INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2003; 41:951–976 (DOI: 10.1002/d.475) A Godunov method for the computation of erosional shallow water transients L. Fraccarollo 1 , H. Capart 2; ∗; † and Y. Zech 3 1 Dipartimento di Costruzioni e Tecnologia Avanzata, Universit a di Messina, and Dipartimento di Ingegneria Civile e Ambientale, Universit a degli Studi di Trento, Italy 2 Department of Civil Engineering, Universit e catholique de Louvain, and Fonds National de la Recherche Scientique, Belgium. Current aliation:Department of Civil Engineering, National Taiwan University, Taiwan, ROC 3 Department of Civil Engineering, Universit e catholique de Louvain, Belgium SUMMARY A Godunov method is proposed for the computation of open-channel ows in conditions of rapid bed erosion and intense sediment transport. Generalized shallow water equations govern the evolution of three distinct interfaces: the water free-surface, the boundary between pure water and a sediment transport layer, and the morphodynamic bottom prole. Based on the HLL scheme of Harten, Lax and Van Leer (1983), a nite volume numerical solver is constructed, then extended to second-order accuracy using Strang splitting and MUSCL extrapolation. Lateralisation of the momentum ux is adopted to handle the non-conservative product associated with bottom slope. Computational results for erosional dam-break waves are compared with experimental measurements and semi-analytical Riemann solutions. Copyright ? 2003 John Wiley & Sons, Ltd. KEY WORDS: nite volume; shallow-water equations; sediment transport; erosional dam-break problem 1. INTRODUCTION Finite volume schemes have matured in recent years into powerful tools for the computation of shallow-water ows over rigid bottom boundaries. Successive developments have produced schemes with good shock-capturing properties [1; 2], second-order accuracy [3; 4], and the ability to deal with irregular bottom proles [5; 6]. Recent applications have further extended the scope from pure water transients to mudows and debris surges over non-erodible bound- aries [7; 8]. Other computational approaches deal with alluvial channels, in which sediment motion is gentle and the bottom boundary evolves slowly [9; 10]. The present work addresses the case of strong erosional ows, encountered in various conditions of geomorphological and engineering interest. These include valley forming oods [11], debris surges rushing down ∗ Correspondence to: H. Capart, Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, 158 Chow-Shan Rd, Taipei 10617, Taiwan, Republic of China. † E-mail: hcapart@peace.hy.ntu.edu.tw Received September 2001 Copyright ? 2003 John Wiley & Sons, Ltd. Revised 16 October 2002