UNCORRECTED PROOF FLD 1489 pp: 1–20 (col.fig.: Nil) PROD. TYPE: COM ED: Vijaya PAGN: Padmashini -- SCAN: PMonica INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (in press) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fld.1489 1 Lattice Boltzmann methods for shallow water flow applications Guido Th¨ ommes 1 , Mohammed Sea¨ ıd 2 and Mapundi K. Banda 3, ∗, † 3 1 Fraunhofer Institut f¨ ur Techno- und Wirtschaftsmathematik, Kaiserslautern 67663, Germany 2 Fachbereich Mathematik, Universit¨ at Kaiserslautern, Kaiserslautern 67663, Germany 5 3 School of Mathematical Sciences, University of KwaZulu-Natal, Scottsville 3209, South Africa SUMMARY 7 We apply the lattice Boltzmann (LB) method for solving the shallow water equations with source terms such as the bed slope and bed friction. Our aim is to use a simple and accurate representation of the 9 source terms in order to simulate practical shallow water flows without relying on upwind discretization or Riemann problem solvers. We validate the algorithm on problems where analytical solutions are available. 11 The numerical results are in good agreement with analytical solutions. Furthermore, we test the method on a practical problem by simulating mean flow in the Strait of Gibraltar. The main focus is to examine the 13 performance of the LB method for complex geometries with irregular bathymetry. The results demonstrate its ability to capture the main flow features. Copyright  2007 John Wiley & Sons, Ltd. 15 Received 17 December 2006; Revised 16 February 2007; Accepted 17 February 2007 KEY WORDS: shallow water equations; lattice Boltzmann method; Strait of Gibraltar 1. INTRODUCTION 17 The lattice Boltzmann (LB) method, also popularly referred to as LBM, is an alternative numerical tool for simulating fluid flows [1]. The method is based on statistical physics and models the fluid 19 flow by tracking the evolution of distribution functions of the fluid particles in discrete phase space. The essential approach in the LB method lies in the recovery of macroscopic fluid flows from 21 the microscopic flow behaviour of the particle movement or the mesoscopic evolution of particle distributions. The basic idea is to replace the nonlinear differential equations of macroscopic 23 fluid dynamics by a simplified description modelled on the kinetic theory of gases. To obtain the hydrodynamic behaviour, the Chapman–Enskog expansion which exploits a small mean free 25 path approximation to describe slowly varying solutions of the underlying kinetic equations is 27 ∗ Correspondence to: Mapundi K. Banda, School of Mathematical Sciences, University of KwaZulu-Natal, Scottsville 3209, South Africa. † E-mail: bandamk@ukzn.ac.za. Contract/grant sponsor: Kaiserslautern University of Technology Contract/grant sponsor: University of KwaZulu-Natal Copyright  2007 John Wiley & Sons, Ltd.