On the boundary treatment in spectral methods for hyperbolic systems
type: Item
instance of: scholarly article
title: On the boundary treatment in spectral methods for hyperbolic systems
zbMATH Open document ID: 0626.65123
DOI: 10.1016/0021-9991(87)90021-0
author: C. Canuto
author: Alfio Quarteroni
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19860012733
review text: Motivated by gas pipeline problems (under slowly varying conditions, without shocks), the authors consider the correct approximation of boundary conditions in spectral methods with Chebyshev collocation and implicit time stepping. Converting a special linear hyperbolic system to characteristic variables, discretizing and taking into account there the outgoing resp. incoming characteristics and converting back to physical variables, they obtain a stable discretization. It turns out that the correct conditions contain the prescribed conditions in linear combination with the collocated differential equations. This approach is used in connection with the schemes of \textit{R. M. Beam} and \textit{R. F. Warming} [ibid. 22, 87-110 (1976; Zbl 0336.76021)] and of \textit{A. Lerat} [C. R. Acad. Sci., Paris, Sér. A 288, 1033-1036 (1979; Zbl 0439.65075)] for nonlinear equations. Computational results are presented for a gas flow problem of industrial relevance. Here the implicit method admits great time steps and gives satisfactory accuracy in less CPU time than an explicit method.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 4018322
zbMATH Keywords: simulation of slow transients in gas transportation networks
zbMATH Keywords: Chebyshev pseudospectral method
zbMATH Keywords: collocation method
zbMATH Keywords: characteristic variables
zbMATH Keywords: gas pipeline problems
zbMATH Keywords: without shocks
zbMATH Keywords: spectral methods
zbMATH Keywords: Chebyshev collocation
zbMATH Keywords: implicit time stepping
Wikidata QID: Q56996714
MaRDI profile type: Publication
OpenAlex ID: W1980592858
cites work: A Chebyshev spectral method for gas transients in pipelines
cites work: Q3740970
cites work: On Numerical Boundary Treatment of Hyperbolic Systems for Finite Difference and Finite Element Methods
cites work: Numerical methods in fluid dynamics. Lectures given at the 3rd 1983 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Como, Italy, July 7-15, 1983
cites work: Q3881842
cites work: A Finite Element Method for First-Order Hyperbolic Systems
description: scientific article; zbMATH DE number 4018322