A robust implicit compact scheme for two-dimensional unsteady flows with a biharmonic stream function formulation

2013 ◽  
Vol 84 ◽  
pp. 141-163 ◽  
Author(s):  
Shuvam Sen ◽  
Jiten C. Kalita ◽  
Murli M. Gupta
Keyword(s):  
Stream Function ◽  
Unsteady Flows ◽  
Compact Scheme ◽  
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.

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