Multigrid solution of the Euler equations on unstructured and adaptive meshes.

*(English)*Zbl 0643.76079
Multigrid methods, 3rd Conf., Copper Mountain/Colo. 1987, Lect. Notes Pure Appl. Math. 110, 413-429 (1988).

[For the entire collection see Zbl 0641.00031.]

A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structure multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structure multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

##### MSC:

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

65Z05 | Applications to the sciences |