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Characteristic Galerkin method for convection-diffusion equations and implicit algorithm using precise integration

Characteristic Galerkin method for convection-diffusion equations and implicit algorithm using... Abstract This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

Characteristic Galerkin method for convection-diffusion equations and implicit algorithm using precise integration

Xikui, Li; Wenhua, Wu
"Acta Mechanica Sinica" , Volume 15 (4): 12 – Nov 1, 1999
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References (17)

Publisher
Springer Journals
Copyright
1999 Chinese Society of Theoretical and Applied Mechanics
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/BF02487935
Publisher site
See Article on Publisher Site

Abstract

Abstract This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional 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.

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: Nov 1, 1999

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