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On the Spectral Difference Method with Modal Filtering Applied to the Euler Equations

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Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 120))

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Abstract

We extend the Spectral Difference method to Proriol-Koornwinder-Dubi-ner-polynomials (PKD) on triangular grids using a two dimensional Lobatto points extension as the set of fluxpoints. These polynomials form an orthogonal basis on triangles and fulfill a singular Sturm-Liouville-problem which can be used to construct modal filters in order to stabilize the scheme for nonlinear conservation laws. To avoid global filtering, we give an outlook of possible edge detection techniques in two dimensions based on the conjugated Fourier partial sum. Finally, we show numerical results for the Spectral Difference method using the proposed filter technique applied to the Euler equations and the nonlinear shock vortex interaction.

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Correspondence to Thomas Sonar .

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Sonar, T., Wirz, M. (2013). On the Spectral Difference Method with Modal Filtering Applied to the Euler Equations. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-33221-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33220-3

  • Online ISBN: 978-3-642-33221-0

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