Contaminant Flow and Transport Simulation in Cracked Porous Media Using Locally Conservative Schemes (Advances in Applied Mathematics and Mechanics, 2012)
The purpose of this paper is to analyze some features of contaminantflow passing through cracked porous medium, such as the influence offracture 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 themathematical model to simulate this problem numerically. Taking intoconsideration of the characteristics of contaminant flow, we employtwo 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 contaminantwastes, which is based on Darcy law. The second one will characterizethe 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 conservativeand compatible algorithms to solve this mathematical model. Specifically,we apply Mixed Finite Element (MFE) method to the flow equation andDiscontinuous Galerkin (DG) method for the transport equation. MFE hasa good convergence rate and numerical accuracy for Darcy velocity. DGis more flexible and can be used to deal with irregular meshes, as wellas little numerical diffusion. With these two numerical means, weinvestigate the sensitivity analysis of different features of contaminantflow in our model, such as diffusion, permeability and fracture density.In particular, we study $K_d$ values which represent the distribution ofcontaminant wastes between the solid and liquid phases. We also make comparisons of two different schemes and discuss the advantages of both methods.