A sparse mesh for compact finite difference-Fourier solvers with radius-dependent spectral resolution in circular domains. (English) Zbl 1350.65090
Summary: 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.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
Keywords:
radial mesh; compact finite differences; CFL condition; elliptic equations; parabolic equations; cylindrical domains; algorithmReferences:
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