Steady-state two-dimensional solutions to the full compressible Navier-Stokes equations are computed for laminar convective motion of a gas in a square cavity with large horizontal temperature differences. Results for air are presented. The ideal-gas law is used and viscosity is given by Sutherland's law. An accurate low-Mach number solver is developed. Hereby an explicit third-order discretization for the convective part and a line-implicit central discretization for the acoustic part and for the diffusive part are used. The semi-implicit line method is formulated in multistage form. Multigrid is used as acceleration technique. A convergence behaviour is obtained which is independent of grid size, grid aspect ratio, Mach number and Rayleigh number. Grid converged results are shown for Rayleigh numbers between 102 and 107. © 2004 Elsevier B.V. All rights reserved.
Vierendeels, J., Merci, B., & Dick, E. (2004). A multigrid method for natural convective heat transfer with large temperature differences. Journal of Computational and Applied Mathematics, 168(1–2), 509–517. https://doi.org/10.1016/j.cam.2003.08.081