High order Godunov mixed methods on tetrahedral meshes for density driven flow simulations in porous media

Journal of Computational Physics

Volumn 208, Issue 1, 2005, Pages 154-174

  Mazzia, Annamaria ^a   Putti, Mario ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Coupled flow and transport equations; High order finite volume; Mixed hybrid finite element; Tetrahedral mesh; Time splitting

Indexed keywords

FINITE ELEMENT METHOD; GROUNDWATER; NUMERICAL METHODS; POROUS MATERIALS;

COUPLED FLOW; COUPLED FLOW AND TRANSPORT EQUATION; COUPLED TRANSPORT; FINITE-VOLUME; FLOW AND TRANSPORT; FLOW EQUATIONS; HIGH ORDER FINITE VOLUME; HIGH-ORDER; HIGHER-ORDER; MIXED HYBRID FINITE ELEMENT; TETRAHEDRAL MESHES; TIME SPLITTING; TRANSPORT EQUATION;

COMPUTATIONAL EFFICIENCY;

EID: 19044369573     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.01.029     Document Type: Article

References (39)

1. C.I. Voss W.R. Souza Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone Water Resour. Res. 23 10 1987 1851-1866
2. O. Kolditz R. Ratke H.J.G. Diersch W. Zielke Coupled groundwater flow and transport: 1. Verification of variable density flow and transport models Adv. Water Resour. 21 1 1998 27-46
3. P. Ackerer A. Younes R. Mose Modeling variable density flow and solute transport in porous medium: 1. Numerical model and verification Transp. Porous Media 35 3 1999 345-373
4. G. Gambolati M. Putti C. Paniconi Three-dimensional model of coupled density-dependent flow and miscible salt transport in groundwater in: J. Bear A.H.-D. Cheng S. Sorek D. Ouazar I. Herrera (Eds.) Seawater Intrusion in Coastal Aquifers; Concepts, Methods and Practices 1999 Kluwer Academic Publishers Dordrecht, The Netherlands 315-362
5. R.A. Wooding S.W. Tyler I. White Convection in groundwater below an evaporating salt lake, 1, Onset of instability Water Resour. Res. 33 6 1997 1199-1217
6. R.A. Wooding S.W. Tyler I. White P.A. Anderson Convection in groundwater below an evaporating salt lake, 2, Evolution of fingers or plumes Water Resour. Res. 33 6 1997 1219-1228
7. S. Oswald, Dichteströmungen in porösen medien: Dreidimensionale experimente und modellierung, Ph.D. thesis, ETH Zürich, 1999
8. H.-J. Diersch O. Kolditz Variable-density flow and transport in porous media: Approaches and challenges Adv. Water Resour. 25 2002 899-944
9. A. Mazzia L. Bergamaschi M. Putti On the reliability of numerical solutions for density dependent flow and transport in groundwater Transp. Porous Media 43 1 2001 65-86
10. K. Johansen W. Kinzelbach S. Oswald G. Wittum The saltpool benchmark problem - numerical simulation of saltwater upconing in a porous medium Adv. Water Resour. 25 2002 335-348
11. C. Cordes M. Putti Accuracy of Galerkin finite elements for the groundwater flow equation in two and three dimensional triangulations Int. J. Numer. Meth. Eng. 52 2001 371-387
12. T. Russel M. Wheeler Finite element and finite difference methods for continuous flows in porous media in: R. Ewing (Ed.) The Mathematics of Reservoir Simulation 1983 SIAM Philadelphia, PA 35-106
13. A. Mazzia L. Bergamaschi M. Putti A time-splitting technique for advection-dispersion equation in groundwater J. Comput. Phys. 157 1 2000 181-198
14. A. Mazzia L. Bergamaschi C.N. Dawson M. Putti Godunov mixed methods on triangular grids for advection-dispersion equations Comput. Geosci. 6 2 2002 123-139
15. L. Bergamaschi, A. Mazzia, M. Putti, A time-splitting technique for the solution of density dependent flow and transport in groundwater, in: L.R. Bentley et al. (Eds.), Computational Methods in Water Resources, Balkema, Rotterdam, 2000, pp. 75-82
16. A. Mazzia M. Putti Mixed-finite element and finite volume discretization for heavy brine solutions in groundwater J. Comput. Appl. Math. 147 1 2002 191-213
