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1.
Liu Xiyu 《数学学报(英文版)》1998,14(1):125-134
This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous
media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary
value problems.
This work is supported in part by NSF of Shandong Province and NNSF of China 相似文献
2.
Gonzalo Alduncin 《Mathematical Methods in the Applied Sciences》2016,39(18):5242-5257
Macro‐hybrid mixed variational models of two‐phase flow, through fractured porous media, are analyzed at the mesoscopic and macroscopic levels. The mesoscopic models are treated in terms of nonoverlapping domain decompositions, in such a manner that the porous rock matrix system and the fracture network interact across rock–rock, rock–fracture, and fracture–fracture interfaces, with flux transmission conditions dualized. Alternatively, the models are scaled to a macroscopic level via an asymptotic process, where the width of the fractures tends to zero, and the fracture network turns out to be an interface system of one less spatial dimension, with variable high permeability. The two‐phase flow is characterized by a fractional flow dual mixed variational model. Augmented two‐field and three‐field variational reformulations are presented for regularization, internal approximations, and macro‐hybrid mixed finite element implementation. Also abstract proximal‐point penalty‐duality algorithms are derived and analyzed for parallel computing. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
Gonzalo Alduncin 《Applicable analysis》2013,92(12):2252-2283
Multidomain mixed nonlinear transport and flow phenomena through elastoviscoplastic porous media is variationally analyzed. Mixed variational formulations of the poro-mechanical system are established via composition duality methods, determining solvability results on the basis of duality principles. The conformation of the coupled physical system corresponds to constrained transport processes driven by a compressible Darcian flow, in a quasistatic elastoviscoplastic deformable subsurface porous media, modeled variationally by primal evolution mixed transport and consolidation, and dual evolution mixed flow and quasistatic deformation. For parallel computing, non-overlapping multidomain decomposition methods based on variational macro-hybridization, are presented and discussed, providing a natural multi-physics approach for the coupled transport flow and deformation system. For computational realizations, internal variational macro-hybrid mixed semi-discrete approximations are given, as well as primal and dual fully discrete semi-implicit time marching schemes. Furthermore, the corresponding coupled transport-flow-deformation system is concluded and analyzed, proposing natural resolution coupling techniques. 相似文献
4.
This paper presents a study of immiscible compressible two‐phase, such as water and gas, flow through double porosity media. The microscopic model consists of the usual equations derived from the mass conservation laws of both fluids, along with the standard Darcy–Muskat law relating the velocities to the pressure gradients and gravitational effects. The problem is written in terms of the phase formulation, that is, where the phase pressures and the phase saturations are primary unknowns. The fractured medium consists of periodically repeating homogeneous blocks and fractures, where the absolute permeability of the medium becomes discontinuous. Consequently, the model involves highly oscillatory characteristics. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. We obtain the convergence of the solutions, and a macroscopic model of the problem is constructed using the notion of two‐scale convergence combined with the dilatation technique. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
This paper presents a method for modeling microgeometric structures of porous media with a predominant using successive cross-sections. The proposed model takes into account the properties of diffusive flow in capillaries. In order to characterize uncertainty and imprecision occurring in geometric features of cross-sections, we introduce the concept of connection degrees as well as tracking degrees based on fuzzy theory. The proposed model can be used for classifying different types of media and finding the relationship between the geometric structure of a porous medium and its physical properties. This model has been successfully applied to polyester yarn structure. 相似文献