Homogenized systems for liquid-vapour transition in unsteady compressible two-phase flow

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In this project, we consider the liquid-vapour flow as a homogenizedmixture of the two phases. The resulting models pose amajor challenge to mathematics, since there are a number ofimportant open questions to be studied. The primary goal is toimprove and validate numerical schemes for such models. Numericalsolutions are needed in many diverse engineering applicationsinvolving phenomena such as liquid sprays or bubblyflows. In order to improve the quality of numerical results weneed to address some mathematical issues concerning the modellingand resulting well-posedness of the equations. Also wewill have to develop a deeper unterstanding of the theory andnumerical methods for hyperbolic systems of equations containingnon-conservative derivatives. Another challenge is phaseextincion, which is related to vacuum states in gas dynamics.Further, it will be necessary to encorporate phase transitioninto the models and numerical computations.