We propose a stabilized Residual Distribution (RD) scheme for the simulation of shallow
water flows. The final discretization is obtained combining the stabilized RD approach …

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 …

Wind-generated surface waves breaking in the nearshore cause an increase in mean water
levels, the wave setup, which can represent a significant fraction of storm surges developing …

In this paper, we construct spatially consistent explicit second order discretizations for time
dependent hyperbolic problems, starting from a given residual distribution (RD) discrete …

In this paper we consider the very high order approximation of solutions of the Euler
equations. We present a systematic generalization of the residual distribution method of [1] …

In this work, we prove the convergence of residual distribution (RD) schemes to dissipative
weak solutions of the Euler equations. We need to guarantee that the RD schemes are …

In this paper we consider the solution of the enhanced Boussinesq equations of Madsen
and Sørensen (1992)[55] by means of residual based discretizations. In particular, we …

We describe fully explicit residual based discretizations of the shallow water equations with
friction on unstructured grids. The schemes are obtained by properly adapting the explicit …

This article describes a number of velocity-based moving mesh numerical methods for
multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists …

This work introduces an extension of the residual distribution (RD) framework to stiff
relaxation problems. The RD is a class of schemes which is used to solve a hyperbolic …