BDF2

Second order backward differentiation formula time integration scheme.

The backwards differencing formula of second order, BDF-2, is a linear, two-step, second-order method. It is A-stable.

Description

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

Ut=A(t,U(t))\dfrac{\partial U}{\partial t} = A(t, U(t))

Using t+2Δtt+2\Delta t for the current time step, t+Δtt+\Delta t for the previous step, and tt for the one before that, BDF-2 can be written:

U(t+2Δt)=43U(t+Δt)13U(t)+23ΔtA(t+2Δt,U(t+2Δt))U(t+2\Delta t) = \dfrac{4}{3}U(t+\Delta t) - \dfrac{1}{3}U(t) + \dfrac{2}{3} \Delta t A \left(t + 2\Delta t, U(t + 2\Delta t) \right)

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