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

TECHNIQUES FOR REARING AND RELEASING NONMIGRATORY CRANES: LESSONS FROM THE MISSISSIPPI SANDHILL CRANE PROGRAM

Captive-reared Mississippi sandhill cranes (Grus canadensis pulla) reared at the Patuxent Wildlife Research Center (patuxent) have been released at the Mississippi Sandhill Crane National Wildlife Refuge (MSCNWR) since 1981. Of 131 birds released through December 1990, 103 were reared by foster parents. The remaining 28 were experimentally hand-reared in 1989 and 1990. After refining release procedures, parent-reared birds have integrated into the wild flock, many have survived, and some have bred. Releases of hand-reared cranes elsewhere in the 1970\u27s were largely unsuccessful. at least in part due to the lack of a lengthy acclimation period. A new hand-rearing protocol holds promise in producing release-worthy birds. The technique employs some features first used in the 1960\u27s (e.g., a costume for the human caretaker and model crane heads used to train chicks to feed). In the mid-1980\u27s, the following features were added: (1) the costumed caretaker was given a visor and feathers, (2) a taxidermic crane head or a hand puppet was held or suspended from the ceiling for use in stimulating chicks to feed, (3) a taxidermic mount of a brooding crane supplied warmth, (4) a full-sized live crane was maintained in an adjacent pen and in visual contact with neonatal young to provide an imprinting model, and (5) a small group of adult (or subadult) cranes was penned adjacent to the outdoor chick pens to provide socialization models. Recent releases of Mississippi sandhill cranes hand-reared according to this protocol and released in Mississippi have had high first-year survival rates. The now-operational technique holds promise for producing large numbers of release-worthy birds