Title: On the Spectral Difference Method with Modal Filtering Applied to the Euler Equations
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.
Publication Year: 2013
Publication Date: 2013-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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