On the downstream boundary conditions for the vorticity-stream function formulation of two-dimensional incompressible flows

1991 ◽  
Vol 85 (2) ◽  
pp. 207-217 ◽  
Author(s):  
T.E. Tezduyar ◽  
J. Liou
Keyword(s):  
Boundary Conditions ◽  
Stream Function ◽  
Incompressible Flows ◽  
Two Dimensional ◽  
Function Formulation ◽  
Stream Function Formulation

scholarly journals Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed A. El-Beltagy ◽  
Mohamed I. Wafa
Keyword(s):  
Stream Function ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Function Formulation ◽  
Mean And Variance ◽  
The Mean ◽  
Stream Function Formulation

A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.

scholarly journals The Turbomachine Blading Design Achieved by Solving the Inverse Field Problem

1987 ◽  
Author(s):  
T. S. Luu ◽  
B. Viney
Keyword(s):  
Boundary Conditions ◽  
Stream Function ◽  
Design Procedure ◽  
Rotational Flow ◽  
Field Problem ◽  
New Approach ◽  
Vorticity Distribution ◽  
Function Formulation ◽  
Stream Function Formulation

This paper describes a design procedure for the determination of the geometry of the blading of the turbomachine with prescribed thickness and bound vorticity distribution. The boundary conditions are discussed in order to have a properly posed field problem. Optimised 2D cascade design example is shown. The quasi 3D “S2” - “S1” stream function formulation is developed. The design of guide vanes downstream of a lateral inlet casing is described. A new approach by introducing a potential like function to treat the 3D rotational flow is also formulated.

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