Fully GPU resident wavelet-based adaptive gridding: application to two-dimensional finite volume hydrodynamic modelling

First order finite volume (FV1) models that use uniform grids are often used in computational engineering, but may become prohibitively costly to run on a fine resolution and/or large areas. To reduce these costs, FV1 models have adopted adaptive gridding or parallelisation on graphics processing units (GPU). FV1 models that combine adaptive gridding and parallelisation usually generate the adaptive grid on the central processing unit (CPU), yielding extra costs for data transfer between the CPU and the GPU. This paper presents a computational innovation that avoids these costs by enabling GPU resident adaptive gridding, based on the multiresolution analysis (MRA) of Haar wavelets (HWs). It combines the indexing of Z order curves, to ensure coalesced access of GPU memory, and a newly adopted Parallel Tree Traversal (PTT) that minimises warp divergence of GPU threads. The resulting GPU resident adaptive gridding method is presented as part of a parallelised, HWFV1 hydrodynamic model (GPU-HWFV1). The model's runtime performance is benchmarked against its CPU predecessor (CPU-HWFV1) and a GPU-FV1 uniform grid model for a range of test cases ran on the finest resolution grid accessible to the HWFV1 models. Tests demonstrate the robustness of the results. As for runtime performance, GPU-HWFV1 is up to 400x faster than CPU-HWFV1, while remaining 30x faster than GPU-FV1 especially in applications that require increased depth in the grid resolution and high sensitivity to resolution refinement. The findings are significant, making a strong case for applying the proposed GPU resident adaptive gridding method to further speed-up FV1 models.