CentralDifference

Implementation of explicit, Central Difference integration without invoking any of the nonlinear solver

Description

Central difference integration is a common explicit integration scheme, typically used in structural dynamics. For a variable, $var element = document.getElementById("moose-equation-2c9312d3-181f-4e5f-93e4-7c13ed44aa10");katex.render("u", element, {displayMode:false,throwOnError:false});$ , at time $var element = document.getElementById("moose-equation-ba28c54c-2d80-4caa-b893-96f8f53c8d29");katex.render("t", element, {displayMode:false,throwOnError:false});$ with a time step, $var element = document.getElementById("moose-equation-bdc1d58a-346f-4003-b6a6-c01f1f046ed9");katex.render("\\Delta t", element, {displayMode:false,throwOnError:false});$ , the central difference approximations for the first and second time derivatives, $var element = document.getElementById("moose-equation-1362302a-c345-4628-a0a5-3c9068939229");katex.render("\\dot{u}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-67251610-3a48-4123-a91d-f0882ab1de9e");katex.render("\\ddot{u}", element, {displayMode:false,throwOnError:false});$ , are given as,

$var element = document.getElementById("moose-equation-b290f041-de15-4189-a388-d23797f23ecb");katex.render("\\begin{aligned} \\mathbf{\\dot{u}}(t) &=& \\frac{\\mathbf{u}(t+\\Delta t)-\\mathbf{u}(t-\\Delta t)}{2 \\Delta t} \\\\ \\mathbf{\\ddot{u}}(t) &=& \\frac{\\mathbf{u}(t+\\Delta t)-2\\mathbf{u}(t)+\\mathbf{u}(t-\\Delta t)}{\\Delta t^2} \\end{aligned}", element, {displayMode:true,throwOnError:false});$

The central difference time integrator derives from the ActuallyExplicitEuler class and therefore circumvents the nonlinear solver. It can be used with consistent, lumped or lump_preconditioned, solve_type options. Information on these solve options can be found on the ActuallyExplicitEuler page.

Input Parameters

solve_typeconsistentThe way to solve the system. A 'consistent' solve uses the full mass matrix and actually needs to use a linear solver to solve the problem. 'lumped' uses a lumped mass matrix with a simple inversion - incredibly fast but may be less accurate. 'lump_preconditioned' uses the lumped mass matrix as a preconditioner for the 'consistent' solve
Default:consistent
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:consistent, lumped, lump_preconditioned
Controllable:No
Description:The way to solve the system. A 'consistent' solve uses the full mass matrix and actually needs to use a linear solver to solve the problem. 'lumped' uses a lumped mass matrix with a simple inversion - incredibly fast but may be less accurate. 'lump_preconditioned' uses the lumped mass matrix as a preconditioner for the 'consistent' solve
use_constant_massFalseIf set to true, will only compute the mass matrix in the first time step, and keep using it throughout the simulation.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If set to true, will only compute the mass matrix in the first time step, and keep using it throughout the simulation.
variablesA subset of the variables that this time integrator should be applied to
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:A subset of the variables that this time integrator should be applied to

Optional 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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Description
Input Parameters