Abstract
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated – a 2D Burgers problem, the “KPP rotating wave” and the Euler system – using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given.
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Acknowledgements
This material is based upon work supported by the National Science Foundation grant DMS-0510650 and DMS-0811041 and partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Guermond, J.L., Pasquetti, R. (2011). Entropy Viscosity Method for High-Order Approximations of Conservation Laws. In: Hesthaven, J., Rønquist, E. (eds) Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15337-2_39
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DOI: https://doi.org/10.1007/978-3-642-15337-2_39
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