Fem For Controlled-Release And Spread Of Solute In Porous Media

Fertilizers and pesticides are widely used in agriculture to improve production efficiency , which brings soil and enviroment pollution. A new technology on controlled-releaseis used in modern agriculture. The choice and optimization of the technology programme can be obtained through the test in the field or laboratory. but the cycle time is too long and the cost is high. Adopting the technology of numerical simulation can greatly save the cost and not be restricted by the time. On the research of the problem about the controlled-release, the general formulas on the processof release are provided and the diffusion caused by the water flowing from high to low arc considered in Friedman[7]. Still in Friedman[7] vertical move and degretation are solved through numerical method, and analystical methods on the process of local release in the equivalent spherical soil region are studied. In Friedman[7] the process of release and flow action are decoupled factitiously, the release is treated as origin and resolved only on one dimension problem. Given velocity field, the finite element method to numerically solve the model about the process of controlled-release coupling the process of spread in three dimension is provided in [9]. In this paper, based on these work, the the finite element method to numerically solve the model about the process of controlled-release. spread coupling the process of flow action in three dimension is studied. The process of spread was characterized by a convection diffusion equation with mechanical dispersion as wellas a boundary condition of the thrid type:The process of controlled-release was governed by a boundary integral oridinary differential equation:Velocity fluid satisfied the following equation:This paper is divided into three chapters.In the first chapter, the details on the coupling system are given.In the second chapter, the semi-discrete finite element numerical scheme is considered and the convergence is analyzed.The error estimate of semi-discrete scheme:Theorem 2.1 Setφ(x) should be bounded below by positive constants and the matrix D(u) should be positive-definite, c(t) and c_h(t) are respectively the solution of equation (2.2.1) and (2.2.3). ThenThis error estimate is lowerthan optimal approximation. Especially in the zero order release stage, the error estimate is up to optima.In the third chapter, the time-discrete finite element numerical scheme is considered and the convergence is analyzed.The error estimate of time-discrctc scheme: Theorem 3.1 Under the conditions of Theorem2.1, set c~m = c(t~m) is the solution of (2.2.1) at the time t = t~m. C_h~m is the solution of the cquation (3.1.1). ThenEspecially in the zero order release stage, the error estimate is up to optima.In this paper the equation of fluid velocity is approximated by a mixed finite element method, and the whole system of controlled-release coupling by a standard Galerkin method. The theory and technique on prior estimate of differential equation as wellas traditional analysis method on the problem of miscible displacement are used when convergences are analyzed.