TAYLOR-GALERKIN-BASED SPECTRAL ELEMENT METHODS FOR CONVECTION-DIFFUSION PROBLEMS

Several explicit Taylor Galerkin-based time integration schemes are pr oposed for the solution of both linear and non-linear convection probl ems with divergence-free velocity. These schemes are based on second-o rder Taylor series of the time derivative. The spatial discretization is performed by a high-order Galerkin spectral element method. For con vection-diffusion problems an operator-splitting technique is given th at decouples the treatment of the convective and diffusive terms. Both problems are then solved using a suitable time scheme. The Taylor Gal erkin methods and the operator-splitting scheme are tested numerically for both convection and convection diffusion problems.