Modeling redox flow battery (RFB) stacks is essential to understand the complex interplay of physical, chemical, and electrochemical processes influencing their performance. While most multiphysics models focus on materials and small-scale devices, only basic lumped circuit or semi-analytical models have been applied to industrial-scale stacks. These models often overlook critical spatially resolved flux distributions and coupled transport phenomena, such as species crossover and shunt currents, which are negligible in single-cell studies but significantly affect stack efficiency and operability. This study examines charge carrier dynamics in fluid electrolytes under electric potential differences across homologous electrodes and membranes, using vanadium chemistry as a case study. Conductive, diffusive, and convective ion motions (V²⁺, V³⁺, VO²⁺, VO₂⁺, H⁺, HSO₄⁻, SO₄²⁻) were modeled via Navier-Stokes, Nernst-Planck, and conservation equations in 3D and 2D finite element simulations in COMSOL Multiphysics®. The approach enables detailed evaluation of interactions between mass transport, charge transport, and electrochemical kinetics, while assessing design parameters like channel geometry, electrode porosity, and membrane properties. Simulations replicated operational conditions under steady-state and transient regimes across multiple charge-discharge cycles, providing insights into battery capacity, state of charge, and efficiency. Shunt current and crossover effects were analyzed in stacks of varying sizes and under different loads, using industrial-scale cells tested at EESCoLab, University of Padova. Results showed that shunt current losses range from under 1% in 5-cell stacks to 7% in 40-cell stacks, increasing at lower loads. Species crossover effects were also more pronounced in larger stacks, significantly impacting coulombic efficiency. These findings align with experimental data. This methodology identifies key factors affecting shunt currents and species crossover, including membrane permeability, electrode porosity, and flow channel design. By bridging the gap between laboratory research and industrial-scale applications, this work contributes to advancing the scalability and cost-effectiveness of next-generation flow batteries.