scholarly journals Partial differential equations for oceanic artificial intelligence

2021 ◽  
Vol 70 ◽  
pp. 137-146
Author(s):  
Jules Guillot ◽  
Guillaume Koenig ◽  
Kadi Minbashian ◽  
Emmanuel Frénod ◽  
Héléne Flourent ◽  
...  
Keyword(s):  
Data Model ◽  
Stokes Equations ◽  
Weather Forecasting ◽  
Navier Stokes ◽  
Model Coupling ◽  
Navier Stokes Equations ◽  
Coupling Approach ◽  
Prediction Systems ◽  
Applications Of Machine Learning ◽  
The One

The Sea Surface Temperature (SST) plays a significant role in analyzing and assessing the dynamics of weather and also biological systems. It has various applications such as weather forecasting or planning of coastal activities. On the one hand, standard physical methods for forecasting SST use coupled ocean- atmosphere prediction systems, based on the Navier-Stokes equations. These models rely on multiple physical hypotheses and do not optimally exploit the information available in the data. On the other hand, despite the availability of large amounts of data, direct applications of machine learning methods do not always lead to competitive state of the art results. Another approach is to combine these two methods: this is data-model coupling. The aim of this paper is to use a model in another domain. This model is based on a data-model coupling approach to simulate and predict SST. We first introduce the original model. Then, the modified model is described, to finish with some numerical results.

The turning couples on an elliptic particle settling in a vertical channel

1994 ◽  
Vol 271 ◽  
pp. 1-16 ◽  
Author(s):  
Peter Y. Huang ◽  
Jimmy Feng ◽  
Daniel D. Joseph
Keyword(s):  
Shear Stress ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Navier Stokes ◽  
Front Face ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Back Face ◽  
The One

We do a direct two-dimensional finite-elment simulation of the Navier–Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of vortex shedding. Turning this way and that is induced by large and unequal values of negative pressure at the rear separation points which are here identified with the two points on the back face where the shear stress vanishes. The main restoring mechanism which turns the broadside of the ellipse perpendicular to the fall is the high pressure at the ‘stagnation point’ on the front face, as in potential flow, which is here identified with the one point on the front face where the shear stress vanishes.

scholarly journals An Algorithm for the Navier-Stokes Problem

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
F.Z. Nouri ◽  
K. Amoura
Keyword(s):  
Nonlinear Problem ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Nous Proposons ◽  
Navier Stokes Equations ◽  
International Audience ◽  
The One ◽  
Work First

International audience This study is a continuation of the one done in [7],[8] and [9] which are based on the work, first derived by Glowinski et al. in [3] and [4] and also Bernardi et al. [1] and [2]. Here, we propose an Algorithm to solve a nonlinear problem rising from fluid mechanics. In [7], we have studied Stokes problem by adapting Glowinski technique. This technique is userful as it decouples the pressure from the velocity during the resolution of the Stokes problem. In this paper, we extend our study to show that this technique can be used in solving a nonlinear problem such as the Navier Stokes equations. Numerical experiments confirm the interest of this discretisation. Cette étude est la continuation des travaux [7],[8] et [9] qui sont basés sur l'étude faite par Glowinski et al. [3] et [4] ainsi que Bernardi et al. (voir [1] et [2]). Ici nous proposons un Algorithme pour résoudre un problème non-linéaire issu de la mécanique des fluides. Dans [7] nous avons étudié le problème de Stokes en adaptant la technique de Glowinski, grace à aquelle, on peut découpler la pression de la vitesse lors de la résolution du problème de Stokes. Dans ce travail, nous étendons notre étude et montrons que cette technique peut être utilisée dans la résolution d'un probème non-linéaire comme les quations de Navier Stokes. Des tests numériques confirment l'intérêt de la discrétisation.

scholarly journals Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory

2021 ◽  
Author(s):  
Yasi Zheng ◽  
Wenjun Liu ◽  
Yadong Liu
Keyword(s):  
Stokes Equations ◽  
Infinite Delay ◽  
Navier Stokes ◽  
Time Behavior ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Bounded Absorbing Set ◽  
Long Time ◽  
The One ◽  
Class Of Functions

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

INTRODUCING OF INTERNAL VISCOUS FRICTION IN EQUATIONS OF BEAM OSCILLATION AS LONG RECTANGULAR STRIP

2021 ◽  
pp. 54-58
Author(s):  
E.M. Zveriaev ◽  
Keyword(s):  
Stokes Equations ◽  
Asymptotic Series ◽  
Viscous Friction ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Dimensional Theory ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Beam Oscillation

Abstract. On the base of the method of simple iterations generalising methods of semi-inverse one of Saint-Venant, Reissner and Timoshenko the one-dimensional theory is constructed using the example of dynamic equations of a plane problem of elasticity theory for a long elastic strip. The resolving equation of that one-dimensional theory coincides with the equation of beam vibrations. The other problems with unknowns are determined without integration by direct calculations. In the initial equations of the theory of elasticity the terms corresponding to the viscous friction in the Navier-Stokes equations are introduced. The asymptotic characteristics of the unknowns obtained by the method of simple iterations allow to search for a solution in the form of expansions of the unknowns into asymptotic series. The resolving equation contains a term that depends on the coefficient of viscous friction.

STATIONARY WEAK SOLUTIONS FOR STOCHASTIC 3D NAVIER–STOKES EQUATIONS WITH LÉVY NOISE

2012 ◽  
Vol 12 (01) ◽  
pp. 1150006 ◽  
Author(s):  
ZHAO DONG ◽  
WENBO V. LI ◽  
JIANLIANG ZHAI
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Probability Measures ◽  
Stationary Probability ◽  
Navier Stokes Equations ◽  
Wiener Processes ◽  
The One ◽  
Levy Noise

We first study the existence of stationary weak solutions of stochastic 3D Navier–Stokes equations involving jumps, and the associated Galerkin stationary probability measures for this case. Then we present a comparison between the Galerkin stationary probability measures for the case driven by Lévy noise and the one driven by Wiener processes.

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