Well-balanced central-upwind scheme for compressible two-phase flows

We design a new well-balanced central-upwind scheme for compressible two-phase flows. The new scheme is an extension of the semi-discrete central-upwind scheme proposed in [1]. The novelty of the presented method is in a special discretization of nonconservative product terms, which are exactly balanced with the numerical fluxes when the method...

ADER scheme for the shallow water equations in channel with irregular bottom elevation

In this paper we develop one dimensional non-linear ADER schemes for the shallow water system with source terms. In contrast to conventional schemes we adopt a formulation given in terms of the free surface elevation and water discharge. Data reconstruction is performed using ENO polynomials both for the conservative variables and for the bottom...

Discontinuous Galerkin Methods for the Shallow-Water Equations with bathymetric terms and dry areas

Shallow-Water Equations are encountered in many applications related to hydraulics, flood propagation or dam break problems. This set of nonlinear hyperbolic equations models a fluid flow in a domain where the depth of the fluid is much lower than its horizontal dimensions. Usually, these equations are treated using Finite Difference, Finite...