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.
Similar content being viewed by others
References
P. R. Spalart and S. R. Allmaras, “A one equation turbulence model for aerodynamic flows,” AIAA. Paper, No. 92-0439 (1992).
B. E. Launder and D. B. Spalding, “The numerical computation of turbulent flows,” Comput. Meth. Appl. Mech. Eng. 3(2), 269–289 (1974).
K. N. Volkov and V. N. Emel’yanov, Modeling of Large Vortices in Turbulent Flow Computations (Fizmatlit, Moscow, 2008) [in Russian].
J. Bredberg, “On the wall boundary condition for turbulence model,” Report of Chalmers University of Technology, No. 00/4 (2000).
S. S. Collis, “Discontinuous Galerkin methods for turbulence simulation,” Stanford University, Center for Turbulence Research. Technical Report (2002).
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).
K. N. Volkov, “Near-wall modeling in computations of turbulent flows on unstructured grids,” Thermophys. Aeromech. 14(1), 107–123 (2007).
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.
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).
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).
K. N. Volkov, “Multigrid techniques as applied to gasdynamic simulation on unstructured meshes,” Comput. Math. Math. Phys. 50, 1837–1850 (2010).
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).
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).
K. Wieghardt and W. Tillman, “On the turbulent friction layer for rising pressure,” NACA Report No. TM-1314 (1951).
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).
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).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.N. Volkov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 2, pp. 336–351.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542514020134