Numerical methods for tracking interfaces

TL;DR: In this paper, a method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described.

TL;DR: Issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids are addressed.

TL;DR: In this paper, the authors consider the formation of droplet clouds or sprays that subsequently burn in combustion chambers, which is caused by interfacial instabilities, such as the Kelvin-Helmholtz instability.

TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.

TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.

TL;DR: SLIC as mentioned in this paper is an alternating-direction method for the geometric approximation of fluid interfaces, which can be used in one, two, or three space dimensions, and it is characterized by the following features: (1) Fluid surfaces are represented locally for each mixed- fluid zone, and these surfaces are defined as a composition of one space dimensional components, one for each coordinate direction.

TL;DR: It is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws using Godunov's and Roe's methods on a self-adjusting mesh.