Mixed Finite Elements and Operator Splitting For Flow and Transport Around a Deep Nuclear Repository
"The aim of my thesis is to model and develop numerical tools adapted to study underground water flow and the propagation of pollutants in a porous medium. The main motivation of this work is a benchmark from GDR Momas and Andra to simulate the 3-D propagation of radionuclides around a deep disposal of nuclear waste.
Firstly, we construct a new mixed finite elements method suitable for general hexahedral meshes. Convergence of the method is proved and shown in numerical experiments. Secondly, we present a method of time dicretisation for the advection equation which allows for the use of different time steps in different subdomains in order to take into account of strong heterogeneities. Finally a numerical method for the calculation of the transport of contaminants is proposed. The techniques above were implemented in a 3-D code and simulation results are shown on the 3-D far field benchmark from GDR Momas and Andra."