A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Journal of Computational Physics
Natural Convection in a Closed Cavity under Stochastic Non-Boussinesq Conditions
SIAM Journal on Scientific Computing
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Journal of Computational Physics
A stochastic variational multiscale method for diffusion in heterogeneous random media
Journal of Computational Physics
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media
Journal of Computational Physics
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Hi-index | 31.48 |
We consider natural convection in flow saturated porous media with random porosity. The porosity is treated as a random field and a stochastic finite element method is developed. The stochastic projection method is considered for the solution of the high-dimensional stochastic Navier-Stokes equations since it leads to the uncoupling of the velocity and pressure degrees of freedom. Because of the porosity dependence of the pressure gradient term in the governing flow equations, one cannot use the first-order projection method. A stabilized stochastic finite element second-order projection method is presented based on a pressure gradient projection. A two-dimensional stochastic problem with moderate and large variation in the random porosity field is examined and the results are compared with Monte-Carlo and sparse grid (Smolyak) collocation approaches. Excellent agreement between these results indicates the effectiveness and accuracy of the proposed methodology.