AN UPWIND NODAL INTEGRAL METHOD FOR INCOMPRESSIBLE FLUID-FLOW

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.