scholarly journals Rescaled expansivity and separating flows

2018 ◽  
Vol 38 (9) ◽  
pp. 4433-4447 ◽  
Author(s):  
Alfonso Artigue ◽  
Keyword(s):  
Separating Flows

scholarly journals Mass-conserving diffusion-based dynamics on graphs

2021 ◽  
pp. 1-49
Author(s):  
J.M BUDD ◽  
Y. VAN GENNIP
Keyword(s):  
Multiscale Modeling ◽  
Classification Problems ◽  
Theoretical Justification ◽  
Finite Graphs ◽  
Discrete Scheme ◽  
Cahn Equation ◽  
Separating Flows ◽  
Special Case ◽  
Appl Math ◽  
Convergence Of The Scheme

An emerging technique in image segmentation, semi-supervised learning and general classification problems concerns the use of phase-separating flows defined on finite graphs. This technique was pioneered in Bertozzi and Flenner (2012, Multiscale Modeling and Simulation10(3), 1090–1118), which used the Allen–Cahn flow on a graph, and was then extended in Merkurjev et al. (2013, SIAM J. Imaging Sci.6(4), 1903–1930) using instead the Merriman–Bence–Osher (MBO) scheme on a graph. In previous work by the authors, Budd and Van Gennip (2020, SIAM J. Math. Anal.52(5), 4101–4139), we gave a theoretical justification for this use of the MBO scheme in place of Allen–Cahn flow, showing that the MBO scheme is a special case of a ‘semi-discrete’ numerical scheme for Allen–Cahn flow. In this paper, we extend this earlier work, showing that this link via the semi-discrete scheme is robust to passing to the mass-conserving case. Inspired by Rubinstein and Sternberg (1992, IMA J. Appl. Math.48, 249–264), we define a mass-conserving Allen–Cahn equation on a graph. Then, with the help of the tools of convex optimisation, we show that our earlier machinery can be applied to derive the mass-conserving MBO scheme on a graph as a special case of a semi-discrete scheme for mass-conserving Allen–Cahn. We give a theoretical analysis of this flow and scheme, proving various desired properties like existence and uniqueness of the flow and convergence of the scheme, and also show that the semi-discrete scheme yields a choice function for solutions to the mass-conserving MBO scheme.

Control of Separating Flows by Thin-Film Actuators

2000 ◽  
Vol 2000 (0) ◽  
pp. 303-306
Author(s):  
Yu FUKUNISHI ◽  
Yuzuru YOKOKAWA
Keyword(s):  
Thin Film ◽  
Separating Flows

scholarly journals Lifting multi-blade flows with interaction

2000 ◽  
Vol 415 ◽  
pp. 203-226 ◽  
Author(s):  
R. G. A. BOWLES ◽  
F. T. SMITH
Keyword(s):  
Rotor Blade ◽  
Periodic Boundary ◽  
Leading Edge ◽  
Main Flow ◽  
Flow Properties ◽  
Central Motion ◽  
Blade System ◽  
Flow Through ◽  
Lift And Drag ◽  
Separating Flows

Planar flow past multiple successive blades and wakes is studied for nearly aligned configurations with normal non-symmetry inducing lift. The typical blade lies relatively near the centreline of the oncoming wake from the preceding blade. The central motion over a wide parameter range is in condensed periodic boundary layers and wakes with fixed displacement, buried within surrounding incident shear flow. This is accompanied, however, by streamwise jumps in the pressure, velocity and mass flux, across the leading edge of each blade, a new and surprising feature which is supported by the combination of incident shears and a solid surface and which is related to the normal flow through the multi-blade system. The leading-edge jumps are required in order to satisfy the equi-pressure condition at the trailing edge. Computational results include separating flows and show the lift and drag, and these are followed by a short-blade analysis which captures the main flow properties explicitly. The results agree qualitatively with experiments and direct simulations for rotor blade flows. The jump feature also extends for example to a single blade immersed in the relatively large wake of an upstream blade.

Transonic Normal Shock-Turbulent Boundary Layer Interaction in Pressure Gradient Flows

1977 ◽  
Author(s):  
A. G. Panaras ◽  
G. R. Inger
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Normal Shock ◽  
Pressure Gradients ◽  
Local Boundary ◽  
Boundary Layer Interaction ◽  
Theoretical Predictions ◽  
Disturbance Analysis ◽  
Separating Flows

A basic theoretical analysis of the interaction of a transonic normal shock wave with a non-separating turbulent boundary layer in a background pressure gradient is given. The method is based on an extension of Inger and Mason’s small disturbance analysis to account for both explicit pressure gradients upstream and downstream of the interaction and the implicit pressure gradient effects on the local boundary layer shape plus the back-effect of the interaction-induced boundary layer thickness growth (blockage) that is important in channel flows and turbomachinery applications. The theory predicts the detailed disturbance pressure and skin friction distributions, including lateral pressure gradients, and is readily imbedded locally in a global calculation scheme involving transonic inviscid and boundary layer prediction codes upstream and downstream of the shock. Good agreement is found between the resulting theoretical predictions and experimental results for non-separating flows.

scholarly journals Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

2019 ◽  
Vol 104 (2-3) ◽  
pp. 579-603 ◽  
Author(s):  
Martin Schmelzer ◽  
Richard P. Dwight ◽  
Paola Cinnella
Keyword(s):  
Machine Learning ◽  
Model Development ◽  
Turbulence Models ◽  
Symbolic Regression ◽  
Systematic Assessment ◽  
Rans Turbulence Models ◽  
Diverging Channel ◽  
Stress Models ◽  
Separating Flows ◽  
Made In

AbstractA novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) 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.

Computations of unsteady separating flows over an oscillating airfoil

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1235-1238
Author(s):  
Sungho Ko ◽  
W. J. McGrosley
Keyword(s):  
Oscillating Airfoil ◽  
Separating Flows
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