Pressure related instabilities of reduced Navier-Stokes equations for internal flows

Order-of-magnitude deletion of the streamwise diffusion terms leads to a reduced form of the Navier-Stokes equations. Solving the reduced equations for internal flows with single-sweep marching algorithms requires a severe minimum streamwise step size to avoid unstable solutions. This behavior is shown to be predominantly due to a single term in the cross-stream momentum equation, uv(x), which introduces a strong elliptic character into the equations. An order-of-magnitude deletion of this term reduces the minimum streamwise step size sufficiently for accurate solutions to be obtained. Further reduction of the transverse momentum equation on an order-of-magnitude basis removes all cross-stream velocity derivatives and completely eliminates the minimum-streamwise-step-size condition for both swirling and nonswirling flows.