Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs,
coastal areas, and other situations in which the water depth is much smaller than the …

In this chapter we describe a general methodology for developing high-order well-balanced
schemes for hyperbolic system with nonconservative products and/or source terms. We …

This review paper describes a class of scheme named “residual distribution schemes” or
“fluctuation splitting schemes”. They are a generalization of Roe's numerical flux in …

We extend recently proposed flux globalization based well-balanced path-conservative
central-upwind schemes to several shallow water models including the Saint-Vevant system …

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-
volume numerical methods for 1D systems of balance laws. The strategy introduced by two …

We propose a new computational approach for embedded boundary simulations of
hyperbolic systems and, in particular, the linear wave equations and the nonlinear shallow …

In this paper, we develop and present an arbitrary high order well-balanced finite volume
WENO method combined with the modified Patankar Deferred Correction (mPDeC) time …

In the context of preserving stationary states, eg lake at rest and moving equilibria, a new
formulation of the shallow water system, called flux globalization has been introduced by …

We propose a new paradigm for designing efficient p-adaptive arbitrary high-order methods.
We consider arbitrary high-order iterative schemes that gain one order of accuracy at each …

A high-order explicit finite difference scheme is derived solving the shallow water equations.
The boundary closures are based on the diagonal-norm summation-by-parts (SBP) …