×

zbMATH — the first resource for mathematics

Numerical solution of steady-state flow through a porous dam. (English) Zbl 0626.76098
A new numerical method is used to solve a classical stationary free boundary problem: the flow through a porous dam. First, the steady-state equation is transformed into an evolution problem equivalent to the original formulation and then we solve this by combining the method of characteristics and the finite element method. The solution of the nonlinear discretized problem is obtained by using a duality iterative algorithm. Finally, numerical results for general geometries are presented.

MSC:
76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alt, H.W., A free boundary problem associated with the flow of ground water, Arch. rat. mech. anal., 64, 111-126, (1977) · Zbl 0371.76079
[2] Alt, H.W., Numerical solution of steady-state porous flow free boundary problems, Numer. math., 36, 73-98, (1980) · Zbl 0447.76074
[3] Baiocchi, C., Su un problema di frontiera libera conneso a questioni di idraulica, Ann. mat. pura appl., 92, 107-127, (1972) · Zbl 0258.76069
[4] Baiocchi, C.; Comincioli, V.; Magenes, E.; Pozzi, G.A., Free boundary problems in the theory of fluid flows through porous media: existence and uniqueness theorems, Ann. mat. pura appl., 97, 1-82, (1973) · Zbl 0343.76036
[5] Baiocchi, C.; Comincioli, V.; Guerri, L.; Volpi, G., Free boundary problems in the theory of fluid flow through porous media: a numerical approach, Calcolo, 10, 1-85, (1973) · Zbl 0296.76052
[6] Baiocchi, C.; Capelo, A., (), 2
[7] Bengue, J.; Ibler, B.; Keraimsi, A.; Labadie, G., A finite element method for Navier-Stokes equations, (), 110-120
[8] Bercovier, M.; Pironneau, O.; Sastri, V., Finite elements characteristics for some parabolic-hyperbolic problems, Appl. math. modelling, 7, 89-96, (1983) · Zbl 0505.65055
[9] Bermudéz, A.; Durany, J., La méthode des caractéristiques pour LES problèmes de convection-diffusion stationnaires, Math. modelling numer. anal., 21, 1, 7-26, (1987) · Zbl 0613.65121
[10] Bermudéz, A.; Durany, J., Application of characteristics method with variable time-step to steady-state convection-diffusion problems, (), 377-386
[11] Bermudéz, A.; Moreno, C., Duality methods for solving variational inequalities, Comput. math. appl., 7, 43-58, (1981) · Zbl 0456.65036
[12] Brezis, H.; Kinderlehrer, D.; Stampacchia, G., Sur une nouvelle formulation du problème de l’écoulement à travers une digue, C.R. acad. sci. Paris, 287, 711-714, (1978) · Zbl 0391.76072
[13] Bruch, J.C.; Sloss, J.M., A variational inequality method applied to free surface seepage from a triangular ditch, Water resources res., 14, 1, 119-124, (1978)
[14] Carrillo, J.; Chipot, M., On the uniqueness of the solution of the dam problem, (), 88-97 · Zbl 0511.35085
[15] Chipot, M., Sur quelques inéquations variationnelles—problème de l’écoulement à travers une digue, ()
[16] Douglas, J.; Russell, T., Numerical methods for convection dominated diffusion problems, SIAM J. numer. anal., 19, 5, 871-885, (1982) · Zbl 0492.65051
[17] Elliott, C.M.; Ockendon, J.R., Weak and variational methods for moving boundary problems, (1982), Pitman London · Zbl 0476.35080
[18] Oden, J.T.; Kikuchi, N., Theory of variational inequalities with applications to problems of flow through porous media, Internat. J. engrg. sci., 18, 1173-1284, (1980) · Zbl 0444.76069
[19] Pironneau, O., On the transport-diffusion algorithm and its applications to the Navier-Stokes equations, Numer. math., 38, 309-332, (1982) · Zbl 0505.76100
[20] Remar, J.; Bruch, J.C.; Sloss, J.M., Axisymmetric free surface seepage, Numer. math., 40, 143-168, (1982) · Zbl 0494.76097
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.