Multi-scale finite element modelling of laminar steady flow through highly permeable porous media

Chemical Engineering Science

Volumn 61, Issue 2, 2006, Pages 586-596

  Parvazinia, M ^a   Nassehi, V ^a   Wakeman, R J ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

Bubble function; Finite element method; Isothermal; Laminar flow; Multi scale modelling; Porous media

Indexed keywords

BUBBLES (IN FLUIDS); EQUATIONS OF MOTION; FINITE ELEMENT METHOD; GALERKIN METHODS; LAGRANGE MULTIPLIERS; LAMINAR FLOW; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; STEADY FLOW;

BRINKMAN EQUATION; BUBBLE FUNCTIONS; ISSOTHERMAL FLOW; MULTI-SCALE MODELING;

POROUS MATERIALS;

FINITE ELEMENT ANALYSIS; LAMINAR FLOW; PERMEABILITY; POROUS MEDIUM; STEADY FLOW;

EID: 27144532381     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2005.07.018     Document Type: Article

References (27)

1. F.M. Allan, and M.H. Hamdan Fluid mechanics of the interface region between two porous layers Applied Mathematics and Computation 128 2002 37 43
2. W. Bai The quadrilateral 'Mini' finite element for the stokes problem Computer Methods in Applied Mechanics and Engineering 143 1997 41 47
3. C. Baiocchi, F. Brezzi, and L.P. Franca Virtual bubbles and Galerkin-least-squares type methods Computer Methods in Applied Mechanics and Engineering 105 1993 125 141
4. K.J. Bathe Finite Element Procedures 1996 Prentice Hall Englewood Cliffs, NJ
5. F. Brezzi, M. Bristeau, L.P. Franca, M. Mallet, and G. Roge A relationship between stablized finite element methods and the Galerkin method with bubble functions Computer Methods in Applied Mechanics and Engineering 96 1992 117 129
6. F. Brezzi, L.P. Franca, T.J.R. Hughes, and A. Russo b = ∫ g Computer Methods in Applied Mechanics and Engineering 145 1997 392 393
7. F. Brezzi, L.P. Franca, and A. Russo Further considerations on residual-free bubbles for advective-diffusive equations Computer Methods in Applied Mechanics and Engineering 166 1998 25 33
8. J. Donea, and A. Huerta Finite Element Methods for Flow Problems 2003 Wiley Chichester, UK
9. L.P. Franca, and C. Farhat Bubble functions prompt unusual stabilized finite element methods Computer Methods in Applied Mechanics and Engineering 123 1995 299 308
10. L.P. Franca, and A. Russo Deriving upwinding, mass lumping and selective reduced integration by residual free bubbles Applied Mathematics Letters 9 1996 83 88
11. L.P. Franca, and A. Russo Unlocking with residual-free bubbles Computer Methods in Applied Mechanics and Engineering 142 1997 361 364
12. L.P. Franca, and A. Russo Mass lumping enamating from residual free bubbles Computer Methods in Applied Mechanics and Engineering 142 1997 353 360
13. Franca, L.P., Hughes, T.J.R., Stenberg, R., 1993. Stabilized finite element methods for the Stokes problem. In: Nicolaides, R.A., Gunzberger, M.D. (Eds.), Incompressible Fluid Dynamics-Trends and Advances. Cambridge University Press, Cambridge.
14. L.P. Franca, C. Farhat, A.P. Macedo, and M. Lesoinne Residual free bubbles for Helemholtz equation Computer Methods in Applied Mechanics and Engineering 40 1997 4003 4009
15. C.F. Gerald, and P.O. Wheatley Applied Numerical Analysis 1984 Addison-Wesley Reading, MA
16. V. Gravimier, W.A. Wall, and E. Ramm A three-level finite element method for the instationary incompressible Navier-Stokes equations Computer Methods in Applied Mechanics and Engineering 193 2004 1323 1366
17. C.T. Hsu, and P. Cheng The Brinkman model for natural convection about a semi-infinite vertical flat plate in a porous medium International Journal of Heat and Mass Transfer 28 1985 683 697
18. T.J.R. Hughes Multi scale phenomena, Green's functions, the Dirichlet - to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods Computer Methods in Applied Mechanics and Engineering 127 1995 381 401
19. T.J.R. Hughes, and J. Stewart A space time formulation for multiscale phenomena Computer Methods in Applied Mechanics and Engineering 74 1996 217 229
20. B.M. Irons A frontal solution for finite element analysis International Journal for Numerical Methods in Engineering 2 1970 5 32
21. M. Kaviany Non-Darcian effects on natural convection in porous media confined between horizontal cylinders International Journal of Heat and Mass Transfer 29 1986 1513 1519
22. V. Nassehi Practical Aspects of Finite Element Modelling of Polymer Processing 2002 Wiley Chichester, UK
23. D.A. Nield, and A. Bejan Convection in Porous Media 1992 Springer New York Inc
24. Parvazinia, M., Nassehi, V., Wakeman, R.J., Ghoreishy, M.H.R., 2006. Finite element modelling of flow through a porous medium between two parallel plates using the Brinkman equation. Transport in Porous Media, in press.
25. Pittman, J.F.T., 1989. Finite elements for field problems. In: Tucker III, C.L. (Ed.), Computer Modelling for Polymer Processing. Hanser Publishers, Munich.
26. J.N. Reddy Applied Functional Analysis and Variational Methods in Engineering 1986 McGraw-Hill New York
27. O.C. Zienkiewicz, and R.L. Taylor The Finite Element Method 1994 McGraw-Hill London