Numerical Solution of Natural Convection Problems Using Radial Point Interpolation Meshless (RPIM) Method Combined with Artificial-Compressibility Model

• Published in: Mathematical and computational applications Vol. 29; no. 3; p. 39
• Main Authors: Pranowo, Santoso, Albertus Joko, Wijayanta, Agung Tri
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-06-2024
• Subjects: Accuracy; Algebra; annulus; Approximation; artificial compressibility; Boundary conditions; Circular cylinders; Compressibility; Crack propagation; Free convection; Heat transfer; Interpolation; Lagrange multiplier; meshless method; Meshless methods; natural convection; Numerical analysis; Numerical methods; Thermal analysis; trapezoidal; Variables
• ISSN: 2297-8747; 1300-686X; 2297-8747
• DOI: 10.3390/mca29030039

A numerical method is used to solve the thermal analysis of natural convection in enclosures. This paper proposes the use of an implicit artificial-compressibility model in conjunction with the Radial Point Interpolation Meshless (RPIM) method to mimic laminar natural convective heat transport. The technique couples the pressure with the velocity components using an artificial compressibility model. The RPIM is used to discretize the spatial terms of the governing equation. We solve the semi-algebraic system implicitly in backward Euler pseudo-time. The proposed method solves two test problems—natural convection in the annulus of concentric circular cylinders and trapezoidal cavity. Additionally, the results are validated using experimental and numerical data available in the literature. Excellent agreement was seen between the numerical results acquired with the suggested method and those obtained through the standard techniques found in the literature.