WEAK SOLUTIONS OF NAVIER–STOKES EQUATIONS CONSTRUCTED BY ARTIFICIAL COMPRESSIBILITY METHOD ARE SUITABLE

We prove that weak solutions constructed by artificial compressibility method are suitable in the sense of Scheffer. Using Hilbertian setting and Fourier transform with respect to time, we obtain non-trivial estimates on the pressure and the time derivative which allow us to pass to the limit.

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

Communications in Contemporary Mathematics ◽

10.1142/s0219199716500644 ◽

2017 ◽

Vol 20 (01) ◽

pp. 1650064 ◽

Cited By ~ 4

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.

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

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891606000914 ◽

2006 ◽

Vol 03 (03) ◽

pp. 575-588 ◽

Cited By ~ 15

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.

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Evaluation of the Artificial Compressibility Method for the Solution of the Incompressible Navier-Stokes Equations

Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics ◽

10.1007/978-3-663-13974-4_20 ◽

1992 ◽

pp. 201-210 ◽

Cited By ~ 5

Author(s):

Yves P. Marx

Keyword(s):

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Artificial Compressibility ◽

Artificial Compressibility Method

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

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-01007 ◽

2011 ◽

Cited By ~ 1

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.

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