scholarly journals The odd-even hopscotch pressure correction scheme for the incompressible Navier-Stokes equations

1987 ◽  
Vol 20 ◽  
pp. 393-402
Author(s):  
J.H.M. Ten Thije Boonkkamp
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Correction Scheme

scholarly journals A Pressure-Correction Scheme for Rotational Navier-Stokes Equations and Its Application to Rotating Turbulent Flows

2011 ◽  
Vol 9 (3) ◽  
pp. 740-755 ◽  
Author(s):  
Dinesh A. Shetty ◽  
Jie Shen ◽  
Abhilash J. Chandy ◽  
Steven H. Frankel
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Correction Scheme ◽  
Diagonalization Method ◽  
Pseudo Spectral

AbstractThe rotational incremental pressure-correction (RIPC) scheme, described in Timmermans et al. [Int. J. Numer. Methods. Fluids., 22 (1996)] and Shen et al. [Math. Comput., 73 (2003)] for non-rotational Navier-Stokes equations, is extended to rotating incompressible flows. The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows. The performance of the scheme and the computational results are compared to the so-called diagonalization method (DM) developed by Morinishi et al. [Int. J. Heat. Fluid. Flow., 22 (2001)]. The RIPC predictions are in excellent agreement with the DM predictions, while being simpler to implement and computationally more efficient. The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions, and can be used in complex geometries and with other suitable boundary conditions.

scholarly journals Immersed Boundary Method for Generalised Finite Volume and Finite Difference Navier-Stokes Solvers

2010 ◽  
Author(s):  
A. Pinelli ◽  
I. Z. Naqavi ◽  
U. Piomelli
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
Integral Conditions ◽  
Navier Stokes Equations ◽  
Correction Scheme ◽  
Grid Points ◽  
Boundary Methods ◽  
Immersed Boundaries

In Immersed Boundary Methods (IBM) the effect of complex geometries is introduced through the forces added in the Navier-Stokes solver at the grid points in the vicinity of the immersed boundaries. Most of the methods in the literature have been used with Cartesian grids. Moreover many of the methods developed in the literature do not satisfy some basic conservation properties (the conservation of torque, for instance) on non-uniform meshes. In this paper we will follow the RKPM method originated by Liu et al. [1] to build locally regularized functions that verify a number of integral conditions. These local approximants will be used both for interpolating the velocity field and for spreading the singular force field in the framework of a pressure correction scheme for the incompressible Navier-Stokes equations. We will also demonstrate the robustness and effectiveness of the scheme through various examples.

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