Abstract: We introduce a global method based on a variant of the Flux Characteristic method described by Ghidaglia et al and designed to simulate two-phase flows. As an example, we use a three equations model with hypotheses of local thermodynamic equilibrium. Here our purpose is to qualify the Finite Volume method of regions where one can find strong gradient of density and free boundary phase transitions. We here consider a complex flow inside an injector-condenser device. The analysis will lead to a variant of the Flux Characteristic method with regularized matrix-valued sign functions. Other applications like water boiling into a hot channel and a fall of pressure in a crack due to friction will be also considered.
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