ImplicitEuler

This is the default time integrator in MOOSE. It is first-order in time, and L-stable, making it suitable to integrate stiff equation systems. It is also known as the backwards Euler method.

Description

With $var element = document.getElementById("moose-equation-b2734881-6b83-45dd-b9ba-2a8f7aa1a9d6");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-4757845d-663e-44f0-900a-ff4d75dcfb4a");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-a940cc77-ae4f-4aee-ad19-8b27db215988");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-cfd9f16a-6d22-44a5-86a3-0a1620c7f701");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, and $var element = document.getElementById("moose-equation-be6f0527-abdc-4a4b-8acc-8fe9e09c7399");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the previous step, the implicit Euler time integration scheme can be written:

var element = document.getElementById("moose-equation-da923cae-386b-4b14-acd8-4389dd0b746f");katex.render("U(t+\\Delta t) = U(t) + \\Delta t A(t+\\Delta t, U(t+\\Delta t))", element, {displayMode:true,throwOnError:false});

This is an implicit system with $var element = document.getElementById("moose-equation-0ad4e50b-2576-4dd8-8306-3a7d7cac8873");katex.render("U(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ , the variable to solve for, appearing on both sides of the equation. We solve this system iteratively, usually with a Newton or Newton-Krylov method as described in the non linear system solve documentation.

Input Parameters

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