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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Spectral Element Method
Convection-diffusion Problems
Galerkin
Operator Splitting
Convection
Divergence-free
Taylor series
Galerkin methods
Time Integration
Galerkin Method
Mathematical operators
Discretization
Higher Order
Derivatives
Derivative
Term

Cite this

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title = "Taylor-Galerkin-based spectral element methods for convection-diffusion problems",
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.",
author = "L.J.P. Timmermans and {Vosse, van de}, F.N. and P.D. Minev",
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journal = "International Journal for Numerical Methods in Fluids",
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Taylor-Galerkin-based spectral element methods for convection-diffusion problems. / Timmermans, L.J.P.; Vosse, van de, F.N.; Minev, P.D.

In: International Journal for Numerical Methods in Fluids, Vol. 18, No. 9, 1994, p. 853-870.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Taylor-Galerkin-based spectral element methods for convection-diffusion problems

AU - Timmermans, L.J.P.

AU - Vosse, van de, F.N.

AU - Minev, P.D.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

U2 - 10.1002/fld.1650180905

DO - 10.1002/fld.1650180905

M3 - Article

VL - 18

SP - 853

EP - 870

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 9

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