Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Crystal growth and dendritic solidification
Journal of Computational Physics
A front-tracking method for dendritic solidification
Journal of Computational Physics
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
Boundary value problems of mathematical physics (vol. 1)
Boundary value problems of mathematical physics (vol. 1)
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
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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.