On the simulation of multicomponent gas flow in porous media

Applied Numerical Mathematics

Volumn 31, Issue 4, 1999, Pages 405-427

  Ewing, Richard E ^a   Wang, Junping ^b   Weekes, Suzanne L ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF WYOMING   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; POROUS MATERIALS;

GODUNOV-TYPE METHOD; MULTICOMPONENT GAS FLOW; NON-DARCY FLOW EQUATIONS;

FLOW OF FLUIDS;

EID: 0033328360     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00006-9     Document Type: Article

References (21)

1. I. Babuska, The finite element method with Lagrangian multiplier, Numer. Math. 20 (1973) 179-192.
2. T.J. Barth, A three-dimensional upwind Euler solver for unstructured meshes, AIAA Paper 91-1548, January 1991.
3. T.J. Barth, B.C. Jespersen, The design and application of upwind schemes on unstructured meshes, AIAA Paper 89-0366, January 1989.
4. F. Brezzi, On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers, RAIRO Anal. Numér. 2 (1974) 129-151.
5. F. Brezzi, J. Douglas, R. Durán, L. Marini, Mixed finite elements for second order elliptic problems in three variables, Numer. Math. 52 (1987) 237-250.
6. F. Brezzi, J. Douglas, M. Fortin, L. Marini, Efficient rectangular mixed finite elements in two and three spaces variables, RAIRO Modél. Math. Anal. Numér. 21 (1987) 581-604.
7. F. Brezzi, J. Douglas, L. Marini, Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985) 217-235.
8. P. Colella, P.R. Woodward, The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys. 54 (1984) 174-201.
9. J. Douglas, J. Wang, A new family of spaces in mixed finite element methods for rectangular elements, Comput. Appl. Math. 12 (1993) 183-197.
10. P. Forchheimer, Wasserbewegung durch boden, Zeit. Ver. Deut. Ing. 45 (1901) 1781-1788.
11. S.K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb. 47 (1959) 271-306.
12. A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high order essentially non-oscillatory schemes III, J. Comput. Phys. 71 (1987) 231-303.
13. S.M. Hassanizadeh, WG. Gray, High velocity flow in porous media, Transp. Porous Media 2 (1987) 521-531.
14. X.-D. Liu, A maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws, SIAM J. Numer. Anal. 30 (1993) 701-716.
15. S. Osher, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal. 21 (1984) 217-235.
16. P. Raviart, J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in: Mathematics Aspects of Finite Element Methods, Lecture Notes in Mathematics, Vol. 606, 1977, pp. 292-315.
17. D. Ruth, H. Ma, On the derivation of the Forchheimer equations by means of the averaging theorem, Transp. Porous Media 7 (1992) 255-264.
18. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal. 21 (1984) 995-1011.
19. J.M. Thomas, Sur L'analyse Numerique des Methodes D'elements Finis Hybrides et Mixtes, Ph.D. Thesis, Université Pierre et Marie Curie, 1977.
20. B. VanLeer, Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme, J. Comput. Phys. 14 (1974) 263-275.
21. J. Wang, T. Mathew, Mixed finite element method over quadrilaterals, in: I.T. Dimov, Bl. Sendov and P. Vassilevski, Eds., Proceedings of The Third International Conference on Advances in Numerical Methods and Applications, World Scientific, 1994, pp. 203-214.