AccelerationByAveraging

An acceleration scheme based on averaging a density over a periodic cycle

Overview

AccelerationByAveraging is an acceleration method that makes a growth prediction for a species based on the average rate of change for a given time period.

The growth of a species for a constant rate of change for a given time period is:

$var element = document.getElementById("moose-equation-ad57ff18-3646-45d7-ab51-b7aac6bdaba8");katex.render("n_{T} - n_{0} = \\frac{\\text{d}n}{\\text{d}t} \\ T", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-127223cd-edca-4b46-ad85-cc4bfb9046e5");katex.render("n_{0}", element, {displayMode:false,throwOnError:false});$ is the species' density at the start of the acceleration, $var element = document.getElementById("moose-equation-db83375f-49b1-4b34-ae02-aea1013ee0f8");katex.render("n_{T}", element, {displayMode:false,throwOnError:false});$ is the density at the end of the acceleration, and $var element = document.getElementById("moose-equation-9dffc772-40a2-459c-8cc9-11091c0310d5");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the time period of the acceleration.

If the rate of change is assumed to linear, then $var element = document.getElementById("moose-equation-84ef92bb-f0d7-482f-86f0-ca5ec21343db");katex.render("\\frac{\\text{d}n}{\\text{d}t}", element, {displayMode:false,throwOnError:false});$ an be estimated by:

$var element = document.getElementById("moose-equation-9dd37da6-78a6-454f-8bb4-659e941a44f6");katex.render("\\frac{\\text{d}n}{\\text{d}t} = \\frac{n_{Ts} - n_{0s}}{t_{s}}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-8a66da11-83f7-4b0d-80eb-2322c57f18cb");katex.render("t_{s}", element, {displayMode:false,throwOnError:false});$ is some sample period of time less than $var element = document.getElementById("moose-equation-5ab76ff7-fb23-4884-9279-805a62149ce6");katex.render("T", element, {displayMode:false,throwOnError:false});$ . The subscripts $var element = document.getElementById("moose-equation-7e8eea7c-25e9-4f41-9df3-2b48e50e3867");katex.render("0s", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-47bc7cba-f8f4-477f-9319-7c21ff1e5921");katex.render("Ts", element, {displayMode:false,throwOnError:false});$ denote the beginning and end of the sample period of time, $var element = document.getElementById("moose-equation-e20dfbec-41a4-4b10-a828-3292f5694761");katex.render("t_{s}", element, {displayMode:false,throwOnError:false});$ , respectively. When converting the density to logarithmic form, AccelerationByAveraging is defined as

$var element = document.getElementById("moose-equation-81ce3cea-eebc-4edb-933c-fd17e5e8a4cd");katex.render("\\exp(N_{j, T}) - \\exp(N_{j, 0}) = \\frac{\\text{d}n}{\\text{d}t} \\ T \\\\[10pt] \\frac{\\text{d}n}{\\text{d}t} = \\frac{\\exp(N_{j, Ts}) - \\exp(N_{j, 0s})}{t_{s}}", element, {displayMode:true,throwOnError:false});$

Where $var element = document.getElementById("moose-equation-60ec34dc-d247-47df-9b22-14b32c3cc0e5");katex.render("N_{j}", element, {displayMode:false,throwOnError:false});$ is the molar density of the species in logarithmic form.

Example Input File Syntax

An example of how to use AccelerationByAveraging can be found in the test file Acceleration_By_Averaging_acceleration.i.

[Kernels]
  [Ar*_AcclerationByAveraging]
    type = AccelerationByAveraging
    variable = Ar*
    density_at_start_cycle = Ar*S
    density_at_end_cycle = Ar*T
    time_of_averaging = 73.74631268e-9
    time_of_acceleration = 2e-6
  []
[]

Input Parameters

density_at_end_cycleThe accelerated density at the end of the cycle in logarithmic form
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The accelerated density at the end of the cycle in logarithmic form
density_at_start_cycleThe accelerated density at the start of the cycle in logarithmic form
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The accelerated density at the start of the cycle in logarithmic form
time_of_accelerationThe time of acceleration
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The time of acceleration
time_of_averagingThe time difference of the averaging
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The time difference of the averaging
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
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
Unit:(no unit assumed)
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.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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

Input Files

(test/tests/accelerations/Acceleration_By_Averaging_acceleration.i)

(test/tests/accelerations/Acceleration_By_Averaging_acceleration.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 'Lymberopoulos_paper.msh'
  []
  [left]
    type = SideSetsFromNormalsGenerator
    normals = '-1 0 0'
    new_boundary = 'left'
    input = file
  []
  [right]
    type = SideSetsFromNormalsGenerator
    normals = '1 0 0'
    new_boundary = 'right'
    input = left
  []
[]

