scholarly journals Asymptotic behavior of classical solutions of a three-dimensional Keller–Segel–Navier–Stokes system modeling coral fertilization

Author(s):  
Myowin Htwe ◽  
Peter Y. H. Pang ◽  
Yifu Wang
1982 ◽  
Vol 120 ◽  
pp. 155-183 ◽  
Author(s):  
Jon Lee

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).


2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Bernard Nowakowski ◽  
Gerhard Ströhmer

AbstractWe investigate the existence and regularity of solutions to the stationary Stokes system and non-stationary Navier–Stokes equations in three dimensional bounded domains with in- and out-lets. We assume that on the in- and out-flow parts of the boundary the pressure is prescribed and the tangential component of the velocity field is zero, whereas on the lateral part of the boundary the fluid is at rest.


Author(s):  
Ghislaine Ngo Boum ◽  
Rodolfo Bontempo ◽  
Isabelle Trébinjac

High accuracy simulation of compressor surge origin and growth is an important challenge for designers of systems using compressors likely to develop that severe instability. Indeed, understanding its driving phenomena, which can be system dependent, is necessary to build an adequate strategy to avoid or control surge emergence. Computational fluid dynamics (CFD) simulations, commonly used to explore flow in the compressor, need then to be extended beyond the compressor as surge is a system scale instability. To get an insight on the path to surge and through surge cycles, a reliable alternative to full three-dimensional (3D) system modeling is used for a turbocharger compressor inserted in an experimental test rig. The air flow in the whole circuit, is modeled with a one-dimensional (1D) Navier Stokes approach which is coupled with a 3D unsteady RANS modeling of the 360 deg air flow in the centrifugal compressor including the volute. Starting from an initial stable flow solution in the system, the back-pressure valve is progressively closed to reduce the massflow and trigger the instability. An entire deep surge loop is simulated and compared with good agreement with the experimental data. The existence of a system-induced convective wave is revealed, and its major role on surge inception at diffuser inlet demonstrated.


Sign in / Sign up

Export Citation Format

Share Document