Abstract
A Least Squares Collocation Meshless Method based on Radial Basis Function (RBF) interpolation is used to solve steady state heat conduction problems on 2D polygonal domains using MATLAB® environment. The point distribution process required by the numerical method can be fully automated, taking account of boundary conditions and geometry of the problem to get higher point distribution density where needed. Several convergence tests have been carried out comparing the numerical results to the corresponding analytical solutions to outline the properties of this numerical approach, considering various combinations of parameters. These tests showed favorable convergence properties in the simple cases considered: along with the geometry flexibility, these features confirm that this peculiar numerical approach can be an effective tool in the numerical simulation of heat conduction problems.
Highlights
The accuracy of standard numerical methods used in Computational Fluid Dynamics (CFD), such as Finite Element, Finite Volume and Spectral Element Methods among others, rely on a high quality discretization of the spatial domain
A wide class of meshless methods which has been the object of recent developments is the one based on Radial Basis Function (RBF) interpolation [4,5,6,7]: this technique accepts only the relative (Euclidean) distance between the points as interpolation parameters
Several computations are carried out considering various combinations of parameters and different types of polygonal 2D domains for a simple Poisson equation to outline the properties of this numerical approach, comparing the computed solution to the corresponding analytical solution
Summary
The accuracy of standard numerical methods used in Computational Fluid Dynamics (CFD), such as Finite Element, Finite Volume and Spectral Element Methods among others, rely on a high quality discretization of the spatial domain. Several computations are carried out considering various combinations of parameters and different types of polygonal 2D domains for a simple Poisson equation to outline the properties of this numerical approach, comparing the computed solution to the corresponding analytical solution. These tests showed that this method can be an effective and robust tool in the numerical simulation of heat conduction problems even in complex shaped domains.
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