The projects develops a breakthough in computational modeling of subsurface heterogeneous geological reservoirs, by developing a novel multi-level multiscale simulation method. The method is called ADM, standing for Adaptive Algebraic Dynamic Multilevel method, and is implemented in our DARSim open-source research & educational simulator. The ADM makes it possible to cross the scale, even in the presence of fractures and complex nonlinear fluid physics. We demonstrate its applicability in real-field environment, specially in dealing with heterogeneities and nonlinearities. The applications of this fundamental modeling project can vary from Geothermal to CCS and Hydrogen Storage.