- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
- computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
- constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
- d_prop_d_actual_mean_enThe corresponding names of the functions that are going to provide the derivative values wrt theactual mean energy for the variables
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The corresponding names of the functions that are going to provide the derivative values wrt theactual mean energy for the variables
- declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
- electronsThe electron density.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The electron density.
- mean_energyThe electron mean energy in log form.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The electron mean energy in log form.
- prop_namesThe names of the properties this material will have
C++ Type:std::vector<std::string>
Controllable:No
Description:The names of the properties this material will have
- prop_valuesThe corresponding names of the functions that are going to provide the values for the variables
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The corresponding names of the functions that are going to provide the values for the variables
ADMMSEEDFRates
Add material properties used for MMS verifications involving properties as a function of electron mean energy.
Overview
ADMMSEEDFRates supplies the electron mean energy dependent coefficients for a user-specifed function for the purposes of methods of manufactured solutions (MMS) verification. This object also calculates the derivative of the electron mean energy dependent coefficients with respect to the electron density and the electron energy density.
Example Input File Syntax
[Materials]
[Material_Coeff_Set2]
type = ADMMSEEDFRates
electrons = em
mean_energy = mean_en
prop_names = 'diffem muem diffmean_en mumean_en'
prop_values = 'diffem muem diffmean_en mumean_en'
d_prop_d_actual_mean_en = 'diffem_coeff muem_coeff diffmean_en_coeff mumean_en_coeff'
[]
[]
Input Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
- output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
- outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
Outputs Parameters
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
- (test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation.i)
- (test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield.i)
- (test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy.i)
(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy.i)
[Mesh]
[geo]
type = FileMeshGenerator
file = '2D_Coupling_Electons_Potential_Ions_MeanEnergy_IC_out.e'
use_for_exodus_restart = true
[]
[]
[Problem]
type = FEProblem
[]
[Variables]
[em]
initial_from_file_var = em
[]
[potential]
initial_from_file_var = potential
[]
[ion]
initial_from_file_var = ion
[]
[mean_en]
initial_from_file_var = mean_en
[]
[]
[Kernels]
#Electron Equations
[em_time_derivative]
type = TimeDerivativeLog
variable = em
[]
[em_diffusion]
type = CoeffDiffusion
variable = em
position_units = 1.0
[]
[em_advection]
type = EFieldAdvection
variable = em
position_units = 1.0
[]
[em_source]
type = BodyForce
variable = em
function = 'em_source'
[]
#Ion Equations
[ion_time_derivative]
type = TimeDerivativeLog
variable = ion
[]
[ion_diffusion]
type = CoeffDiffusion
variable = ion
position_units = 1.0
[]
[ion_advection]
type = EFieldAdvection
variable = ion
position_units = 1.0
[]
[ion_source]
type = BodyForce
variable = ion
function = 'ion_source'
[]
#Potential Equations
[potential_diffusion]
type = CoeffDiffusionLin
variable = potential
position_units = 1.0
[]
[ion_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = ion
potential_units = V
[]
[em_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = em
potential_units = V
[]
#Electron Energy Equations
[mean_en_time_deriv]
type = TimeDerivativeLog
variable = mean_en
[]
[mean_en_advection]
type = EFieldAdvection
variable = mean_en
position_units = 1.0
[]
[mean_en_diffusion]
type = CoeffDiffusion
variable = mean_en
position_units = 1.0
[]
[mean_en_joule_heating]
type = JouleHeating
variable = mean_en
em = em
position_units = 1.0
potential_units = V
[]
[mean_en_source]
type = BodyForce
variable = mean_en
function = 'energy_source'
[]
[]
[AuxVariables]
[potential_sol]
[]
[mean_en_sol]
[]
[em_sol]
[]
[ion_sol]
[]
[]
[AuxKernels]
[potential_sol]
type = FunctionAux
variable = potential_sol
function = potential_fun
[]
[mean_en_sol]
type = FunctionAux
variable = mean_en_sol
function = mean_en_fun
[]
[em_sol]
type = FunctionAux
variable = em_sol
function = em_fun
[]
[ion_sol]
type = FunctionAux
variable = ion_sol
function = ion_fun
[]
[]
[Functions]
#Material Variables
#Electron diffusion coeff.
[diffem_coeff]
type = ConstantFunction
value = 0.05
[]
#Electron mobility coeff.
[muem_coeff]
type = ConstantFunction
value = 0.01
[]
#Electron energy diffusion coeff.
[diffmean_en_coeff]
type = ParsedFunction
vars = 'diffem_coeff'
vals = 'diffem_coeff'
value = '5.0 / 3.0 * diffem_coeff'
[]
#Electron energy mobility coeff.
[mumean_en_coeff]
type = ParsedFunction
vars = 'muem_coeff'
vals = 'muem_coeff'
value = '5.0 / 3.0 * muem_coeff'
[]
#Ion diffusion coeff.
[diffion]
type = ConstantFunction
value = 0.1
[]
#Ion mobility coeff.
[muion]
type = ConstantFunction
value = 0.025
[]
[N_A]
type = ConstantFunction
value = 1.0
[]
[ee]
type = ConstantFunction
value = 1.0
[]
[diffpotential]
type = ConstantFunction
value = 0.01
[]
#Manufactured Solutions
#The manufactured electron density solution
[em_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 0.2*sin(2*pi*t)*cos(pi*y) + 1.0 + cos(pi/2*x)) / N_A)'
[]
#The manufactured ion density solution
[ion_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 1.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
#The manufactured electron density solution
[potential_fun]
type = ParsedFunction
vars = 'ee diffpotential'
vals = 'ee diffpotential'
value = '-(ee*(2*cos((pi*x)/2) + cos(pi*y)*sin(2*pi*t)))/(5*diffpotential*pi^2)'
[]
#The manufactured electron energy solution
[energy_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'sin(pi*y) + sin(2*pi*t)*cos(pi*y)*sin(pi*y) + 0.75 + cos(pi/2*x)'
[]
[mean_en_fun]
type = ParsedFunction
vars = 'energy_fun em_fun'
vals = 'energy_fun em_fun'
value = 'log(energy_fun) + em_fun'
[]
#Electron diffusion coeff.
[diffem]
type = ParsedFunction
vars = 'diffem_coeff energy_fun'
vals = 'diffem_coeff energy_fun'
value = 'diffem_coeff * energy_fun'
[]
#Electron mobility coeff.
[muem]
type = ParsedFunction
vars = 'muem_coeff energy_fun'
vals = 'muem_coeff energy_fun'
value = 'muem_coeff * energy_fun'
[]
#Electron energy diffusion coeff.
[diffmean_en]
type = ParsedFunction
vars = 'diffmean_en_coeff energy_fun'
vals = 'diffmean_en_coeff energy_fun'
value = 'diffmean_en_coeff * energy_fun'
[]
#Electron energy mobility coeff.
[mumean_en]
type = ParsedFunction
vars = 'mumean_en_coeff energy_fun'
vals = 'mumean_en_coeff energy_fun'
value = 'mumean_en_coeff * energy_fun'
[]
#Source Terms in moles
#The electron source term.
