Abstract
We present new invariant domain preserving finite volume schemes for the compressible Euler and Navier–Stokes–Fourier systems. The schemes are entropy stable and preserve positivity of density and internal energy. More importantly, their convergence towards a strong solution of the limit system has been proved rigorously in [9, 11]. We will demonstrate their accuracy and robustness on a series of numerical experiments.
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Acknowledgement
M. Lukáčová-Medviďová has been partially supported by the German Science Foundation under the grants TRR 146 Multiscale simulation methods for soft matter systems and TRR 165 Waves to weather. H. Mizerová and B. She have received funding from the Czech Science Foundation (GAČR), Grant Agreement 18–05974S. The Institute of Mathematics of the Czech Academy of Sciences is supported by RVO:67985840.
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Lukáčová-Medviďová, M., Mizerová, H., She, B. (2021). New Invariant Domain Preserving Finite Volume Schemes for Compressible Flows. In: Muñoz-Ruiz, M.L., Parés, C., Russo, G. (eds) Recent Advances in Numerical Methods for Hyperbolic PDE Systems. SEMA SIMAI Springer Series, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-030-72850-2_6
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