An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems (Communications in Computational Physics, 2018)
In this paper, we present an efficient rescaling scheme for computing thelong-time dynamics of expanding interfaces. The idea is to design an adaptive time-spacemapping such that in the new time scale, the interfaces evolves logarithmicallyfast at early growth stage and exponentially fast at later times. The new spatial scaleguarantees the conservation of the area/volume enclosed by the interface. Comparedwith the original rescaling method in [J. Comput. Phys. 225(1) (2007) 554–567], thisadaptive scheme dramatically improves the slow evolution at early times when thesize of the interface is small. Our results show that the original three-week computationin [J. Comput. Phys. 225(1) (2007) 554–567] can be reproduced in about oneday using the adaptive scheme. We then present the largest and most complicatedHele-Shaw simulation up to date.