[em_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '((2*pi*cos(2*pi*t)*cos(pi*y))/5 - (diffem_coeff*pi^2*sin((pi*x)/2)^2)/4 -
diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t)) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 + (diffem_coeff*pi^2*(5*sin(pi*y) +
cos(pi*y)*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/5 -
(ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) - (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(10*diffpotential) + (ee*muem_coeff*cos((pi*x)/2)*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) +
(ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential) +
(ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos(pi*y) - sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(5*diffpotential) + (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(pi*cos(pi*y) -
(pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)) / N_A'
[]
#The ion source term.
[ion_source]
type = ParsedFunction
vars = 'ee diffpotential diffion muion N_A'
vals = 'ee diffpotential diffion muion N_A'
value = '((diffion*pi^2*(9*cos((pi*x)/2) + 40*sin(pi*y)))/40 +
(9*ee*muion*sin((pi*x)/2)^2)/(100*diffpotential) -
(ee*muion*cos((pi*x)/2)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(10*diffpotential) -
(ee*muion*cos(pi*y)*sin(2*pi*t)*sin(pi*y))/(5*diffpotential) -
(ee*muion*cos(pi*y)*sin(2*pi*t)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(5*diffpotential)) / N_A'
[]
[energy_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '(((4*cos((pi*x)/2) + 4*sin(pi*y) +
4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(172*ee*muem_coeff*cos(2*pi*t)^2 - 282*ee*muem_coeff +
180*ee*muem_coeff*cos((pi*x)/2)^2 + 160*ee*muem_coeff*cos((pi*x)/2)^3 +
664*ee*muem_coeff*cos(pi*y)^2 - 480*ee*muem_coeff*cos(pi*y)^4 - 66*ee*muem_coeff*cos((pi*x)/2) -
296*ee*muem_coeff*sin(pi*y) + 200*diffem_coeff*diffpotential*pi^2 -
664*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2 + 480*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^4 +
364*ee*muem_coeff*cos(pi*y)*sin(2*pi*t) - 90*ee*muem_coeff*cos((pi*x)/2)*sin(pi*y) +
75*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2) + 140*diffem_coeff*diffpotential*pi^2*sin(pi*y) +
16*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2) - 8*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2 +
176*ee*muem_coeff*cos(2*pi*t)^2*sin(pi*y) - 320*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t) +
200*ee*muem_coeff*cos((pi*x)/2)^2*sin(pi*y) + 464*ee*muem_coeff*cos(pi*y)^2*sin(pi*y) +
300*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)^2 - 1200*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2 +
160*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*sin(pi*y) +
104*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t) -
40*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^3*sin(2*pi*t) + 408*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) +
96*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) + 160*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*sin(pi*y) -
2000*diffem_coeff*diffpotential*pi^2*cos(pi*y)^3*sin(2*pi*t) +
400*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2*sin(pi*y) - 32*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2 -
464*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) + 186*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
272*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 1260*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t) +
500*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*sin(pi*y) - 408*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) -
96*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) -
400*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
448*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
240*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
48*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
100*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y)))/(960*diffpotential) +
(pi*cos(2*pi*t)*cos(pi*y)*(4*cos((pi*x)/2) + 24*sin(pi*y) + 20*cos((pi*x)/2)*sin(pi*y) + 20*sin(pi*y)^2 +
8*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3))/10 - (5*diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/12 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*((5*cos((pi*x)/2))/3 +
(5*sin(pi*y))/3 + (cos(pi*y)*sin(2*pi*t))/3 + 5/3))/4 - diffem_coeff*pi^2*(cos(pi*y) - sin(2*pi*t) +
2*cos(pi*y)^2*sin(2*pi*t))^2*((5*cos((pi*x)/2))/3 + (5*sin(pi*y))/3 + (cos(pi*y)*sin(2*pi*t))/3 + 5/3) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4)*((5*cos((pi*x)/2))/3 +
(5*sin(pi*y))/3 + (cos(pi*y)*sin(2*pi*t))/3 + 5/3))/4 - (diffem_coeff*pi^2*(5*cos(pi*y) -
sin(2*pi*t)*sin(pi*y))*(cos(pi*y) - sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/3 + (ee*sin(2*pi*t)*sin(pi*y)*(diffem_coeff*(pi*cos(pi*y) -
(pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) -
(ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)))/(5*diffpotential*pi) +
diffem_coeff*pi^2*sin(pi*y)*(4*cos(pi*y)*sin(2*pi*t) + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4)*((5*cos((pi*x)/2))/3 + (5*sin(pi*y))/3 +
(cos(pi*y)*sin(2*pi*t))/3 + 5/3) - (ee*sin((pi*x)/2)^2*(4*cos((pi*x)/2) + 4*sin(pi*y) +
4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(10*ee*muem_coeff + 10*ee*muem_coeff*cos((pi*x)/2) +
10*ee*muem_coeff*sin(pi*y) + 25*diffem_coeff*diffpotential*pi^2 +
2*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)))/(1000*diffpotential^2*pi^2)) / N_A'
[]
[em_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + cos(pi/2*x)) / N_A)'
[]
[ion_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
[mean_en_ICs]
type = ParsedFunction
vars = 'em_ICs'
vals = 'em_ICs'
value = 'log(32. + cos(pi/2*x)) + em_ICs'
[]
[]
[BCs]
[potential_BC]
type = FunctionDirichletBC
variable = potential
function = 'potential_fun'
boundary = '0 1 2 3'
preset = true
[]
[em_BC]
type = FunctionDirichletBC
variable = em
function = 'em_fun'
boundary = '0 1 2 3'
preset = true
[]
[ion_BC]
type = FunctionDirichletBC
variable = ion
function = 'ion_fun'
boundary = '0 1 2 3'
preset = true
[]
[energy_BC]
type = FunctionDirichletBC
variable = mean_en
function = 'mean_en_fun'
boundary = '0 1 2 3'
preset = true
[]
[]
[Materials]
[field_solver]
type = FieldSolverMaterial
potential = potential
[]
[Material_Coeff]
type = GenericFunctionMaterial
prop_names = 'e N_A'
prop_values = 'ee N_A'
[]
[ADMaterial_Coeff_Set1]
type = ADGenericFunctionMaterial
prop_names = 'diffpotential diffion muion'
prop_values = 'diffpotential diffion muion'
[]
[Material_Coeff_Set2]
type = ADMMSEEDFRates
electrons = em
mean_energy = mean_en
prop_names = 'diffem muem diffmean_en mumean_en'
prop_values = 'diffem muem diffmean_en mumean_en'
