East Asian J. Appl. Math., 15 (2025), pp. 591-614.
Published online: 2025-06
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2024-056.270624}, url = {http://global-sci.org/intro/article_detail/eajam/24157.html} }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.