A comparison of numerical schemes for the GPU-accelerated simulation of variably-saturated groundwater flow

The optimal strategy to numerically solve the Richards equation is problem-dependent, especially on GPUs because an efficient numerical scheme on CPU might not scale well on GPU. In this work, four numerical schemes are coded to investigate their parallel performance on CPU and GPU. The results indicate that the scaling of Richards solvers on GPU is affected by the numerical scheme, the linear system solver, the soil constitutive model, the code structure, the problem size and the adaptive time stepping strategies. Compared with CPU, parallel simulations on GPU exhibit stronger variance in the scaling of different code sections. The poorly-scaled components could deteriorate the overall scaling. Under all circumstances, using a GPU significantly enhances computational speed, especially for large problems. Clearly, GPU computing have significant potential in accelerating large-scale hydrological simulations, but care must be taken on the design and implementation of the model structure.

Automated summary

The optimal strategy for solving the Richards equation numerically depends on the specific problem, particularly when using GPUs. This study investigates the parallel performance of four numerical schemes on both CPUs and GPUs. The results show that the scaling of Richards solvers on GPUs is influenced by various factors. Compared to CPUs, parallel simulations on GPUs exhibit significant variation in scaling across different code sections, with poorly-scaled components potentially impacting overall performance. Nonetheless, using GPUs can greatly enhance computational speed, especially for large-scale problems.