235 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
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
A multigrid multilevel Monte Carlo method using high-order finite-volume scheme for lognormal diffusion problems
The aim of this paper is to show that a high-order discretization can be used to improve the convergence of a multilevel
Monte Carlo method for elliptic partial differential equations with lognormal random coefficients in combination with
the multigrid solution method. To demonstrate this, we consider a fourth-order accurate finite-volume discretization.
With the help of the Matérn family of covariance functions, we simulate the coefficient field with different degrees
of smoothness. The idea behind using a fourth-order scheme is to capture the additional regularity in the solution
introduced due to higher smoothness of the random field. Second-order schemes previously utilized for these types of
problems are not able to fully exploit this additional regularity. We also propose a practical way of combining a full
multigrid solver with the multilevel Monte Carlo estimator constructed on the same mesh hierarchy. Through this
integration, one full multigrid solve at any level provides a valid sample for all the preceding Monte Carlo levels. The
numerical results show that the fourth-order multilevel estimator consistently outperforms the second-order variant.
In addition, we observe an asymptotic gain for the standard Monte Carlo estimator
Estimation of Model Error Using Bayesian Model-Scenario Averaging with Maximum a Posterori-Estimates
International audienceThe lack of an universal modelling approach for turbulence in Reynolds-Averaged Navier–Stokes simulations creates the need for quantifying the modelling error without additional validation data. Bayesian Model-Scenario Averaging (BMSA), which exploits the variability on model closure coefficients across several flow scenarios and multiple models, gives a stochastic, a posteriori estimate of a quantity of interest. The full BMSA requires the propagation of the posterior probability distribution of the closure coefficients through a CFD code, which makes the approach infeasible for industrial relevant flow cases. By using maximum a posteriori (MAP) estimates on the posterior distribution, we drastically reduce the computational costs. The approach is applied to turbulent flow in a pipe at Re= 44,000 over 2D periodic hills at Re=5600, and finally over a generic falcon jet test case (Industrial challenge IC-03 of the UMRIDA project)
Probabilistic surrogate modeling of offshore wind-turbine loads with chained Gaussian processes
Heteroscedastic Gaussian process regression, based on the concept of chained
Gaussian processes, is used to build surrogates to predict site-specific loads
on an offshore wind turbine. Stochasticity in the inflow turbulence and
irregular waves results in load responses that are best represented as random
variables rather than deterministic values. Moreover, the effect of these
stochastic sources on the loads depends strongly on the mean environmental
conditions -- for instance, at low mean wind speeds, inflow turbulence produces
much less variability in loads than at high wind speeds. Statistically, this is
known as heteroscedasticity. Deterministic and most stochastic surrogates do
not account for the heteroscedastic noise, giving an incomplete and potentially
misleading picture of the structural response. In this paper, we draw on the
recent advancements in statistical inference to train a heteroscedastic
surrogate model on a noisy database to predict the conditional pdf of the
response. The model is informed via 10-minute load statistics of the
IEA-10MW-RWT subject to both aero- and hydrodynamic loads, simulated with
OpenFAST. Its performance is assessed against the standard Gaussian process
regression. The predicted mean is similar in both models, but the
heteroscedastic surrogate approximates the large-scale variance of the
responses significantly better.Comment: 10 pages. To be published in the IOP Journal of Physics: Conference
Series. To be presented at TORQUE 202
Simplex-stochastic collocation method with improved scalability
The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling
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