Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for
solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new
but have gained rapid popularity in numerical solutions of hyperbolic partial differential …

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 …

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 …

In this work, we design an arbitrary high order accurate nodal discontinuous Galerkin
spectral element type method for the one dimensional shallow water equations. The novel …

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

Hyperbolic conservation laws with source terms often admit steady state solutions where the
fluxes and source terms balance each other. To capture this balance and near-equilibrium …

The shallow water equations model flows in rivers and coastal areas and have wide
applications in ocean, hydraulic engineering, and atmospheric modeling. In “**ng et al. Adv …