TABLE OF CONTENTS The flow of incompressible fluids with large (discontinuous) density variations (interfaces) occurs in widespread applications. Water/air free surface flow is a classical example, e.g., a water drop falling into a pool of water. Other important examples are the filling of a cast metal mold with a molten metal alloy; the production and transport of micron-sized ink drops during inkjet printer operation; environmental and combustion problems, as well as many applications in mechanical, aerospace and chemical engineering industries. Reliable simulation of these types of flows demands a numerical model with accuracy, fidelity, and robustness (see Chap. 6 for an introduction).
In this chapter we will focus on a particularly useful application of high-resolution methods to incompressible flows, that is flows with large density variations. As the numerical methods have become more robust and economical, their use in analyzing industrial processes has increased. With this increased emphasis it is worthwhile to briefly review the details of methods that are useful in simulating such flows.
There are several prototypical examples of variable density mixing flows. These flows have different character starting with a shear layer including a density difference across the shear. Many examples are driven by gravity, for example, either a rising bubble (a hot less dense fluid) below a cooler one, and a Rayleigh-Taylor instability where a higher density fluid lies over a lower density fluid in gravity...
