## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2013 (2013), Article ID 903618, 14 pages.

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

Mohamed A. El-Beltagy and Mohamed I. Wafa

#### Abstract

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.

#### Article information

**Source**

J. Appl. Math., Volume 2013 (2013), Article ID 903618, 14 pages.

**Dates**

First available in Project Euclid: 14 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1394808094

**Digital Object Identifier**

doi:10.1155/2013/903618

**Mathematical Reviews number (MathSciNet)**

MR3092003

**Zentralblatt MATH identifier**

06950928

#### Citation

El-Beltagy, Mohamed A.; Wafa, Mohamed I. Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation. J. Appl. Math. 2013 (2013), Article ID 903618, 14 pages. doi:10.1155/2013/903618. https://projecteuclid.org/euclid.jam/1394808094