Preconditioned conjugate gradients for solving the transient Boussinesq equations in three-dimensional geometries

1988 ◽  
Vol 8 (3) ◽  
pp. 283-303 ◽  
Author(s):  
S. Dupont ◽  
J. M. Marchal
Keyword(s):  
Three Dimensional ◽  
Boussinesq Equations ◽  
Conjugate Gradients ◽  
Preconditioned Conjugate Gradients

The eruptive regime of mass-transfer-driven Rayleigh–Marangoni convection

2016 ◽  
Vol 791 ◽  
Author(s):  
Thomas Köllner ◽  
Karin Schwarzenberger ◽  
Kerstin Eckert ◽  
Thomas Boeck
Keyword(s):  
Concentration Distribution ◽  
Marangoni Convection ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Navier Stokes ◽  
Flow Structures ◽  
Rayleigh Convection ◽  
Marangoni Effects ◽  
Validation Experiments

The transfer of an alcohol, 2-propanol, from an aqueous to an organic phase causes convection due to density differences (Rayleigh convection) and interfacial tension gradients (Marangoni convection). The coupling of the two types of convection leads to short-lived flow structures called eruptions, which were reported in several previous experimental studies. To unravel the mechanism underlying these patterns, three-dimensional direct numerical simulations and corresponding validation experiments were carried out and compared with each other. In the simulations, the Navier–Stokes–Boussinesq equations were solved with a plane interface that couples the two layers including solutal Marangoni effects. Our simulations show excellent agreement with the experimentally observed patterns. On this basis, the origin of the eruptions is explained by a two-step process in which Rayleigh convection continuously produces a concentration distribution that triggers an opposing Marangoni flow.

The effect of ordering on preconditioned conjugate gradients

1989 ◽  
Vol 29 (4) ◽  
pp. 635-657 ◽  
Author(s):  
Iain S. Duff ◽  
Gérard A. Meurant
Keyword(s):  
Conjugate Gradients ◽  
Preconditioned Conjugate Gradients

ON THE REGULARITY OF THREE-DIMENSIONAL ROTATING EULER–BOUSSINESQ EQUATIONS

1999 ◽  
Vol 09 (07) ◽  
pp. 1089-1121 ◽  
Author(s):  
A. BABIN ◽  
A. MAHALOV ◽  
B. NICOLAENKO
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Boussinesq Equations ◽  
Stable Stratification ◽  
Primitive Equations ◽  
Time Interval ◽  
Regular Solutions ◽  
Time Intervals ◽  
Long Time

The 3-D rotating Boussinesq equations (the "primitive" equations of geophysical fluid flows) are analyzed in the asymptotic limit of strong stable stratification. The resolution of resonances and a nonstandard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on infinite time intervals of regular solutions to the viscous 3-D "primitive" equations is proven for initial data in Hα, α≥ 3/4. Existence on a long-time interval T*of regular solutions to the 3-D inviscid equations is proven for initial data in Hα, α > 5/2 (T*→∞ as the frequency of gravity waves →∞).

scholarly journals Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Zhaohui Dai ◽  
Xiaosong Wang ◽  
Lingrui Zhang ◽  
Wei Hou
Keyword(s):  
Weak Solutions ◽  
Blow Up ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Interpolation Inequality ◽  
Embedding Theorem ◽  
The Earth ◽  
The Cauchy Problem ◽  
Homogeneous Besov Space ◽  
Blow Up Criterion

The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressurepin the homogeneous Besov spaceḂ∞,∞0.

scholarly journals Some Regularity Criteria for the 3D Boussinesq Equations in the Class L20,T;B˙∞,∞-1

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zujin Zhang
Keyword(s):  
Temperature Gradient ◽  
Velocity Gradient ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Regularity Criteria ◽  
Deformation Tensor

We consider the three-dimensional Boussinesq equations and obtain some regularity criteria via the velocity gradient (or the vorticity, or the deformation tensor) and the temperature gradient.

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