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Comparison of macro- and microscopic solutions of the Riemann problem I. Supercritical shock tube and expansion into vacuum

Hitz, Timon; Heinen, Matthias; Vrabec, Jadran; Munz, Claus-Dieter

The Riemann problem is a fundamental concept in the development of numerical methods for the macroscopic flow equations. It allows the resolution of discontinuities in the solution, such as shock waves, and provides a powerful tool for the construction of numerical flux functions. A natural extension of the Riemann problem involves two phases, a liquid and a vapour phase which undergo phase change at the material boundary. For this problem, we aim at a comparison with the macroscopic solution from molecular dynamics simulations. In this work, as a first step, the macroscopic solution of two important Riemann problem scenarios, the supercritical shock tube and the expansion into vacuum, were compared to microscopic solutions produced by molecular dynamics simulations. High fidelity equations of state were used to accurately approximate the material behaviour of the model fluid. The results of both scenarios compare almost perfect with each other. During the vacuum expansion, the fluid obtained a state of non-equilibrium, where the microscopic and macroscopic solutions start to diverge. A limiting case was shown, where liquid droplets appeared in the expansion fan, which was approximated by the macroscopic solution, assuming an undercooled vapour.
Published in: Journal of Computational Physics, 10.1016/j.jcp.2019.109077, Elsevier