Heun

Heun's (aka improved Euler) time integration method.

Heun's (or "improved Euler") time integration method is second-order accurate in time. It is a two-step explicit method and a special case of the 2nd-order Runge-Kutta method.

Description

With $var element = document.getElementById("moose-equation-c6f8419d-74cd-454b-99e3-6e0ee3151699");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-7f73b567-1e2d-417f-9e5e-a67a236990ff");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-fdef9049-efc5-41ad-8d51-5e6a96c42903");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-88152859-05ce-4fc2-bc3f-1a906b1009b6");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, and $var element = document.getElementById("moose-equation-03043249-9972-47c3-8232-607ed2cbd40a");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the previous step, Heun's method can be written:

var element = document.getElementById("moose-equation-8af9d9d6-4c4c-4b1a-9565-7a3bd3a1345f");katex.render("U(t+\\Delta t) = U(t) + \\dfrac{\\Delta t}{2} \\left(A(t, U(t)) + A(t,U(t) + \\Delta t A(t, U(t)) ) \\right)", 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-c566a1de-f736-4dcf-b977-cbb63551bc68");katex.render("\\begin{array}{c|cc} 0 & 0 \\\\ 1 & 1 & 0 \\\\ \\hline & 1/2 & 1/2 \\end{array}", element, {displayMode:true,throwOnError:false});

warning

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

warning

ExplicitRK2-derived TimeIntegrators (ExplicitMidpoint, Heun, Ralston) and other multistage TimeIntegrators are known not to work with Materials/AuxKernels that accumulate 'state' and should be used with caution.

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