Lattice Gas Simulation of 2-D Viscous Fingering

Abstract

Incompressible two-fluid viscous flows in homogeneous porous media are governed by Darcy’s law and the diffusion equation [1], i.e. respectively:

$$\begin{array}{*{20}c} {\nabla p = - \mu \text{u},} & {\nabla \cdot \text{u} = 0;} & {\frac{{\text{d}c}} {{\text{d}t}} = D\nabla ^2 c.} \\ \end{array}$$

((1))