d_prop_d_actual_mean_en = 'diffem_coeff muem_coeff diffmean_en_coeff mumean_en_coeff'
[]
[Charge_Signs]
type = GenericConstantMaterial
prop_names = 'sgnem sgnion sgnmean_en'
prop_values = '-1.0 1.0 -1.0'
[]
[]
[Postprocessors]
[em_l2Error]
type = ElementL2Error
variable = em
function = em_fun
[]
[ion_l2Error]
type = ElementL2Error
variable = ion
function = ion_fun
[]
[potential_l2Error]
type = ElementL2Error
variable = potential
function = potential_fun
[]
[mean_en_l2Error]
type = ElementL2Error
variable = mean_en
function = mean_en_fun
[]
[h]
type = AverageElementSize
[]
[]
[Preconditioning]
active = 'smp'
[smp]
type = SMP
full = true
[]
[fdp]
type = FDP
full = true
[]
[]
[Executioner]
type = Transient
start_time = 50
end_time = 51
# dt = 0.008
dt = 0.02
automatic_scaling = true
compute_scaling_once = false
petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
solve_type = NEWTON
line_search = none
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = 'lu NONZERO 1.e-10'
scheme = bdf2
nl_abs_tol = 1e-13
[]
[Outputs]
perf_graph = true
[out]
type = Exodus
interval = 10
[]
[]
(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation.i)
[Mesh]
[geo]
type = FileMeshGenerator
file = '2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_IC_out.e'
use_for_exodus_restart = true
[]
[]
[Problem]
type = FEProblem
[]
[Variables]
[em]
initial_from_file_var = em
[]
[potential]
initial_from_file_var = potential
[]
[ion]
initial_from_file_var = ion
[]
[mean_en]
initial_from_file_var = mean_en
[]
[]
[Kernels]
#Electron Equations
[em_time_derivative]
type = TimeDerivativeLog
variable = em
[]
[em_diffusion]
type = CoeffDiffusion
variable = em
position_units = 1.0
[]
[em_advection]
type = EFieldAdvection
variable = em
position_units = 1.0
[]
[em_source]
type = BodyForce
variable = em
function = 'em_source'
[]
#Ion Equations
[ion_time_derivative]
type = TimeDerivativeLog
variable = ion
[]
[ion_diffusion]
type = CoeffDiffusion
variable = ion
position_units = 1.0
[]
[ion_advection]
type = EFieldAdvection
variable = ion
position_units = 1.0
[]
[ion_source]
type = BodyForce
variable = ion
function = 'ion_source'
[]
#Potential Equations
[potential_diffusion]
type = CoeffDiffusionLin
variable = potential
position_units = 1.0
[]
[ion_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = ion
potential_units = V
[]
[em_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = em
potential_units = V
[]
#Electron Energy Equations
[mean_en_time_deriv]
type = TimeDerivativeLog
variable = mean_en
[]
[mean_en_advection]
type = EFieldAdvection
variable = mean_en
position_units = 1.0
[]
[mean_en_diffusion]
type = CoeffDiffusion
variable = mean_en
position_units = 1.0
[]
[mean_en_diffusion_correction]
type = ThermalConductivityDiffusion
variable = mean_en
em = em
position_units = 1.0
[]
[mean_en_joule_heating]
type = JouleHeating
variable = mean_en
em = em
position_units = 1.0
potential_units = V
[]
[mean_en_source]
type = BodyForce
variable = mean_en
function = 'energy_source'
[]
[]
[AuxVariables]
[potential_sol]
[]
[mean_en_sol]
[]
[em_sol]
[]
[ion_sol]
[]
[]
[AuxKernels]
[potential_sol]
type = FunctionAux
variable = potential_sol
function = potential_fun
[]
[mean_en_sol]
type = FunctionAux
variable = mean_en_sol
function = mean_en_fun
[]
[em_sol]
type = FunctionAux
variable = em_sol
function = em_fun
[]
[ion_sol]
type = FunctionAux
variable = ion_sol
function = ion_fun
[]
[]
[Functions]
#Material Variables
#Electron diffusion coeff.
[diffem_coeff]
type = ConstantFunction
value = 0.05
[]
#Electron mobility coeff.
[muem_coeff]
type = ConstantFunction
value = 0.01
[]
#Electron energy diffusion coeff.
[diffmean_en_coeff]
type = ParsedFunction
vars = 'diffem_coeff'
vals = 'diffem_coeff'
value = '5.0 / 3.0 * diffem_coeff'
[]
#Electron energy mobility coeff.
[mumean_en_coeff]
type = ParsedFunction
vars = 'muem_coeff'
vals = 'muem_coeff'
value = '5.0 / 3.0 * muem_coeff'
[]
#Ion diffusion coeff.
[diffion]
type = ConstantFunction
value = 0.1
[]
#Ion mobility coeff.
[muion]
type = ConstantFunction
value = 0.025
[]
[N_A]
type = ConstantFunction
value = 1.0
[]
[ee]
type = ConstantFunction
value = 1.0
[]
[diffpotential]
type = ConstantFunction
value = 0.01
[]
#Manufactured Solutions
#The manufactured electron density solution
[em_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 0.2*sin(2*pi*t)*cos(pi*y) + 1.0 + cos(pi/2*x)) / N_A)'
[]
#The manufactured ion density solution
[ion_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 1.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
#The manufactured electron density solution
[potential_fun]
type = ParsedFunction
vars = 'ee diffpotential'
vals = 'ee diffpotential'
value = '-(ee*(2*cos((pi*x)/2) + cos(pi*y)*sin(2*pi*t)))/(5*diffpotential*pi^2)'
[]
#The manufactured electron energy solution
[energy_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'sin(pi*y) + sin(2*pi*t)*cos(pi*y)*sin(pi*y) + 0.75 + cos(pi/2*x)'
[]
[mean_en_fun]
type = ParsedFunction
vars = 'energy_fun em_fun'
vals = 'energy_fun em_fun'
value = 'log(energy_fun) + em_fun'
[]
#Electron diffusion coeff.
[diffem]
type = ParsedFunction
vars = 'diffem_coeff energy_fun'
vals = 'diffem_coeff energy_fun'
value = 'diffem_coeff * energy_fun'
[]
#Electron mobility coeff.
[muem]
type = ParsedFunction
vars = 'muem_coeff energy_fun'
vals = 'muem_coeff energy_fun'
value = 'muem_coeff * energy_fun'
[]
#Electron energy diffusion coeff.
[diffmean_en]
type = ParsedFunction
vars = 'diffmean_en_coeff energy_fun'
vals = 'diffmean_en_coeff energy_fun'
value = 'diffmean_en_coeff * energy_fun'
[]
#Electron energy mobility coeff.
[mumean_en]
type = ParsedFunction
vars = 'mumean_en_coeff energy_fun'
vals = 'mumean_en_coeff energy_fun'
value = 'mumean_en_coeff * energy_fun'
[]
#Source Terms in moles
#The electron source term.
[em_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '((2*pi*cos(2*pi*t)*cos(pi*y))/5 - (diffem_coeff*pi^2*sin((pi*x)/2)^2)/4 -
diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t)) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 + (diffem_coeff*pi^2*(5*sin(pi*y) +
cos(pi*y)*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/5 -
(ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) - (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(10*diffpotential) + (ee*muem_coeff*cos((pi*x)/2)*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) +
(ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential) +
(ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos(pi*y) - sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(5*diffpotential) + (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(pi*cos(pi*y) -
(pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)) / N_A'
[]
#The ion source term.
