Objective: The conventional Fontan circulation deviates the superior vena cava (SVC = 1/3 of the systemic venous return) toward the right lung (3/5 of total lung volume) and the inferior vena cava (IVC = 2/3 of the systemic venous return) toward the left lung (2/5 of total lung volume). A “physiological” Fontan deviating the SVC toward the left lung and the IVC toward the right lung was compared with the conventional setting by computational fluid dynamics, studying whether this setting achieves a more favorable hemodynamics than the conventional Fontan circulation. Materials and Methods: An in-silico 3D parametric model of the Fontan procedure was developed using idealized vascular geometries with invariant sizes of SVC, IVC, right pulmonary artery (RPA), and left pulmonary artery (LPA), steady inflow velocities at IVC and SVC, and constant equal outflow pressures at RPA and LPA. These parameters were set to perform finite-volume incompressible steady flow simulations, assuming a single-phase, Newtonian, isothermal, laminar blood flow. Numerically converged finite-volume mass and momentum flow balances determined the inlet pressures and the outflow rates. Numerical closed-path integration of energy fluxes across domain boundaries determined the flow energy loss rate through the Fontan circulation. The comparison evaluated: (1) mean IVC pressure; (2) energy loss rate; (3) kinetic energy maximum value throughout the domain volume. Results: The comparison of the physiological vs. conventional Fontan provided these results: (1) mean IVC pressure 13.9 vs. 14.1 mmHg (= 0.2 mmHg reduction); (2) energy loss rate 5.55 vs. 6.61 mW (= 16% reduction); (3) maximum kinetic energy 283 vs. 396 J/m3 (= 29% reduction). Conclusions: A more physiological flow distribution is accompanied by a reduction of mean IVC pressure and by substantial reductions of energy loss rate and of peak kinetic energy. The potential clinical impact of these hemodynamic changes in reducing the incidence and severity of the adverse long-term effects of the Fontan circulation, in particular liver failure and protein-losing enteropathy, still remains to be assessed and will be the subject of future work.