A sparse mesh for Compact Finite Difference-Fourier solvers with radius-dependent spectral resolution in circular domains

This paper presents a new method for the resolution of elliptic and parabolic equations in circular domains. It can be trivially extended to cylindrical domains. The algorithm uses a mixed Fourier-Compact Finite Difference method. The main advantage of the method is achieved by a new concept of mesh. The topology of the new grid keeps constant the aspect ratio of the cells, avoiding the typical clustering for radial structured meshes at the center. The reduction of the number of nodes has as a consequence the reduction in memory consumption. In the case of fluid mechanics problems, this technique also increases the time step for a constant Courant number. Several examples are given in the paper which show the potential of the method.