GPU acceleration for general conservation equations and its application to several engineering problems

Abstract

Presented is a general method for conservation equations called SHLL (split HLL) applied using Graphics Processing Unit (GPU) acceleration. The SHLL method is a purely vector-split approximation of the classical HLL method (Harten et al., 1983 [1]) which assumes the presence of local wave propagation in the algebraic derivation of fluxes across cell surfaces. The conventional HLL flux expression terms are interface-split and wave propagation velocities estimated (where required) based on local conditions. Due to the highly local nature of the SHLL fluxes, the scheme is very efficiently applied to GPU computation since the flux, initialisation and update phases of the computation are all vectorized processes. The SHLL scheme is applied to GPU computating using Nvidia’s CUDA package. Numerical schemes are presented for solutions to the general transport (convection–diffusion) equation, Euler Equations and Shallow Water Equations with results presented for several benchmark gas and shallow water flow engineering problems. Computational times are compared between high-end GPU (Nvidia C1060) and CPU (Intel Xeon 3.0 GHz, 32 MB cache) systems with reported speedups of over 67 times when applied to two dimensional simulations with multi-million cell numbers.