[Problem]
  type = FEProblem
[]

[Variables]
  [Ar*]
  []
[]

[AuxVariables]
  [em]
  []
  [Ar+]
  []
  [mean_en]
  []
  [potential]
  []
  [Ar*S]
  []
  [Ar*T]
  []
[]

[Kernels]
  [Ar*_AcclerationByAveraging]
    type = AccelerationByAveraging
    variable = Ar*
    density_at_start_cycle = Ar*S
    density_at_end_cycle = Ar*T
    time_of_averaging = 73.74631268e-9
    time_of_acceleration = 2e-6
  []
[]

[BCs]
  [Ar*_physical_right_diffusion]
    type = LogDensityDirichletBC
    variable = Ar*
    boundary = 'right'
    value = 1e-5
  []
  [Ar*_physical_left_diffusion]
    type = LogDensityDirichletBC
    variable = Ar*
    boundary = 'left'
    value = 1e-5
  []
[]

#MultiApp used to calculate the non-accelerated density for 1RF cycle.
#This is used to get A*T (density at end of cycle)
[MultiApps]
  [Sub]
    type = FullSolveMultiApp
    input_files = 'Acceleration_By_Averaging_acceleration_sub.i'
  []
[]

[Transfers]
  [em_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = em
    variable = em
  []
  [Ar+_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = Ar+
    variable = Ar+
  []
  [mean_en_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = mean_en
    variable = mean_en
  []
  [potential_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = potential
    variable = potential
  []
  [Ar*_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = Ar*
    variable = Ar*
  []

  [Ar*T_from_sub]
    type = MultiAppCopyTransfer
    from_multi_app = Sub
    source_variable = Ar*
    variable = Ar*T
  []
[]

[Preconditioning]
  active = 'smp'
  [smp]
    type = SMP
    full = true
  []

  [fdp]
    type = FDP
    full = true
  []
[]

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -ksp_type'
  petsc_options_value = 'lu NONZERO 1.e-10 fgmres'
[]

[Outputs]
  perf_graph = true
  [out]
    type = Exodus
  []
[]

(test/tests/accelerations/Acceleration_By_Averaging_acceleration.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 'Lymberopoulos_paper.msh'
  []
  [left]
    type = SideSetsFromNormalsGenerator
    normals = '-1 0 0'
    new_boundary = 'left'
    input = file
  []
  [right]
    type = SideSetsFromNormalsGenerator
    normals = '1 0 0'
    new_boundary = 'right'
    input = left
  []
[]

[Problem]
  type = FEProblem
[]

[Variables]
  [Ar*]
  []
[]

[AuxVariables]
  [em]
  []
  [Ar+]
  []
  [mean_en]
  []
  [potential]
  []
  [Ar*S]
  []
  [Ar*T]
  []
[]

[Kernels]
  [Ar*_AcclerationByAveraging]
    type = AccelerationByAveraging
    variable = Ar*
    density_at_start_cycle = Ar*S
    density_at_end_cycle = Ar*T
    time_of_averaging = 73.74631268e-9
    time_of_acceleration = 2e-6
  []
[]

[BCs]
  [Ar*_physical_right_diffusion]
    type = LogDensityDirichletBC
    variable = Ar*
    boundary = 'right'
    value = 1e-5
  []
  [Ar*_physical_left_diffusion]
    type = LogDensityDirichletBC
    variable = Ar*
    boundary = 'left'
    value = 1e-5
  []
[]

#MultiApp used to calculate the non-accelerated density for 1RF cycle.
#This is used to get A*T (density at end of cycle)
[MultiApps]
  [Sub]
    type = FullSolveMultiApp
    input_files = 'Acceleration_By_Averaging_acceleration_sub.i'
  []
[]

[Transfers]
  [em_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = em
    variable = em
  []
  [Ar+_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = Ar+
    variable = Ar+
  []
  [mean_en_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = mean_en
    variable = mean_en
  []
  [potential_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = potential
    variable = potential
  []
  [Ar*_to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = Sub
    source_variable = Ar*
    variable = Ar*
  []

  [Ar*T_from_sub]
    type = MultiAppCopyTransfer
    from_multi_app = Sub
    source_variable = Ar*
    variable = Ar*T
  []
[]

[Preconditioning]
  active = 'smp'
  [smp]
    type = SMP
    full = true
  []

  [fdp]
    type = FDP
    full = true
  []
[]

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -ksp_type'
  petsc_options_value = 'lu NONZERO 1.e-10 fgmres'
[]

[Outputs]
  perf_graph = true
  [out]
    type = Exodus
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files