ExplicitTVDRK2

Explicit TVD (total-variation-diminishing) second-order Runge-Kutta time integration method.

Description

The method Gottlieb and Shu (1998) consists of two stages:

Stage 1.

var element = document.getElementById("moose-equation-c07a9d29-aadf-4a35-b695-653f797e9256");katex.render("R_{NL} = M(U^{(1)}-U^n)/\\Delta t - F(t^n,U^n)", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-8c02a526-3319-4251-bf74-4f01d4668115");katex.render("t^{(1)} = t^{n} + \\Delta t = t^{n+1}", element, {displayMode:true,throwOnError:false});

Stage 2.

var element = document.getElementById("moose-equation-bbac1e3b-02a5-4f97-9139-0fb5d450fc69");katex.render("R_{NL} = M(2U^{(2)}-U^{(1)}-U^n)/(2\\Delta t) - (1/2)F(t^{(1)},U^{(1)})", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-b9173255-6417-47d2-95b4-42b789b85508");katex.render("U^{n+1} = U^{(2)}", element, {displayMode:true,throwOnError:false});

The method requires two mass matrix (linear) system solves per timestep. Although strictly speaking these are "two stage" methods, we treat the "update" step as a third stage, since in finite element analysis the update step requires a mass matrix solve.

warning

To use the explicit TimeIntegrators derived from this method, you must generally add "implicit=false" to the Kernels, Materials, etc. used in your simulation, so that MOOSE evaluates them correctly! An important exception are TimeDerivative kernels, which should never be marked "implicit=false".

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

References

S. Gottlieb and C. W. Shu. Total variation diminishing runge-kutta schemes. Mathematics of computation of the American Mathematical Society, 67(221):73–85, 1998.

@article{gottlieb1998,
    author = "Gottlieb, S. and Shu, C. W.",
    title = "Total variation diminishing Runge-Kutta schemes",
    year = "1998",
    journal = "Mathematics of computation of the American Mathematical Society",
    volume = "67",
    number = "221",
    pages = "73-85"
}

Description
Input Parameters
References