Abstract
A non-linear parabolic system is derived to describe compressible nuclear waste disposal contamination in porous media . Galerkin method is applied for the pressure equation . For the concentration of the brine of the fluid, a kind of partial upwind finite element scheme is constructed. A numerical application is included to demonstrate certain aspects of the theory and illustrate the capabilities of the kind of partial upwind finite element approach.
Highlights
The proposed disposal of high-level nuclear waste in underground repositories is an important environmental topic for many countries
The model for compressible flow and transport of contaminated brine in porous media can be described by a differential system that can be put into the following form [2]
We used the system with large coupled of strongly non-linear partial differential equations which arise from the contamination of nuclear waste in porous media .We used a Galerkin method for the pressure equation and a kind of partial upwind finite element method for the concentration.For the compressible case, we obtained the error estimates for approximate Darcy velocity U, concentrations C in L (0,T~, L2 ( )) .From the numerical results presented in this application, we have got a kind of partial upwind finite element method for triangular element convergent to the exact solution and in comparison with Galerkin method, we found that a kind of partial upwind finite element method much more accurate than Galerkin method
Summary
The proposed disposal of high-level nuclear waste in underground repositories is an important environmental topic for many countries. Decisions on the feasibility and safety of the various sites and disposal methods will be based, in part, on numerical models for describing the flow of contaminated brines and groundwater through porous or fractured media under severe thermal regimes caused by the radioactive contaminants. The non-linear couplings between the unknowns are important in modeling the correct physics of flow. In this model one obtain a convection-diffusion equations which represent a mathematical model for a case of diffusion phenomena in which underlying flow is present ; w and b w correspond to the transport of w through the diffusion process and the convection effects, respectively, where and denoted respectively the gradient operator and the Laplacian operator in the spatial coordinates. For more details of this subject see [7, 6, and 4]
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