▪ Abstract We provide an overview of level set methods, introduced by Osher and Sethian,
for computing the solution to fluid-interface problems. These are computational techniques …

A variety of numerical techniques are available for tracking moving interfaces. In this review,
we concentrate on techniques that result from the link between the partial differential …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

In this paper, we review the recent development of phase-field models and their numerical
methods for multi-component fluid flows with interfacial phenomena. The models consist of a …

This is the second edition of a well-received book providing the fundamentals of the theory
hyperbolic conservation laws. Several chapters have been rewritten, new material has been …

Interface problems arise in many applications. For example, when there are two different
materials, such as water and oil, or the same material but at different states, such as water …

A simple second order accurate and fully Eulerian numerical method is presented for the
simulation of multifluid compressible flows, governed by the stiffened gas equation of state …

Numerical approximation of the five-equation two-phase flow of Kapila et al.[AK Kapila, R.
Menikoff, JB Bdzil, SF Son, DS Stewart, Two-phase modeling of deflagration-to-detonation …

A simple shock-capturing approach to multicomponent flow problems is developed for the
compressible Euler equations with a stiffened gas equation of state in multiple space …

The aim of this paper is to propose a method for dealing with the problem of mesh
deformation (or mesh evolution) in the context of free and moving boundary problems, in …