scholarly journals Stochastic Navier-Stokes Equations with Artificial Compressibility in Random Durations

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Hong Yin
Keyword(s):  
Incompressible Flow ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Finite Dimensional

The existence and uniqueness of adapted solutions to the backward stochastic Navier-Stokes equation with artificial compressibility in two-dimensional bounded domains are shown by Minty-Browder monotonicity argument, finite-dimensional projections, and truncations. Continuity of the solutions with respect to terminal conditions is given, and the convergence of the system to an incompressible flow is also established.

scholarly journals On the construction of suitable weak solutions to the 3D Navier–Stokes equations in a bounded domain by an artificial compressibility method

2017 ◽  
Vol 20 (01) ◽  
pp. 1650064 ◽  
Author(s):  
Luigi C. Berselli ◽  
Stefano Spirito
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation.

scholarly journals A DISPERSIVE APPROACH TO THE ARTIFICIAL COMPRESSIBILITY APPROXIMATIONS OF THE NAVIER–STOKES EQUATIONS IN 3D

2006 ◽  
Vol 03 (03) ◽  
pp. 575-588 ◽  
Author(s):  
DONATELLA DONATELLI ◽  
PIERANGELO MARCATI
Keyword(s):  
Weak Solution ◽  
Stokes Equations ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Dispersive Approach ◽  
Incompressible Navier Stokes Equation

In this paper we study how to approximate the Leray weak solutions of the incompressible Navier–Stokes equations. In particular we describe an hyperbolic version of the so-called artificial compressibility method investigated by J. L. Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimates of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier–Stokes equation.

scholarly journals Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier–Stokes equations

2013 ◽  
Vol 143 (5) ◽  
pp. 905-927 ◽  
Author(s):  
Margaret Beck ◽  
C. Eugene Wayne
Keyword(s):  
Decay Rate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Long Time ◽  
High Reynolds

Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows, where they often emerge on timescales much shorter than the viscous timescale, and then dominate the dynamics for very long time intervals. In this paper we propose a dynamical systems explanation of the metastability of an explicit family of solutions, referred to as bar states, of the two-dimensional incompressible Navier–Stokes equation on the torus. These states are physically relevant because they are associated with certain maximum entropy solutions of the Euler equations, and they have been observed as one type of metastable state in numerical studies of two-dimensional turbulence. For small viscosity (high Reynolds number), these states are quasi-stationary in the sense that they decay on the slow, viscous timescale. Linearization about these states leads to a time-dependent operator. We show that if we approximate this operator by dropping a higher-order, non-local term, it produces a decay rate much faster than the viscous decay rate. We also provide numerical evidence that the same result holds for the full linear operator, and that our theoretical results give the optimal decay rate in this setting.

scholarly journals The Finite-Dimensional Uniform Attractors for the Nonautonomous g-Navier-Stokes Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Delin Wu
Keyword(s):  
Fractal Dimension ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Uniform Attractor ◽  
Navier Stokes Equations ◽  
Finite Dimensional ◽  
Uniform Attractors

We consider the uniform attractors for the two dimensional nonautonomous g-Navier-Stokes equations in bounded domain . Assuming , we establish the existence of the uniform attractor in and . The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.

Solution of three-dimensional incompressible flow problems

1977 ◽  
Vol 82 (2) ◽  
pp. 309-319 ◽  
Author(s):  
S. M. Richardson ◽  
A. R. H. Cornish
Keyword(s):  
Stream Function ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Vector Potentials

A method for solving quite general three-dimensional incompressible flow problems, in particular those described by the Navier–Stokes equations, is presented. The essence of the method is the expression of the velocity in terms of scalar and vector potentials, which are the three-dimensional generalizations of the two-dimensional stream function, and which ensure that the equation of continuity is satisfied automatically. Although the method is not new, a correct but simple and unambiguous procedure for using it has not been presented before.

scholarly journals On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations

2005 ◽  
Vol 462 (2066) ◽  
pp. 459-479 ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Takeshi Taniguchi
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stochastic Version ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We prove the existence and uniqueness of solutions for a stochastic version of the three-dimensional Lagrangian averaged Navier–Stokes equation in a bounded domain. To this end, we previously prove some existence and uniqueness results for an abstract stochastic equation and justify that our model falls within this framework.

scholarly journals Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Eduardo Renteria Casas
Keyword(s):  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Arbitrary Dimensions ◽  
Parameter Ranges

Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \bWmop)$ for $p$ and $q$ in  appropriate parameter ranges are proven. The case of spatially measured-valued inhomogeneities is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions with $1 < p, q < \infty$ arbitrary.

Artificial Compressibility Method and Preconditioning Method for Solving Two Dimensional Incompressibile Flow

2011 ◽  
Author(s):  
Hyungro Lee ◽  
Einkeun Kwak ◽  
Seungsoo Lee
Keyword(s):  
Mach Number ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Preconditioning Method

In this study, two commonly used numerical methods for the analysis of incompressible flows (or low Mach number flows), Chorins’ artificial compressibility method and Wiess and Smith’s preconditioning method are compared. Also, the convergence characteristics of two methods are numerically investigated for two-dimensional laminar and turbulent flows. Although the two methods have similar governing equations, the eigensystems and other details are very different. The eigensystems of the artificial compressibility method and the preconditioning method are analytically examined. An artificial compressibility code that solves the incompressible RANS (Reynolds Averaged Navier-Stokes) equations is newly developed for the study. An artificial compressibility code and a well-verified existing low Mach number code uses Roe’s approximate Riemann solver in conjunction with a cell centered finite volume method. Using MUSCL extrapolation with nonlinear limiters, 2nd order spatial accuracy is achieved while maintaining TVD (total variation diminishing) property. AF-ADI (approximate factorization-alternate direction implicit) method is used to get the steady solution for both codes. Menter’s k–ω SST turbulence model is used for the analysis of turbulent flows. Navier-Stokes equations and the turbulence model equations are solved in a loosely coupled manner.

scholarly journals Computer Simulation of Water Flow Animation Based on Two-Dimensional Navier-Stokes Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Rushi Cao ◽  
Ruyun Cao
Keyword(s):  
Computer Graphics ◽  
Boundary Conditions ◽  
Water Flow ◽  
Stokes Equations ◽  
Simulation Method ◽  
Fluid Simulation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

Simulation of water flow animation is a significant and challenging subject in computer graphics. With the continuous development of computational fluid dynamics and computer graphics, many more effective simulation methods have been developed, and fluid animation simulation has developed rapidly. In order to obtain realistic flow animation, one of the key aspects is to simulate flow motion. Based on the two-dimensional Navier-Stokes equations, a mathematical model is established to solve the boundary conditions required by the physical flow field of water. The coordinate transformation formula is introduced to transform the irregular physical area into a regular square calculation area, and then, the specific expressions of the liberalized Navier-Stokes equation, continuity equation, pressure Poisson equation, and dimensionless boundary conditions are given. Using animation software to sequence graphics and images of all kinds of control and direct operation of the relevant instructions, through the computer technology to simulate the flow of animation, based on the stability of fluid simulation method and simulation efficiency, so as to make realistic flow animation. The results show that FluidsNet has considerable performance in accelerating large scene animation simulation on the basis of ensuring the rationality of prediction, and the motion of water wave is realistic. The application of computer successfully simulates water flow.

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