High Resolution Time Integration for the Spherical Harmonics Equations

We present a high resolution time integration method for the spherical harmonics equations based on the L-Trap method of Duraisamy, et al. This method is equivalent to the Crank-Nicolson method in smooth regions of the solution and changes form in non-smooth regions of the solution to avoid artificial oscillations in the solution. The method is nonlinear in the sense that the time integration used in each cell depends on the solution there. We use a quasi-linear type approach to solve the nonlinear equations that arise. Results from test problems demonstrate the necessity of a non-oscillatory method and the effectiveness of this particular approach.