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Formulation of wall boundary conditions in turbulent flow computations on unstructured meshes

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Abstract

Features of the formulation and numerical implementation of wall boundary conditions in turbulent flow computations on unstructured meshes are discussed. A method is proposed for implementing weak wall boundary conditions for a finite-volume discretization of the Reynolds-averaged Navier-Stokes equations on unstructured meshes. The capabilities of the approach are demonstrated in several gasdynamic simulations in comparison with the method of near-wall functions. The influence of the near-wall resolution on the accuracy of the computations is analyzed, and the grid dependence of the solution is compared in the case of the near-wall function method and weak boundary conditions.

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References

  1. P. R. Spalart and S. R. Allmaras, “A one equation turbulence model for aerodynamic flows,” AIAA. Paper, No. 92-0439 (1992).

    Google Scholar 

  2. B. E. Launder and D. B. Spalding, “The numerical computation of turbulent flows,” Comput. Meth. Appl. Mech. Eng. 3(2), 269–289 (1974).

    Article  MATH  Google Scholar 

  3. K. N. Volkov and V. N. Emel’yanov, Modeling of Large Vortices in Turbulent Flow Computations (Fizmatlit, Moscow, 2008) [in Russian].

    Google Scholar 

  4. J. Bredberg, “On the wall boundary condition for turbulence model,” Report of Chalmers University of Technology, No. 00/4 (2000).

    Google Scholar 

  5. S. S. Collis, “Discontinuous Galerkin methods for turbulence simulation,” Stanford University, Center for Turbulence Research. Technical Report (2002).

    Google Scholar 

  6. K. N. Volkov, “Wall boundary conditions and grid dependence of the solution in turbulent flow computations on unstructured grids,” Vychisl. Metody Program. 7(1), 211–223 (2006).

    Google Scholar 

  7. K. N. Volkov, “Near-wall modeling in computations of turbulent flows on unstructured grids,” Thermophys. Aeromech. 14(1), 107–123 (2007).

    Article  Google Scholar 

  8. M. Kato and B. E. Launder, “The modeling of turbulent flow around stationary and vibrating square cylinders,” Proceedings of the 9th Symposium on Turbulent Shear Flows, August 16–18, 1993 (Kyoto, Japan, 1993), Vol. 9, pp. 10.4.1–10.4.6.

    Google Scholar 

  9. M. A. Leschziner and W. Rodi, “Calculation of annular and twin parallel jets using various discretization schemes and turbulent-model variations,” J. Fluids Eng. 103, 353–360 (1981).

    Article  Google Scholar 

  10. K. N. Volkov, “Unstructured-grid finite-volume discretization of the Navier-Stokes equations based on high-resolution difference schemes,” Comput. Math. Math. Phys. 48, 1181–1202 (2008).

    Article  Google Scholar 

  11. K. N. Volkov, “Multigrid techniques as applied to gasdynamic simulation on unstructured meshes,” Comput. Math. Math. Phys. 50, 1837–1850 (2010).

    Article  MathSciNet  Google Scholar 

  12. K. N. Volkov, “Preconditioning of the Euler and Navier-Stokes equations in low-velocity flow simulation on unstructured grid,” Comput. Math. Math. Phys. 49, 1789–1804 (2009).

    Article  MathSciNet  Google Scholar 

  13. S. Deck, P. Duveau, P. d’Espiney, and P. Guillen, “Development and application of Spalart-Allmaras one-equation turbulence model to three-dimensional supersonic complex configurations,” Aerospace Sci. Technol. 6(3), 171–183 (2002).

    Article  MATH  Google Scholar 

  14. K. Wieghardt and W. Tillman, “On the turbulent friction layer for rising pressure,” NACA Report No. TM-1314 (1951).

    Google Scholar 

  15. D. A. Yoder and N. J. Georgiadis, “Implementation and validation of the Chien k-ɛ turbulence model in the WIND Navier-Stokes code,” AIAA Paper, No. 99-0745 (1999).

    Google Scholar 

  16. A. J. H. Teekaram, C. J. P. Forth, and T. V. Jones, “Film cooling in the presence of mainstream pressure gradients,” J. Turbomachinery 113, 484–492 (1991).

    Article  Google Scholar 

  17. K. N. Volkov, “The effect of pressure gradient and localized injection on turbulent heat transfer on a flat plate,” High Temp. 44, 414–421 (2006).

    Article  Google Scholar 

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Correspondence to K. N. Volkov.

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Original Russian Text © K.N. Volkov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 2, pp. 336–351.

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Volkov, K.N. Formulation of wall boundary conditions in turbulent flow computations on unstructured meshes. Comput. Math. and Math. Phys. 54, 353–367 (2014). https://doi.org/10.1134/S0965542514020134

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