Small-time existence for the three-dimensional navier-stokes equations for an incompressible fluid with a free surface

1996 ◽  
Vol 133 (4) ◽  
pp. 299-331 ◽  
Author(s):  
Atusi Tani
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Small Time ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Existence

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

Modélisation tridimensionnelle de l'écoulement au voisinage d'un aménagement portuaire

1989 ◽  
Vol 16 (6) ◽  
pp. 829-844
Author(s):  
A. Soulaïmani ◽  
Y. Ouellet ◽  
G. Dhatt ◽  
R. Blanchet
Keyword(s):  
Free Surface ◽  
Computational Analysis ◽  
Stokes Equations ◽  
A Priori ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Solution Algorithm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Flows

This paper is devoted to the computational analysis of three-dimensional free surface flows. The model solves the Navier-Stokes equations without any a priori restriction on the pressure distribution. The variational formulation along with the solution algorithm are presented. Finally, the model is used to study the hydrodynamic regime in the vicinity of a projected harbor installation. Key words: free surface flows, three-dimensional flows, finite element method.

Existence of global weak solution for quantum Navier–Stokes system

2020 ◽  
Vol 31 (05) ◽  
pp. 2050038
Author(s):  
Jianwei Yang ◽  
Gaohui Peng ◽  
Huiyun Hao ◽  
Fengzhen Que
Keyword(s):  
Stokes System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Data ◽  
Global Weak Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dependent Viscosity ◽  
Time Existence ◽  
Cold Pressure

In this paper, the barotropic compressible quantum Navier–Stokes equations with a density-dependent viscosity in a three-dimensional torus is studied. By introducing a cold pressure to handle the convection term, we prove the global-in-time existence of weak solutions to quantum Navier–Stokes equations for large data in the sense of standard definition.

Numerical Analysis of Hydrodynamics and Heat Transfer of a Free Surface Circular Jet Impinging Onto a Substrate

2007 ◽  
Author(s):  
Hitoshi Fujimoto ◽  
Shinya Dejima ◽  
Albert Y. Tong ◽  
Takayuki Hama ◽  
Hirohiko Takuda
Keyword(s):  
Heat Transfer ◽  
Free Surface ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Liquid Jets ◽  
Flow Profile ◽  
Navier Stokes Equations ◽  
Incompressible Viscous Fluids ◽  
Impact Angles

The present paper is concerned with three-dimensional numerical simulations of hydrodynamics and convective heat transfer of a free surface liquid jet impinging onto a hot substrate. The Navier-Stokes equations for unsteady incompressible viscous fluids are used and are solved numerically by a finite difference method. The numerical model is validated by comparing the results with experiments conducted by other researchers under the conditions of normal impingement. Oblique impingement of liquid jets onto a substrate is treated. It is found that the stagnation point does not coincide with the geometric jet center on the solid surface. The deviation increases with decreasing impact angles, i.e. increasing degree of obliqueness. The peak of local Nusselt number is also shifted in accordance with the flow profile. The velocity and temperature distributions are examined in detail to better understand the physics of the oblique impingement phenomena.

Hydrodynamic Impact of a Falling Body upon a Viscous Incompressible Fluid

1977 ◽  
Vol 21 (03) ◽  
pp. 165-181
Author(s):  
Buford R. Koehler ◽  
C. F. Kettleborough
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Hydrodynamic Impact ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Pressure Distributions

The hydrodynamic impact of a falling body upon a viscous incompressible fluid is investigated by the development and solution of a mathematical model which simulates the impact of a rigid flat-bottomed body upon the quiescent free surface of viscous incompressible water. A one-dimensional compressible air layer exists between the falling body and the water free surface. Velocity and pressure distributions within the air layer are calculated using the continuity equation and the one-dimensional momentum equation derived from the Navier-Stokes equations. The water free surface is allowed to deform as the air pressures acting on it increase. The two-dimensional rectangular coordinate form of the Navier-Stokes equations for an incompressible fluid is applied to the water. A normalization scheme is used which causes the water free surface to appear straight and simplifies the application of free-surface boundary conditions. Water velocities are calculated from the momentum and continuity equations. Pressures are calculated using the pressure equation derived from the Navier-Stokes equations. Air-water interface velocities are obtained from boundary-layer relations. The governing equations of the air layer and water region are expressed in finite difference form and are solved on a high-speed digital computer. The behavior of the air layer before impact is discussed. Air layer velocity and pressure distributions are obtained. The influence of the air layer on the water is studied. Pressure and velocity distributions in the water are obtained before and at the instant of impact. Pressure distributions and pressure histories compare favorably with available experimental data. Corresponding plots of the moving free surface show the actual shape of the compressible air region. A slight variation in the body deadrise angle is found to significantly change impact pressures and the shape of the pressure distributions.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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