A criterion of orthogonality on the assumption and restrictions in subgrid-scale modelling of turbulence

Abstract In order to shed light on understanding the subgrid-scale (SGS) modelling methodology, we analyze and define the concepts of assumption and restriction in the modelling procedure, then show by a generalized derivation that if there are multiple stationary restrictions in a modelling, the corresponding assumption function must satisfy a criterion of orthogonality. Numerical tests using one-dimensional nonlinear advection equation are performed to validate this criterion. This study is expected to inspire future research on generally guiding the SGS modelling methodology.

[1]  Liang Shao,et al.  Subgrid modeling of anisotropic rotating homogeneous turbulence , 2005 .

[2]  Lian-Ping Wang,et al.  Effects of subgrid-scale modeling on time correlations in large eddy simulation , 2001 .

[3]  L. Fang,et al.  Applying the Kolmogorov equation to the problem of subgrid modeling for Large-Eddy Simulation of turbulence , 2009 .

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

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

[6]  Bo Li,et al.  Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation , 2014 .

[7]  Rainer Friedrich,et al.  A Non-Linear SGS Model Based On The Spatial Velocity Increment , 2006 .

[8]  Jung Yul Yoo,et al.  Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation , 2005 .

[9]  L. Fang,et al.  A new dynamic formula for determining the coefficient of Smagorinsky model , 2011 .

[10]  J. Ferziger,et al.  Improved subgrid-scale models for large-eddy simulation , 1980 .

[11]  Jean-Pierre Bertoglio,et al.  Recent understanding on the subgrid-scale modeling of large-eddy simulation in physical space , 2014 .

[12]  M. Lesieur,et al.  New Trends in Large-Eddy Simulations of Turbulence , 1996 .

[13]  L. Fang,et al.  Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence , 2015, 1511.06501.

[14]  A. Leonard.  Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows , 1975 .

[15]  M. Breuer.  A CHALLENGING TEST CASE FOR LARGE EDDY SIMULATION: HIGH REYNOLDS NUMBER CIRCULAR CYLINDER FLOW , 2000, Proceeding of First Symposium on Turbulence and Shear Flow Phenomena.

[16]  Liang Shao,et al.  A new dynamic subgrid eddy viscosity model with application to turbulent channel flow , 2004 .

[17]  Le Fang,et al.  Multiscale three-point velocity increment correlation in turbulent flows , 2014 .

[18]  Marcel Lesieur,et al.  Turbulence in fluids , 1990 .

[19]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[20]  Jean-Pierre Bertoglio,et al.  Corrections to the scaling of the second-order structure function in isotropic turbulence , 2010 .

[21]  Jean-Pierre Bertoglio,et al.  An improved velocity increment model based on Kolmogorov equation of filtered velocity , 2009 .

[22]  Eliot Fried,et al.  A-priori testing of alpha regularisation models as subgrid-scale closures for large-eddy simulations , 2013 .

[23]  Yue Yang,et al.  Space-Time Correlations and Dynamic Coupling in Turbulent Flows , 2017 .

[24]  Liang Shao,et al.  A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence , 2007, Journal of Fluid Mechanics.

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

[26]  Shiyi Chen,et al.  Constrained subgrid-scale stress model for large eddy simulation , 2008 .

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