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 $var element = document.getElementById("moose-equation-d3d2545b-d184-4143-a3c6-faa6993677d9");katex.render("U", element, {displayMode:false,throwOnError:false});$ , the vector of nonlinear variables, and $var element = document.getElementById("moose-equation-9c52b805-90dd-4b23-9744-43db73efe24c");katex.render("A", element, {displayMode:false,throwOnError:false});$ , a nonlinear operator, we write the PDE of interest as:

var element = document.getElementById("moose-equation-960185cf-6604-4cf7-827e-d201362a242f");katex.render("\\dfrac{\\partial U}{\\partial t} = A(t, U(t))", element, {displayMode:true,throwOnError:false});

Using $var element = document.getElementById("moose-equation-68332992-b93e-42a2-b29d-e28e2ef6d617");katex.render("t+2\\Delta t", element, {displayMode:false,throwOnError:false});$ for the current time step, $var element = document.getElementById("moose-equation-12fb7169-98ba-442b-aeb9-54ae5c234768");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ for the previous step, and $var element = document.getElementById("moose-equation-3ffa7fe4-0f9d-462d-a905-0612774f4f62");katex.render("t", element, {displayMode:false,throwOnError:false});$ for the one before that, BDF-2 can be written:

var element = document.getElementById("moose-equation-fc0b1ba5-5638-49d2-b090-d93e07609a10");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