Extensions to the Roe and HLL method have been previously formulated in order to solve
the Shallow Water equations in the presence of source terms. These were named the …

In this study, a novel two-dimensional finite-volume method on unstructured triangular
meshes for two-layer shallow water flows is developed. First, the one-dimensional relaxation …

In this paper, we present a well-balanced numerical scheme for the frictional two-layer
shallow water equations (2LSWE) over variable bottom topography and under a rigid-lid …

The shock instability problem commonly arises in flow simulations involving strong shocks,
particularly when employing high-order schemes, limiting their applications in hypersonic …

In this paper, continuous research is undertaken to explore the underlying mechanism of
numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting …

This study examines how the variability of the Manning coefficient (n) affects the position of
hydraulic jumps downstream of hydraulic structures. Using a robust finite volume method …

This paper proposes a novel energy-balanced numerical scheme for the two-layer shallow
water equations (2LSWEs) that accurately captures internal hydraulic jumps without …

High order methods are becoming increasingly popular in shallow water flow modeling
motivated by their high computational efficiency (ie the ratio between accuracy and …

This article presents a numerical technique that ensures the exact solution of stationary
shockwaves, known as the hydraulic jump, for the one‐dimensional shallow water equations …

A high order finite difference numerical scheme is developed for the shallow water
equations on curvilinear meshes based on an alternative flux formulation of the weighted …