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Spectral element benchmark simulations of natural convection in two-dimensional cavities. (English) Zbl 1090.76051
Summary: We report the results of spectral element simulations of natural convection in two-dimensional cavities. In particular, a detailed comparison is performed with the reference data for the 8:1 cavity at $$Ra=3.4 \times 10^5$$ recently described by M. A. Christon et al. [ibid. 40, No. 8, 953–980 (2002; Zbl 1025.76042)]. The Navier-Stokes equations augmented by Boussinesq approximation to represent buoyancy effects are solved by a numerical method based on a spectral element discretization and operator splitting. The computed solutions agree closely with the reference data for both the square and rectangular cavity configurations.

##### MSC:
 76M22 Spectral methods applied to problems in fluid mechanics 76M20 Finite difference methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 80A20 Heat and mass transfer, heat flow (MSC2010)
##### Keywords:
Boussinesq approximation; operator splitting
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