The numerical modelling of advective transport in the presence of fluid pressure transients

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 30, Issue 7, 2006, Pages 615-634

  Selvadurai, A Patrick S ^a   Dong, W ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Advective transport; Piezo conduction equation; Stabilized numerical methods; Time and mesh adaptive schemes; Transport from cavities

Indexed keywords

BOUNDARY CONDITIONS; COMPRESSIBILITY; FOURIER TRANSFORMS; MATHEMATICAL MODELS; POROUS MATERIALS; STEADY FLOW; TRANSPORT PROPERTIES;

ADVECTIVE TRANSPORT; DARCY FLOW; FLOW VELOCITY DISTRIBUTION; FLUID PRESSURE TRANSIENTS; PIEZO-CONDUCTION EQUATION;

FLUID DYNAMICS;

BOUNDARY CONDITIONS; COMPRESSIBILITY; FLUID DYNAMICS; FOURIER TRANSFORMS; MATHEMATICAL MODELS; POROUS MATERIALS; STEADY FLOW; TRANSPORT PROPERTIES;

COMPRESSIBLE FLOW; DARCY LAW; FLUID FLOW; NUMERICAL METHOD; NUMERICAL MODEL; POROUS MEDIUM;

EID: 33745078545     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.494     Document Type: Article

References (30)

1. Bear J. Dynamics of Fluids in Porous Media. Dover Publications: New York, 1972.
2. Bear J, Verruijt A. Modelling Groundwater Flow and Pollution. D. Reidel Publ. Co.: Dordrecht, The Netherlands, 1990.
3. Bear J, Bachmat Y. Introduction to Modelling of Transport Phenomena in Porous Media. D. Reidel Publ. Co.: Dordrecht, The Netherlands, 1992.
4. Banks RB. Growth and Diffusion Phenomena: Mathematical Frameworks and Applications. Springer: Berlin, 1994.
5. Charbeneau R. Groundwater Hydraulics, and Pollutant Transport. Prentice-Hall: Upper Saddle River, NJ, 1999.
6. Selvadurai APS. Partial Differential Equations in Mechanics, vols. 1 and 2. Springer: Berlin, 2000.
7. Selvadurai APS. The advective transport of a chemical from a cavity in a porous medium. Computers and Geotechnics 2002; 29:525-546.
8. Selvadurai APS. Contaminant migration from an axisymmetric source in a porous medium. Water Resources Research 2003; 39(8):1204, WRR 001742.
9. Selvadurai APS. On the advective-diffusive transport in porous media in the presence of time-dependent velocities. Geophysical Research Letters 2004; 31(13):L13505.
10. Selvadurai APS. Advective transport from a penny-shaped crack in a porous medium and an associated uniqueness theorem. International Journal for Numerical and Analytical Methods in Geomechanics 2004; 28:191-208.
11. Biot MA. General theory of three-dimensional consolidation. Journal of Applied Physics 1941; 12:155-164.
12. Lewis RW, Schrefler BA. The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. Wiley: New York, 1998.
13. Barenblatt GI, Entov VM, Ryzhik VM. Theory of Fluid Flows Through Natural Rocks. Kluwer Academic Publishers: Dordrecht, The Netherlands, 1990.
14. Selvadurai APS. Some remarks on the elastic drive equation. In Environmental Geomechanics, Vulliet L, Laloui L, Schrefler BA (eds). EPFL Press: Switzerland, 2002; 253-258.
15. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Computer Methods in Applied Mechanics and Engineering 1998; 156:185-210.
16. Wang Y, Hutter K. Comparisons of numerical methods with respect to convectively dominated problems. International Journal for Numerical Methods in Fluids 2001; 37:721-745.
17. Hughes TJR, Brooks A. A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure. In Finite Elements in Fluids, Gallagher RH et al. (eds). Wiley: Chichester, U.K., 1982; 47-65.
18. Dong W, Selvadurai APS. Chemical transport in a fluid-saturated porous media. Proceeding of the 9th Symposium on Numerical Models in Geomechanics - NUMOG IX, Ottawa, Canada, 2004: 355-362.
19. Oñate E, García J, Idelsohn S. Computation of the stabilization parameter for the finite element solution of advective-diffusive problems. International Journal for Numerical Methods in Fluids 1997; 25:1385-1407.
20. Carey GF, Jiang BN. Least squares finite element method and pre-conditioned conjugate gradient solution. International Journal for Numerical Methods in Engineering 1987; 24:1283-1296.
21. Wendland E, Schmid GA. Symmetrical streamline stabilization scheme for high advective transport. International Journal for Numerical and Analytical Methods in Geomechanics 2000; 24:29-45.
22. Raymond WH, Garder A. Selective damping in a Galerkin method for solving wave problems with variable grids. Monthly Weather Review 1976; 104:1583-1590.
23. Donea J, Giulian S, Laval H, Quartapelle L. Time-accurate solution of advection-diffusion problem by finite elements. Computer Methods in Applied Mechanics and Engineering 1984; 45:123-145.
24. Vichnevetsky R, Bowles JB. Fourier Analysis of Numerical Approximations of Hyperbolic Equations. SIAM: Philadelphia, PA, 1982.
25. Pereira JMC, Pereira JCF. Fourier analysis of several finite difference schemes for the one-dimensional unsteady convection-diffusion equation. International Journal for Numerical Methods in Fluids 2001; 36:417-439.
26. Selvadurai APS, Dong W. A time-adaptive scheme for the accurate solution of the advective-transport equation with a transient flow velocity. Computer Modeling in Engineering Science 2006, in press.
27. Eriksson K, Johnson C. Adaptive finite element methods for parabolic problems. I: A linear model problem. SIAM Journal on Numerical Analysis 1991; 28:43-77.
28. Carslaw H, Jaeger JC. Heat Conduction in Solids. Oxford University Press: Oxford, 1959.
29. Carey GF. Adaptive refinement and nonlinear fluid problems. Computer Methods in Applied Mechanics and Engineering 1979; 17/18:541-560.
30. George PL. Automatic Mesh Generation - Application to Finite Element Methods. Wiley: Chichester, 1991.