[ion_source]
type = ParsedFunction
vars = 'ee diffpotential diffion muion N_A'
vals = 'ee diffpotential diffion muion N_A'
value = '((diffion*pi^2*(9*cos((pi*x)/2) + 40*sin(pi*y)))/40 +
(9*ee*muion*sin((pi*x)/2)^2)/(100*diffpotential) -
(ee*muion*cos((pi*x)/2)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(10*diffpotential) -
(ee*muion*cos(pi*y)*sin(2*pi*t)*sin(pi*y))/(5*diffpotential) -
(ee*muion*cos(pi*y)*sin(2*pi*t)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(5*diffpotential)) / N_A'
[]
[energy_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '(((4*cos((pi*x)/2) + 4*sin(pi*y) + 4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(172*ee*muem_coeff*cos(2*pi*t)^2 -
282*ee*muem_coeff + 180*ee*muem_coeff*cos((pi*x)/2)^2 + 160*ee*muem_coeff*cos((pi*x)/2)^3 +
664*ee*muem_coeff*cos(pi*y)^2 - 480*ee*muem_coeff*cos(pi*y)^4 - 66*ee*muem_coeff*cos((pi*x)/2) -
296*ee*muem_coeff*sin(pi*y) + 200*diffem_coeff*diffpotential*pi^2 -
664*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2 + 480*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^4 +
364*ee*muem_coeff*cos(pi*y)*sin(2*pi*t) - 90*ee*muem_coeff*cos((pi*x)/2)*sin(pi*y) +
75*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2) + 140*diffem_coeff*diffpotential*pi^2*sin(pi*y) +
16*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2) - 8*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2 +
176*ee*muem_coeff*cos(2*pi*t)^2*sin(pi*y) - 320*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t) +
200*ee*muem_coeff*cos((pi*x)/2)^2*sin(pi*y) + 464*ee*muem_coeff*cos(pi*y)^2*sin(pi*y) +
300*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)^2 - 1200*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2 +
160*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*sin(pi*y) +
104*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t) -
40*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^3*sin(2*pi*t) +
408*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) + 96*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) +
160*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*sin(pi*y) -
2000*diffem_coeff*diffpotential*pi^2*cos(pi*y)^3*sin(2*pi*t) +
400*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2*sin(pi*y) -
32*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2 -
464*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
186*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) + 272*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
1260*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t) +
500*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*sin(pi*y) -
408*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) -
96*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) -
400*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
448*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
240*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
48*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
100*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y)))/(960*diffpotential) +
(pi*cos(2*pi*t)*cos(pi*y)*(4*cos((pi*x)/2) + 24*sin(pi*y) + 20*cos((pi*x)/2)*sin(pi*y) + 20*sin(pi*y)^2 +
8*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3))/10 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/4 - diffem_coeff*pi^2*(cos(pi*y) - sin(2*pi*t) +
2*cos(pi*y)^2*sin(2*pi*t))^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 -
diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) - sin(2*pi*t) +
2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) +
(ee*sin(2*pi*t)*sin(pi*y)*(diffem_coeff*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) - (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)))/(5*diffpotential*pi) +
diffem_coeff*pi^2*sin(pi*y)*(4*cos(pi*y)*sin(2*pi*t) + 1)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) -
(ee*sin((pi*x)/2)^2*(4*cos((pi*x)/2) + 4*sin(pi*y) +
4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(10*ee*muem_coeff + 10*ee*muem_coeff*cos((pi*x)/2) +
10*ee*muem_coeff*sin(pi*y) + 25*diffem_coeff*diffpotential*pi^2 +
2*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)))/(1000*diffpotential^2*pi^2)) / N_A'
[]
[em_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + cos(pi/2*x)) / N_A)'
[]
[ion_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
[mean_en_ICs]
type = ParsedFunction
vars = 'em_ICs'
vals = 'em_ICs'
value = 'log(32. + cos(pi/2*x)) + em_ICs'
[]
[]
[BCs]
[potential_BC]
type = FunctionDirichletBC
variable = potential
function = 'potential_fun'
boundary = '0 1 2 3'
preset = true
[]
[em_BC]
type = FunctionDirichletBC
variable = em
function = 'em_fun'
boundary = '0 1 2 3'
preset = true
[]
[ion_BC]
type = FunctionDirichletBC
variable = ion
function = 'ion_fun'
boundary = '0 1 2 3'
preset = true
[]
[energy_BC]
type = FunctionDirichletBC
variable = mean_en
function = 'mean_en_fun'
boundary = '0 1 2 3'
preset = true
[]
[]
[Materials]
[field_solver]
type = FieldSolverMaterial
potential = potential
[]
[Material_Coeff]
type = GenericFunctionMaterial
prop_names = 'e N_A'
prop_values = 'ee N_A'
[]
[ADMaterial_Coeff_Set1]
type = ADGenericFunctionMaterial
prop_names = 'diffpotential diffion muion'
prop_values = 'diffpotential diffion muion'
[]
[Material_Coeff_Set2]
type = ADMMSEEDFRates
electrons = em
mean_energy = mean_en
prop_names = 'diffem muem diffmean_en mumean_en'
prop_values = 'diffem muem diffmean_en mumean_en'
d_prop_d_actual_mean_en = 'diffem_coeff muem_coeff diffmean_en_coeff mumean_en_coeff'
[]
[Charge_Signs]
type = GenericConstantMaterial
prop_names = 'sgnem sgnion sgnmean_en'
prop_values = '-1.0 1.0 -1.0'
[]
[]
[Postprocessors]
[em_l2Error]
type = ElementL2Error
variable = em
function = em_fun
[]
[ion_l2Error]
type = ElementL2Error
variable = ion
function = ion_fun
[]
[potential_l2Error]
type = ElementL2Error
variable = potential
function = potential_fun
[]
[mean_en_l2Error]
type = ElementL2Error
variable = mean_en
function = mean_en_fun
[]
[h]
type = AverageElementSize
[]
[]
[Preconditioning]
active = 'smp'
[smp]
type = SMP
full = true
[]
[fdp]
type = FDP
full = true
[]
[]
[Executioner]
type = Transient
start_time = 50
end_time = 51
# dt = 0.008
dt = 0.02
automatic_scaling = true
compute_scaling_once = false
petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
solve_type = NEWTON
line_search = none
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = 'lu NONZERO 1.e-10'
scheme = bdf2
nl_abs_tol = 1e-13
[]
[Outputs]
perf_graph = true
[out]
type = Exodus
interval = 10
[]
[]
(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield.i)
[Mesh]
