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 cross-
sectional 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 well-
balanced 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.