Space-time spectral element method for one-dimensional nonlinear advection-diffusion problems
type: Item
instance of: scholarly article
title: Space-time spectral element method for one-dimensional nonlinear advection-diffusion problems
zbMATH Open document ID: 0827.65098
author: Eduard Moses
author: U. Zrahia
author: A. L. Yarin
author: P. Z. Bar-Yoseph
published in: Journal of Computational Physics
publication date: 1995-08-02T00:00:00Z
review text: The following space-time Galerkin spectral element methods are developed and applied to solve the Burgers equation with small viscosity: (a) coupled methods, consisting of an explicit method for hyperbolic dominated equations and an implicit method for parabolic dominated equations; (b) two splitting methods which solve the hyperbolic substep explicitly and the parabolic one implicitly (one uses spectral elements in the explicit part and the other uses the Adams-Bashforth multistep method). A subcycling technique, in which several convective steps are taken for each implicit viscous step is also investigated for the two splitting methods. A stability analysis of the four methods is performed and subsequent results are debated. A convergence study and a comparison of computer execution time for the four methods is made and the results are discussed. Comparative study leads to the conclusion that the space-time spectral element splitting method with subcycling is superior to the other methods presented in terms of robustness and computer execution time. The number of subcycles should be kept low (2-3) in order to avoid significant loss of accuracy. The coupled explicit method is also applied to the solution of equations for non-isothermal flow of an ideal gas with temperature dependent properties in a cylindrical duct of variable radius.
reviewed by: Fuhua Ling
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 772376
zbMATH Keywords: space-time Galerkin spectral element methods
zbMATH Keywords: Burgers equation
zbMATH Keywords: coupled methods
zbMATH Keywords: splitting methods
zbMATH Keywords: Adams-Bashforth multistep method
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: non-isothermal flow of an ideal gas
MaRDI profile type: Publication
full work available at URL: jcph.1995.1116
OpenAlex ID: W1966948822
DOI: 10.1006/JCPH.1995.1116
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description: scientific article; zbMATH DE number 772376