Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids

A finite-difference formulation is applied to track solid-liquid boundaries on a fixed underlying grid. The interface is not of finite thickness but i s treated as a discontinuity and is explicitly tracked. The imposition of b oundary conditions exactly on a sharp interface that passes through the Car tesian grid is performed using simple stencil readjustments in the vicinity of the interface. Attention is paid to formulating difference schemes that are globally second-order accurate in x and t. Error analysis and grid ref inement studies are performed for test problems involving the diffusion and convection-diffusion equations, and for stable solidification problems. Is sues concerned with stability and change of phase of grid points in the evo lution of solid-liquid phase fronts are also addressed. It is demonstrated that the field calculation is second-order accurate while the position of t he phase front is calculated to first-order accuracy. Furthermore, the accu racy estimates hold for the cases where there is a property jump across the interface. Unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work. The results indi cate the need to begin an effort to benchmark computations of instability p henomena. (C) 1999 Academic Press.