Numerical methods for geothermal energy

Study of a complex system in porous medium, with as main unknowns the pressure and the speed of the flow, the mechanical displacement and the temperature, and resolution by numerical diagrams (Finite volumes method, finite elements method). We aim to prove the convergence of numerical algorithms for the homogenized problem, using iterative schemes. First, the objective is to produce numerical diagrams for the resolution of these problems, and to prove the convergence of the methods. In addition, certain coefficients present in the differential system are not necessarily known (permeability on the ground, …). We can apply a Monte-Carlo method to express numerical results. We then propose to derive homogenization methods for micro-macro scaling, by random realizations of Poisson-Voronoi tessellation.