A novel deterministic symbolic regression method SpaRTA is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.
Computational Fluid Dynamics analyses of high Reynolds-number flows mostly rely on the Reynolds-Averaged Navier-Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical closure coefficients, calibrated on a set of simple reference flows. Predicting new flows using a single closure model with nominal values for the closure coefficients may lead to biased predictions. Bayesian Model-Scenario Averaging is a statistical technique providing an optimal way to combine the predictions of several competing models calibrated on various sets of data (scenarios). The method allows to obtain a stochastic estimate of a Quantity-of-Interest in an unmeasured prediction scenario by i) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and ii) by computing a weighted posterior predictive distribution. While step ii) has a negligible computational cost, step i) requires a large number of samples of the solver.
The loss factor is often determined in building acoustics by measuring the structure-borne reverberation time. To do this, elements under test are excited either by a hammer or by a shaker. In several experiments with sand-lime brick walls, measured loss factors turned out to be significantly larger when hammer excitation was used instead of shaker excitation. A thorough investigation of this effect was then performed using hammer blows of different strengths and a 250-kg shaker. This way, forces are in the same order of magnitude for both excitations. Measurement results lead to the conclusion that large forces may create a nonlinear structural response. The nonlinearity is observed for a sand-lime brick wall without plastering but not for a lightweight composite wall and also not for a monolithic concrete wall. The assumption of nonlinear behaviour is furthermore supported by an additional investigation where alarm pistol shots were used to excite a sand-lime brick wall with very large airborne sound pressure levels. The airborne sound insulation of the wall turned out to be nonlinear, that is, it increased with increasing sending room levels.
This work presents developments towards a deterministic symbolic regression method to derive algebraic Reynolds-stress models for the Reynolds-Averaged Navier-Stokes (RANS) equations. The models are written as tensor polynomials, for which optimal coefficients are found using Bayesian inversion. These coefficient fields are the targets for the symbolic regression. A method is presented based on a regularisation strategy in order to promote sparsity of the inferred models and is applied to high-fidelity data. By being data-driven the method reduces the assumptions commonly made in the process of model development in order to increase the predictive fidelity of algebraic models.
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.The Reynolds-Averaged Navier-Stokes (RANS) equations combined with turbulence closure models are widely utilized in engineering to predict flows with high Reynolds number. These turbulence closure models are used to obtain an approximate Reynolds stress tensor that is responsible for coupling the mean flow with turbulence. Although many turbulence models exist in the literature, there is no single model that generalizes well to all classes of turbulent flows [1,2]. Specifically, the performance depends on the modeling assumptions and the type of flow used to calibrate the so-called closure coefficients that are needed as inputs to a turbulence model.Since the dominant source of error in the flow prediction comes from the turbulence modeling, a number of approaches have already been developed for the model-form uncertainty quantification (UQ) of RANS simulations, see e.g. [3,4] for recent reviews. The majority of these approaches are based on the perturbation of baseline RANS models. One way to achieve this is by injecting uncertainties in the closure coefficients [5,6,7,8] of turbulence models. Another more general physics-based approaches exists, which typically introduces randomness directly into the modeled Reynolds Stress Tensor (RST), either by perturbing its eigenvalues [9,10,11], tensor invariants [12,13] or the entire RST field [14]. One can also classify these stochastic models in terms of global and local perturbation (in space). For global approaches, such as in [5,6,7,10], the magnitude of perturbations in closure coefficients, eigenvalues of RST, etc. is the same throughout the flow domain. This translates to a low-dimensional UQ problem which can be efficiently handled by deterministic sampling techniques like stochastic collocation or just by simulating flows for Email addresses: pkumar@cwi.nl (Prashant Kumar), m.schmelzer@tudelft.nl (Martin Schmelzer), r.p.dwight@tudelft.nl (Richard P. Dwight) arXiv:1811.00872v1 [physics.comp-ph] 1 Nov 2018
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