Relaxation schemes for curvature-dependent front propagation

✍ Scribed by Shi Jin; Markos A. Katsoulakis; Zhouping Xin

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 298 KB
• Volume: 52
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/(sici)1097-0312(199912)52:12<1587::aid-cpa4>3.0.co;2-a

✦ Synopsis

In this paper we study analytically and numerically a novel relaxation approximation for front evolution according to a curvature-dependent local law. In the Chapman-Enskog expansion, this relaxation approximation leads to the levelset equation for transport-dominated front propagation, which includes the mean curvature as the next-order term. This approach yields a new and possibly attractive way of calculating numerically the propagation of curvature-dependent fronts. Since the relaxation system is a symmetrizable, semilinear, and linearly convective hyperbolic system without singularities, the relaxation scheme captures the curvature-dependent front propagation without discretizing directly the complicated yet singular mean curvature term.