Chavent, G.; Salzano, G. A finite-element method for a 1-D water flooding problem with gravity. (English) Zbl 0489.76106 J. Comput. Phys. 45, 307-344 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 21 Documents MSC: 76T99 Multiphase and multicomponent flows 76M99 Basic methods in fluid mechanics 65C20 Probabilistic models, generic numerical methods in probability and statistics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 82C70 Transport processes in time-dependent statistical mechanics Keywords:wall effect; one-dimensional immiscible displacement of oil by water; presence of gravity yields nomonotone transport term; saturation equation; degenerate nonlinear diffusion term; Bardos-Leroux-Nedelec boundary conditions in pure transport case; methods of Raviart-Thomas and Lesaint-Raviart for approximating diffusion and transport terms; technique of Godunov; water injection rate; capillary forces PDF BibTeX XML Cite \textit{G. Chavent} and \textit{G. Salzano}, J. Comput. Phys. 45, 307--344 (1982; Zbl 0489.76106) Full Text: DOI References: [1] Bardos, C.L.; Leroux, A.Y.; Nedelec, J.C., Rapp. interne CMA, 38, (1978) [2] Raviart, P.A.; Thomas, J.M., A mixed finite element method for second order elliptic problem, () · Zbl 0362.65089 [3] Lesaint, P.; Raviart, P.A., () [4] Godunov, S.K., Mat. sb., 47, 3, 271, (1959) [5] Chavent, G., About the identification and modelling of miscible or immiscible displacement in porous media, () · Zbl 0436.93018 [6] Chavent, G.; Cohen, G., () [7] Salzano, G., Rapp. INRIA, 2, (1980) [8] Marle, C., Cours de production, Vol. IV, (1965), Technip · Zbl 0127.17408 [9] Chavent, G., () [10] Chavent, G., Rapp. lab., 260, (1977) [11] Gagneux, G., J. Méc., 19, 2, 1-31, (1980) [12] Leroux, A.Y., Approximation de quelques problèmes hyperbolique nonlinéaires, () [13] Van Leer, B., J. comput. phys., 23, 3, 276-299, (1977) [14] Cohen, G., Résolution numérique et identification pour une équation quasiparabolique non-linéaire Dégénérée de diffusion et transport en dimension un, Thèse de 3ème cycle, (1978) [15] Jaffré, J., Comput. fluids, 8, 177-188, (1980) [16] Jaffré, J., Rapp. INRIA, 37, (1980) [17] Cohen, G.; Chavent, G.; Espy, M., () 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.