High pressure induced freezing and thawing processes are investigated by means of modelling and numerical simulation. The enthalpy-porosity model is reformulated in terms of conservation equations of mass, momentum and heat for a compressible medium. It can be shown that convective fluid motion has a major influence on the formation of the ice front. Furthermore, due to a vanishing density anomaly under high pressure, natural convection exhibits a different behaviour than under low pressure thus the formation of the ice front under high pressure obeys different mechanisms than that under ambient pressure. (C) 2003 Elsevier Ltd. All rights reserved.