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Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number

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Bibliographic Details
Title: Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number
Authors: G.C. Bourantas, E.D. Skouras, V.C. Loukopoulos, G.C. Nikiforidis
Source: Computer Modeling in Engineering & Sciences ; ISSN: 1526-1492 (Print) ; ISSN: 1526-1506 (Online) ; Volume 59 ; Issue 1
Publisher Information: Tech Science Press
Publication Year: 2019
Subject Terms: Meshfree point collocation method, Velocity-vorticity formulation, 2D incompressible Navier-Stokes equations, Velocity correction method
Description: A meshfree point collocation method has been developed for the velocity-vorticity formulation of two-dimensional, steady state incompressible Navier-Stokes equations. Particular emphasis was placed on the application of the velocity-correc -tion method, ensuring the continuity equation. The Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity conditions that make the matrix of the system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through two representative, well-known, and established benchmark problems. The numerical scheme was also applied to a case with irregular geometry for marginally high Reynolds numbers.
Document Type: article in journal/newspaper
File Description: application/pdf
Language: English
Relation: https://doi.org/10.3970/cmes.2010.059.031
DOI: 10.3970/cmes.2010.059.031
Availability: https://doi.org/10.3970/cmes.2010.059.031
Rights: info:eu-repo/semantics/openAccess ; https://creativecommons.org/licenses/by/4.0/
Accession Number: edsbas.A6EE6939
Database: BASE
Description
Abstract:A meshfree point collocation method has been developed for the velocity-vorticity formulation of two-dimensional, steady state incompressible Navier-Stokes equations. Particular emphasis was placed on the application of the velocity-correc -tion method, ensuring the continuity equation. The Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity conditions that make the matrix of the system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through two representative, well-known, and established benchmark problems. The numerical scheme was also applied to a case with irregular geometry for marginally high Reynolds numbers.
DOI:10.3970/cmes.2010.059.031