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

  • Carl Philipp Zinner EMAIL logo and Hans Christian Öttinger
Published/Copyright: October 11, 2018

Abstract

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.

Acknowledgment

We thank Henning Struchtrup and Manuel Torrilhon for many helpful discussions. We are particularly grateful to Henning Struchtrup for revealing an error in [41].

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Received: 2018-07-17
Revised: 2018-08-31
Accepted: 2018-09-10
Published Online: 2018-10-11
Published in Print: 2019-01-28

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