A well-balanced solver for the Saint Venant equations with variable cross-section

In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable crosssectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation a wellbalanced solver is developed, assuring the C-property and depth positivity. The performance of this method is studied in several test cases focusing on accurate capturing of steady states.