In this paper, we propose a fully coupled flow-geomechanics simulator using the mixed finite element method. The mathematical model, including mass conservation of fluid, Darcy's law for velocity, and force equilibrium of solid skeleton, is derived in the framework of Biot's consolidation theory. Pore pressure, fluid velocity and solid displacement are chosen as primary variables. This has the advantage of satisfying element-wise mass conservation and describing the velocity in a continuous way, instead of as a derived value of pressure, as in traditional simulator.

This mixed model is then discretized in appropriate finite element spaces. Specifically, we use a Discontinuous Galerkin space for pressure, a Brezzi-Douglas-Marini space for fluid velocity, and a Continuous Galerkin space for solid displacement. The system of equations is solved in a fully coupled scheme, which ensures second order convergence and stability.

Afterwards, the resulted model is validated by a wide range of benchmark problems, including the consolidation problems of Terzaghi, Mandel and Cryer. In all cases, our numerical results are in agreement with the analytical solutions, which illustrates the effectiveness of our simulator, especially in capturing the Mandel-Cryer effect accurately.