Since high performance separations can be achieved, design and modeling of the Dual Reflux Pressure Swing Adsorption (DRPSA) process are topics of great interest. DRPSA is a cyclic process whose dynamic behavior requires an accurate description of the steep gradients of concentrations, which develop and propagate along the bed during the process. Moreover, this process is intrinsically non-stationary. Therefore, Cyclic Steady State (CSS) can be established, which requires simulating the process dynamics for a large (even undefined) number of cycles. The complexity in representing DRPSA dynamics is the reason why research efforts have been recently spent to develop numerical models detailed enough to reliably describe the separation evolution. A suitable spatial discretization of the system equations is needed in order to be sure that the results do not depend on the selected grid size. At the same time, as the number of grid points increases, the time required for the simulation increases too. Therefore, in this work, we propose a general and effective strategy to automatically select a spatial discretization, which guarantees that the simulation results are grid-independent and, at the same time, that the true CSS is reached with a minimal computational effort. To do this, we resort to approaches available in literature for Pressure Swing Adsorption processes and formulate a new strategy tailored for DRPSA. This approach has been applied together with the Finite Volume Method as numerical discretization approach, but it can be adapted to any numerical strategy.