On the mathematical analysis of the artificial compressibility method

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Yoshiyuki Kagei
Keyword(s):  
Mathematical Analysis ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

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 Implementation of the fractional-step, artificial compressibility with pressure projection (FSAC-PP) method into openfoam for unsteady flows

2021 ◽  
Vol 11 (5) ◽  
pp. 85-91
Author(s):  
Jesús Miguel Sánchez Gil ◽  
Tom-Robin Teschner ◽  
László Könözsy
Keyword(s):  
Time Derivative ◽  
Unsteady Flows ◽  
Time Discretization ◽  
Projection Methods ◽  
Fractional Step ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Start Up ◽  
2D Flow ◽  
Pressure Projection

Commercial and open-source CFD solvers rely mostly on incompressible approximate projection methods to overcome the pressure-velocity decoupling, such as the SIMPLE (Patankar, 1980) or PISO (Issa, 1986) algorithm. Incompressible methods based on the Artificial Compressibility method (Chorin, 1967) lack a mechanism to evolve in time and need to be supplemented by a real time derivative through the dual time scheme. The current study investigates the implementation of the explicit dual time discretization of the Artificial Compressibility method into OpenFOAM and extends on that by applying the dual time scheme to the incompressible FSAC-PP method (Könözsy, 2012). Applied to the Couette 2D flow at Re=100 and Re=1000, results show that for both methods accurate time evolutions of the velocity profiles are presented, where the FSAC-PP methods seemingly produces smoother profiles compared to the AC method, especially during the start-up of the simulation.

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.

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