کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
756712 | 1462739 | 2013 | 11 صفحه PDF | دانلود رایگان |
In this paper we propose and analyze a high order numerical method to solve the Stokes equations with random coefficients. A stochastic Galerkin approach, based on a finite dimensional Karhunen–Loève decomposition technique for the stochastic inputs, is used to reduce the original stochastic Stokes equations into a set of deterministic equations for the expansion coefficients. Then a PN×PN-2PN×PN-2 spectral method, together with a block Jacobi iteration is applied to solve the resulting problem. We establish the well-posedness of the weak formulation and its discrete counterpart. Moreover, we provide a rigorous convergence analysis and demonstrate exponential convergence with respect to the degrees of the polynomials chaos expansion used for the approximation in the random direction. Finally, a series of numerical tests is presented to support the theoretical results.
Journal: Computers & Fluids - Volume 71, 30 January 2013, Pages 250–260