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Journal of Non-Equilibrium Thermodynamics

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Numerical Stability with Help from Entropy: Solving a Set of 13 Moment Equations for Shock Tube Problem

Carl Philipp Zinner
  • Corresponding author
  • formerly ETH Zürich, Department of Materials, Polymer Physics, HCP F 48.1, Leopold-Ruzicka-Weg 4, CH-8093 Zürich, Switzerland
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Hans Christian Öttinger
  • ETH Zürich, Department of Materials, Polymer Physics, HCP F 47.2, Leopold-Ruzicka-Weg 4, CH-8093 Zürich, Switzerland
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  • Other articles by this author:
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Published Online: 2018-10-11 | DOI: https://doi.org/10.1515/jnet-2018-0038


The shock structures of a 13 moment generalized hydrodynamics system of rarefied gases are simulated. These are first order hyperbolic equations derived from the Boltzmann equation. The investigated moment system stands out due to having an entropy evolution. In addition, a particular interest arises from the fact that the equations not only contain nonconservative products, but also provide the key to solving this mathematical and numerical issue by means of a simple substitution utilizing the physical entropy evolution. The apparent success of this method warrants investigation and provides a new perspective and starting point for finding general approaches to nonconservative products and irreversible processes. Furthermore, the system shows physically accurate results for low Mach numbers and is able to reveal the nonequilibrium entropy profile across a shock wave.

Keywords: conservation laws; hyperbolicity; relaxation; moment equations; entropy


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About the article

Received: 2018-07-17

Revised: 2018-08-31

Accepted: 2018-09-10

Published Online: 2018-10-11

Citation Information: Journal of Non-Equilibrium Thermodynamics, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204, DOI: https://doi.org/10.1515/jnet-2018-0038.

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