scholarly journals Breaking the Kolmogorov Barrier in Model Reduction of Fluid Flows

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 26 ◽  
Author(s):  
Shady E. Ahmed ◽  
Omer San
Keyword(s):  
Energy Spectrum ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Piecewise Linear ◽  
Fluid Flows ◽  
Reduced Order ◽  
Temporal Complexity ◽  
Comparable Accuracy ◽  
The Cost ◽  
Modal Truncation

Turbulence modeling has been always a challenge, given the degree of underlying spatial and temporal complexity. In this paper, we propose the use of a partitioned reduced order modeling (ROM) approach for efficient and effective approximation of turbulent flows. A piecewise linear subspace is tailored to capture the fine flow details in addition to the larger scales. We test the partitioned ROM for a decaying two-dimensional (2D) turbulent flow, known as 2D Kraichnan turbulence. The flow is initiated using an array of random vortices, corresponding to an arbitrary energy spectrum. We show that partitioning produces more accurate and stable results than standard ROM based on a global application of modal decomposition techniques. We also demonstrate the predictive capability of partitioned ROM through an energy spectrum analysis, where the recovered energy spectrum significantly converges to the full order model’s statistics with increased partitioning. Although the proposed approach incurs increased memory requirements to store the local basis functions for each partition, we emphasize that it permits the construction of more compact ROMs (i.e., of smaller dimension) with comparable accuracy, which in turn significantly reduces the online computational burden. Therefore, we consider that partitioning acts as a converter which reduces the cost of online deployment at the expense of offline and memory costs. Finally, we investigate the application of closure modeling to account for the effects of modal truncation on ROM dynamics. We illustrate that closure techniques can help to stabilize the results in the inertial range, but over-stabilization might take place in the dissipative range.

Lattice Boltzmann for Turbulence Modeling

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Turbulence Modeling ◽  
Real Life ◽  
Practical Interest ◽  
Reynolds Numbers ◽  
Full Resolution ◽  
To Come ◽  
Highly Turbulent Flows ◽  
Main Ideas

This chapter introduces the main ideas behind the application of LBE methods to the problem of turbulence modeling, namely the simulation of flows which contain scales of motion too small to be resolved on present-day and foreseeable future computers. Many real-life flows of practical interest exhibit Reynolds numbers far too high to be directly simulated in full resolution on present-day computers and arguably for many years to come. This raises the challenge of predicting the behavior of highly turbulent flows without directly simulating all scales of motion which take part to turbulence dynamics, but only those that fall within the computer resolution at hand.

Review of Recent Advances in the Study of Unsteady Turbulent Internal Flows

1995 ◽  
Vol 48 (4) ◽  
pp. 189-212 ◽  
Author(s):  
G. J. Brereton ◽  
R. R. Mankbadi
Keyword(s):  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Unsteady Flows ◽  
Turbulence Models ◽  
Research Area ◽  
Transition To Turbulence ◽  
Measurement Technology ◽  
Internal Flows ◽  
Recent Advances ◽  
The Many

Turbulent flow which undergoes organized temporal unsteadiness is a subject of great importance to unsteady aerodynamic and thermodynamic devices. Of the many classes of unsteady flows, those bounded by rigid smooth walls are particularly amenable to fundamental studies of unsteady turbulence and its modeling. These flows are presently being given increased attention as interest grows in the prospect of predicting non-equilibrium turbulence and because of their relevance to turbulence–acoustics interactions, in addition to their importance as unsteady flows in their own right. It is therefore timely to present a review of recent advances in this area, with particular emphasis placed on physical understanding of the turbulent processes in these flows and the development of turbulence models to predict them. A number of earlier reviews have been published on unsteady turbulent flows, which have tended to focus on specific aspects of certain flows. This review is intended to draw together, from the diverse literature on the subject, information on fundamental aspects of these flows which are relevant to improved understanding and development of predictive models. Of particular relevance are issues of instability and transition to turbulence in reciprocating flows, the robustness of coherent structures in wall-bounded flows to forced perturbations (in contrast to the relative ease of manipulation in free shear flows), unsteady scalar transport, improved measurement technology, recent contributions to target data for model testing and the quasi-steady and non-steady rapid distortion approaches to turbulence modeling in these flows. The present article aims to summarize recent contributions to this research area, with a view to consolidating comprehension of the well-known basics of these flows, and drawing attention to critical gaps in information which restrict our understanding of unsteady turbulent flows.

