Abstract
LES quality assessment is very important in view of predictive LES applications. Recently Klein [1] proposed to evaluate the numerical as well as the modeling error in a LES using an approach based on Richardson extrapolation, where it is assumed that the modeling error scales like a power law. In order to apply this approach, the scaling exponent for the numerical error with respect to the filter width has to be known in advance. This scaling law will be explored for three different configurations: a channel flow, a plane jet and a swirling recirculating flow. Theoretical argumentation [2, 3] leads to a scaling of m = 2/3. The current findings suggest to use Δ4/3 for flow configurations operating at moderate Reynolds numbers. The resulting scaling exponent will be used to assess the quality of LES simulations of these configurations.
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References
M. Klein. An attempt to assess the quality of large eddy simulations in the context of implicit filtering. Flow, Turbulence and Combustion, 75: 131–147, 2005.
S.B. Pope. Turbulent Flows. Cambridge Universtiy Press, 2000.
P. Sagaut. Large Eddy Simulation for Incompressible Flows. Springer, 1998.
S.B. Pope. Ten questions concerning the large-eddy-simulation of turbulent flows. New Journal of Physics, 6(35), 2004.
A. Nakayama and S.N. Vengadesan. On the influence of numerical schemes and subgrid-stress models on large eddy simulation of turbulent flow past a square cylinder. International Journal for Numerical Methods in Fluids, 38:227–253, 2002.
P.J. Roache. Verification and validation in computational science and engineering. Hermosa Publishers, Albuquerque, 1998.
B.J. Geurts and J. Fröhlich. A framework for predicting accuracy limitations in large eddy simulations. Physics of Fluids, 14(6):L41–L44, 2002.
F.K. Chow and P. Moin. A further study of numerical errors in large-eddy simulations. Journal of Computational Physics, 184:366–380, 2003.
A.G. Kravchenko and P. Moin. On the effect of numerical errors in large eddy simulation of turbulent flows. Journal of Computational Physics, 131:310–322, 1997.
J. Meyers, B.J. Geurts, and M. Baelmans. Database analysis of errors in large-eddy simulation. Physics of Fluids, 15(9):2740–2755, 2003.
B. Vreman, B. Geurts, and H. Kuerten. Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer. International Journal for Numerical Methods in Fluids, 22:297–311, 1996.
U. Schumann and R.A. Sweet. A direct method for the solution of Poisson's equation with Neumann boundary conditions on a staggered grid of arbitrary size. Journal of Computational Physics, 20:171–182, 1976.
M. Klein, A. Sadiki, and J. Janicka. Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation. International Journal of Heat and Fluid Flow, 24(6):785–794, 2003.
M. Freitag and M. Klein. Direct numerical simulation of a recirculating, swirling flow. Flow, Turbulence and Combustion, 75:51–66, 2005.
R.D. Moser, J. Kim, and N.N. Mansour. Direct numerical simulation of turbulent channel flow up to Reô = 590. Physics of Fluids, 11(4): 943–945, 1999.
M. Klein, A. Sadiki, and J. Janicka. A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. Journal of Computational Physics, 186:652–665, 2003.
J.O. Hinze. Turbulence. McGraw-Hill, 1959.
J. Kim, P. Moin, and R. Moser. Turbulence statistics in fully developed channel flow at low Reynolds number. Journal Fluid Mechanics, 177: 133–166, 1987.
C. Schneider, A. Dreizler, and J. Janicka. Fluid dynamical analysis of atmospheric reacting and isothermal swirling flows. Flow, Turbulence and Combustion, 74:103–127, 2005.
J.M. Beer and N.A. Chigier. Combustion Aerodynamics. Applied Science Publishers, London, 1972.
I.B. Celik, Z.N. Cehreli, and I. Yavuz. Index of resolution quality for large eddy simulations. ASME Journal of Fluids Engineering, 127:949–958, 2005.
M. Freitag and M. Klein. An improved method to assess the quality of large eddy simulations in the context of implicit filtering. Journal of Turbulence, in press, 2006.
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Klein, M., Freitag, M., Janicka, J. (2007). Numerical Determination of the Scaling Exponent of the Modeled Subgrid Stresses for Eddy Viscosity Models. In: Kassinos, S.C., Langer, C.A., Iaccarino, G., Moin, P. (eds) Complex Effects in Large Eddy Simulations. Lecture Notes in Computational Science and Engineering, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34234-2_12
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DOI: https://doi.org/10.1007/978-3-540-34234-2_12
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