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Author: Dreyer, Wolfgang × Subject: conservation laws ×

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    Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Dreyer, Wolfgang; Hantke, Maren; Warnecke, Gerald
    We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The mass transfer is modeled by a kinetic relation. We prove existence and uniqueness results. Further, we construct the exact solution for Riemann problems. We derive analogous results for the cases of initially one phase with resulting condensation by compression or evaporation by expansion. Further we present numerical results for these cases. We compare the results to similar problems without phase transition.
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    On balance laws for mixture theories of disperse vapor bubbles in liquid with phase change
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Hantke, Maren; Warnecke, Gerald
    We study averaging methods for the derivation of mixture equations for disperse vapor bubbles in liquids. The carrier liquid is modeled as a continuum, whereas simplified assumptions are made for the disperse bubble phase. An approach due to Petrov and Voinov is extended to derive mixture equations for the case that there is a phase transition between the carrier liquid and the vapor bubbles in water. We end up with a system of balance laws for a multi-phase mixture, which is completely in divergence form. Additional non-differential source terms describe the exchange of mass, momentum and energy between the phases. The sources depend explicitly on evolution laws for the total mass, the radius and the temperature of single bubbles. These evolution laws are derived in a prior article and are used to close the system. Finally numerical examples are presented.