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Solution of Incompressible Turbulent Flow by a Mesh-Free Method

R. Vertnik1, B. Šarler2

Štore-Steel, Techical Development, E-mail:
University of Nova Gorica, Laboratory for Multiphase Processes, Slovenia, E-mail:

Computer Modeling in Engineering & Sciences 2009, 44(1), 65-96.


The application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of incompressible turbulent flow is explored in this paper. The turbulent flow equations are described by the low - Re number k-emodel with Jones and Launder [Jones and Launder (1971)] closure coefficients. The involved velocity, pressure, turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The velocity, turbulent kinetic energy and dissipation equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively, based on the Chorin's fractional step method [Chorin 1967]. The adaptive upwinding technique, proposed by the Lin and Atluri [Lin and Atluri (2000)] is used because of the convection dominated situation. The solution procedure is represented in 2D. Three test cases have been performed: laminar flow in a channel with Re = 100, turbulent flow in a channel with Re = 12300 and turbulent flow in a channel with 1/6 backward facing step with Re = 5000. The solution is compared with the analytical solution in the first case, with the experiment [Laufer (1948)] and commercial code Fluent in the second case, and with the experiment [Jovi\'c and Driver (1994)], commercial code Fluent and direct numerical simulation [Le, Moin and Kim (1997)] in the third case. All numerical examples include non-uniform spatial discretisation. A reasonably good agreement between the solutions has been achieved. The advantages of the represented mesh-free approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward applicability in non-uniform node arrangements.


Cite This Article

Vertnik, R., Šarler, B. (2009). Solution of Incompressible Turbulent Flow by a Mesh-Free Method. CMES-Computer Modeling in Engineering & Sciences, 44(1), 65–96.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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