Solving the Savage-Hutter equations for granular avalanche flows with a second-order Godunov type method on GPU

In this article, we apply Davis's second-order predictor-corrector Godunov type method to numerical solution of the Savage-Hutter equations for modeling granular avalanche flows. The method uses monotone upstream-centered schemes for conservation laws (MUSCL) reconstruction for conservative variables and Harten-Lax-van Leer contact (HLLC) scheme for numerical fluxes. Static resistance conditions and stopping criteria are incorporated into the algorithm. The computation is implemented on graphics processing unit (GPU) by using compute unified device architecture programming model. A practice of allocating memory for two-dimensional array in GPU is given and computational efficiency of two-dimensional memory allocation is compared with one-dimensional memory allocation. The effectiveness of the present simulation model is verified through several typical numerical examples. Numerical tests show that significant speedups of the GPU program over the CPU serial version can be obtained, and Davis's method in conjunction with MUSCL and HLLC schemes is accurate and robust for simulating granular avalanche flows with shock waves. As an application example, a case with a teardrop-shaped hydraulic jump in Johnson and Gray's granular jet experiment is reproduced by using specific friction coefficients given in the literature.