The purpose of this paper is to analyze some features of contaminant
flow passing through cracked porous medium, such as the influence of
fracture network on the advection and diffusion of contaminant species,
the impact of adsorption on the overall transport of contaminant wastes.
In order to precisely describe the whole process, we firstly 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 describe the total flow of contaminant
wastes, which is based on Darcy law. The second one will characterize
the adsorption, diffusion and convection behavior of contaminant species,
which describes most features of contaminant flow we are interested in.
After the construction of numerical model, we apply locally conservative
and compatible algorithms to solve this mathematical model. Specifically,
we apply Mixed Finite Element (MFE) method to the flow equation and
Discontinuous Galerkin (DG) method for the transport equation. MFE has
a good convergence rate and numerical accuracy for Darcy velocity. DG
is more flexible and can be used to deal with irregular meshes, as well
as little numerical diffusion. With these two numerical means, we
investigate the sensitivity analysis of different features of contaminant
flow in our model, such as diffusion, permeability and fracture density.
In particular, we study $K_d$ values which represent the distribution of
contaminant wastes between the solid and liquid phases. We also make comparisons of two different schemes and discuss the advantages of both methods.