Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

This paper presents a well-balanced numerical scheme for simulating frictional shallow
flows over complex domains involving wetting and drying. The proposed scheme solves, in …

A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow
water equations has been first introduced in A. Kurganov and D. Levy, Central-upwind …

Shallow water equations with a non-flat bottom topography have been widely used to model
flows in rivers and coastal areas. An important difficulty arising in these simulations is the …

Shallow water equations with nonflat bottom have steady state solutions in which the flux
gradients are nonzero but exactly balanced by the source term. It is a challenge to design …

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a
numerical scheme shall capture such flows efficiently, it should be able to preserve the …

A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial
equilibrium solutions, where the effects of convective fluxes and source terms cancel each …

Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero
but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) …

We consider the solution of the Saint-Venant equations with topographic source terms on 2D
unstructured meshes by a finite volume approach. We first present a stable and positivity …

We consider in this work the discontinuous Galerkin discretization of the nonlinear shallow
water equations on unstructured triangulations. In the recent years, several improvements …