Noniterative time stepping schemes with adaptive truncation error control for the solution of Richards equation

Water Resources Research

Volumn 38, Issue 10, 2002, Pages 29-1-29-10

  Kavetski, Dmitri ^a   Binning, Philip ^a   Sloan, Scott W ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Adaptive integration; Noniterative time stepping; Richards equation; Thomas Gladwell scheme

Indexed keywords

ITERATIVE METHODS; LINEARIZATION; SOILS;

RICHARDS EQUATIONS;

WATER RESOURCES;

ERROR; ITERATIVE TECHNIQUE; PRESSURE;

EID: 0036822365     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2001wr000720     Document Type: Article

References (24)

1. Abriola, L. M., and J. R. Lang, Self-adaptive hierarchic finite element solution of the one-dimensional unsaturated flow equation, Int. J. Numer. Methods Fluids, 10, 227-246, 1990.
2. Bergamaschi, L., and M. Putti, Mixed finite elements and Newton-type linearizations for the solution of Richards' equation, Int. J. Numer. Methods Eng., 45, 1025-1046, 1999.
3. Celia, M. A., E. T. Bouloutas, and R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26, 1483-1496, 1990.
4. Cooley, R. L., Some new procedures for numerical solution of variably saturated flow problems, Water Resour. Res., 19, 1271-1285, 1983.
5. Culham, W. E., and R. S. Varga, Numerical methods for time-dependent non-linear boundary-value problems, J. Soc. Pet. Eng., 11, 374-388, 1971.
6. Fassino, C., and G. Manzini, Fast-secant algorithms for the non-linear Richards equation, Commun. Numer. Methods Eng., 14, 921-930, 1998.
7. Grifoll, J., and Y. Cohen, A front-tracking numerical algorithm for liquid infiltration into nearly dry soils, Water Resour. Res., 35, 2579-2585, 1999.
8. Huyakorn, P. S., and G. F. Pinder, Computational Methods in Subsurface Flow, Academic, San Diego, Calif., 1985.
9. Huyakorn, P. S., S. D. Thomas, and B. M. Thompson, Techniques for making finite element algorithms competitive in modeling flow in variably saturated porous media, Water Resour. Res., 20, 1099-1115, 1984.
10. Jones, J. E., and C. S. Woodward, Preconditioning Newton-Krylov methods for variably saturated flow, in XIII International Conference on Computational Methods in Water Resources, edited by G. F. Pinder, pp. 101-106, A. A. Balkema, Brookfield, Vt., 2000.
11. Kavetski, D. N., P. Binning, and S. W. Sloan, Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation, Adv. Water Resour., 24, 595-605, 2001.
12. Kavetski, D., P. Binning, and S. W. Sloan, Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow, Int. J. Numer. Methods Eng., 53, 1301-1322, 2002.
13. Lehmann, F., and P. H. Ackerer, Comparison of iterative methods for improved solutions of the fluid flow equation in partially saturated porous media, Transp. Porous Media, 31, 275-292, 1998.
14. Miller, C. T., G. A. Williams, C. T. Kelley, and M. D. Tocci, Robust solution of Richards' equation for nonuniform porous media, Water Resour. Res., 34, 2599-2610, 1998.
15. Ortega, J. M., and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic, San Diego, Calif., 1970.
16. Paniconi, C., and M. Putti, A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems, Water Resour. Res., 30, 3357-3374, 1994.
17. Paniconi, C., A. A. Aldama, and E. F. Wood, Numerical evaluation of iterative and noniterative methods for the solution of the nonlinear Richards equation, Water Resour. Res., 27, 1147-1163, 1991.
18. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed., Cambridge Univ. Press, New York, 1992.
19. Rathfelder, K., and L. M. Abriola, Mass conservative numerical solutions of the head-based Richards equation, Water Resour. Res., 30, 2579-2586, 1994.
20. Sloan, S. W., and A. J. Abbo, Blot consolidation analysis with automatic time stepping and error control, part 1, Theory and implementation, Int. J. Numer. Anal. Methods Geomech., 23, 467-492, 1999.
21. Thomas, R. M., and I. Gladwell, Variable-order variable-step algorithms for second-order systems, part 1, The methods, Int. J. Numer. Methods Eng., 26, 39-53, 1988.
22. Tocci, M. D., C. T. Kelly, and C. T. Miller, Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines, Adv. Water Resour., 20, 1-14, 1997.
23. Williams, G. A., and C. T. Miller, An evaluation of temporally adaptive transformation approaches for solving Richards' equation, Adv. Water Resour., 22, 831-840, 1999.
24. Wood, W. L., Practical Time Stepping Schemes, Oxford Univ. Press, New York, 1990.