Skip to main content
Article thumbnail
Location of Repository

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1, Reference solutions \ud

By Patrick Le Quéré, Catherine Weisman, Henri Paillère, Jan Vierendeels, Erik Dick, Roland Becker, Malte Braack and James C. W. Locke


There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, (constant property and variable property cases) and (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established

Topics: QA, QC
Publisher: EDP Sciences
Year: 2005
OAI identifier:

Suggested articles


  1. (1992). A Chebyshev collocation algorithm for 2D Non-Boussinesq convection. doi
  2. (1999). A Multigrid semi-implicit line-method for viscous incompressible and low-Mach number flows on high aspect ratio grids. doi
  3. (1997). Guide, Finite Element Analysis Toolbox, British Energy,
  4. (1986). Natural Convection in an enclosed vertical air layer with large horizontal temperature differences. doi
  5. (1983). Natural convection of air in a square cavity: a benchmark solution. doi
  6. (1983). Natural convection of air in a square cavity: a comparison exercice. doi
  7. (1999). Numerical simulation of laminar flames at low Mach number with adaptive finite elements. Combustion Theory and Modelling, doi
  8. (1967). Numerical solution of the system of two-dimensional unsteady Navier-Stokes equations for a compressible gas in a closed region. Fluid Dyn. doi
  9. (1982). On the filtering of sound from the Navier-Stokes equations. Sandia National Laboratories report SAND82-8257
  10. (1991). Qu´ er´ e, Accurate solutions to the square differentially heated cavity at high Rayleigh number. doi
  11. (2000). Qu´ er´ e, Modelling and simulation of natural convection flows with large temperature differences: a benchmark problem for low Mach number solvers,
  12. (2002). Solution of a stationary benchmark problem for natural convection with high temperature difference. doi
  13. (1976). The Validity of the Boussinesq approximation for liquids and gases. doi
  14. (1980). Unsteady natural convection in a rectangular cavity. doi
  15. (2002). Verification and validation in Computational Fluid Dynamics. Sandia National Laboratories report SAND2002-0529 doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.