Abstract
With respect to the possible presence of discontinuities in the solutions of nonlinear wave propagation problems high order methods have to be provided with a dose of supplementary numerical dissipation, otherwise the approximate solution may severely suffer from the presence of Gibbs oscillations. To prevent these oscillations from rendering the scheme unstable we apply the spectral filtering framework to the DG method on triangular grids. The corresponding spectral filter has been derived in [18] from a spectral viscosity formulation and is applied adaptively in order to restrict artificial viscosity to shock locations. Furthermore, the image processing technique of DTV filtering is shown to be a useful postprocessor. Numerical experiments are carried out for the two-dimensional Euler equations where we show results for the Shu-Osher shock–density wave interaction problem as well as the interaction of a moving vortex with a stationary shock.
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Ortleb, S., Meister, A., Sonar, T. (2011). Adaptive Spectral Filtering and Digital Total Variation Postprocessing for the DG Method on Triangular Grids: Application to the Euler Equations. 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_45
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DOI: https://doi.org/10.1007/978-3-642-15337-2_45
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