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 $var element = document.getElementById("moose-equation-adbd7414-7bbf-4450-9f43-8a5d3a8b0db3");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-f26ae07e-2a47-4d24-ae1d-9af324abf26f");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-a745d5de-4a59-40eb-867b-511cb566e04f");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-f811e138-e129-42ec-8f4a-0d65df0f7b49");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, and $var element = document.getElementById("moose-equation-e686ed70-97ed-4147-916f-3dc9dad6df1a");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the previous step, Heun's method can be written:

var element = document.getElementById("moose-equation-e238ec0d-2a89-478a-b35e-47cd418f088d");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-84b5da8f-c434-48b8-95b2-1d9cbe379fd9");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