Solution of Poisson Equation on Unstructured Grids

Solutions of the Poisson and the Helmholtz-type equations are often required in geophysical flow simulations. Examples are, in the incompressible/anelastic approximation for nonhydrostatic mesoscale models and in the vorticity-streamfunction formulation for simple global circulation models. In this paper a methodology for solving the Poisson equation on unstructured adaptive grids is presented. The algorithms for reducing the matrix bandwidth are discussed and the solver is validated against analytical solutions of benchmark cases.