Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast.: II.: Numerical study

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers, and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed far the linear dispersion results. We show that the method may be a useful alternative to more traditional methods. [S1063-651X(99)08308-7].