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ARTICLE

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

by G.C. Bourantas¹, E.D. Skouras², V.C. Loukopoulos⁴, G.C. Nikiforidis¹

1 Department of Medical Physics, School of Medicine, University of Patras, GR 26500, Rion, Greece.
2 Department of Chemical Engineering, University of Patras, GR 26500, Rion, Greece.
3 Institute of Chemical Engineering and High Temperature Chemical Processes - Foundation for Research and Technology, P.O. Box 1414, GR-26504, Patras, Rion, Greece.
4 Department of Physics, University of Patras, Patras, 26500, Rion, Greece.

Computer Modeling in Engineering & Sciences 2010, 59(1), 31-64. https://doi.org/10.3970/cmes.2010.059.031

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.

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