EVOLUTION FILTRATION PROBLEMS WITH SEAWATER INTRUSION: TWO-PHASE FLOW DUAL MIXED VARIATIONAL ANALYSIS

doi:10.1016/S0252-9602(15)30046-1

Abstract

Abstract:

Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.

Key words: two-phase flow in coastal aquifers, fractional two-phase flow, dual mixed variational analysis, macro-hybrid variational formulations, augmented exactly penalized duality algorithms, proximation semi-implicit time marching schemes

CLC Number:

35A15

Gonzalo ALDUNCIN. EVOLUTION FILTRATION PROBLEMS WITH SEAWATER INTRUSION: TWO-PHASE FLOW DUAL MIXED VARIATIONAL ANALYSIS[J].Acta mathematica scientia,Series B, 2015, 35(5): 1142-1162.

Trendmd

References

[1] Chen Z, Ewing R. Mathematical analysis of reservoir models. SIAM J Math Anal, 1999, 30:431-453
[2] Chen Z. Degenerate two-phase incompressible flow I, existence, uniqueness and regularity of a weak solution. J Differ Equ, 2001, 171:203-232
[3] Alduncin G. Composition duality methods for mixed variational inclusions. Appl Math Opt, 2005, 52:311-348
[4] Alduncin G. Composition duality methods for evolution mixed variational inclusions. Nonlinear Analysis:Hybrid Syst, 2007, 1:336-363
[5] Alduncin G. Macro-hybrid variational formulations of constrained boundary value problems. Numerical Funct Anal Opt, 2007, 28:751-774
[6] Alduncin G. Analysis of evolution macro-hybrid mixed variational problems. Int J Math Anal, 2008, 2:663-708
[7] Alduncin G. Primal and dual evolution macro-hybrid mixed variational inclusions. Int J Math Anal, 2011, 5:1631-1664
[8] Alduncin G. Parallel proximal-point algorithms for constrained problems in mechanics//Yang L T, Paprzycki M. Practical Applications of Parallel Computing. New York:Nova Science, 2003:69-88
[9] Alduncin G. Analysis of augmented three-field macro-hybrid mixed finite element schemes. Analysis in Theory and Applications, 2009, 25:254-282
[10] Alduncin G. Evolution filtration problems with seawater intrusion:Macro-hybrid primal mixed variational analysis. Front Eng Mech Research, 2013, 2:22-27
[11] Esquivel-Avila J, Alduncin G. Qualitative analysis of evolution filtration free boundary problems//Proceedings of the Second World Congress on Computational Mechanics. Stuttgart:University of Stuttgart, 1990:658-661
[12] Baiocchi C, Comincioli V, Magenes E, et al. Free boundary problems in the theory of fluid flow through porous media:existence and uniqueness theorems. Ann Mat Pura Appl, 1973, 4:1-82
[13] Torelli A. Su un proplema a frontiera libera di evoluzione. Bolletino U M I, 1975, 11(4):559-570
[14] Torelli A. On a free boundary value problem connected with a non steady phenomenon. Ann Sc Norm Super Pisa Cl Sci, 1977, IV:33-58
[15] Friedman A, Torelli A. A free boundary problem connected with non-steady filtration in porous media. Num Anal, TMA, 1977, 1:503-545
[16] Gilardi G. A new approach to evolution free boundary problem. Commun Partial Differ Equ, 1979, 4:1099-1122
[17] DiBenedetto E, Friedman A. Periodic behaviour for the evolutionary dam and related free boundary problems. Commun Partial Differ Equ, 1986, 11:1297-1377
[18] Arbogast T. The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow. Nonlinear Analysis, 1992, 19:1009-1031
[19] Alduncin G. Variational formulations of nonlinear constrained boundary value problems. Nonlinear Analysis, 2010, 72:2639-2644
[20] Girault V, Raviart P A. Finite Element Methods for Navier-Stokes Equations. Berlin:Springer-Verlag, 1986
[21] Alduncin G. Composition duality principles for mixed variational inequalities. Math Comput Model, 2005, 41:639-654
[22] Alduncin G. Mixed variational modeling of multiphase flow and transport in the subsurface. Far East J Appl Math, 2012, 71:1-42
[23] Alduncin G. Numerical resolvent methods for macro-hybrid mixed variational inequalities. Num Funct Anal Opt, 1998, 19:667-696
[24] Temam R. Analyse Numérique. Paris:Presses Universitaires de France, 1970
[25] Alduncin G, Vera-Guzmán N. Parallel proximal-point algorithms for mixed finite element models of flow in the subsurface. Commun Numer Methods Eng, 2004, 20:83-104
[26] Alduncin G, Esquivel-Ávila J, Vera-Guzmán N. Steady filtration problems with seawater intrusion:macro-Hybrid penalized finite element approximations. Int J Num Methods in Fluids, 2005, 49:935-957
[27] Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods. New York:Springer-Verlag, 1991
[28] Roberts J E, Thomas J-M. Mixed and hybrid methods//Ciarlet P G, Lions J L. Handbook of Numerical Analysis, Vol II. Amsterdam:North-Holland, 1991:523-639
[29] Fortin M, Glowinski R (eds). Méthodes de Lagrangien Augmenté:Applications à la Résolution Numérique de Problèmes aux Limites. Paris:Dunod-Bordas, 1982
[30] Gabay D. Application de la méthode des multiplicateurs aux inéquations variationnelles//Fortin M, Glowinski R. Méthodes de Lagrangien Augmenté. Paris:Dunod-Bordas, 1982:279-307
[31] Glowinski R. Numerical Methods for Nonlinear Variational Problems. New York:Springer-Verlag, 1984
[32] Glowinski R, Le Tallec P. Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. Philadelphia:SIAM, 1989
[33] Mosco U. Dual variational inequalities. J Math Anal Appl, 1972, 40:202-206