Abstract
Anon-linear parabolic system is derived to describe incompressible nuclear waste disposal contamination in porous media. Galerkin method is applied for the pressure equation. For the concentration, a kind of partial upwind finite element scheme is constructed. The finite element solution satisfies discrete maximum principle and converges to the solution in norm )) (
Highlights
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
A fully discrete formulation is given in some detail to present key ideas that are essential in code development
Summary
The proposed disposal of high-level nuclear waste in underground repositories is an important environmental topic for many countries. The non-linear couplings between the unknowns are important in modeling the correct physics properties of flow. In this model, we 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 operater and the Laplacian operator in the spatial coordinates. In this paper we will consider the fluid flow in porous media using a Galerkin method for the pressure equation and a kind of partial upwind finite element scheme is constructed for the convection dominated saturation (or concentration).
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