Abstract
Mesh partitioning is significant to the efficiency of parallel computational fluid dynamics simulations. The most time-consuming parts of parallel computational fluid dynamics simulations are iteratively solving linear systems derived from partial differential equation discretizations. This article aims at mesh partitioning for better iterative convergence feature of this procedure. For typical computational fluid dynamics simulations in which partial differential equations are discretized and solved after the mesh is partitioned, numerical information of the linear systems is not available yet during mesh partitioning. We propose to construct approximations for matrix elements and theoretically find out that for finite-volume-based problems, the face area can approximate the corresponding matrix element well. A mesh partitioning scheme using the matrix value approximations for better iterative convergence behavior is implemented and numerically testified. The results show that our method can capture the most important factor influencing the matrix values and achieve partitions with good performance throughout the simulations with non-uniform meshes. The novel partitioning strategy is general and easy to implement in various partitioning packages.
Highlights
It is widely known that large-scale computational fluid dynamics (CFD) simulations usually require a large amount of computational effort
There are two important issues when we attempt to use matrix value approximations in mesh partitioning for better iterative convergence feature: 1. How should we indicate the matrix values on the mesh level before the partial differential equations (PDEs) discretization? we should work out easy and appropriate approximations for the values of off-diagonal matrix entries derived from the discretization on the mesh
The partitioning heuristics only need to guarantee that the load imbalance (LIB) be restricted within 5%
Summary
It is widely known that large-scale computational fluid dynamics (CFD) simulations usually require a large amount of computational effort. Parallel computing is introduced to help solve these problems within acceptable time. For a parallel CFD problem, the core procedure is solving the partial differential equations (PDEs) in parallel. In many CFD platforms such as Fluent Inc.[1] and OpenFOAM,[2] in the preprocessing phase, mesh is first generated from the geometry and partitioned into several sub-domains. The governing equations are discretized on the partitioned mesh and the problem is eventually transformed into solving a sequence of linear systems in parallel. Up to 80% of the CPU time for a flow
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