[geo]
type = FileMeshGenerator
file = '2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield_IC_out.e'
use_for_exodus_restart = true
[]
[]
[Problem]
type = FEProblem
[]
[Variables]
[em]
initial_from_file_var = em
[]
[potential]
initial_from_file_var = potential
[]
[ion]
initial_from_file_var = ion
[]
[mean_en]
initial_from_file_var = mean_en
[]
[Ex]
initial_from_file_var = Ex
[]
[Ey]
initial_from_file_var = Ey
[]
[]
[Kernels]
#Electron Equations
[em_time_derivative]
type = TimeDerivativeLog
variable = em
[]
[em_diffusion]
type = CoeffDiffusion
variable = em
position_units = 1.0
[]
[em_advection]
type = EFieldAdvection
variable = em
position_units = 1.0
[]
[em_source]
type = BodyForce
variable = em
function = 'em_source'
[]
#Ion Equations
[ion_time_derivative]
type = TimeDerivativeLog
variable = ion
[]
[ion_diffusion]
type = CoeffDiffusion
variable = ion
position_units = 1.0
[]
[ion_advection]
type = EffectiveEFieldAdvection
variable = ion
u = Ex
v = Ey
position_units = 1.0
[]
[ion_source]
type = BodyForce
variable = ion
function = 'ion_source'
[]
#Potential Equations
[potential_diffusion]
type = CoeffDiffusionLin
variable = potential
position_units = 1.0
[]
[ion_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = ion
potential_units = V
[]
[em_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = em
potential_units = V
[]
#Eff. Efield
[EffEfield_X_time_deriv]
type = TimeDerivative
variable = Ex
[]
[EffEfield_X_ForceBody]
type = EffectiveEField
variable = Ex
nu = 5.0
component = 0
position_units = 1.0
[]
[EffEfield_Y_time_deriv]
type = TimeDerivative
variable = Ey
[]
[EffEfield_Y_ForceBody]
type = EffectiveEField
variable = Ey
nu = 5.0
component = 1
position_units = 1.0
[]
#Electron Energy Equations
[mean_en_time_deriv]
type = TimeDerivativeLog
variable = mean_en
[]
[mean_en_advection]
type = EFieldAdvection
variable = mean_en
position_units = 1.0
[]
[mean_en_diffusion]
type = CoeffDiffusion
variable = mean_en
position_units = 1.0
[]
[mean_en_diffusion_correction]
type = ThermalConductivityDiffusion
variable = mean_en
em = em
position_units = 1.0
[]
[mean_en_joule_heating]
type = JouleHeating
variable = mean_en
em = em
position_units = 1.0
potential_units = V
[]
[mean_en_source]
type = BodyForce
variable = mean_en
function = 'energy_source'
[]
[]
[AuxVariables]
[potential_sol]
[]
[mean_en_sol]
[]
[em_sol]
[]
[ion_sol]
[]
[Ex_sol]
[]
[Ey_sol]
[]
[]
[AuxKernels]
[potential_sol]
type = FunctionAux
variable = potential_sol
function = potential_fun
[]
[mean_en_sol]
type = FunctionAux
variable = mean_en_sol
function = mean_en_fun
[]
[em_sol]
type = FunctionAux
variable = em_sol
function = em_fun
[]
[ion_sol]
type = FunctionAux
variable = ion_sol
function = ion_fun
[]
[Ex_sol]
type = FunctionAux
variable = Ex_sol
function = Ex_fun
[]
[Ey_sol]
type = FunctionAux
variable = Ey_sol
function = Ey_fun
[]
[]
[Functions]
#Material Variables
#Electron diffusion coeff.
[diffem_coeff]
type = ConstantFunction
value = 0.05
[]
#Electron mobility coeff.
[muem_coeff]
type = ConstantFunction
value = 0.01
[]
#Electron energy diffusion coeff.
[diffmean_en_coeff]
type = ParsedFunction
vars = 'diffem_coeff'
vals = 'diffem_coeff'
value = '5.0 / 3.0 * diffem_coeff'
[]
#Electron energy mobility coeff.
[mumean_en_coeff]
type = ParsedFunction
vars = 'muem_coeff'
vals = 'muem_coeff'
value = '5.0 / 3.0 * muem_coeff'
[]
#Ion diffusion coeff.
[diffion]
type = ConstantFunction
value = 0.1
[]
#Ion mobility coeff.
[muion]
type = ConstantFunction
value = 0.025
[]
[N_A]
type = ConstantFunction
value = 1.0
[]
[ee]
type = ConstantFunction
value = 1.0
[]
[diffpotential]
type = ConstantFunction
value = 0.01
[]
#Manufactured Solutions
#The manufactured electron density solution
[em_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 0.2*sin(2*pi*t)*cos(pi*y) + 1.0 + cos(pi/2*x)) / N_A)'
[]
#The manufactured ion density solution
[ion_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 1.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
#The manufactured electron density solution
[potential_fun]
type = ParsedFunction
vars = 'ee diffpotential'
vals = 'ee diffpotential'
value = '-(ee*(2*cos((pi*x)/2) + cos(pi*y)*sin(2*pi*t)))/(5*diffpotential*pi^2)'
[]
#The manufactured electron energy solution
[energy_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'sin(pi*y) + sin(2*pi*t)*cos(pi*y)*sin(pi*y) + 0.75 + cos(pi/2*x)'
[]
[mean_en_fun]
type = ParsedFunction
vars = 'energy_fun em_fun'
vals = 'energy_fun em_fun'
value = 'log(energy_fun) + em_fun'
[]
#The manufactured eff. Efield solution
[Ex_fun]
type = ParsedFunction
vars = 'ee diffpotential'
vals = 'ee diffpotential'
value = '-(ee*exp(-5*t)*sin((pi*x)/2)*(exp(5*t) - 1))/(5*diffpotential*pi)'
[]
[Ey_fun]
type = ParsedFunction
vars = 'ee diffpotential'
vals = 'ee diffpotential'
value = '-(2*ee*exp(-5*t)*sin(pi*y))/(4*diffpotential*pi^2 + 25*diffpotential) -
(ee*sin(pi*y)*(5*sin(2*pi*t) - 2*pi*cos(2*pi*t)))/(diffpotential*pi*(4*pi^2 + 25))'
[]
#Electron diffusion coeff.
[diffem]
type = ParsedFunction
vars = 'diffem_coeff energy_fun'
vals = 'diffem_coeff energy_fun'
value = 'diffem_coeff * energy_fun'
[]
#Electron mobility coeff.
[muem]
type = ParsedFunction
vars = 'muem_coeff energy_fun'
vals = 'muem_coeff energy_fun'
value = 'muem_coeff * energy_fun'
[]
#Electron energy diffusion coeff.
[diffmean_en]
type = ParsedFunction
vars = 'diffmean_en_coeff energy_fun'
vals = 'diffmean_en_coeff energy_fun'
value = 'diffmean_en_coeff * energy_fun'
[]
#Electron energy mobility coeff.
[mumean_en]
type = ParsedFunction
vars = 'mumean_en_coeff energy_fun'
vals = 'mumean_en_coeff energy_fun'
value = 'mumean_en_coeff * energy_fun'
[]
#Source Terms in moles
#The electron source term.
[em_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '((2*pi*cos(2*pi*t)*cos(pi*y))/5 - (diffem_coeff*pi^2*sin((pi*x)/2)^2)/4 -
diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t)) + (diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 + (diffem_coeff*pi^2*(5*sin(pi*y) +
cos(pi*y)*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/5 -
(ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) -
(ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(10*diffpotential) +
(ee*muem_coeff*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) +
(ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential) + (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos(pi*y) -
sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(5*diffpotential) +
(ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)) / N_A'
[]
#The ion source term.
