An enriched shifted boundary method to account for moving fronts

Abstract

We present an extension of the shifted boundary method to simulate partial differential equations with moving internal interfaces. The objective is to apply the method to phase change problems modelled by the Stefan equation which is a parabolic heat equation with a discontinuity separating two phases, moving at a speed given by the normal flux jump. To obtain an accurate prediction of the temperature field on both sides of the discontinuity, and of the position of the discontinuity itself, we propose a variant of the shifted boundary method adapted to problems with moving fronts. This method is based on an enriched mixed form proposed by some of the present authors, which preserves a uniform second order accuracy in space and time. Stabilization terms are added on the whole domain to ensure convergence.