Fractional step artificial compressibility schemes for the unsteady incompressible Navier–Stokes equations

2007 ◽  
Vol 36 (5) ◽  
pp. 974-986 ◽  
Author(s):  
H.S. Tang ◽  
Fotis Sotiropoulos
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Fractional Step ◽  
Navier Stokes Equations ◽  
Artificial Compressibility

scholarly journals A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

2014 ◽  
Vol 16 (5) ◽  
pp. 1135-1180 ◽  
Author(s):  
László Könözsy ◽  
Dimitris Drikakis
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Fractional Step ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Flow Problems ◽  
Dual Time Stepping ◽  
Pressure Projection ◽  
The Stability

AbstractThis paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

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 A divergence free fractional step method for the Navier-Stokes equations on non-staggered grids

2010 ◽  
Vol 51 ◽  
pp. 654 ◽  
Author(s):  
Steven William Armfield ◽  
Nicholas Williamson ◽  
Michael Kirkpatrick ◽  
Robert Street
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equations ◽  
Staggered Grids ◽  
Divergence Free
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