AEC Classifier: A Tree-Based Classifier with Error Control for Medical Disease Diagnosis and Other Applications

2021 ◽  
Vol 15 (02) ◽  
pp. 241-262
Author(s):  
Wasif Bokhari ◽  
Ajay Bansal
Keyword(s):  
Error Control ◽  
Binary Classification ◽  
False Negative ◽  
Disease Diagnosis ◽  
False Negatives ◽  
Medical Disease ◽  
Unique Nature ◽  
Comparable Accuracy ◽  
The Cost ◽  
Roc Score

In medical disease diagnosis, the cost of a false negative could greatly outweigh the cost of a false positive. This is because the former could cost a life, whereas the latter may only cause medical costs and stress to the patient. The unique nature of this problem highlights the need of asymmetric error control for binary classification applications. In this domain, traditional machine learning classifiers may not be ideal as they do not provide a way to control the number of false negatives below a certain threshold. This paper proposes a novel tree-based binary classification algorithm that can control the number of false negatives with a mathematical guarantee, based on Neyman–Pearson (NP) Lemma. This classifier is evaluated on the data obtained from different heart studies and it predicts the risk of cardiac disease, not only with comparable accuracy and AUC-ROC score but also with full control over the number of false negatives. The methodology used to construct this classifier can be expanded to many more use cases, not only in medical disease diagnosis but also beyond as shown from analysis on different diverse datasets.

scholarly journals Data-Driven Filtered Reduced Order Modeling of Fluid Flows

2018 ◽  
Vol 40 (3) ◽  
pp. B834-B857 ◽  
Author(s):  
X. Xie ◽  
M. Mohebujjaman ◽  
L. G. Rebholz ◽  
T. Iliescu
Keyword(s):  
Fluid Flows ◽  
Reduced Order Modeling ◽  
Data Driven ◽  
Reduced Order

scholarly journals Hybrid Turbulence Models: Recent Progresses and Further Researches

2019 ◽  
Vol 130 ◽  
pp. 01013
Author(s):  
Hariyo Priambudi Setyo Pratomo ◽  
Fandi Dwiputra Suprianto ◽  
Teng Sutrisno
Keyword(s):  
Turbulent Flows ◽  
Turbulence Modeling ◽  
A Priori ◽  
Computational Cost ◽  
Turbulence Models ◽  
Turbulence Scale ◽  
Research Activities ◽  
Daunting Task ◽  
Active Research ◽  
Inherent Nature

Turbulence simulation remains one of the active research activities in computational engineering. Along with the increase in computing power and the prime motivation of improving the accuracy of statistical turbulence modeling approaches and reducing the expensive computational cost of both direct numerical and large turbulence scale- resolving simulations, various hybrid turbulence models being capable of capturing unsteadiness in the turbulence are now accessible. Nevertheless this introduces the daunting task to select an appropriate method for different cases as one can not know a priori the inherent nature of the turbulence. It is the aim of this paper to address recent progresses and further researches within a branch of the hybrid RANS-LES models examined by the first author as simple test cases but generating complex turbulent flows are available from experimentation. In particular, failure of a seamless hybrid formulation not explicitly dependent on the grid scale is discussed. From the literature, it is practical that at least one can go on with confidence when choosing a potential hybrid model by intuitively distinguishing between strongly and weakly unstable turbulent flows.

Use of Experimental Data for an Efficient Description of Turbulent Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S240-S245 ◽  
Author(s):  
N. Aubry
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Original System ◽  
Navier Stokes ◽  
Lorenz Attractor ◽  
Wall Region ◽  
Lorenz Equations ◽  
Chaotic Solution

The proper orthogonal decomposition (POD), also called Karhunen-Loe`ve expansion, which extracts ‘coherent structures’ from experimental data, is a very efficient tool for analyzing and modeling turbulent flows. It has been shown that it converges faster than any other expansion in terms of kinetic energy (Lumley 1970). First, the POD is applied to the chaotic solution of the Lorenz equations. The dynamics of the Lorenz attractor is reconstructed by only the first three POD modes. In the second part of this paper, we show how the POD can be used in turbulence modeling. The particular case studied is the wall region of a turbulent boundary layer. In this flow, the velocity field is expanded into POD modes in the normal direction and Fourier modes in the streamwise and spanwise directions. Dynamical systems are obtained by Galerkin projections of the Navier Stokes equations onto the different modes. Aubry et al. (1988) applied the technique to derive and study a ten dimensional representation which reproduced qualitatively the bursting event experimentally observed. It is shown that streamwise modes, absent in Aubry et al.’s model, participate to the bursting events. This agrees remarkably well with experimental observations. In both examples, the dynamics of the original system is very well recovered from the contribution of only a few modes.

Fast Solution of Transient Elastohydrodynamic Line Contact Problems Using the Trajectory Piecewise Linear Approach

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Daniel Maier ◽  
Corinna Hager ◽  
Hartmut Hetzler ◽  
Nicolas Fillot ◽  
Philippe Vergne ◽  
...  
Keyword(s):  
Piecewise Linear ◽  
Contact Problems ◽  
Galerkin Projection ◽  
Line Contact ◽  
Reduced Order ◽  
Fast Solution ◽  
Speed Up ◽  
Newton Raphson ◽  
First Time ◽  
Piecewise Linear Approach

In order to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton–Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton–Raphson based method at a high accuracy.

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