Department of Applied Mathematics, University of Waterloo
We will present two talks on the numerical methods used in a two-dimensional internal gravity wave model named IGW, which solves the time-dependent, incompressible Navier-Stokes equations. The numerical scheme in IGW is a projection method based on works by Bell, Colella and Glaz (1989), Bell, Solomon and Szymaczak (1989) and Bell and Marcus (1992). Unlike the previous projection methods, this method is of second-order temporal accuracy and the nonlinear advection terms are treated using a second-order Godunov-type procedure.
This first talk focuses on the time stepping of the numerical method. We obtain a temporal discretization that is second-order accurate by introducing a half-step step between the advection and the projection steps. A higher order Godunov scheme is then applied to the interpolated velocities to determine the numerical fluxes at the cell edges.