Abstract
In this paper we will approach the shock tube problem, or mathematically speaking the Riemann problem with extended thermodynamics. Extended thermodynamics (ET) provides dissipative field equations which are symmetric hyperbolic [1]. Thus, the solution to the shock-tube-problem may be obtained using the well known analytic and numerical methods for hyperbolic systems.
We will observe a large number of acceleration and shock waves for the systems of extended thermodynamics. Due to the dissipation, these waves are strongly damped and the systems of ET lead to diffusive solutions of the Riemann problem - although we are dealing with hyperbolic systems.
Furthermore we investigate the start-up phase of the shock tube. For very small times the large systems of ET are needed for a physically valid description. It will be shown numerically that the solution of ET for the start-up phase converges to the solution of the free-flight-equation.
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Au, J.D., Reitebuch, D., Torrilhon, M., Weiss, W. (2001). The Riemann-Problem in Extended Thermodynamics. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_9
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DOI: https://doi.org/10.1007/978-3-0348-8370-2_9
Publisher Name: Birkhäuser, Basel
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