Time Step Parameter#
Time step parameter = <float>
Description / Usage#
This card allows the user to vary the time integration scheme. The usual settings are:
Backward Euler method (1st order in time)
Trapezoid rule (2nd order in time)
This is a sample card that sets the time integration scheme to Trapezoidal rule:
Time step parameter = 0.5
One should usually use the Trapezoid rule. When a large time step \(\Delta t\) is used the Trapezoid rule can exhibit oscillations. If such a large \(\Delta t\) is required then the Backward Euler method can be used (it will damp oscillations), albeit at a cost of accuracy.
If we designate the time step parameter as \(\theta\), the solution at time step \(n\) as \(y^n\), and the PDE to be solved as
then the time integration method takes the form
Note that there is no choice of finite \(\theta\) that will yield a Forward Euler method. See Gartling (1987) for more information.
For porous flow problems with mass lumping, you should always choose backward Euler method.
SAND86-1816: NACHOS 2: A Finite Element Computer Program for Incompressible Flow Problems - Part 2 - User’s Manual, Gartling, David K. (September, 1987).