This report is the third intermediate report of the StimDesign project which will finish in June next year. The focus is here solely on our two dimensional numerical developments. We report advances on the different building blocks of our numerical model: fracture mechanics solver with frictional contacts and cohesive forces, finite volume discretization for fluid flow and fully coupled hydro-mechanical solvers. This reports documents in depth the mathematical formulation as well as the numerical discretization. Notably a new scheme to account for both frictional contact of shear crack as well as opening mode is presented and tested on a series of tests examples. Tests of our implementation of algorithms based on hierarchical matrices for the acceleration of the solution of linear systems arising in the boundary element methods is also documented. We report significant speedup and reduction in memory requirements. Finally, two studies which have or will soon be submitted for publication are put in appendix. The first study investigate the effect of shear induced dilatancy on the transition from aseismic to seismic in the context of fluid injection in a planar fault. The second study investigates the possibility of remote activation / nucleation (in a frictional weakening zone) due to the stress transfer associated with the propagation of a purely aseismic crack due to fluid injection in a friction neutral layer.