A rapidly converging phase field model

Abstract

We propose a phase field model that approximates its limiting sharp interface model (free boundary problem) up to second order in interface thickness. A broad range of double-well potentials can be utilized so long as the dynamical coefficient in the phase equation is adjusted appropriately. This model thereby assures that computation with particular value of interface thickness ε, will differ at most by O(ε2) from the limiting sharp interface problem. As an illustration, the speed of a traveling wave of the phase field model is asymptotically expanded to demonstrate that it differs from the speed of the traveling wave of the limit problem by O(ε2).