  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 for the linear dispersion
results. We show that the method may be a useful alternative to more
traditional methods.
