Scaling laws in large scale simulations of the Saffman-Taylor instability

We present new large scale simulations of the Saffman-Taylor instability driven by a constant massflux. In contrast to viscous fingering driven by a constant {\em pressure jump}, we observe at late time simultaneous ramification of the fingers and coarsening of the ``fjords.'' This may explain the new asymptotic scaling regime where the interface dynamics is described by a power-law relation for a measure of interfacial stretching vs. time. We present detailed comparisons with experimental data from the literature.