High Rayleigh Number Laminar-Free Convection in Cavities: New Benchmark Solutions

The fully matrix-inversion-free artificial compressibility (AC), characteristic based split (CBS) algorithm is used to produce a stable and accurate solution for high Rayleigh number natural convection in rectangular cavities. Two benchmark problems are solved using the AC-CBS scheme: the classical differentially heated (DH) cavity, and a cavity subject to temperature boundary conditions on its sides, which is proposed here as a new benchmark. For the DH cavity problem, the dependence of the solution on the computational grid is highlighted, and it is shown how the horizontal velocity is more sensitive than the other calculated quantities. For the newly proposed benchmark, the numerical results are compared to experimental data that has recently appeared in the open literature.