ACCURACY OF FINITE-VOLUME DISCRETIZATIONS FOR THE BIFURCATING NATURAL-CONVECTION FLOW IN A SQUARE CAVITY

This study investigates the numerical accuracy of the finite-volume di scretization for the natural-convection flow of air in a square cavity with differentially heated vertical walls and adiabatic horizontal wa lls. The regime of high Rayleigh numbers is considered, in which the s teady flow bifurcates to a periodic unsteady flow. Investigated is how the accuracy depends on (1) the numerical discretization scheme for t he convective fluxes and (2) the number of grid points. The fourth-ord er central interpolation scheme for the convective derivative turns ou t to be the most accurate scheme. At least 240(2) grid points are requ ired to obtain good accuracy for the amplitude of the oscillations.