Taylor-Galerkin-based spectral element methods for convection-diffusion problems |
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Authors: | L. J. P. Timmermans F. N. Van De Vosse 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. |
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Keywords: | Convection-diffusion problems Operator-splitting Taylor-Galerkin time integration Spectral element method |
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