3,239 research outputs found
Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo
A multilevel Monte Carlo (MLMC) method for quantifying model-form
uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS)
simulations is presented. Two, high-dimensional, stochastic extensions of the
RANS equations are considered to demonstrate the applicability of the MLMC
method. The first approach is based on global perturbation of the baseline eddy
viscosity field using a lognormal random field. A more general second extension
is considered based on the work of [Xiao et al.(2017)], where the entire
Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For
two fundamental flows, we show that the MLMC method based on a hierarchy of
meshes is asymptotically faster than plain Monte Carlo. Additionally, we
demonstrate that for some flows an optimal multilevel estimator can be obtained
for which the cost scales with the same order as a single CFD solve on the
finest grid level.Comment: 40 page
IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
This paper proposes an extension of the Multi-Index Stochastic Collocation
(MISC) method for forward uncertainty quantification (UQ) problems in
computational domains of shape other than a square or cube, by exploiting
isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC
algorithm is very natural since they are tensor-based PDE solvers, which are
precisely what is required by the MISC machinery. Moreover, the
combination-technique formulation of MISC allows the straight-forward reuse of
existing implementations of IGA solvers. We present numerical results to
showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio
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