A local mass conservation method for the level set method applied to capillary incompressible flow

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In the case of incompressible flow, the level set method does not ensure mass conservation and it has to be enforced. The usual global mass conservation presents unacurracy in the case of separated phases of one fluid. In this paper, we propose an alternative local mass conservation based local volume fluxes. We apply our method to test cases where one fluid separates in disconnected parts (motion of two separated liquid volumes, break-up due to surface tension).