A Meshless Method for Modeling Convective Heat Transfer

A meshless method is used in a projection-based approach to solve the primitive equations for fluid flow with heat transfer. The method is easy to implement in a MATLAB format. Radial basis functions are used to solve two benchmark test cases: natural convection in a square enclosure and flow with forced convection over a backward facing step. The results are compared with two popular and widely used commercial codes: COMSOL, a finite element model, and FLUENT, a finite volume-based model.Copyright © 2010 by ASME

[1]  Darrell W. Pepper,et al.  Benchmark problems for heat transfer codes : presented at the Winter Annual Meeting of the American Society of Mechanical Engineers, Anaheim, California, November 8-13, 1992 , 1992 .

[2]  G. D. Davis.  Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[3]  D. Eppstein,et al.  MESH GENERATION AND OPTIMAL TRIANGULATION , 1992 .

[4]  Darrell W. Pepper,et al.  CONVECTIVE HEAT TRANSFER DOWNSTREAM OF A 3-D BACKWARD-FACING STEP , 2002 .

[5]  D. Brian Spalding.  Numerical simulation of natural convection in porous media , 1984 .

[6]  Nam Mai-Duy,et al.  An efficient indirect RBFN‐based method for numerical solution of PDEs , 2005 .

[7]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[8]  D. Gartling.  A test problem for outflow boundary conditions—flow over a backward-facing step , 1990 .

[9]  R. Franke.  A Critical Comparison of Some Methods for Interpolation of Scattered Data , 1979 .

[10]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[11]  Andrew D. Back,et al.  Radial Basis Functions , 2001 .

[12]  Darrell Pepper.  Meshless methods for PDEs , 2010, Scholarpedia.

[13]  Darrell W. Pepper,et al.  An h-adaptive finite element method for turbulent heat transfer , 2010 .

[14]  Nagamani Devi Kalla.  Solution of Heat Transfer and Fluid Flow problems using meshless Radial Basis Function method , 2008 .

[15]  Božidar Šarler.  Towards a mesh-free computation of transport phenomena , 2002 .

[16]  George N. Barakos,et al.  Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions , 1994 .

[17]  A. Rajagopal,et al.  Mesh free Galerkin method based on natural neighbors and conformal mapping , 2008 .

[18]  Xiang-Yang Li,et al.  Point placement for meshless methods using Sphere packing and Advancing Front methods , 2001 .

[19]  Alain J. Kassab,et al.  A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics , 2009 .

[20]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[21]  Darrell W. Pepper,et al.  Application of an hp-Adaptive FEM for Solving Thermal Flow Problems , 2007 .

[22]  S. Atluri,et al.  The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods , 2002 .