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Keywords:

  • Finite volume;
  • Multigrid;
  • Numerical accuracy;
  • Natural convection;
  • Bench-mark solution

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 104, 105 and 106 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.