Parallel linear multigrid algorithms for the acceleration of compressible flow calculations.

*(English)*Zbl 0978.76055From the conclusion: The objective of this paper is to develop a flow solution technique that offers a good compromise between parallel and numerical efficiency. The proposed solver is built around two main components: I. A widely adopted strategy for the SPMD parallelization of finite element type calculations. This strategy maximizes the parallel efficiency of the resulting solver by explicitly enforcing data locality through domain partitioning techniques. Moreover, by using standard message passing environments such as PVM or MPI, the portability of the solver is also guaranteed; II. A multigrid acceleration technique for the solution of large sparse linear systems arising from linearized implicit time integration techniques or dynamic mesh deformation procedures. A multigrid by volume agglomeration strategy has been selected for which the multigrid hierarchy can be automatically generated using the sole data given by the finest discretization of the computational domain. This aspect is of particular importance in the context of the SPMD parallelization strategy considered in this study: the problem of generating local data structures for coarse grid topologies and data exchange at submesh interfaces is treated in parallel without resorting to an appropriate (multimesh) partitioning technique. The resulting parallel flow solver has been extensively tested and evaluated in the two-dimensional case. Its application to three-dimensional problems is currently done in the context of the N3S-NATUR industrial CFD package; preliminary results have been presented here for steady Euler flows.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76M10 | Finite element methods applied to problems in fluid mechanics |

76N15 | Gas dynamics (general theory) |

65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |

65Y05 | Parallel numerical computation |

##### Keywords:

SPMD parallelization; message passing environment; multigrid acceleration technique; large sparse linear systems; linearized implicit time integration; dynamic mesh deformation; volume agglomeration strategy; N3S-NATUR industrial CFD package; Euler flows##### Software:

Wesseling
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\textit{G. Carré} et al., Comput. Methods Appl. Mech. Eng. 184, No. 2--4, 427--448 (2000; Zbl 0978.76055)

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