Multi-species simulation of porous sand and water mixtures
The simulation of fluid mixing under the Eulerian framework often suffers from numerical dissipation issues. In this paper, we present a mass-preserving convection scheme that offers direct control on the shape of the interface. The key component of this scheme is a sharpening term built upon the diffusive flux of a user-specified kernel function. To determine the thickness of the ideal interface during fluid mixing, we perform theoretical analysis on a one-dimensional diffusive model using the Fick's law of diffusion. By explicitly controlling the interface thickness using a spatio-temporally varying kernel variable, we can use our scheme to produce realistic fluid mixing effects 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.