Stefan Number-Insensitive Numerical Simulation of the Enthalpy Method for Stefan Problems Using the Space-Time CE/SE Method

Abstract

An improvement is introduced to the conservation element and solution element (CE/SE) phase-change scheme presented previously. The improvement addresses a well-known weakness in numerical simulations of the enthalpy method when the Stefan number (the ratio of sensible to latent heat) is small (less than 0.1). Behavior of the improved scheme, at the limit of small Stefan numbers, is studied and compared with that of the original scheme. It is shown that high dissipative errors, associated with small Stefan numbers, do not occur using the new scheme.

Notes

¹There is a dissipation term that automatically acts only in the neighborhood of the discontinuities and serves as a means of suppressing nonphysical oscillations without affecting the solution at the smooth regions [28].