TY - JOUR
T1 - An HOC Finite Difference Scheme for the Steady Natural Convection Problem Based on the Velocity-Vorticity Method
AU - Wang , Tao
AU - Liu , Tiegang
AU - Wang , Kun
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 591
EP - 614
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2024-056.270624
UR - https://global-sci.org/intro/article_detail/eajam/24157.html
KW - Navier-Stokes equation, Boussinesq hypothesis, velocity-vorticity method, fourth-order compact scheme, natural convection problem.
AB - <p style="text-align: justify;">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.</p>