Efficient steady-state solution techniques for variably saturated groundwater flow

Advances in Water Resources

Volumn 26, Issue 8, 2003, Pages 833-849

  Farthing, Matthew W ^a   Kees, Christopher E ^b   Coffey, Todd S ^c   Kelley, C T ^b   Miller, Cass T ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Pseudo transient continuation; Richards' equation; Steady state

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; ITERATIVE METHODS; NONLINEAR SYSTEMS;

RICHARD'S EQUATION;

GROUNDWATER FLOW;

FLOW MODELING; GROUNDWATER; SATURATED MEDIUM; STEADY FLOW;

FLOW MODELING; GROUNDWATER FLOW; PHREATIC ZONE; STEADY FLOW;

EID: 0042267435     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(03)00076-9     Document Type: Article

References (40)

1. Anderson E. Bai Z. Bischof C. Demmel J. Dongarra J. Du Croz J.et al LAPACK Users' Guide 1992 SIAM Philadelphia, PA
2. Ashcraft C. Grimes R. Spooles: An object-oriented sparse matrix library Proceedings of the 1999 SIAM Conference on Parallel Processing for Scientific Computing March 22-24, San Antonio 1999 SIAM
3. Ashcraft C, Grimes R. SPOOLES homepage. Technical Report http:// www.netlib.org/linalg/spooles/spooles.2.2.html , 1999
4. Baca R.G. Chung J.N. Mulla D.J. Mixed transform finite element method for solving the non-linear equation for flow in variably saturated porous media Int. J. Numer. Methods Fluids 24 1997 441-455
5. Balay S. Gropp W.D. McInnes L.C. Smith B.F. Efficient management of parallelism in object oriented numerical software libraries Arge E. Bruaset A.M. Langtangen H.P. Modern software tools in scientific computing 1997 163-202 Birkhauser Boston, MA
6. Balay S, Gropp WD, McInnes LC, Smith BF. PETSc homepage. Technical Report http://www.mcs.anl.gov/petsc , Argonne National Laboratory, 1998
7. Balay S, Gropp WD, McInnes LC, Smith BF. PETSc 2.0 users manual. Technical Report ANL-95/11- Revision 2.0.28, Argonne National Laboratory, 2000
8. Bergamaschi L. Putti M. Mixed finite elements and Newton-type linearization for the solution of Richards' equation Int. J. Numer. Methods Eng. 45 1999 1025-1046
9. Celia M.A. Bouloutas E.T. Zarba R.L. A general mass-conservative numerical solution for the unsaturated flow equation Water Resour. Res. 26 7 1990 1483-1496
10. Chounet L.M. Hilhorst D. Jouron C. Kelanemer Y. Nicolas P. Simulation of water flow and heat transfer in soils by means of a mixed finite element method Adv. Water Resour. 22 5 1999 445-460
11. Coffey TS. Temporal and pseudo-temporal numerical integration methods. PhD thesis, North Carolina State University, Raleigh, NC, 2002
12. Duff I.S. van der Vorst H.A. Developments and trends in the parallel solution of linear systems Parallel Comput. 25 13-14 1999 1931-1970
13. Eisenstat S.C. Walker H.F. Choosing the forcing terms in an inexact Newton method SIAM J. Sci. Comput. 17 1996 16-32
14. Farthing M.W. Kees C.E. Miller C.T. Mixed finite element methods and higher-order temporal approximations Adv. Water Resour. 25 1 2002 85-101
15. Forsyth P.A. Wu Y.-S. Pruess K. Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media Adv. Water Resour. 18 1995 25-38
16. Gropp W.D. Keyes D.E. McInnes L.C. Tidriri M.D. Globalized Newton- Krylov-Schwarz algorithms and software for parallel implicit CFD Int. J. High Performance Comput. Appl. 14 2 2000 102-136
17. Gupta A. Recent advances in direct methods for solving unsymmetric sparse systems of linear equations Assoc. Comput. Machinery, Trans. Math. Software 28 3 2002 301-324
