Abstract
We propose a sub-cell procedure for the stabilization of cell-centered Lagrangian numerical schemes for the computation of compressible gas dynamics. This procedure is intended to stabilize the mesh, indeed cell-centered schemes are already stable for shocks since they are based on a Riemann solver technology. In this work we focus on the basic principles and on the compatibility with the entropy. We show that a sub-cell decomposition into four triangles is always mesh-stable provided the scheme is entropy increasing. Numerical examples serve as illustration. We also discuss the consistency issue.
MSC2010: 65M08, 65M12, 65Z99, 76M12
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Acknowledgements
he first author kindly acknowledges the support of CEA.
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Després, B., Labourasse, E. (2011). Towards stabilization of cell-centered Lagrangian methods for compressible gas dynamics. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_34
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DOI: https://doi.org/10.1007/978-3-642-20671-9_34
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