Time Explicit Integrator

After discretization in space, an explicit ordinary system of differential equations is obtained. The standard procedure is to integrate the DG system of equations with the explicit Runge-Kutta family of methods.

The combination is in the literature denoted RK-DG. Often, a p+1 order RK method is combined with p:th order shape functions. See Ref. 1 for details. The new integrator supports a CFL-based time step regulator. The stability limitation for the time step k is of the sort

where C is a moderate constant.

COMSOL Multiphysics can compute the largest time step k based on the smallest mesh size h, the order of the shape functions, and the maximum wave speed in the domain. Under Time stepping, select From expressions to automatically compute the largest stable time step k. Under Cell time scale expressions add wahw.wtc as the variable for the Estimate of Maximum Wave Speed when using The Wave Form PDE Interface.

• Time Explicit Solver • Introduction to Solvers and Studies