Numerical study of natural convective heat transfer with large temperature differences (Q2729156)

The paper considers the steady-state laminar two-dimensional convective motion of gas in a square cavity with large horizontal temperature differences. No Boussinesq or low-Mach number approximations of Navier-Stokes equations are used. The ideal-gas law is used, and viscosity is given by Sutherland's law. To solve the full Navier-Stokes equations, the authors develop an accurate low-Mach number solver consisting of an explicit third-order discretization for convective part, and a line-implicit central discretization of acoustic part and diffusive part, respectively. A multigrid method is used as a convergence accelerator. The time needed for calculation varies linearly with the number of grid cells. Computation is made on a \(512\times 512\) stretched grid with maximum aspect ratio 80. Results are shown for a variety of Rayleigh numbers with temperature difference of 0.6. Streamline patterns and temperature distributions as well as averaged pressure and averaged Nusselt number are determined and shown on graphs and tables. The authors show that the accuracy of the discretization method is very good, and that the convergence of the method is very fast, independent of the Rayleigh number, the number of grid cells and grid aspect ratio.