Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Committee Chair/Advisor

Sun, Shu y

Committee Member

Rebholz , Leo

Committee Member

Yoon , Jeong R


The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous media, such as the influence of fracture network on the advection and diffusion of contaminant species, the adsorption impact of contaminant wastes on the overall transport flow and so on. In order to precisely describe the whole process, we firstly need to build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation, the other is reactive transport equation. The first equation is used to depict the total flow of contaminant wastes, which based on Darcy law. The second one will characterize the adsorption, diffusion and convection behavior of contaminant species, which summarizes most features of contaminant flow we are interested in. After the construction of numerical model, we apply different tools to solve this mathematical model. There are two delicate measures for us to consider first. One is Mixed Finite Element (MFE) method, the other is Discontinuous Galerkin (DG) method. Both methods are locally conservative. MFE has a good convergence rate and numerical accuracy. DG is more flexible and can be used to deal with irregular meshes, as well as high-order accuracy. With these two numerical means, we investigate the sensitivity analysis of different features of contaminant flow in our model, such as diffusion, permeability, fracture density, Kd values which represent the distribution of contaminant wastes between the solid and liquid phases. We also make comparison of two different schemes and discuss advantages of both methods.



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