[ion_source]
type = ParsedFunction
vars = 'ee diffpotential diffion muion N_A'
vals = 'ee diffpotential diffion muion N_A'
value = '((diffion*pi^2*(9*cos((pi*x)/2) + 40*sin(pi*y)))/40 +
(9*ee*muion*exp(-5*t)*sin((pi*x)/2)^2*(exp(5*t) - 1))/(100*diffpotential) -
(ee*muion*exp(-5*t)*cos((pi*x)/2)*(exp(5*t) - 1)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(10*diffpotential) -
(ee*muion*exp(-5*t)*cos(pi*y)*(2*pi + 5*exp(5*t)*sin(2*pi*t) -
2*pi*exp(5*t)*cos(2*pi*t))*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(diffpotential*(4*pi^2 + 25)) -
(ee*muion*exp(-5*t)*cos(pi*y)*sin(pi*y)*(2*pi + 5*exp(5*t)*sin(2*pi*t) -
2*pi*exp(5*t)*cos(2*pi*t)))/(diffpotential*(4*pi^2 + 25))) / N_A'
[]
[energy_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '(((4*cos((pi*x)/2) + 4*sin(pi*y) + 4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(172*ee*muem_coeff*cos(2*pi*t)^2 -
282*ee*muem_coeff + 180*ee*muem_coeff*cos((pi*x)/2)^2 + 160*ee*muem_coeff*cos((pi*x)/2)^3 +
664*ee*muem_coeff*cos(pi*y)^2 - 480*ee*muem_coeff*cos(pi*y)^4 -
66*ee*muem_coeff*cos((pi*x)/2) - 296*ee*muem_coeff*sin(pi*y) +
200*diffem_coeff*diffpotential*pi^2 - 664*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2 +
480*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^4 + 364*ee*muem_coeff*cos(pi*y)*sin(2*pi*t) -
90*ee*muem_coeff*cos((pi*x)/2)*sin(pi*y) + 75*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2) +
140*diffem_coeff*diffpotential*pi^2*sin(pi*y) + 16*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2) -
8*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2 + 176*ee*muem_coeff*cos(2*pi*t)^2*sin(pi*y) -
320*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t) + 200*ee*muem_coeff*cos((pi*x)/2)^2*sin(pi*y) +
464*ee*muem_coeff*cos(pi*y)^2*sin(pi*y) + 300*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)^2 -
1200*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2 + 160*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*sin(pi*y) +
104*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t) - 40*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^3*sin(2*pi*t) +
408*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) + 96*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) +
160*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*sin(pi*y) -
2000*diffem_coeff*diffpotential*pi^2*cos(pi*y)^3*sin(2*pi*t) + 400*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2*sin(pi*y) -
32*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2 - 464*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
186*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) + 272*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
1260*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t) + 500*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*sin(pi*y) -
408*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) -
96*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) -
400*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
448*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
240*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
48*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 80*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
100*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y)))/(960*diffpotential) +
(pi*cos(2*pi*t)*cos(pi*y)*(4*cos((pi*x)/2) + 24*sin(pi*y) + 20*cos((pi*x)/2)*sin(pi*y) + 20*sin(pi*y)^2 +
8*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3))/10 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1))/4 - diffem_coeff*pi^2*(cos(pi*y) - sin(2*pi*t) +
2*cos(pi*y)^2*sin(2*pi*t))^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) +
(ee*sin(2*pi*t)*sin(pi*y)*(diffem_coeff*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) - (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)))/(5*diffpotential*pi) +
diffem_coeff*pi^2*sin(pi*y)*(4*cos(pi*y)*sin(2*pi*t) + 1)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) -
(ee*sin((pi*x)/2)^2*(4*cos((pi*x)/2) + 4*sin(pi*y) +
4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(10*ee*muem_coeff + 10*ee*muem_coeff*cos((pi*x)/2) +
10*ee*muem_coeff*sin(pi*y) + 25*diffem_coeff*diffpotential*pi^2 +
2*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)))/(1000*diffpotential^2*pi^2)) / N_A'
[]
[em_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + cos(pi/2*x)) / N_A)'
[]
[ion_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
[mean_en_ICs]
type = ParsedFunction
vars = 'em_ICs'
vals = 'em_ICs'
value = 'log(32. + cos(pi/2*x)) + em_ICs'
[]
[]
[BCs]
[potential_BC]
type = FunctionDirichletBC
variable = potential
function = 'potential_fun'
boundary = '0 1 2 3'
preset = true
[]
[em_BC]
type = FunctionDirichletBC
variable = em
function = 'em_fun'
boundary = '0 1 2 3'
preset = true
[]
[ion_BC]
type = FunctionDirichletBC
variable = ion
function = 'ion_fun'
boundary = '0 1 2 3'
preset = true
[]
[energy_BC]
type = FunctionDirichletBC
variable = mean_en
function = 'mean_en_fun'
boundary = '0 1 2 3'
preset = true
[]
[Ex_BC]
type = FunctionDirichletBC
variable = Ex
function = 'Ex_fun'
boundary = '0 1 2 3'
preset = true
[]
[Ey_BC]
type = FunctionDirichletBC
variable = Ey
function = 'Ey_fun'
boundary = '0 1 2 3'
preset = true
[]
[]
[Materials]
[field_solver]
type = FieldSolverMaterial
potential = potential
[]
[Material_Coeff]
type = GenericFunctionMaterial
prop_names = 'e N_A'
prop_values = 'ee N_A'
[]
[ADMaterial_Coeff_Set1]
type = ADGenericFunctionMaterial
prop_names = 'diffpotential diffion muion'
prop_values = 'diffpotential diffion muion'
[]
[Material_Coeff_Set2]
type = ADMMSEEDFRates
electrons = em
mean_energy = mean_en
prop_names = 'diffem muem diffmean_en mumean_en'
prop_values = 'diffem muem diffmean_en mumean_en'
d_prop_d_actual_mean_en = 'diffem_coeff muem_coeff diffmean_en_coeff mumean_en_coeff'
[]
[Charge_Signs]
type = GenericConstantMaterial
prop_names = 'sgnem sgnion sgnmean_en'
prop_values = '-1.0 1.0 -1.0'
[]
[]
[Postprocessors]
[em_l2Error]
type = ElementL2Error
variable = em
function = em_fun
[]
[ion_l2Error]
type = ElementL2Error
variable = ion
function = ion_fun
[]
[potential_l2Error]
type = ElementL2Error
variable = potential
function = potential_fun
[]
[mean_en_l2Error]
type = ElementL2Error
variable = mean_en
function = mean_en_fun
[]
[Ex_l2Error]
type = ElementL2Error
variable = Ex
