Numerical methods based on discontinuous Galerkin and finite volume methods for shallow water model and applications

Abstract

Shallow water equations (SWE) can be used to model many real flow problems such as dam break, tsunami and flood. In this dissertation, we have developed three numerical schemes for solving these equations. The first scheme is the wellbalanced discontinuous Galerkin (DG) method with weighted average flux (WAF) for one-dimensional SWE. The second scheme is developed to obtain more realistic results for the one-dimensional flow, where the one-dimensional SWE is considered for arbitrary cross-sectional areas, based on the finite volume method (FVM). And the third scheme is developed to solve real world flows by considering the two-dimensional SWE based on the well-balanced FVM with WAF.