An HOC Finite Difference Scheme for the Steady Natural Convection Problem Based on the Velocity-Vorticity Method
Year: 2025
Author: Tao Wang, Tiegang Liu, Kun Wang
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 591–614
Abstract
A high-order compact finite difference scheme for solving natural convection problems using velocity-vorticity formulation of the incompressible Navier-Stokes equations is presented. The basic idea of the method is to regard all controlling equations as the Poisson-type. We construct a fourth-order finite difference scheme for the velocity-vorticity equation based on the nine-point stencils for each Poisson-type equation. Next we give an example with an exact solution to verify that the scheme has the fourth-order accuracy. Finally, numerical solutions for the model problem of natural convection in a square heating cavity are presented to show the reliability and effectiveness of this method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2024-056.270624
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 591–614
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Navier-Stokes equation Boussinesq hypothesis velocity-vorticity method fourth-order compact scheme natural convection problem.