The use of neural networks and operators to solve partial differential equations that govern fluid flow is carried out in a simulation-free, physics-informed approach, where the residual of the governing equation calculated via automatic differentiation across the neural network is the loss function used for training. One issue with this approach is that simulating highly nonlinear flows such as high Reynolds number flows is challenging, even in laminar settings. We propose a new simulation-free approach for training PINNs using a residual loss based on a discrete numerical scheme instead of automatic differentiation. This loss function also requires a new grid-based PINNs training strategy. Using the loss landscape, we demonstrate why our new loss function works better than the automatic differentiation-based loss function. We also demonstrate how to implement our grid-based training for complex geometry. Simulations using the new neural model for high Reynolds number fluid flow and complex geometry test cases are showcased and compared with automatic differentiation approaches. The results show that our new discrete loss function and training strategy take less computational time, converge faster than automatic differentiation, and can be used to simulate nonlinear flows efficiently.