A level set variational formulation for coupled phase change/mass transfer problems: application to freezing of biological systems

Traditionally, the difficulty of applying variational principles to a moving boundary problem lies in the unknown sub-domains over which to perform integration. The level set method (Osher and Sethian, J. Comput. Phys. 79 (1988) 12) has offered a new perspective to this problem. In this paper, we will use the standard level set equations to recast the governing equations describing solidification processes into a novel level set-based variational principle (weak form). This leads to a generalized formulation which does not depend on any particular form of the level set function. The "jump" conditions on the moving interface are naturally incorporated into domain integrals by using the Dirac delta function. As such, a fixed mesh approach is afforded by using standard Galerkin's method in the finite element formulation. The capabilities of the proposed computational method are demonstrated through a numerical example pertaining to the freezing of biological cell suspensions.

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