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All-Vanadium Redox Flow Batteries (VRFBs) are emerging as a novel technology for stationary energy storage. Numerical models are useful for exploring the potential performance of such devices, optimizing the structure and operating condition of cell stacks, and studying its interfacing to the electrical grid. A one-dimensional steady-state multiphysics model of a single VRFB, including mass, charge and momentum transport and conservation, and coupled to a kinetic model for electrochemical reactions, is first presented. This model is then extended, including reservoir equations, in order to simulate the VRFB charge and discharge dynamics. These multiphysics models are discretized by the finite element method in a commercial software package (COMSOL). Numerical results of both static and dynamic 1D models are compared to those from 2D models, with the same parameters, showing good agreement. This motivates the use of reduced models for a more efficient system simulation.