@Article{AAMM-3-3,
author = {Vertnik, Robert and Šarler, Božidar},
title = {Local Collocation Approach for Solving Turbulent Combined Forced and Natural Convection Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2011},
volume = {3},
number = {3},
pages = {259--279},
abstract = {<p style="text-align: justify;">An application of the meshless Local Radial Basis Function Collocation
Method (LRBFCM) [22, 30–33] in solution of incompressible turbulent combined
forced and natural convection is for the first time explored in the present paper.
The turbulent flow equations are described by the low-Re number $k − ε$ model with
Launder and Sharma [23] and Abe et al. [1] closure coefficients. The involved temperature,
velocity, pressure, turbulent kinetic energy and dissipation fields are represented
on overlapping 5-noded sub-domains through the collocation by using
multiquadrics Radial Basis Functions (RBF). The involved first and second order
partial derivatives of the fields are calculated from the respective derivatives of the
RBF&#39;s. The involved equations are solved through the explicit time stepping. The
pressure-velocity coupling is based on Chorin&#39;s fractional step method [11]. The
adaptive upwinding technique, proposed by Lin and Atluri [27], is used because
of the convection dominated situation. The solution procedure is represented for
a 2D upward channel flow with differentially heated walls. The results have been
assessed by achieving a reasonable agreement with the direct numerical simulation
of Kasagi and Nishimura [20] for Reynolds number 4494, based on the channel
width, and Grashof number 9.6 × 10<sup>5</sup>. 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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-10s2-01},
url = {https://global-sci.com/article/73592/local-collocation-approach-for-solving-turbulent-combined-forced-and-natural-convection-problems}
}