We investigate both optical and electrical properties of organic solar cells (OSCs) incorporating 2D periodic metallic back grating as an anode. Using a unified finite-difference approach, the multiphysics modeling framework for plasmonic OSCs is established to seamlessly connect the photon absorption with carrier transport and collection by solving the Maxwell's equations and semiconductor equations (Poisson, continuity, and drift-diffusion equations). Due to the excited surface plasmon resonance, the significantly nonuniform and extremely high exciton generation rate near the metallic grating are strongly confirmed by our theoretical model. Remarkably, the nonuniform exciton generation indeed does not induce more recombination loss or smaller open-circuit voltage compared to 1D multilayer standard OSC device. The increased open-circuit voltage and reduced recombination loss by the plasmonic OSC are attributed to direct hole collections at the metallic grating anode with a short transport path. The work provides an important multiphysics understanding for plasmonic organic photovoltaics.