Using hierarchical Cartesian grids with multigrid acceleration

This paper describes the use of a multigrid strategy on hierarchical Cartesian grids for the simulation of small amplitude inviscid waves in a tank. Quadtree grid generation by recursive subdivision is described and the grid storage system discussed along with the associated grid operations, such as neighbour finding and identification of empty cells. A multigrid strategy using a novel global approach is discussed with respect to its application to quadtree grids. A comparative study is presented of the performance of multigrid parameters, such as number of iterations at each level, grid visiting schedules and different prolongation operators. It is shown that quadtree grids are ideally suited to a multigrid strategy when the solution of the elliptic Laplace's equation is sought, with savings of the order of 90% in CPU time with respect to a non‐multigrid solution.