Open Access
2013 Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation
Mohamed A. El-Beltagy, Mohamed I. Wafa
J. Appl. Math. 2013: 1-14 (2013). DOI: 10.1155/2013/903618


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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Mohamed A. El-Beltagy. Mohamed I. Wafa. "Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation." J. Appl. Math. 2013 1 - 14, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950928
MathSciNet: MR3092003
Digital Object Identifier: 10.1155/2013/903618

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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