Numerical methods for shallow water equations

Shallow water equations are widely used to model flows in rivers and coastal areas. A good numerical method for solving these systems should accurately capture both the steady states and their small perturbations, should perform well when computing dry or hear dry states and should be simple, accurate, and robust. We introduce a second-order central-upwind scheme that satisfies the above mentioned properties and prove that it is well-balanced and positivity preserving. This scheme belongs to the class of Godunov-type semi-discrete central-upwind schemes which are an attractive alternative to other existing methods because they are simple (no Riemann problem solvers are employed), universal, and can be used as a "black-box solver".