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Publication
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A proof of existence is given for a stationary model of alloy solidification. The system is composed of heat equation, solute equation and Navier-Stokes equations. In rite latter Carman-Kozeny penalization of porous medium models the mushy zone. The problem is first regularized and a sequence of regularized solutions is built thanks to Leray-Schauder's fixed point Theorem. A solution is then extracted by compactness argument.
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir
Serge Vaudenay, Bénédikt Minh Dang Tran