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)

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

Reducing bias and quantifying uncertainty in watershed flux estimates: the R package loadflex

Many ecological insights into the function of rivers and watersheds emerge from quantifying the flux of solutes or suspended materials in rivers. Numerous methods for flux estimation have been described, and each has its strengths and weaknesses. Currently, the largest practical challenges in flux estimation are to select among these methods and to implement or apply whichever method is chosen. To ease this process of method selection and application, we have written an R software package called loadflex that implements several of the most popular methods for flux estimation, including regressions, interpolations, and the special case of interpolation known as the period-weighted approach. Our package also implements a lesser-known and empirically promising approach called the “composite method,” to which we have added an algorithm for estimating prediction uncertainty. Here we describe the structure and key features of loadflex, with a special emphasis on the rationale and details of our composite method implementation. We then demonstrate the use of loadflex by fitting four different models to nitrate data from the Lamprey River in southeastern New Hampshire, where two large floods in 2006–2007 are hypothesized to have driven a long-term shift in nitrate concentrations and fluxes from the watershed. The models each give believable estimates, and yet they yield different answers for whether and how the floods altered nitrate loads. In general, the best modeling approach for each new dataset will depend on the specific site and solute of interest, and researchers need to make an informed choice among the many possible models. Our package addresses this need by making it simple to apply and compare multiple load estimation models, ultimately allowing researchers to estimate riverine concentrations and fluxes with greater ease and accuracy

Computational uncertainty in hybrid atomistic-continuum frameworks

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Over the past decade micro and nanofluidics emerged as vital tools in the ongoing drive towards the development of nano-scale analysis and manufacturing systems. Accurate numerical modelling of the phenomena involved at these scales is ssential in order to speed up the industrial design process for nanotechnology. However a parameter often ignored in hybrid simulations is the uncertainty level introduced in the numerical modelling of phenomena taking place at micro and nanoscales. The main interest of the present study is the propagation of the inherent atomistic fluctuations to the continuum solver in the case of multiscale modelling and hybrid solvers

Quantifying Eulerian Eddy Leakiness in an Idealized Model

An idealized eddy‐resolving ocean basin, closely resembling the North Pacific Ocean, is simulated using MITgcm. We identify rotationally coherent Lagrangian vortices (RCLVs) and sea surface height (SSH) eddies based on the Lagrangian and Eulerian framework, respectively. General statistical results show that RCLVs have a much smaller coherent core than SSH eddies with the ratio of radius is about 0.5. RCLVs are often enclosed by SSH anomaly contours, but SSH eddy identification method fails to detect more than half of RCLVs. Based on their locations, two types of eddies are classified into three categories: overlapping RCLVs and SSH eddies, nonoverlapping SSH eddies, and nonoverlapping RCLVs. Using Lagrangian particles, we examine the processes of leakage and intrusion around SSH eddies. For overlapping SSH eddies, over the lifetime, the material coherent core only accounts for about 25% and about 50% of initial water leak from eddy interior. The remaining 25% of water can still remain inside the boundary, but only in the form of filaments outside the coherent core. For nonoverlapping SSH eddies, more water leakage (about 60%) occurs at a faster rate. Guided by the number and radius of SSH eddies, fixed circles and moving circles are randomly selected to diagnose the material flux around these circles. We find that the leakage and intrusion trends of moving circles are quite similar to that of nonoverlapping SSH eddies, suggesting that the material coherence properties of nonoverlapping SSH eddies are not significantly different from random pieces of ocean with the same size