DNS of Mixed Convection in Enclosed 3D-Domains with Interior Boundaries

  • Olga ShishkinaEmail author
  • Andrei Shishkin
  • Claus Wagner
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 13)


Engineering problems of climate control in buildings, cars or aircrafts, where the temperature must be regulated to maintain comfortable and healthy conditions, can be formulated as mixed convection problems, in which the flows are determined both by buoyancy and by inertia forces, while neither of these forces dominate. The objective of the present study is to investigate by means of Direct Numerical Simulations (DNS) instantaneous and statistical characteristics of turbulent mixed convection flows around heated obstacles which take place in indoor ventilation problems for Grashof number up to 1.0e11 and Reynolds numbers based on the height of the domain and the inlet velocity up to 1.0e5. The chosen computational domain, which is a parallelepiped with four parallelepiped obstacles inside, can be assumed as a generic room in indoor ventilation problems. The DNS of turbulent convective flows are carried out with a fourth order accurate finite volume code solving the three-dimensional incompressible Navier–Stokes equations in Boussinesq approximation.


Direct Numerical Simulation Mixed Convection Thermal Plume Interior Boundary Fast Solver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors are grateful to the Deutsche Forschungsgemeinschaft (DFG) for supporting this work.


  1. 1.
    Chorin A. J. & Marsden J. E. (1993) A Mathematical Introduction to Fluid Mechanics. Springer Series: Texts in Applied Mathematics, 4, Springer-Verlag.Google Scholar
  2. 2.
    Grötzbach G. (1983) Spatial resolution requirements for direct numerical simulation of Rayleigh–Bénard convection, J. Comput. Phys. 49: 241–264.zbMATHCrossRefGoogle Scholar
  3. 3.
    Leonard A. & Winckelmans G. S. (1999) A tensor-diffusivity subgrid model for Large-Eddy Simulation, Caltech ASCI technical report, cit-asci-tr043, 043.Google Scholar
  4. 4.
    Schumann U. & Sweet R. A. (1976) A direct method for the solution of Poisson’s equation with Neumann boundary conditions on a staggered grid of arbitrary size, J. Comput. Phys. 20: 171–182.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Shishkina O., Shishkin A. & Wagner C. (2009) Simulation of turbulent thermal convection in complicated domains, J. Comput. Appl. Maths 226, 336–344.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Shishkina O. & Wagner C. (2008) Analysis of sheet-like thermal plumes in turbulent Rayleigh–Bénard convection, J. Fluid Mech. 599: 383–404.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Shishkina O. & Wagner C. (2007) A fourth order finite volume scheme for turbulent flow simulations in cylindrical domains, Comput. Fluids 36: 484–497.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Shishkina O. V. (2007) The Neumann stability of high-order symmetric schemes for convection–diffusion problems, Siberian Mathematical J. 48: 1141–1146.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Verzicco R. & Camussi R. (2003) Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell, J. Fluid Mech. 477: 19–49.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.DLR-Institute of Aerodynamics and Flow TechnologyGöttingenGermany

Personalised recommendations