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Spectral and High Order Methods for Partial Differential Equations pp 411–418Cite as

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 76))

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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References

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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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Authors and Affiliations

  1. Department of Mathematics, Texas A & M University, College Station, TX, USA

    J. L. Guermond

  2. Lab. J. A. Dieudonné (CFD group), UMR CNRS 6621, Nice-Sophia Antipolis University, Nice, France

    R. Pasquetti

Authors
  1. J. L. Guermond
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  2. R. Pasquetti
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Corresponding author

Correspondence to J. L. Guermond .

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Editors and Affiliations

  1. , Division of Applied Mathematics, Brown University, George Street 182, Providence, 02912, Rhode Island, USA

    Jan S. Hesthaven

  2. , Department of Mathematical Sciences, Norwegian University of Science and Tech, Trondheim, 7491, Norway

    Einar M. Rønquist

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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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