Spectral methods (Fourier Galerkin, Fourier pseudospectral, Chebyshev Tau, Chebyshev collocation, spectral element) and standard finite differences are applied to solve the Burgers equation with small viscosity (). This equation admits a (nonsingular) thin internal layer that must be resolved if accurate numerical solutions are to be obtained. From the reported computations, it appears that spectral schemes offer the best accuracy, especially if coordinate transformation or elemental subdivision is used to resolve the regions of large variation of the dependent variable.
%0 Journal Article
%1 basdevant86:CF-14-23
%A Basdevant, C.
%A Deville, M.
%A Haldenwang, P.
%A Lacroix, J. M.
%A Onazzoni, J.
%A Peyret, R.
%A Orlandi, P.
%A Patera, A. T.
%D 1986
%J Computers & Fluids
%K usyd 76m20-finite-difference-methods-in-fluid-mechanics 76m22-spectral-methods-in-fluid-mechanics
%P 23--41
%R 10.1016/0045-7930(86)90036-8
%T Spectral and Finite Difference Solution of the Burgers Equation
%U http://dx.doi.org/10.1016/0045-7930(86)90036-8
%V 14
%X Spectral methods (Fourier Galerkin, Fourier pseudospectral, Chebyshev Tau, Chebyshev collocation, spectral element) and standard finite differences are applied to solve the Burgers equation with small viscosity (). This equation admits a (nonsingular) thin internal layer that must be resolved if accurate numerical solutions are to be obtained. From the reported computations, it appears that spectral schemes offer the best accuracy, especially if coordinate transformation or elemental subdivision is used to resolve the regions of large variation of the dependent variable.
@article{basdevant86:CF-14-23,
abstract = {{Spectral methods (Fourier Galerkin, Fourier pseudospectral, Chebyshev Tau, Chebyshev collocation, spectral element) and standard finite differences are applied to solve the Burgers equation with small viscosity (). This equation admits a (nonsingular) thin internal layer that must be resolved if accurate numerical solutions are to be obtained. From the reported computations, it appears that spectral schemes offer the best accuracy, especially if coordinate transformation or elemental subdivision is used to resolve the regions of large variation of the dependent variable.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Basdevant, C. and Deville, M. and Haldenwang, P. and Lacroix, J. M. and Onazzoni, J. and Peyret, R. and Orlandi, P. and Patera, A. T.},
biburl = {https://www.bibsonomy.org/bibtex/221fd2899e226a47f91ff36a5ded5397c/gdmcbain},
citeulike-article-id = {2440875},
citeulike-linkout-0 = {http://dx.doi.org/10.1016/0045-7930(86)90036-8},
doi = {10.1016/0045-7930(86)90036-8},
interhash = {66bf48f79c0bcf920f2d02e92072137e},
intrahash = {21fd2899e226a47f91ff36a5ded5397c},
journal = {Computers \& Fluids},
keywords = {usyd 76m20-finite-difference-methods-in-fluid-mechanics 76m22-spectral-methods-in-fluid-mechanics},
pages = {23--41},
posted-at = {2008-02-28 10:09:49},
priority = {2},
timestamp = {2019-10-21T03:18:52.000+0200},
title = {Spectral and Finite Difference Solution of the {Burgers} Equation},
url = {http://dx.doi.org/10.1016/0045-7930(86)90036-8},
volume = 14,
year = 1986
}