Level set methods and sloshing problems

Abstract

Level set methods are powerful numerical techniques for tracking the motion of an interface. Many applications arise in such areas as fluid flow simulations, medical science, and image processing. In fluid flow simulations, tracking the interface between two fluid flow phases is often difficult. Among the mathematical models that can be used to analyze fluid flow are the shallow water equations and Navier-Stokes equations. An important class of fluid flow problems is known as sloshing problems. These problems are concerned with the sloshing of a fluid in a tank, and they arise in the automotive, aerospace, and ship-building industries. In this thesis we consider the modelling of sloshing problems using shallow water equations and Navier-Stokes equations. Whereas the shallow water equations include a function that models the fluid interface, the Navier-Stokes equations do not. In this latter case, however, one can use the level set approach to track the fluid interface. Given the fluid velocity as obtained from the Navier-Stokes equations, one can use it to evolve the interface using the level set approach. We develop a MATLAB based implementation and provide numerical results to demonstrate this approach.