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During reverse osmosis (RO) membrane filtration, performance is dramatically affected by fouling, which concurrently decreases the permeate flux while increasing the energy required to operate the system. Comprehensive design and optimization of RO systems are best served by an understanding of the coupling between membrane shape, local flow field, and fouling; however, current studies focus exclusively on simplified steady-state models that ignore the dynamic coupling between fluid flow, solute transport, and foulant accumulation. We developed a customized solver (SUMs: Stanford University Membrane Solver) under the open source finite volume simulator OpenFOAM to solve transient Navier–Stokes, advection–diffusion, and adsorption–desorption equations for foulant accumulation. We implemented two permeate flux reduction models at the membrane boundary: the resistance-in-series (RIS) model and the effective-pressure-drop (EPD) model. The two models were validated against filtration experiments by comparing the equilibrium flux, pressure drop, and fouling pattern on the membrane. Both models not only predict macroscopic quantities (e.g., permeate flux and pressure drop) but also the fouling pattern developed on the membrane, with a good match with experimental results. Furthermore, the models capture the temporal evolution of foulant accumulation and its coupling with flux reduction.