Department of Applied Mathematics, University of Waterloo
The numerical scheme in IGW is a projection method based on methods developed by Bell, Colella and Glaz (1989), Bell, Solomon and Szymaczak (1989) and Bell and Marcus (1992). This projection method can only be used if the projected variables are divergence-free, i.e., the flow is incompressible.
We have described the time stepping, spatial and temporal accuracy of the numerical method in the previous talk. In this second talk, we will restrict our attention to the construction of the projection matrix. We have applied the Boussinesq approximation to eliminate the projection operator from depending on time. The projection is then approximated by using a local basis of discretely divergence-free vector fields. Lastly, we discuss the elimination of boundary dependence of the projection by introducing appropriate left and right boundary conditions.