This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It
differs from previous expositions on the subject in that the accent is put on the development …

In this paper, we prove the existence of global weak solutions to the compressible two-fluid
Navier–Stokes equations in three dimensional space. The pressure depends on two …

This article focuses on the design of semi-implicit schemes that are fully well-balanced for
the one-dimensional shallow water equations, that is, schemes that preserve all smooth …

We consider the system of partial differential equations governing the one-dimensional flow
of two superposed immiscible layers of shallow water. The difficulty in this system comes …

The purpose of this paper is to explore a viscous two-phase liquid–gas model relevant for
well and pipe flow. Our approach relies on applying suitable modifications of techniques …

This paper focuses on the extension of the Weighted Average Flux (WAF) scheme for the
numerical simulation of two-phase gas–liquid flow by imposing velocity equilibrium and …

This paper describes a numerical discretization of the compressible Euler equations with a
gravitational potential. A pertinent feature of the solutions to these inhomogeneous …

Abstract The second-order Van-Leer MUSCL schemes are actually one of the most popular
high order schemes for fluid dynamic computations. In the frame work of the Euler equations …

A hierarchy of relaxation two-phase flow models is considered, formulated as hyperbolic
relaxation systems with source terms. The relaxation terms cause volume, heat, and mass …

We present here a three-fluid three-pressure model to describe three-field patterns or three-
phase flows. The basic ideas rely on the counterpart of the two-fluid two-pressure model …