Lattice Boltzmann method for two-dimensional shallow water equations with CUDA

This paper presents the Lattice Boltzmann method (LBM) for two dimensional shallow water equations to simulate dam break problem. We implemented sequential code and compared it with the exact solution. Then, we implemented three parallel programs with the Compute Unified Device Architecture (CUDA). The first parallel version is a straightforward implementation. The second parallel version reduces the calculations of distribution function in the LBM. The third parallel program has fixed the branch divergence problem with branch distribution. Speed up for the third parallel program is increased approximately 2.1x from the first parallel program, and it is increased approximately 22.7x from the sequential program version.

I. Introduction

Shallow water equations [1] are the hyperbolic partial differential equations that can be applied to predict or study shallow water flows in river or sea. Due to their complexities in solving the equations, we need efficient and accurate numerical methods to approximate the equations. In this work, we apply the Lattice Boltzmann method [3] (LBM) for solving the equations in two dimensions. The advantage of this method is that it is easy to implement using parallel computing. So, it can reduce computational time for the case of very large computational domain. The parallel computations have been done by using NVIDIA CUDA Technology [4] such that it can improve the computational efficiency on both CPU and GPU computations. We will modify the sequential algorithm proposed by Zhou [1] to be new parallel versions to increase the speed of numerical simulations where the case study is dam-break simulation over a wet bed