Abstract

As a part of the effort of constructing fundamentally physics based numerical model for growth of a phase in solid-to-solid phase transformations, a suitable mathematical description for advancing phase front and its numerical solution are required. The advection equation can be used for simulating the propagating phase front. However, it is well known that simple explicit finite difference solution in this case is unstable. Averaging of the spatial derivative provides useful stabilization for the numerical scheme, but exacerbates numerical dissipation and broadening of the continuous function describing the diffuse phase front. Numerical experiments were made, where these problems were observed. Simple solution procedures were introduced that effectively solved the problems for time scales that were required for the numerical solver to operate in the designed context.