ExplicitEuler

Time integration using the explicit Euler method.

The explicit Euler method is only first-order accurate in time.

Description

With $var element = document.getElementById("moose-equation-ce64e767-1c86-48f1-a1d2-ec3f839ee775");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-45df8df0-8584-485a-89b3-f91bd8f55806");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-35918650-4fc1-4a37-affa-8b1bf9f8447e");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-88bd167b-f534-47ec-9e1e-bd14eb33c183");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, and $var element = document.getElementById("moose-equation-9cec073f-bb62-4619-9cfd-46714a9fb100");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the previous step, the explicit Euler method can be written:

var element = document.getElementById("moose-equation-d74159a7-6e13-4894-ae65-85db1f803691");katex.render("U(t+\\Delta t) = U(t) + \\Delta t A(t, U(t))", element, {displayMode:true,throwOnError:false});

This method can be expressed as a Runge-Kutta method with the following Butcher Tableau:

var element = document.getElementById("moose-equation-dff69ae7-4ca8-4330-ba5a-6889c3b253c8");katex.render("\\begin{array}{c|c} 0 & 0 \\\\ \\hline & 1 \\end{array}", element, {displayMode:true,throwOnError:false});

note

The ActuallyExplicitEuler implements the same algorithm but without forming the non linear system, making it faster and use less memory.

warning

All kernels except time-(derivative)-kernels should have the parameter implicit=false to use this time integrator.

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