An Eulerian-Lagrangian substructuring domain decomposition method for unsteady-state advection-diffusion equations

Numerical Methods for Partial Differential Equations

Volumn 17, Issue 6, 2001, Pages 565-583

  Wang, Hong ^a   Al Lawatia, Mohamed ^b  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b SULTAN QABOOS UNIVERSITY   (Oman)

Author keywords

Advection diffusion equations; Characteristic methods; Domain decomposition methods; Eulerian Lagrangian methods; Neumann Dirichlet algorithm

Indexed keywords

EID: 0035499494     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.1027     Document Type: Article

References (28)

1. B. F. Smith, P. E. Bjørstad, and W. D. Gropp, Domain decomposition: parallel multilevel methods for elliptic partial differential equations, Cambridge University Press, Cambridge, UK, 1996.
2. P. Bjørstad and O. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures, SIAM J Numer Anal 23 (1986), 1093-1120.
3. R. Rannacher and G. Zhou, Analysis of a domain-splitting method for nonstationary convection-diffusion problems, East-West J Num Math 2 (1994), 151-172.
4. X. C. Cai, Additive Schwarz algorithms for parabolic convection-diffusion equations, Numer Math 60 (1991), 41-61.
5. X. C. Cai, Multiplicative Schwarz methods for parabolic problems, SIAM J Sci Comp 15 (1994), 587-603.
6. M. Ciccoli, Adaptive domain decomposition algorithms and finite volume/finite element approximation for advection-diffusion equations, J Sci Comp 11 (1996), 299-341.
7. F. Gastaldi, L. Gastaldi, and A. Quarteroni, Adaptive domain decomposition methods for advection dominated equations, East-West J Numer Math 4 (1996), 165-206.
8. R. Trotta, Multidomain finite elements for advection-diffusion equations, Appl Numer Math 21 (1996), 91-118.
9. B. A. Finlayson, Numerical methods for problems with moving fronts, Ravenna Park Publ, Seattle, 1992.
10. H. Wang, H. K. Dahle, R. E. Ewing, M. S. Espedal, R. C. Sharpley, and S. Man, An ELLAM scheme for advection-diffusion equations in two dimensions, SIAM J Sci Comp 20 (1999), 2160-2194.
11. H. Wang, R. E. Ewing, G. Qin, S. L. Lyons, M. Al-Lawatia, and S. Man, A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations, J Comp Phys 152 (1999), 120-163.
12. J. P. Benque and J. Ronat, "Quelques difficulties des modeles numeriques en hydraulique," Glowinski and Lions, editors, Computing methods in applied sciences and engineering, North Holland, Amsterdam, 1982, pp 471-494.
13. 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 Num Anal 19 (1982), 871-885.
14. G. F. Pinder and H. H. Cooper, A numerical technique for calculating the transient position of the saltwater front, Water Resources Res 6 (1970), 875-882.
15. O. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations, Num Math 38 (1982), 309-332.
16. X. Tai, T. Johansen, H. Dahle, and M. Espedal, "A characteristic domain splitting method," Glowinski, et al., editors, Domain decomposition methods in science and engineering, Proc Eighth Int Conf Domain Decomp Meth, Wiley, New York, 1997, pp 317-323,
17. 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 Resources 13 (1990), 187-206.
18. H. Wang, R. Ewing, and T. Russell, Eulerian-Lagrangian localized adjoint methods for convection-diffusion equations and their convergence analysis, IMA J Numer Anal 15 (1995), 405-459.
19. M. Al-Lawatia, R. C. Sharpley, and H. Wang, Second-order characteristic methods for advection-diffusion equations and comparison to other schemes, Adv Water Resources 22 (1999), 741-768.
20. H. Wang, A family of ELLAM schemes for advection-diffusion-reaction equations and their convergence analyses, Numer Methods PDEs 14 (1998), 739-780.
21. R. W. Healy and T. F. Russell, Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method, Adv Water Res 21 (1998), 11-26.
22. T. F. Russell and R. V. Trujillo, "Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimensions," Gambolati, et al., editors, Computational methods in surface hydrology, Springer-Verlag, Berlin, 1990, pp 357-363.
23. H. Wang, An optimal-order error estimate for an ELLAM scheme for two-dimensional linear advection-diffusion equations, SIAM J Numer Anal 37 (2000), 1338-1368.
24. P. J. Binning and M. A. Celia, A finite volume Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equations in two-dimensional multi-phase flow systems. Water Resource Res 32 (1996), 103-114.
25. J. W. Barrett and K. W. Morton, Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems, Comp Meth Appl Mech Eng 45 (1984), 97-122.
26. I. Christie, D. F. Griffiths, A. R. Mitchell, and O. C. Zienkiewicz, Finite element methods for second order differential equations with significant first derivatives, Int J Num Eng 10 (1976), 1389-1396.
27. L. Marini and A. Quarteroni, A relaxation procedure for domain decomposition methods using finite elements, Numer Math 55 (1989), 575-598.
28. H. Wang, D. Liang, R. E. Ewing, S. L. Lyons, and G. Qin, An ELLAM-MFEM solution technique for compressible fluid flows in porous media with point sources and sinks, J Comp Phys 159 (2000), 344-376.