function = Ex_fun
[]
[Ey_l2Error]
type = ElementL2Error
variable = Ey
function = Ey_fun
[]
[h]
type = AverageElementSize
[]
[]
[Preconditioning]
active = 'smp'
[smp]
type = SMP
full = true
[]
[fdp]
type = FDP
full = true
[]
[]
[Executioner]
type = Transient
start_time = 50
end_time = 51
# dt = 0.008
dt = 0.02
automatic_scaling = true
compute_scaling_once = false
petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
solve_type = NEWTON
line_search = none
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = 'lu NONZERO 1.e-10'
scheme = bdf2
nl_abs_tol = 1e-13
[]
[Outputs]
perf_graph = true
[out]
type = Exodus
interval = 10
[]
[]
(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy.i)
[Mesh]
[geo]
type = FileMeshGenerator
file = '2D_Coupling_Electons_Potential_Ions_MeanEnergy_IC_out.e'
use_for_exodus_restart = true
[]
[]
[Problem]
type = FEProblem
[]
[Variables]
[em]
initial_from_file_var = em
[]
[potential]
initial_from_file_var = potential
[]
[ion]
initial_from_file_var = ion
[]
[mean_en]
initial_from_file_var = mean_en
[]
[]
[Kernels]
#Electron Equations
[em_time_derivative]
type = TimeDerivativeLog
variable = em
[]
[em_diffusion]
type = CoeffDiffusion
variable = em
position_units = 1.0
[]
[em_advection]
type = EFieldAdvection
variable = em
position_units = 1.0
[]
[em_source]
type = BodyForce
variable = em
function = 'em_source'
[]
#Ion Equations
[ion_time_derivative]
type = TimeDerivativeLog
variable = ion
[]
[ion_diffusion]
type = CoeffDiffusion
variable = ion
position_units = 1.0
[]
[ion_advection]
type = EFieldAdvection
variable = ion
position_units = 1.0
[]
[ion_source]
type = BodyForce
variable = ion
function = 'ion_source'
[]
#Potential Equations
[potential_diffusion]
type = CoeffDiffusionLin
variable = potential
position_units = 1.0
[]
[ion_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = ion
potential_units = V
[]
[em_charge_source]
type = ChargeSourceMoles_KV
variable = potential
charged = em
potential_units = V
[]
#Electron Energy Equations
[mean_en_time_deriv]
type = TimeDerivativeLog
variable = mean_en
[]
[mean_en_advection]
type = EFieldAdvection
variable = mean_en
position_units = 1.0
[]
[mean_en_diffusion]
type = CoeffDiffusion
variable = mean_en
position_units = 1.0
[]
[mean_en_joule_heating]
type = JouleHeating
variable = mean_en
em = em
position_units = 1.0
potential_units = V
[]
[mean_en_source]
type = BodyForce
variable = mean_en
function = 'energy_source'
[]
[]
[AuxVariables]
[potential_sol]
[]
[mean_en_sol]
[]
[em_sol]
[]
[ion_sol]
[]
[]
[AuxKernels]
[potential_sol]
type = FunctionAux
variable = potential_sol
function = potential_fun
[]
[mean_en_sol]
type = FunctionAux
variable = mean_en_sol
function = mean_en_fun
[]
[em_sol]
type = FunctionAux
variable = em_sol
function = em_fun
[]
[ion_sol]
type = FunctionAux
variable = ion_sol
function = ion_fun
[]
[]
[Functions]
#Material Variables
#Electron diffusion coeff.
[diffem_coeff]
type = ConstantFunction
value = 0.05
[]
#Electron mobility coeff.
[muem_coeff]
type = ConstantFunction
value = 0.01
[]
#Electron energy diffusion coeff.
[diffmean_en_coeff]
type = ParsedFunction
vars = 'diffem_coeff'
vals = 'diffem_coeff'
value = '5.0 / 3.0 * diffem_coeff'
[]
#Electron energy mobility coeff.
[mumean_en_coeff]
type = ParsedFunction
vars = 'muem_coeff'
vals = 'muem_coeff'
value = '5.0 / 3.0 * muem_coeff'
[]
#Ion diffusion coeff.
[diffion]
type = ConstantFunction
value = 0.1
[]
#Ion mobility coeff.
[muion]
type = ConstantFunction
value = 0.025
[]
[N_A]
type = ConstantFunction
value = 1.0
[]
[ee]
type = ConstantFunction
value = 1.0
[]
[diffpotential]
type = ConstantFunction
value = 0.01
[]
#Manufactured Solutions
#The manufactured electron density solution
[em_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 0.2*sin(2*pi*t)*cos(pi*y) + 1.0 + cos(pi/2*x)) / N_A)'
[]
#The manufactured ion density solution
[ion_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((sin(pi*y) + 1.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
#The manufactured electron density solution
[potential_fun]
type = ParsedFunction
vars = 'ee diffpotential'
vals = 'ee diffpotential'
value = '-(ee*(2*cos((pi*x)/2) + cos(pi*y)*sin(2*pi*t)))/(5*diffpotential*pi^2)'
[]
#The manufactured electron energy solution
[energy_fun]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'sin(pi*y) + sin(2*pi*t)*cos(pi*y)*sin(pi*y) + 0.75 + cos(pi/2*x)'
[]
[mean_en_fun]
type = ParsedFunction
vars = 'energy_fun em_fun'
vals = 'energy_fun em_fun'
value = 'log(energy_fun) + em_fun'
[]
#Electron diffusion coeff.
[diffem]
type = ParsedFunction
vars = 'diffem_coeff energy_fun'
vals = 'diffem_coeff energy_fun'
value = 'diffem_coeff * energy_fun'
[]
#Electron mobility coeff.
[muem]
type = ParsedFunction
vars = 'muem_coeff energy_fun'
vals = 'muem_coeff energy_fun'
value = 'muem_coeff * energy_fun'
[]
#Electron energy diffusion coeff.
[diffmean_en]
type = ParsedFunction
vars = 'diffmean_en_coeff energy_fun'
vals = 'diffmean_en_coeff energy_fun'
value = 'diffmean_en_coeff * energy_fun'
[]
#Electron energy mobility coeff.
[mumean_en]
type = ParsedFunction
vars = 'mumean_en_coeff energy_fun'
vals = 'mumean_en_coeff energy_fun'
value = 'mumean_en_coeff * energy_fun'
[]
#Source Terms in moles
#The electron source term.
[em_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '((2*pi*cos(2*pi*t)*cos(pi*y))/5 - (diffem_coeff*pi^2*sin((pi*x)/2)^2)/4 -
diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t)) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 + (diffem_coeff*pi^2*(5*sin(pi*y) +
cos(pi*y)*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/5 -
(ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) - (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(10*diffpotential) + (ee*muem_coeff*cos((pi*x)/2)*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) +
(ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*(cos((pi*x)/2) + sin(pi*y) +
(cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential) +
(ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos(pi*y) - sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) +
sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(5*diffpotential) + (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(pi*cos(pi*y) -
(pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)) / N_A'
[]
#The ion source term.