17. C.T. Simmons K.A. Narayan R.A. Wooding On a test case for density-dependent groundwater flow and solute transport model: The salt lake problem Water Resour. Res. 35 12 1999 3607-3620
18. S.M. Hassanizadeh T. Leijnse A non-linear theory of high-concentration-gradient dispersion in porous media Adv. Water Resour. 18 4 1995 203-215
19. S.M. Hassanizadeh T. Leijnse On the modeling of brine transport in porous media Water Resour. Res. 24 3 1988 321-330
20. C.N. Dawson High resolution upwind-mixed finite element methods for advection diffusion equations with variable time-stepping Numer. Meth. PDE 11 1995 525-538
21. T.J. Barth, D.C. Jespersen, The design and application of upwind schemes on unstructured meshes, AIAA paper 89-0366, 1989, pp. 1-12
22. A. Mazzia M. Putti Investigation of extension of high order finite volume schemes from triangles to tetrahedra in: D.K.R. Herbin (Ed.) Finite Volumes for Complex Applications III, Problems and Perspectives 2002 Hermes Penton Science London 413-420
23. E. Godlewski P. Raviart Numerical Approximation of Hyperbolic Systems of Conservation Laws 1996 Springer New York
24. L.J. Durlofsky B. Engquist S. Osher Triangle based adaptive stencils for the solution of hyperbolic conservation laws J. Comput. Phys. 98 1992 64-73
25. M.E. Hubbard Multidimensional slope limiters for MUSCL-type Finite Volume schemes on unstructured grids J. Comput. Phys. 155 1 1999 54-74
26. P. Batten C. Lambert D. Causon Positively conservative high-resolution convection schemes for unstructured meshes Int. J. Numer. Meth. Eng. 39 1996 1821-1838
27. H. Yan, G. Urbin, D. Knight, A.A. Zheltovodov, Compressible large eddy simulation using unstructured grid: Supersonic boundary layer and compression ramps, in: 10th International Conference on Methods of Aerophysical Research, Novosibirsk, Russia, 2000, pp. 1-8
28. Y. Coudiere J.-P. Vila P. Villedieu Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem Math. Model. Numer. Anal. 33 3 1999 493-516
29. E. Bertolazzi G. Manzini A cell-centered second-order accurate finite volume method for convection-diffusion problems in unstructured meshes Math. Model. Meth. Appl. Sci. 14 8 2004 1235-1260
30. A. Harten S. Osher B. Engquist S.R. Chakravarthy Some results on uniformly high-order accurate essentially nonoscillatory schemes Appl. Numer. Math. 2 1986 347-377
31. A. Harten B. Engquist S.R. Chakravarthy Uniformly high-order accurate essentially nonoscillatory schemes. iii J. Comput. Phys. 71 1987 231-303
32. H.-J.G. Diersch O. Kolditz Coupled groundwater flow and transport: 2. Thermohaline and 3D convection systems Adv. Water Resour. 21 1998 401-425
33. J. Bear Hydraulics of Groundwater 1979 McGraw-Hill New York
34. G. Dagan Theory of solute transport by groundwater Annu. Rev. Fluid Mech. 19 1987 183-215
35. L. Bergamaschi M. Putti Mixed finite elements and Newton-like linearization for the solution of Richard's equation Int. J. Numer. Meth. Eng. 45 8 1999 1025-1046
36. A. Mazzia M. Putti Three dimensional godunov mixed methods on tetrahedra for the advection-dispersion equation in: W.G.G.S.M. Hassanizadeh R.J. Schotting G. Pinder (Eds.) Computational Methods in Water Resources, Developments in Water Resources, 47 vol. 1 2002 Elsevier Amsterdam 381-388
37. F. Brezzi M. Fortin Mixed and Hybrid Finite Element Methods 1991 Springer Berlin
38. 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 3 1993 701-716
39. C.M. D'Haese M. Putti C. Paniconi N.E. Verhoest F.D. Troch Assessment of initial solution estimates and adaptive vs. heuristic time stepping for variably saturated flow in: C. Miller (Ed.) Computational Methods in Water Resources vol. 1 2004 Elsevier Amsterdam 545-556