ImplicitMidpoint

Second-order Runge-Kutta (implicit midpoint) time integration.

The implicit midpoint method is second-order accurate. As a Gauss-Legendre method it is A-stable.

Description

With , the vector of nonlinear variables, and , a nonlinear operator, we write the PDE of interest as:

Using for the current time step, and for the previous step, the implicit midpoint integration scheme can be written:

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

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