Simulation of Fluid Mixing with Interface Control

Abstract

The simulation of fluid mixing under the Eulerian framework often su ers from numerical dissipation issues. In this paper, we present a mass-preserving convection scheme that o ers direct control on the shape of the interface. The key component of this scheme is a sharpening term built upon the di usive flux of a userspecified kernel function. To determine the thickness of the ideal interface during fluid mixing, we perform theoretical analysis on a one-dimensional di usive model using the Fick's law of di usion. By explicitly controlling the interface thickness using a spatio-temporally varying kernel variable, we can use our scheme to produce realistic fluid mixing e ects without numerical dissipation artifacts. We can also use the scheme to control interface changes between two fluids, due to temperature, pressure, or external energy input. This convection scheme is compatible with many advection methods and it has a small computational overhead.