An Implicit Scheme for Solving the Convection-Diffusion-Reaction Equation in Two Dimensions

Journal of Computational Physics

Volumn 164, Issue 1, 2000, Pages 123-142

  Sheu, Tony W H ^a   Wang, S K ^a   Lin, R K ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Fourier stability analysis; Modified equation analysis; Monotonicity; Nodally exact; Two dimensional convection diffusion reaction equation

Indexed keywords

COMPUTATIONAL EFFICIENCY; DIFFUSION IN LIQUIDS; HEAT CONVECTION;

CONVECTION-DIFFUSION-REACTION EQUATIONS; FOURIER; FOURIER STABILITY ANALYSE; IMPLICIT SCHEMES; MODIFIED EQUATION ANALYSIS; MONOTONICITY; NODALLY EXACT; STABILITY ANALYZE; TWO-DIMENSIONAL; TWO-DIMENSIONAL CONVECTION-DIFFUSION-REACTION EQUATION;

DIFFERENTIAL EQUATIONS;

EID: 0009072490     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6588     Document Type: Article

References (18)

1. Harari I., Hughes T. J. R. Finite element methods for the Helmholtz equation in an exterior domain: Model problems. Comput. Methods Appl. Mech. Eng. 87:1991;59.
2. Ilinca F., Pelletier D. Positivity preservation and adaptive solution for the k-ε model of turbulence. AIAA J. 36:1998;44.
3. Crochet M. J., Davies A. R., Walters K. Numerical Simulation of Non-Newtonian Flow. 1984.
4. Leboucher L. Monotone scheme and boundary conditions for finite volume simulation of magnetohynamic internal flows at high Hartmann number. J. Comput. Phys. 150:1999;181.
5. Ataie-Ashtini B., Lockington D. A., Volker R. E. Numerical correction of finite difference solution of the advection-dispersion equation with reaction. J. Contam. Hydrol. 23:1996;149.
6. Hossain M. A. Modeling advective-dispersive transport with reaction: An accurate explicit finite difference model. Appl. Math. Comput. 102:1999;101.
7. Hossain M. A., Yonge D. R. On Galerkin models for transport in groundwater. Appl. Math. Comput. 100:1999;249.
8. Harari I., Hughes T. J. R. Stabilized finite element methods for steady advection-diffusion with production. Comput. Methods Appl. Mech. Eng. 115:1994;165.
9. Idelsohn S., Nigro N., Storti M., Buscaglia G. A Petrov-Galerkin formulation for advection-reaction-diffusion problems. Comput. Methods Appl. Mech. Eng. 136:1996;27.
10. Ascher U. M., Mattheij Robert M. M., Russell Robert D. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. 1988.
11. Doolan E. P., Miller J. J. H., Schilders W. H. A. Uniform Numerical Methods for Problems with Initial and Boundary Layers. 1980.
12. Tezdugar T., Park Y. Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput. Methods Appl. Mech. Eng. 59:1986;307.
13. R. Codina, A shock-capturing anisotropic diffusion for the finite element solution of the diffusion-convection-reaction equation, in, Finite Elements in Fluids, New Trends and Applications, Part 1, edited by, K. Morgan, Pineridge, Swansea, 1993, p, 67.
14. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Comput. Methods Appl. Mech. Eng. 156:1998;185.
15. Polezhaev V. I. Numerical solution of the system of two-dimensional unsteady Navier-Stokes equations for a compressible gas in a closed region. Fluid Dyn. 2:1967.
16. Warming R. F., Hyette B. J. The modified equation approach to the stability and accuracy analysis of finite-difference methods. J. Comput. Phys. 14:1974;159.
17. Meis T., Marcowitz U. Applied Mathematical Science Series. Numerical Solution of Partial Differential Equations. 22:1981.
18. Yu X. Finite difference methods for the reduced water wave equation. Comput. Methods Appl. Mech. Eng. 154:1998;265.