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On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations. (English) Zbl 1353.76039
Summary: We give a brief overview on high-order accurate shock capturing schemes with the aim of applications in compressible turbulence simulations. The emphasis is on the basic methodology and recent algorithm developments for two classes of high-order methods: the weighted essentially non-oscillatory and discontinuous Galerkin methods.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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