Numerical simulation of freezing process using the BEM

Abstract

The boundary element method is applied for numerical simulation of the freezing process proceeding in biological tissue under the influence of cylindrical cryoprobe. From the mathematical point of view the problem discussed belongs to the group of moving boundaries ones for which the mushy zone sub-region (intermediate phase) is considered. In this paper the mathematical model of the process is formulated using the fixed domain approach and a parameter called the substitute thermal capacity determines the evolution of latent heat. On a stage of numerical computations the generalized variant of the alternating phase truncation method (APTM) is applied and the basic mathematical model is rebuilt by the introduction of the enthalpy function. The boundary element method together with APTM leads to the simple and effective numerical algorithm because the difficulties connected with the non-linear problem modelling can be omitted. In the final part of the paper the results of computations are shown.