scholarly journals New variational principles for locating periodic orbits of differential equations

2011 ◽  
Vol 369 (1944) ◽  
pp. 2211-2218 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Luis M. Fazendeiro ◽  
Jonas Lätt ◽  
Hui Tang ◽  
Peter V. Coveney
Keyword(s):  
Periodic Orbits ◽  
Variational Principles ◽  
Stokes Equations ◽  
Iterative Algorithms ◽  
Navier Stokes ◽  
Unstable Periodic Orbits ◽  
Navier Stokes Equations ◽  
New Methods ◽  
Discrete Representations

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier–Stokes equations, simulated using the lattice Boltzmann equation.

scholarly journals Unstable periodic orbits in the Lorenz attractor

2011 ◽  
Vol 369 (1944) ◽  
pp. 2345-2353 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Aaron Brown ◽  
Jonas Lätt ◽  
Hui Tang ◽  
Luis M. Fazendeiro ◽  
...  
Keyword(s):  
Periodic Orbits ◽  
Stokes Equations ◽  
Traditional Approach ◽  
Navier Stokes ◽  
Lorenz Attractor ◽  
Time Averaging ◽  
Unstable Periodic Orbits ◽  
Lorenz Equations ◽  
Navier Stokes Equations ◽  
Generic Orbit

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computation of unstable periodic orbits of the driven Navier–Stokes equations, which can be simulated using the lattice Boltzmann method.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

scholarly journals Exact and limiting solutions of fluid flow for axially oscillating cylindrical pipe and annulus

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
U. K. Sarkar ◽  
Nirmalendu Biswas
Keyword(s):  
Velocity Distribution ◽  
High Frequency ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Cylindrical Pipe ◽  
Navier Stokes Equations ◽  
Cylindrical Annulus

AbstractThe Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis has been given for the determination of approximate velocity distributions for the high frequency and low frequency or quasi-static limits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distribution inside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocity distribution inside an axially oscillating cylindrical pipe of radius $${\bar R_o}$$ R ¯ o and the velocity distribution outside an axially oscillating cylindrical pipe of radius $${\bar R_i}$$ R ¯ i , where $${\bar R_i}$$ R ¯ i and $${\bar R_o}$$ R ¯ o are the inner and outer radii of the axially oscillating annulus, respectively.

scholarly journals Determination of air and hydrofoil pressure coefficient by laser doppler anemometry

2010 ◽  
Vol 37 (1) ◽  
pp. 17-35
Author(s):  
Slavica Ristic ◽  
Mirjana Puharic ◽  
Marina Kutin ◽  
Dusan Matic
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Laser Doppler Anemometry ◽  
Pressure Coefficient ◽  
Laser Doppler ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advantages And Disadvantages ◽  
Axial Pump

Some results of experiments performed in water cavitation tunnel are presented. Pressure coefficient (Cp) was experimentally determined by Laser Doppler Anemometry (LDA) measurements. Two models were tested: model of airplane G4 (Super Galeb) and hydrofoil of high speed axial pump. These models are not prepared for conventional pressure measurements, so that LDA is applied for Cp determination. Numerical results were obtained using a code for average Navier-Stokes equations solutions. Comparisons between computational and experimental results prove the effectiveness of the LDA. The advantages and disadvantages of LDA application are discussed. Flow visualization was made by air bubbles.

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