CHARACTERIST IC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION*

ABSTRACT: This paper presents a finite element procedure for solving tran-sient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integra-tion method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equa-tion, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration pro-cedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the uncondi-tional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability. KEY WORDS: convection-diffusion equation, characteristic Galerkin method, finite element procedure, precise integration, implicit algorith