Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. 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.Singapore: World SCientific, 2007.
The results have been assessed by achieving a reasonable agreement with the direct numerical simulation of Kasagi and Nishimura for Reynolds number 4494, based on the channel width, and Grash of number 9.6×10 5. The solution procedure is represented for a 2D upward channel flow with differentially heated walls. The adaptive upwinding technique, proposed by Lin and Atluri, is used because of the convection dominated situation. The pressure-velocity coupling is based on Chorin’s fractional step method. The involved equations are solved through the explicit time stepping. The involved first and second order partial derivatives of the fields are calculated from the respective derivatives of the RBF’s. 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 turbulent flow equations are described by the low-Re number к – ε model with Launder and Sharma and Abe et al. An application of the meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of incompressible turbulent combined forced and natural convection is for the first time explored in the present paper.
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