## Abstract

We present a Newton method to compute the stochastic solution of the steady incompressible Navier-Stokes equations with random data (boundary conditions, forcing term, fluid properties). The method assumes a spectral discretization at the stochastic level involving a orthogonal basis of random functionals (such as Polynomial Chaos or stochastic multi-wavelets bases). The Newton method uses the unsteady equations to derive a linear equation for the stochastic Newton increments. This linear equation is subsequently solved following a matrix-free strategy, where the iterations consist in performing integrations of the linearized unsteady Navier-Stokes equations, with an appropriate time scheme to allow for a decoupled integration of the stochastic modes. Various examples are provided to demonstrate the efficiency of the method in determining stochastic steady solution, even for regimes where it is likely unstable.

Original language | English (US) |
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Pages (from-to) | 1566-1579 |

Number of pages | 14 |

Journal | Computers and Fluids |

Volume | 38 |

Issue number | 8 |

DOIs | |

State | Published - Sep 2009 |

Externally published | Yes |

### Bibliographical note

Funding Information:This work is supported by the Agence Nationale de la Recherche, Project ASRMEI, Grant No. ANR-08-JCJC-0022-01.

## ASJC Scopus subject areas

- General Computer Science
- General Engineering