An upwind nodal solution method is developed for the steady, two-dimen
sional flow of an incompressible fluid. The formulation is based on th
e nodal integral method, which uses transverse integrations, analytica
l solutions of the one-dimensional averaged equations, and node-averag
ed uniqueness constraints to derive the discretized nodal equations. T
he derivation introduces an exponential upwind bias by retaining the s
treamwise convection term in the homogeneous part of the transverse-in
tegrated convection-diffusion equation. The method is adapted to the s
tream function-vorticity form of the Navier-Stokes equations, which ar
e solved over a nonstaggered nodal mesh. A special nodal scheme is use
d for the Poisson stream function equation to properly account for the
exponentially varying vorticity source. Rigorous expressions for the
velocity components and the no-slip vorticity boundary condition are d
erived from the stream function formulation. The method is validated w
ith several benchmark problems. An idealized purely convective flow of
a scalar step function indicates that the nodal approximation errors
are primarily dispersive, not dissipative, in nature. Results for idea
lized and actual recirculating driven-cavity flows reveal a significan
t reduction in false diffusion compared with conventional finite diffe
rence techniques.