An efficient diffusion model for viscous fingering

Abstract

Viscous fingering is one of the most important factors to produce realistic diffusion among two miscible fluids with differing viscosities. Diffusion-limited Aggregation (DLA) has been a popular choice for the synthesis of the viscous fingering effect. However, as DLA provides a mere description of aggregation process, it is not clear how to apply the DLA model into conventional 3D fluid simulation equations. The DLA model first generates a shape description of the viscous fingering effect. The shape description is changed to a fluid flow region by the application of dilation and erosion operators. The flow region is then filled with the directions which will guide the fluid motion in a simulation. The directions are converted into a form of external force by means of a linear feedback system. Our results show that the DLA model can generate the viscous fingering effect effectively in a single phase simulation without relying on a high resolution grid. Our method is semi-physical due to the employment of DLA and is easy to implement, as the underlying concept is simple. Computational overhead is also negligible from the conventional fluid simulation.