A new exact Riemann solver for the shallow water equations with a discontinuous bottom is
proposed. The algorithm is based on the approach to overcome the non-uniqueness of the …

This paper is concerned with the development of well-balanced high order numerical
schemes for systems of balance laws with a linear flux function, whose coefficients may be …

The Riemann problem for the shallow water equations with discontinuous topography is
considered. In a general case the exact solution of this problem is not unique, which …

In this paper, the solution of the Riemann Problem for the one-dimensional, free-surface
Shallow Water Equations over a bed step is analyzed both from a theoretical and a …

In this article we present a new numerical procedure for solving exactly the Riemann
problem of compressible two-phase flow models containing non-conservative products …

In this paper we deal with the numerical computation of one-dimensional, unsteady, free-
surface flows over mobile-bed. We focus on flows characterized by high concentration of …

We studied the shallow water equations of nonlinear conservation laws. First we studied the
parametrisation of nonlinear elementary waves and hence we present the solution to the …

Hillslope hydrology is a very important part of research based on watershed hydrology. In
this study, we focus on water flow over a soil surface with vegetation in a hydrographic …

We determine completely the Riemann solutions to the shallow water equations with a
bottom step, including the dry bed problem. The nonstrict hyperbolicity of this first-order …

This work considers the numerical approximation of the shallow-water equations. In this
context, one faces three important issues related to the well-balanced, positivity and entropy …