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

Abstract

SUMMARYSeveral 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.

On the streamfunction–vorticity formulation in sliding bi-period frames: Application to bulk behavior for polymer blends

“…The procedure we follow here in the context of spectral elements is similar to the mortar finite element method [9]. A spectral element method [10,11] is used, since this method is suitable for capturing interfaces with a small interfacial thickness [12]. Similar to a finite element method, the computational domain X is divided into N el non-overlapping sub-domains X e , but now a spectral approximation is applied on each element.…”

“…The streamfunction formulation leads to a biharmonic equation (11) which, within a variational context, leads to severe continuity requirements. Therefore Eq.…”

Diffuse interface modeling of the morphology and rheology of immiscible polymer blends

“…To discretize the governing equations a spectral element method 16,17 is used, since this method is suitable for capturing interfaces with a small interfacial thickness. 18 Similar to any regular finite element method, the computational domain ⍀ is divided into N el non-overlapping sub-domains ⍀ e , but now a spectral approximation is applied on each element.…”

Characteristic-based operator-splitting finite element method for Navier-Stokes equations

“…It has flexible format and good stability. Timmermans et al [9] solved the pure convection-diffusion equation by T-G-based operator-splitting spectral element method. In the model, the convective equation was solved by T-G method.…”

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