▪ Abstract We present an overview of the lattice Boltzmann method (LBM), a parallel and
efficient algorithm for simulating single-phase and multiphase fluid flows and for …

This book is intended primarily as a textbook for second-year undergraduate students in
mathematics, mathematical physics, and engineering. The book is designed as a first …

A level set approach for computing solutions to incompressible two-phase flow is presented.
The interface between the two fluids is considered to be sharp and is described as the zero …

▪ Abstract We review the development of diffuse-interface models of hydrodynamics and
their application to a wide variety of interfacial phenomena. These models have been …

The level set method was devised by S. Osher and JA Sethian (1988, J. Comput. Phys. 79,
12–49) as a simple and versatile method for computing and analyzing the motion of an …

Fast Marching Methods are numerical schemes for computing solutions to the nonlinear
Eikonal equation and related static Hamilton--Jacobi equations. Based on entropy-satisfying …

We develop a fast method to localize the level set method of Osher and Sethian (1988, J.
Comput. Phys. 79, 12) and address two important issues that are intrinsic to the level set …

▪ 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 …

One of the fundamental problems in simulating the motion of sharp interfaces between
immiscible fluids is a description of the transition that occurs when the interfaces merge and …

Developments in many modern applications are encountering rapid escalation in heat
dissipation, coupled with a need to decrease the size of thermal management hardware …