Abstract
In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial basis functions (RBFs) have been popularly used as high-accuracy interpolants of function values at scattered locations. In this paper, we apply the polyharmonic splines (PHS) as the RBF together with appended polynomial and solve the heat conduction equation in several geometries using a collocation procedure. We demonstrate the expected exponential convergence of the numerical solution as the degree of the appended polynomial is increased. The method holds promise to solve several different governing equations in thermal sciences.
Original language | English (US) |
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Pages (from-to) | 1-27 |
Number of pages | 27 |
Journal | Computational Thermal Sciences |
Volume | 14 |
Issue number | 3 |
DOIs | |
State | Published - 2022 |
Keywords
- heat conduction problems
- meshless method
- polyharmonic splines
- radial basis function
ASJC Scopus subject areas
- Energy Engineering and Power Technology
- Surfaces and Interfaces
- Fluid Flow and Transfer Processes
- Computational Mathematics