A hybrid Laplace-Galerkin method for thermo-hydro-mechanical coupling in fluid saturated porous media: Application for borehole problems

A hybrid Laplace-Galerkin method is proposed for modeling thermo-hydro-mechanical coupled problems of fluid saturated porous media in unsteady state regime. It consists of transforming the weak form equations into the Laplace space where they are solved by the Galerkin finite element method. Results in time space are then obtained by the Stehfest method of inverse Laplace transformation. This technique does not require any time stepping comparing to the traditional implicit or explicit time discretization method. Its exactitude is confirmed by comparing with existent analytical results as well as the one obtained by the implicit time stepping method.