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A Stochastic Galerkin Method for the Fokker–Planck–Landau Equation with Random Uncertainties Read chapter Read first chapter

2018 | OriginalPaper | Chapter

A Phase-Field Model for Flows with Phase Transition

Authors : Mirko Kränkel, Dietmar Kröner

Published in: Theory, Numerics and Applications of Hyperbolic Problems II

Publisher: Springer International Publishing

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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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previous chapter Weakly Coupled Systems of Conservation Laws on Moving Surfaces
next chapter Mathematical Theory of Two-Phase Geochemical Flow with Chemical Species
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Metadata
Title
A Phase-Field Model for Flows with Phase Transition
Authors
Mirko Kränkel
Dietmar Kröner
Copyright Year
2018
Book
Theory, Numerics and Applications of Hyperbolic Problems II

Print ISBN: 978-3-319-91547-0

Electronic ISBN: 978-3-319-91548-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91548-7_19

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