Combining Mixed Finite Element Method And Finite Volume Element Method For Miscible Displacement In Porous Media

In recent years, with the development of agriculture and industry, the discharge of large amount of waste gas, waste water and industrial residue, the widely use of pesti-cides and fertilizer, the increasing growth of radioactive wastes when using the nuclear energy, the increasing garbage caused by population growth and urbanization are caus-ing more and more damages. The intentional or accidental release of chemical wastes on soils has further stimulated current interests in the movement of chemicals. Displace-ment studies have become important tools in soil physics, particularly for predicting the movement of pesticide, nitrates, heavy metals and other solutes through soils.Convection-Dispersion Equation is one of basic motion equations about solute trans-port in soil. This simple model has a solid physics foundation and could describe the transport of solute, heat, reaction diffusion process, etc. However, according to the complexity of the practical conditions, this model cannot be used in the field of large scale solute transport problems. In aggregated media, soils are composed of slowly and quickly conducting pore sequences, the liquid-filled, dead-end pores or immobile wa-ter exists. One way to account for the transport and immobile water is to partition the liquid phase into mobile and immobile regions, to limit convective-dispersive transport to the mobile liquid region, and to assume that diffusion is responsible for the exchange of solute between the mobile and immobile regions. In [21] the movement of a chemical through a absorbing porous medium with a lateral or intra-aggregated diffusion was con-sidered. Mobile water is located inside the larger pores and Immobile water is located inside aggregates and at the contact points of aggregates and/or particles. A dynamic soil region is located sufficiently close to the mobile water phase for equilibrium be-tween the solute in the mobile liquid and that absorbed by this part of the soil mass. A stagnant soil region, where sorption is diffusion limited, is located mainly around the micro-pores inside the aggregates or along dead-end water pockets. Sorption occurs here only after the chemicals have diffused through the liquid barrier of the immobile liquid phase. The non-equilibrium solute transport two-region model(TRM) is based on the convection-dispersion model. Two-Region Model have taken the immobile water, influ-ence of absorption and degradation into account, which is more accurately to describe the solute transport process in soil.For more complex problems, it is difficult to present the analytical solutions and nu- merical simulation is a kind of effective method. The basic numerical simulation method is FDM and FEM, but the traditional FDM are not efficient for some models with con-vection term. Due to the hyperbolic properties of convection-dominate dispersion equa-tions, the central difference formula often cause numerical dispersion and oscillation even it has two-order precision in space. The characteristics combing the difference or finite element method can be better to reflect the first-order hyperbolic properties of convection-dispersion equations. The characteristic methods, discrete the equation along the characteristic line according to physical and mechanical properties, can effectively overcome nonphysical oscillation and reduce truncation errors and greatly improve the calculation accuracy. Cui Ming and ZhangDe sheng had impled the characteristic finite element method to two-region model and made an assay of numerical calculation. In this article, In chapter two, based on the same numerical approximation theory, we adopt the mixed finite element method combing the finite volume element method to attain the numerical results and analyze the related error estimates. Meanwhile, we give a one-dimensional simple model.