This paper presents numerical techniques for coupled simulations with different time scales and space discretizations for reservoir flow and geomechanics. We use an explicitly coupled approach together with an iterative coupling to increase stability and reduce time discretization error. An error indicator is proposed to determine when displacement must be updated and whether the explicit or iterative coupling technique is required. Under this setting, one geomechanics calculation is performed for several reservoir flow steps. For time steps without geomechanics updates linear extrapolated pore volume is used for porous flow calculations. The resulting algorithm is computationally more efficient than the iterative coupling, and it is more stable and accurate than the loosely coupled technique. In the event that different meshes are used for the reservoir flow and geomechanics models, special treatments are required for the integration of the coupling terms over each element. To avoid complex 3D grid intersection calculations we propose to divide an element into a number of subelements and apply the midpoint integration rule over each subelement. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method for coupled simulations with different time and space discretizations. Copyright 2005, Society of Petroleum Engineers.