A High Performance GPU Implementation of the Lattice Boltzmann Method with Open Boundary Conditions for Solving the Shallow Water Equations in Real Scenarios

Abstract

For the past two decades, the lattice Boltzmann method has proven to be an accurate and efficient alternative for solving the shallow water equations. This system of equations describes the evolution of the free-surface of a fluid and it is applicable in open ocean simulations, such as tsunamis. In this work, an efficient GPU implementation of the lattice Boltzmann method for solving the shallow water equations is developed. A model for the treatment of open boundary conditions is proposed. The presented model is validated theoretically and experimentally. Several theorems are established and proven in order to ensure the well-balanced property of the method in arbitrary nodes and boundary nodes. Numerical experiments consists in a lake at rest, cylindrical dam break flows over flat and complex bathymetries, and real scenarios of tsunami. A deep analysis on the efficience of the method is performed. The code is parallelized under the “single instruction, multiple thread” model used when working with CUDA for developing GPU accelerated applications. Several low level optimizations have been studied and applied in order to achieve a competitive performance with respect to those reported in the literature. Additionally, an exhaustive performance analysis of different methods to integrate boundary conditions in a unified CUDA kernel for a time step is presented. Finally, an open source framework of the method has been implemented. This framework aims to be applicable to other systems of equations under minimum modifications.