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Spectral computations of one dimensional inviscid compressible flows. (English) Zbl 0561.76076
The pseudo spectral Chebyshev method is applied to one-dimensional inviscid compressible flows in a finite shock tube. A conservation property for the pseudo-spectral Chebyshev approximation is established analogous to that given by Lax and Wendroff for the pseudo-spectral Fourier approximation. A new spectral filtering method is introduced to achieve a high resolution treatment of shock and contact discontinuities. This involves a low pass filter for stabilization together with a post processing Schuman filter to retrieve smoothed results with localised discontinuities from the noisy but stable calculations. This latter step involves a priori determination of the location of the discontinuities from an examination of the spectral coefficients.
Reviewer: M.Thompson

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M99 Basic methods in fluid mechanics
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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