Modelling of an Underground Waste Disposal Site by Upscaling and Simulation with Domain Decomposition Method

Abstract

We derive an upscaled but accurate 2D model of the global behavior of an underground radioactive waste disposal. This kind of computation occurs in safety assessment process. Asymptotic development of the solution leads to solve terms of order 1 on more regular and steady-state auxiliary problems. Neumann-Dirichlet domain decomposition methods, with non matching spectral grids, are performed to solve those auxiliary problems. Fourier and Chebychev polynomials approximation of the solution are used depending on boundary conditions implemented on subdomains. Since spectral representation of the solution or its derivatives allows accurate mappings between the interfaces of the different grids, we speed up the convergence of the Neumann-Dirichlet method by the Aitken acceleration which is sensitive to the accuracy of the representation of the iterate solution on the artificial interfaces. In order to enforce regularity for the spectral approximation, some regular extensions and filtering techniques on the artificial interfaces for the right hand side of the problem and the iterate solution are implemented.