18. Jenkins E.W. Kees C.E. Kelley C.T. Miller C.T. An aggregation-based domain decomposition preconditioner for groundwater flow SIAM J. Sci. Comput. 23 2 2001 430-441
19. Jones J.E. Woodward C.S. Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems Adv. Water Resour. 24 7 2001 763-774
20. Kavetski D. Binning P. Sloan S.W. Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards' equation Adv. Water Resour. 24 2001 595-605
21. Kees C.E. Miller C.T. C++ implementations of numerical methods for solving differential-algebraic equations: Design and optimization considerations Assoc. Comput. Machinery, Trans. Math. Software 25 4 1999 377-403
22. Kees C.E. Miller C.T. Higher order time integration methods for two-phase flow Adv. Water Resour. 25 2 2002 159-177
23. Kelley C.T. Iterative methods for linear and nonlinear equations 1995 SIAM Philadelphia, PA
24. Kelley C.T. Keyes D.E. Convergence analysis of pseudo-transient continuation SIAM J. Numer. Analysis 35 2 1998 508-523
25. Knoll D.A. McHugh P.R. Enhanced nonlinear iterative techniques applied to nonequilibrium plasma flow SIAM J. Sci. Comput. 19 1 1998 291-301
26. Lehmann F. Ackerer Ph. Comparison of iterative methods for improved solutions of the fluid flow equation in partially saturated porous media Transport Porous Media 31 3 1998 275-292
27. Miller C.T. Christakos G. Imhoff P.T. McBride J.F. Pedit J.A. Trangenstein J.A. Multiphase flow and transport modeling in heterogeneous porous media: Challenges and approaches Adv. Water Resour. 21 2 1998 77-120
28. Miller C.T. Williams G.A. Kelley C.T. Tocci M.D. Robust solution of Richards' equation for non-uniform porous media Water Resour. Res. 34 10 1998 2599-2610
29. Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media Water Resour. Res. 12 3 1976 513-522
30. Paniconi C. Putti M. A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems Water Resour. Res. 30 12 1994 3357-3374
31. Paniconi C. Putti M. Newton-type linearization and line search methods for unsaturated flow models Aral M.M. Advances in groundwater pollution control and remediation NATO ASI Series 2: Environment vol. 9 1996 155-172 Kluwer Academic
32. Parlange J.-Y. Hogarth W.L. Barry D.A. Parlange M.B. Haverkamp R. Ross P.J. et al Analytical approximations to the solution of Richards' equation with applications to infiltration, ponding, and time compression approximation Adv. Water Resour. 23 1999 189-194
33. Rathfelder K. Abriola L.M. Mass conservative numerical solutions of the head-based Richards equation Water Resour. Res. 30 9 1994 2579-2586
34. Simunek J, Vogel T, van Genuchten MTh. The SWMS code for simulating water flow and solute transport in two-dimensional variably saturated media. Technical Report Research Report 132, US Salinity Laboratory, Agricultural Research Service, US Department of Agriculture, Riverside, CA, 1994
35. Tocci M.D. Kelley C.T. Miller C.T. Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines Adv. Water Resour. 20 1 1997 1-14
36. Tocci M.D. Kelley C.T. Miller C.T. Kees C.E. Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions Comput. Geosci. 2 4 1999 291-309
37. van Genuchten M.Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils Soil Sci. Soc. Am. J. 44 1980 892-898
38. Williams G.A. Miller C.T. Kelley C.T. Transformation approaches for simulating flow in variably saturated porous media Water Resour. Res. 36 4 2000 923-934
39. Wu Y.-S. Forsyth P.A. On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media J. Contaminant Hydrol. 48 2001 277-304
40. Zaidel J. Russo D. Estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils Water Resour. Res. 28 9 1992 2285-2295