Analysis of errors occurring in large eddy simulation

We analyse the effect of second- and fourth-order accurate central finite-volume discretizations on the outcome of large eddy simulations of homogeneous, isotropic, decaying turbulence at an initial Taylor–Reynolds number Reλ=100. We determine the implicit filter that is induced by the spatial discretization and show that a higher order discretization also induces a higher order filter, i.e. a low-pass filter that keeps a wider range of flow scales virtually unchanged. The effectiveness of the implicit filtering is correlated with the optimal refinement strategy as observed in an error-landscape analysis based on Smagorinsky's subfilter model. As a point of reference, a finite-volume method that is second-order accurate for both the convective and the viscous fluxes in the Navier–Stokes equations is used. We observe that changing to a fourth-order accurate convective discretization leads to a higher value of the Smagorinsky coefficient CS required to achieve minimal total error at given resolution. Conversely, changing only the viscous flux discretization to fourth-order accuracy implies that optimal simulation results are obtained at lower values of CS. Finally, a fully fourth-order discretization yields an optimal CS that is slightly lower than the reference fully second-order method.

[1]  B. Geurts,et al.  A framework for predicting accuracy limitations in large-eddy simulation , 2002 .

[2]  B. Geurts,et al.  Mixing in manipulated turbulence , 2006, physics/0601164.

[3]  Bernardus J. Geurts,et al.  Numerically induced high-pass dynamics in large-eddy simulation , 2005 .

[4]  Gaston H. Gonnet,et al.  Scientific Computation , 2009 .

[5]  M. Germano,et al.  Turbulence: the filtering approach , 1992, Journal of Fluid Mechanics.

[6]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[7]  W. L. Ijzerman,et al.  Signal Representation and Modeling of Spatial Structures in Fluids , 2000 .

[8]  P. Moin,et al.  On the Effect of Numerical Errors in Large Eddy Simulations of Turbulent Flows , 1997 .

[9]  B. Geurts,et al.  Large-eddy simulation of the turbulent mixing layer , 1997, Journal of Fluid Mechanics.

[10]  F. Beux,et al.  The effect of the numerical scheme on the subgrid scale term in large-eddy simulation , 1998 .

[11]  Comparison of subgrid-models in large eddy simulation of the temporal mixing layer , 1994 .

[12]  Fotini Katopodes Chow,et al.  The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering , 2003, Journal of Fluid Mechanics.

[13]  B. Geurts Elements of direct and large-eddy simulation , 2003 .

[14]  梶島 岳夫 乱流の数値シミュレーション = Numerical simulation of turbulent flows , 2003 .

[15]  P. Sagaut Large Eddy Simulation for Incompressible Flows , 2001 .

[16]  S. Pope Turbulent Flows: FUNDAMENTALS , 2000 .

[17]  S Ghosal AN ANALYSIS OF NUMERICAL ERROR IN LARGE EDDY SIMULATION OF TURBULENCE , 1996 .

[18]  C. Meneveau,et al.  Scale-Invariance and Turbulence Models for Large-Eddy Simulation , 2000 .

[19]  P. Moin,et al.  Numerical Simulation of Turbulent Flows , 1984 .

[20]  P. Moin,et al.  A General Class of Commutative Filters for LES in Complex Geometries , 1998 .

[21]  Johan Meyers,et al.  A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model , 2007, J. Comput. Phys..

[22]  B. Geurts,et al.  Database-analysis of errors in Large-Eddy Simulation , 2003 .

[23]  P. Sagaut BOOK REVIEW: Large Eddy Simulation for Incompressible Flows. An Introduction , 2001 .

[24]  Bernardus J. Geurts,et al.  COMPARISON OF NUMERICAL SCHEMES IN LARGE-EDDY SIMULATION OF THE TEMPORAL MIXING LAYER , 1996 .

[25]  P Sagaut,et al.  Large Eddy Simulation for Incompressible Flows: An Introduction. Scientific Computation Series , 2002 .

[26]  B. Geurts Inverse modeling for large-eddy simulation , 1997 .