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 $var element = document.getElementById("moose-equation-9be45d17-cb01-4e11-85c7-65058a700140");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-75380dc8-ea5f-4bef-94fc-b670ad376432");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-7fe99a6e-a6ed-42bf-a113-ccc6c2e3bdd8");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-496d8963-a570-4fb6-99ee-be2243435c99");katex.render("t+2\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, $var element = document.getElementById("moose-equation-cfc4a9ad-ddf6-4065-be0f-7c0855050a3a");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the previous step, and $var element = document.getElementById("moose-equation-89e47321-acf5-41c3-be86-e26c231e7003");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the one before that, BDF-2 can be written:

var element = document.getElementById("moose-equation-364e3feb-d096-47e0-9176-b74fef94f2c3");katex.render("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)", element, {displayMode:true,throwOnError: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

Description
Input Parameters