Domain decomposition methods for contaminant transport in fractured porous media
Abstract
Contaminant transport in 3-dimensional totally fractured porous media is considered. It can be modeled as an interconnected system of fractures separating the porous rocks (the matrix) into a collection of blocks. The governing partial differential equations of the model consist of two subsystems--one describing the flow in the fractures, and the other describing the flow in the matrix blocks. The main objective of this thesis is to develop an efficient algorithm for the numerical solution of the problem. An operator splitting technique is developed to satisfy the requirement that the potential and the concentration of the mixture be continuous on the boundaries of the matrix blocks at each time level. This splitting technique effectively reduces storage requirements and the overall computation time. Due to high velocity in the fractures, the fracture concentration equation is discretized by the method of characteristics in time and by the Raviart-Thomas-Nedelec mixed finite element method of index 0, RTN(0) in space. The matrix concentration equation is discretized by a backward Euler scheme and the standard trilinear Galerkin method. The pressure equation is approximated by RTN(0) and the trilinear Galerkin method for the fractures and the matrix blocks, respectively. In the numerical simulation of the dual-porosity transport problems, approximation of the fracture system is the more costly portion. The equations for different matrix blocks are naturally decoupled, while the fracture concentration requires a global solver at each time step. For the fracture system, domain decomposition iterative procedures are employed: a nonoverlapping procedure for the pressure and velocity, and a fictitious overlapping procedure for the concentration equation. Convergence arguments for the iterative algorithms are presented. Numerical results are shown to demonstrate the effectiveness of the algorithms. Conclusions and possible applications are indicated.
Degree
Ph.D.
Advisors
Douglas, Purdue University.
Subject Area
Mathematics|Geophysics|Environmental science
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