Instability, vortex shedding, and numerical convergence

1988 ◽  
pp. 42-55 ◽  
Author(s):  
Christopher Anderson ◽  
Claude Greengard ◽  
Michael Henderson
Keyword(s):  
Vortex Shedding ◽  
Numerical Convergence

Evolution of unstable system.

2015 ◽  
Vol 9 (3) ◽  
pp. 2487-2502 ◽  
Author(s):  
Igor V. Lebed
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Stokes Flow ◽  
Stable Solution ◽  
The State ◽  
Unstable System ◽  
Unstable Flow ◽  
Unstable Solutions ◽  
Vortex Shedding Modes ◽  
Hydrodynamics Equations

Scenario of appearance and development of instability in problem of a flow around a solid sphere at rest is discussed. The scenario was created by solutions to the multimoment hydrodynamics equations, which were applied to investigate the unstable phenomena. These solutions allow interpreting Stokes flow, periodic pulsations of the recirculating zone in the wake behind the sphere, the phenomenon of vortex shedding observed experimentally. In accordance with the scenario, system loses its stability when entropy outflow through surface confining the system cannot be compensated by entropy produced within the system. The system does not find a new stable position after losing its stability, that is, the system remains further unstable. As Reynolds number grows, one unstable flow regime is replaced by another. The replacement is governed tendency of the system to discover fastest path to depart from the state of statistical equilibrium. This striving, however, does not lead the system to disintegration. Periodically, reverse solutions to the multimoment hydrodynamics equations change the nature of evolution and guide the unstable system in a highly unlikely direction. In case of unstable system, unlikely path meets the direction of approaching the state of statistical equilibrium. Such behavior of the system contradicts the scenario created by solutions to the classic hydrodynamics equations. Unstable solutions to the classic hydrodynamics equations are not fairly prolonged along time to interpret experiment. Stable solutions satisfactorily reproduce all observed stable medium states. As Reynolds number grows one stable solution is replaced by another. They are, however, incapable of reproducing any of unstable regimes recorded experimentally. In particular, stable solutions to the classic hydrodynamics equations cannot put anything in correspondence to any of observed vortex shedding modes. In accordance with our interpretation, the reason for this isthe classic hydrodynamics equations themselves.

Some modeling issues on trailing-edge vortex shedding

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 787-793
Author(s):  
Wei Ning ◽  
Li He
Keyword(s):  
Vortex Shedding ◽  
Trailing Edge ◽  
Edge Vortex

COMPARISON OF LES WITH DSM, k-ε AND EXPERIMENTS FORTURBULENT VORTEX SHEDDING FLOW PAST 2D SQUARE CYLINDER

1994 ◽  
Vol 59 (459) ◽  
pp. 49-56 ◽  
Author(s):  
Shigehiro SAKAMOTO ◽  
Akashi MOCHIDA ◽  
Shuzo MURAKAMI ◽  
Wolfgang RODI
Keyword(s):  
Vortex Shedding ◽  
Square Cylinder ◽  
Flow Past

scholarly journals Asymmetric vortex shedding in the wake of an abruptly expanding annular jet

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Maarten Vanierschot ◽  
Mustafa Percin ◽  
Bas W. van Oudheusden
Keyword(s):  
Vortex Shedding ◽  
Asymmetric Vortex ◽  
Annular Jet

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

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