A cache-efficient reordering method for unstructured meshes with applications to wall-resolved large-eddy simulations

Abstract

Unstructured meshes provide a distinct advantage for handing complex geometries. However, the low cache utilization due to mesh-related data access patterns raises particular challenges in achieving a high computing efficiency for large-eddy simulations. We propose a geometrical-based mesh reordering method to improve cache utilization. The proposed method utilizes a Hilbert space-filling curve that passes through each cell once, guiding the reordering of the cells of the unstructured mesh. The reordering enables neighboring cells to be stored in contiguous areas of memory as much as possible. The performance of the proposed method is validated by two- and three-dimensional unstructured meshes. According to the memory and spatial distances, the proposed reordering method significantly improves data localities. Consequently, the cache hit rate is increased and the computing efficiency is improved. The proposed reordering method is then applied to large-eddy simulations of flows around an underwater vehicle model with ReL=1.2×106. To fully resolve the near-wall flows, an unstructured mesh consisting of 1.476 billion cells is used, which is partitioned into 12800 subdomains. The computed velocity profiles, pressure and friction coefficients are in good agreement with the experimental measurements. The computational costs are reduced by using the proposed reordering method.