Numerical Methods For Fluid Flow In Deformed Porous Media

The solid medium consist of holes connected each other and located randomly with different shape and size is called porous medium.Due to the very high pressure and temperature the porous media endured,the porous media tends to change in shape completely and partly. So the porous media has the property of deformation. We name this kind of media compressible porous media.Knowledge about the dynamic flow conditions of porous media is of the utmost importance in industrial application such as Papermaking. Increasing the efficiency of the press section of paper machines is an attractive route to achieving energy savings,which is recognized as the problem of fluid flow in deformed porous media[1]. Great efforts have been made to develop numerical simulation tools for papermaking to predict and control the water removal during the wet pressing of paper webs. A comprehensive review of articles treating the dynamics of water flow during wet pressing has been published by El-Hosseiny(1991).This article deals with the dynamic behavious during filtration and wet pressing of compressible porous media[2]. this article introduces a new coordinate system y on the basis of previous coordinate system z,which deforms with the medium. An parabolic equation is developed which void ratio changes with time tand spaccy Furthermore,we give Galerkin numerical solution of the equation and error estimates of the finite element solution and location function z have been shown. Galerkin numerical solution of all kinds of equations have been discussed in [3]-[9].The whole dissertation consists of three chapters. In the chapter 1 ,we discussed the physical background,basic concepts and mathematical model.The section 1 disussed some basic physical concepts.The section 2 discussed mathematical model of one-dimensional problem of fluid flow in porous media.and some marks.In the chapter 2,we discussed semi-discrete form and convergence analysis of deformed porous media problem.The section 1 disussed the variational form and semi-discrete form of deformed porous media problem.In section 2,we give conver-gence analysis and error estimate of semi-discrete form.Im section 3,we give error estimate of semi-discrete form of location function z,In the chapter 3,we discussed fully discrete form and convergence analysis ofde-formed porous media problem.The section 1 disussed fully discrete form of deformed porous media problem.In section 2,we give convergence analysis and error estimate of fully discrcte form.In section 3,wc give error estimate of fully discrete form of location function z.