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Closure conditions for non-equilibrium multi-component models

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Abstract

A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production, thermodynamical stability, Galilean invariance and mathematical properties such as hyperbolicity, subcharacteristic property and existence of an entropy–entropy flux pair. For the relaxation of chemical potentials, a two-component and a three-component models for vapor–water and gas–water–vapor, respectively, are considered.

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Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

    S. Müller

  2. Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, 39016, Magdeburg, Germany

    M. Hantke

  3. Center for Computational Engineering Sciences, RWTH Aachen University, Schinkelstr. 2, 52062, Aachen, Germany

    P. Richter

Authors
  1. S. Müller
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  2. M. Hantke
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  3. P. Richter
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Correspondence to S. Müller.

Additional information

Communicated by Andreas Öchsner.

The P. Richter acknowledges funding by the Friedrich-Naumann-Stiftung für die Freiheit.

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Müller, S., Hantke, M. & Richter, P. Closure conditions for non-equilibrium multi-component models. Continuum Mech. Thermodyn. 28, 1157–1189 (2016). https://doi.org/10.1007/s00161-015-0468-8

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  • DOI: https://doi.org/10.1007/s00161-015-0468-8

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