Benchmark data on laminar Rayleigh–Bénard convection in a stratified supercritical fluid: A case of two-dimensional flow in a square cell

We simulate numerically steady-state Rayleigh–Bénard convection slightly above the stability threshold in a stratified supercritical fluid. We use a two-dimensional approximation and consider one roll contained in a square cell. Simulations are performed by two different numerical codes. First code is based on the complete Navier–Stokes equations, and second one is a low Mach number approximation with filtering sound and stratification effects. We consider conditions in which an influence of adiabatic temperature gradient is significant. Solutions found on the basis of two mathematical models are matched in a special fashion to find a contribution of adiabatic temperature gradient and specify common features independent of whether the governing equations are able to predict a stratification effect. We perform a comparison with known analytical and experimental results and propose our solutions as benchmark data for supercritical Rayleigh–Bénard convection.