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Spectral methods for the Euler equations. I. Fourier methods and shock capturing. (English) Zbl 0554.76060

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put into historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock- capturing approaches are also presented. Fourier shock-capturing techniques are evaluated using a one-dimensional, periodic astrophysical ”nozzle” problem.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M99 Basic methods in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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