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Abstract
This study investigates the numerical accuracy of the finite-volume discretization for the natural-convection flow of air in a square cavity with differentially heated vertical walls and adiabatic horizontal walls. The regime of high Rayleigh numbers is considered, in which the steady flow bifurcates to a periodic unsteady flow. Investigated is how the accuracy depends on (1) the numerical discretization scheme for the convective fluxes and (2) the number of grid points. The fourth-order central interpolation scheme for the convective derivative turns out to be the most accurate scheme. At least 2402 grid points are required to obtain good accuracy for the amplitude of the oscillations.