A $\operatorname{log}$-type non-local flow of convex curves

2021 ◽  
Vol 29 (5) ◽  
pp. 1157-1182
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Ke Shi
Keyword(s):  
Local Flow ◽  
Convex Curves ◽  
Non Local

Linear amplification factor transport equation for stationary crossflow instabilities in supersonic boundary layers

2020 ◽  
pp. 095441002095499
Author(s):  
Jiakuan Xu
Keyword(s):  
Transport Equation ◽  
Boundary Layers ◽  
Amplification Factor ◽  
Reynolds Numbers ◽  
Linear Stability Theory ◽  
Local Flow ◽  
Flow Parameters ◽  
Compressible Boundary Layers ◽  
Non Local ◽  
Flow Variables

Based on the database from linear stability theory (LST) analysis, a local amplification factor transport equation for stationary crossflow (CF) waves in low-speed boundary layers was developed in 2019. In this paper, the authors try to extend this transport equation to compressible boundary layers based on local flow variables. The similarity equations for compressible boundary layers are introduced to build the function relations between non-local variables and local flow parameters. Then, compressibility corrections are taken into account to modify the source term of the transport equation. Through verifications of different sweep angles, Reynolds numbers, angles of attack, Mach numbers, and different cross-section geometric shapes, the rationality and correctness of the new transport equation established in this paper are illustrated.

scholarly journals Control of the continuity equation with a non local flow

2010 ◽  
Vol 17 (2) ◽  
pp. 353-379 ◽  
Author(s):  
Rinaldo M. Colombo ◽  
Michael Herty ◽  
Magali Mercier
Keyword(s):  
Continuity Equation ◽  
Local Flow ◽  
Non Local

A non-local expanding flow of convex closed curves in the plane

2020 ◽  
pp. 2050115
Author(s):  
Ke Shi
Keyword(s):  
Numerical Experiment ◽  
Additional Assumption ◽  
Euclidean Plane ◽  
Blow Up ◽  
Time Interval ◽  
Initial Curve ◽  
Closed Curves ◽  
Convex Curves ◽  
Non Local

This paper presents a new non-local expanding flow for convex closed curves in the Euclidean plane which increases both the perimeter of the evolving curves and the enclosed area. But the flow expands the evolving curves to a finite circle smoothly if they do not develop singularity during the evolving process. In addition, it is shown that an additional assumption about the initial curve will ensure that the flow exists on the time interval [Formula: see text]. Meanwhile, a numerical experiment reveals that this flow may blow up for some initial convex curves.

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