Finite volume multigrid prediction of laminar natural convection: Bench‐mark solutions

TLDR

The study introduces a finite volume multigrid procedure to predict laminar natural convection flows efficiently and accurately on very fine grids. The method employs a fully conservative finite volume scheme with second‑order central differencing, starting from a coarse 10×10 grid and iteratively refining to finer grids while considering Rayleigh numbers 10⁴–10⁶. Computing times grow linearly with the number of control volumes, and the approach yields grid‑independent solutions with second‑order monotonic convergence and accuracy within 0.01% on grids up to 640×640 for a closed cavity with side‑wall temperature differences.

Abstract

Abstract A finite volume multigrid procedure for the prediction of laminar natural convection flows is presented, enabling efficient and accurate calculations on very fine grids. The method is fully conservative and uses second‐order central differencing for convection and diffusion fluxes. The calculations start on a coarse (typically 10 × 10 control volumes) grid and proceed to finer grids until the desired accuracy or maximum affordable storage is reached. The computing times increase thereby linearly with the number of control volumes. Solutions are presented for the flow in a closed cavity with side walls at different temperatures and insulated top and bottom walls. Rayleigh numbers of 10 4 , 10 5 and 10 6 are considered. Grids as fine as 640 × 640 control volumes are used and the results are believed to be accurate to within 0–01%. Second‐order monotonic convergence to grid‐independent values is observed for all predicted quantities.