A Variational Multiscale Stabilized Finite Element Method for Stochastic Advection-Diffusion and Stochastic Incompress- ible Flow
نویسندگان
چکیده
An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the linear stochastic scalar advection-diffusion equation and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element method (SSFEM). Generalized polynomial chaos and Karhunen-Loève expansion techniques are used for representation of uncertain quantities. A parallel finite element implementation using cluster specific implementation of BLAS I and BLAS II and a preconditioned parallel GMRES solver with restart capability were developed for the parallel solution of the stochastic partial differential equations. The proposed stabilized method is demonstrated by examining flow past a cylinder with uncertainties in the inflow boundary conditions.
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