Taylor-Galerkin-based spectral element methods for convection-diffusion problems

L.J.P. Timmermans, F.N. Vosse, van de, P.D. Minev

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Abstract

Several explicit Taylor-Galerkin-based time integration schemes are proposed for the solution of both linear and non-linear convection problems with divergence-free velocity. These schemes are based on second-order Taylor series of the time derivative. The spatial discretization is performed by a high-order Galerkin spectral element method. For convection-diffusion problems an operator-splitting technique is given that decouples the treatment of the convective and diffusive terms. Both problems are then solved using a suitable time scheme. The Taylor-Galerkin methods and the operator-splitting scheme are tested numerically for both convection and convection-diffusion problems.
Original languageEnglish
Pages (from-to)853-870
Number of pages18
JournalInternational Journal for Numerical Methods in Fluids
Volume18
Issue number9
DOIs
Publication statusPublished - 1994

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