Accelerating FVM-Based Parallel Fluid Simulations with Better Grid Renumbering Methods

Abstract

Grid renumbering techniques have been shown to be effective in improving the efficiency of computational fluid dynamics (CFD) numerical simulations based on the finite volume method (FVM). However, with the increasing complexity of real-world engineering scenarios, there is still a huge challenge to choose better sequencing techniques to improve parallel simulation performance. This paper designed an improved metric (MDMP) to evaluate the structure of sparse matrices. The metric takes the aggregation of non-zero elements inside the sparse matrix as an evaluation criterion. Meanwhile, combined with the features of the cell-centered finite volume method supporting unstructured grids, we proposed the cell quotient (CQ) renumbering algorithm to further reduce the maximum bandwidth and contours of large sparse matrices with finite volume discretization. Finally, with real-world engineering cases, we quantitatively analyzed the evaluation effect of MDMP and the optimization effect of different renumbering algorithms. The results showed that the classical greedy algorithm reduces the maximum bandwidth of the sparse matrix by at most 60.34% and the profile by 95.38%. Correspondingly, the CQ algorithm reduced them by at most 92.94% and 98.70%. However, in terms of MDMP, the CQ algorithm was 83.43% less optimized than the Greedy algorithm. In terms of overall computational speed, the Greedy algorithm was optimized by a maximum of 38.19%, and the CQ algorithm was optimized by a maximum of 27.31%. The above is in accordance with the evaluation results of the MDMP metric. Thus, our new metric can more accurately evaluate the renumbering method for numerical fluid simulations, which is of great value in selecting a better mesh renumbering method in engineering applications of CFD.