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A Phase-Field Model for Flows with Phase Transition

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Theory, Numerics and Applications of Hyperbolic Problems II (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 237))

Abstract

There are many mathematical models for describing compressible or incompressible flows with phase transition. In this contribution, we will focus on the Navier–Stokes–Korteweg model [12] (Appl Math Comput 272, part 2, 309–335, 2016) and a phase-field model: The compressible Navier–Stokes–Allen–Cahn model (NSAC) is able to model compressible two-phase flows including surface tension effects and phase transitions. In this contribution, we will present a discontinuous Galerkin scheme for the NSAC model. The scheme is designed to fulfill a discrete version of the free energy inequality, which is the second law of thermodynamics in the isothermal case. For situations near the thermodynamic equilibrium, this property suppresses so-called parasitic currents, which are unphysical velocity fields near the phase boundary.

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Authors and Affiliations

  1. Abteilung für angewandte Mathematik, University of Freiburg, Hermann-Herder-Str 10, 79104, Freiburg, Germany

    Mirko Kränkel & Dietmar Kröner

Authors
  1. Mirko Kränkel
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  2. Dietmar Kröner
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Correspondence to Dietmar Kröner .

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Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Kränkel, M., Kröner, D. (2018). A Phase-Field Model for Flows with Phase Transition. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_19

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