Relaxation schemes for curvature-dependent front propagation

In this paper we study analytically and numerically a novel relaxation appr oximation for front evolution according to a curvature-dependent local law. In the Chapman-Enskog expansion, this relaxation approximation leads to th e level-set equation for transport-dominated front propagation, which inclu des the mean curvature as the next-order term. This approach yields a new a nd possibly attractive way of calculating numerically the propagation of cu rvature-dependent fronts. Since the relaxation system is a symmetrizable, s emilinear, and linearly convective hyperbolic system without singularities, the relaxation scheme captures the curvature-dependent front propagation w ithout discretizing directly the complicated yet singular mean curvature te rm. (C) 1999 John Wiley & Sons, Inc.