Nonstandard Methods for the Convective Transport Equation with Nonlinear Reactions

Numerical Methods for Partial Differential Equations

Volumn 14, Issue 4, 1998, Pages 467-485

  Kojouharov, Hristo V ^a   Chen, Benito M ^a  

^a UNIVERSITY OF WYOMING   (United States)

Author keywords

Convection reaction equations; Convective flows; Exact finite difference schemes; Lagrangian methods; Reactive solute transport problems

Indexed keywords

EID: 0345082597     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199807)14:4<467::AID-NUM3>3.0.CO;2-I     Document Type: Article

References (19)

1. K. W. Morton, Numerical Solution of Convection-Diffusion Problems, Chapman & Hall, London, 1996.
2. B. Liu, M. B. Allen, H. Kojouharov, and B. Chen, "Finite-element solution of reaction-diffusion equations with advection." In Computational Methods in Water Resources XI, Vol. 1: Computational Methods in Subsurface Flow and Transport Problems, 3-12, A. A. Aldama, J. Aparicio, C. A. Brebbia, W. G. Gray, I. Herrera, and G. F. Pinder, Eds., Computational Mechanics Publications, Southampton Boston, 1996.
3. W. G. Gray, and G. F. Pinder, "An analysis of the numerical solution of the transport equation." Water Resour. Res. 12, 547-555 (1976).
4. C. Johnson and J. Saranen, "Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations." Math. Comp. 47, 1-18 (1986).
5. J. Douglas Jr. and T. F. Russell, "Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures." SIAM J. Numer. Anal. 19, 871-885 (1982).
6. M. A. Celia, T. F. Russell, I. Herrera, and R. E. Ewing, "An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation." Adv. Water Resour. 13, 187-206 (1990).
7. M. B. Allen and B. Liu, "A modified method of characteristics incorporating streamline diffusion." Numer. Meth. P. D. E. 11, 155-174 (1995).
8. R. W. Healy and T. F. Russell, "A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation." Water Resour. Res. 29, 2399-2413 (1993).
9. T. Arbogast and M. F. Wheeler, "A characteristics-mixed finite element method for advection-dominated transport problems." SIAM J. Numer. Anal. 32, 404-424 (1995).
10. J. Douglas, Jr., F. Furtado, and F. Pereira, "On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs." Comp. Geosciences 1, 155-190 (1997).
11. J. D. Murray, Mathematical Biology, Springer, Berlin, 1993.
12. P. S. Huyakorn and G. F. Pinder, Computational Methods in Subsurface Flow, Academic Press, New York, 1983.
13. A. R. Mitchell and D. F. Griffiths, The Finite Difference Method in Partial Differential Equations, John Wiley & Sons, New York, 1980.
14. F. John, Partial Differential Equations, Springer-Verlag, New York, 1991.
15. R. E. Mickens, "Exact solutions to a finite-difference model of nonlinear reaction-advection equation: Implications for numerical analysis." Numer. Methods Partial Diff. Eq. 5, 313-325 (1989).
16. D. W. Peaceman, Fundamentals of the Numerical Reservoir Simulation, Elsevier, Amsterdam, 1977.
17. M. B. Allen and E. L. Isaacson, Numerical Analysis for Applied Science, John Wiley & Sons, New York, 1997.
18. R. E. Mickens, "Difference equation models of differential equations having zero local truncation errors." In Differential Equations, I. W. Knowles and R. T. Lewis, Eds., North-Holland, Amsterdam, 1984, pp. 445-449.
19. H. R. Reddy and R. M. Ford, "Analysis of biodegradation and bacterial transport: Comparison of models with kinetic and equilibrium bacterial adsorption." J. Contam. Hydrol. 22, 271-287 (1996).