[ion_source]
type = ParsedFunction
vars = 'ee diffpotential diffion muion N_A'
vals = 'ee diffpotential diffion muion N_A'
value = '((diffion*pi^2*(9*cos((pi*x)/2) + 40*sin(pi*y)))/40 +
(9*ee*muion*sin((pi*x)/2)^2)/(100*diffpotential) -
(ee*muion*cos((pi*x)/2)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(10*diffpotential) -
(ee*muion*cos(pi*y)*sin(2*pi*t)*sin(pi*y))/(5*diffpotential) -
(ee*muion*cos(pi*y)*sin(2*pi*t)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(5*diffpotential)) / N_A'
[]
[energy_source]
type = ParsedFunction
vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
value = '(((4*cos((pi*x)/2) + 4*sin(pi*y) +
4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(172*ee*muem_coeff*cos(2*pi*t)^2 - 282*ee*muem_coeff +
180*ee*muem_coeff*cos((pi*x)/2)^2 + 160*ee*muem_coeff*cos((pi*x)/2)^3 +
664*ee*muem_coeff*cos(pi*y)^2 - 480*ee*muem_coeff*cos(pi*y)^4 - 66*ee*muem_coeff*cos((pi*x)/2) -
296*ee*muem_coeff*sin(pi*y) + 200*diffem_coeff*diffpotential*pi^2 -
664*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2 + 480*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^4 +
364*ee*muem_coeff*cos(pi*y)*sin(2*pi*t) - 90*ee*muem_coeff*cos((pi*x)/2)*sin(pi*y) +
75*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2) + 140*diffem_coeff*diffpotential*pi^2*sin(pi*y) +
16*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2) - 8*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2 +
176*ee*muem_coeff*cos(2*pi*t)^2*sin(pi*y) - 320*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t) +
200*ee*muem_coeff*cos((pi*x)/2)^2*sin(pi*y) + 464*ee*muem_coeff*cos(pi*y)^2*sin(pi*y) +
300*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)^2 - 1200*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2 +
160*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*sin(pi*y) +
104*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t) -
40*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^3*sin(2*pi*t) + 408*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) +
96*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) + 160*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*sin(pi*y) -
2000*diffem_coeff*diffpotential*pi^2*cos(pi*y)^3*sin(2*pi*t) +
400*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2*sin(pi*y) - 32*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2 -
464*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) + 186*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
272*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 1260*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t) +
500*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*sin(pi*y) - 408*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) -
96*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) -
400*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
448*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
240*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
48*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
80*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
100*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y)))/(960*diffpotential) +
(pi*cos(2*pi*t)*cos(pi*y)*(4*cos((pi*x)/2) + 24*sin(pi*y) + 20*cos((pi*x)/2)*sin(pi*y) + 20*sin(pi*y)^2 +
8*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3))/10 - (5*diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/12 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*((5*cos((pi*x)/2))/3 +
(5*sin(pi*y))/3 + (cos(pi*y)*sin(2*pi*t))/3 + 5/3))/4 - diffem_coeff*pi^2*(cos(pi*y) - sin(2*pi*t) +
2*cos(pi*y)^2*sin(2*pi*t))^2*((5*cos((pi*x)/2))/3 + (5*sin(pi*y))/3 + (cos(pi*y)*sin(2*pi*t))/3 + 5/3) +
(diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4)*((5*cos((pi*x)/2))/3 +
(5*sin(pi*y))/3 + (cos(pi*y)*sin(2*pi*t))/3 + 5/3))/4 - (diffem_coeff*pi^2*(5*cos(pi*y) -
sin(2*pi*t)*sin(pi*y))*(cos(pi*y) - sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/3 + (ee*sin(2*pi*t)*sin(pi*y)*(diffem_coeff*(pi*cos(pi*y) -
(pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) -
(ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) +
sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)))/(5*diffpotential*pi) +
diffem_coeff*pi^2*sin(pi*y)*(4*cos(pi*y)*sin(2*pi*t) + 1)*(cos((pi*x)/2) + sin(pi*y) +
cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4)*((5*cos((pi*x)/2))/3 + (5*sin(pi*y))/3 +
(cos(pi*y)*sin(2*pi*t))/3 + 5/3) - (ee*sin((pi*x)/2)^2*(4*cos((pi*x)/2) + 4*sin(pi*y) +
4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(10*ee*muem_coeff + 10*ee*muem_coeff*cos((pi*x)/2) +
10*ee*muem_coeff*sin(pi*y) + 25*diffem_coeff*diffpotential*pi^2 +
2*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)))/(1000*diffpotential^2*pi^2)) / N_A'
[]
[em_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + cos(pi/2*x)) / N_A)'
[]
[ion_ICs]
type = ParsedFunction
vars = 'N_A'
vals = 'N_A'
value = 'log((3.0 + 0.9*cos(pi/2*x)) / N_A)'
[]
[mean_en_ICs]
type = ParsedFunction
vars = 'em_ICs'
vals = 'em_ICs'
value = 'log(32. + cos(pi/2*x)) + em_ICs'
[]
[]
[BCs]
[potential_BC]
type = FunctionDirichletBC
variable = potential
function = 'potential_fun'
boundary = '0 1 2 3'
preset = true
[]
[em_BC]
type = FunctionDirichletBC
variable = em
function = 'em_fun'
boundary = '0 1 2 3'
preset = true
[]
[ion_BC]
type = FunctionDirichletBC
variable = ion
function = 'ion_fun'
boundary = '0 1 2 3'
preset = true
[]
[energy_BC]
type = FunctionDirichletBC
variable = mean_en
function = 'mean_en_fun'
boundary = '0 1 2 3'
preset = true
[]
[]
[Materials]
[field_solver]
type = FieldSolverMaterial
potential = potential
[]
[Material_Coeff]
type = GenericFunctionMaterial
prop_names = 'e N_A'
prop_values = 'ee N_A'
[]
[ADMaterial_Coeff_Set1]
type = ADGenericFunctionMaterial
prop_names = 'diffpotential diffion muion'
prop_values = 'diffpotential diffion muion'
[]
[Material_Coeff_Set2]
type = ADMMSEEDFRates
electrons = em
mean_energy = mean_en
prop_names = 'diffem muem diffmean_en mumean_en'
prop_values = 'diffem muem diffmean_en mumean_en'
d_prop_d_actual_mean_en = 'diffem_coeff muem_coeff diffmean_en_coeff mumean_en_coeff'
[]
[Charge_Signs]
type = GenericConstantMaterial
prop_names = 'sgnem sgnion sgnmean_en'
prop_values = '-1.0 1.0 -1.0'
[]
[]
[Postprocessors]
[em_l2Error]
type = ElementL2Error
variable = em
function = em_fun
[]
[ion_l2Error]
type = ElementL2Error
variable = ion
function = ion_fun
[]
[potential_l2Error]
type = ElementL2Error
variable = potential
function = potential_fun
[]
[mean_en_l2Error]
type = ElementL2Error
variable = mean_en
function = mean_en_fun
[]
[h]
type = AverageElementSize
[]
[]
[Preconditioning]
active = 'smp'
[smp]
type = SMP
full = true
[]
[fdp]
type = FDP
full = true
[]
[]
[Executioner]
type = Transient
start_time = 50
end_time = 51
# dt = 0.008
dt = 0.02
automatic_scaling = true
compute_scaling_once = false
petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
solve_type = NEWTON
line_search = none
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = 'lu NONZERO 1.e-10'
scheme = bdf2
nl_abs_tol = 1e-13
[]
[Outputs]
perf_graph = true
[out]
type = Exodus
interval = 10
[]
[]