A preserving scheme for phase-change with sharp interface using the extreme mesh deformation approach (X-MESH)
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We consider the solidification process of water with a sharp interface model using the so-called Stefan phase-change model. We are interested to see whether or not it is possible to find a numerical scheme preserving the energy balance in each phase even for front propagation over long distances or for topological changes (ice nucleation or coalescence of fronts). We show that a new approach called X-MESH (extreme mesh deformation approach) has interesting properties towards building energy-preserving scheme. The X-MESH is based on ALE techniques but uses a twist: nodes located on the front vary with time. From one time-step to the next, some nodes may join and some others may leave the front. A peculiar aspect of the X-MESH is that some elements may reach zero measure in the deformation mesh process. The benefit of these unusual possibilities is that front moving over long distance as well as topological changes are easily taken into account.
