ExplicitEuler

Time integration using the explicit Euler method.

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

Description

With $var element = document.getElementById("moose-equation-623afddc-c1ee-408e-a08e-d071ef8ba647");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-0d6bf841-4f58-4c45-8f95-43569c3a5371");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-3c735bca-fc0c-40e1-a091-e064dcb4ca45");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-6760c1ee-a30c-49f7-b773-56aa85f79718");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, and $var element = document.getElementById("moose-equation-83f63c63-df5c-43a8-9c5a-fa123bebf039");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the previous step, the explicit Euler method can be written:

var element = document.getElementById("moose-equation-ac7711c3-dae0-4498-9fc3-c85fe36a187e");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-b66328b1-f8da-476a-a4b8-05faa7e17eec");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