Abstract

I present a new algorithm for solving the streamfunction-vorticity equations in irregular, multiply connected regions. To avoid mesh generation difficulties associated with unstructured, body fitted grids, I embed the irregular domain in a uniform Cartesian mesh. The governing partial differential equations are discretized using standard finite volume and finite difference methods away from the irregular boundary. Near the irregular boundary, special discretizations are used to impose boundary conditions. I solve the vorticity transport equation using the high-resolution algorithms in the clawpack package and capacity form differencing to handle the irregular geometry. By modifying the capacity function for small cells cut by the boundary, I can avoid the small cell instability problem associ...

Citations