A finite element LES methodology for anisotropic inhomogeneous meshes

Large eddy simulation techniques offer a wealth of valuable information for engineering design purposes, but in many cases the required mesh resolution is prohibitive. Combining the dynamic LES procedure with unstructured mesh adaptivity offers a robust and efficient way of capturing the inhomogeneity and anisotropy of complex turbulent flows. However, this may result in a non-vanishing commutation error due to the filter employed. The inverse Helmholtz filter is used here with a tensor definition of filter width related to the local element size and shape. The formulation, verification and validation of a finite element methodology, designed to yield maximal accuracy from moderate mesh resolution with minimal ad hoc procedures, is described. Results for the 3D backward facing step obtained using the open source CFD code Fluidity are presented. Using adaptive meshing, closer agreement to DNS was obtained compared to fixed meshes while using 60% fewer nodes.

[1]  Hervé Jeanmart,et al.  On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation , 2001, Journal of Fluid Mechanics.

[2]  Darryl D. Holm,et al.  Alpha-modeling Strategy for LES of Turbulent Mixing , 2002, nlin/0202012.

[3]  James G. Brasseur,et al.  A resolvable subfilter-scale model specific to large-eddy simulation of under-resolved turbulence , 2001 .

[4]  Hans Kuerten,et al.  Large-eddy simulation of the temporal mixing layer using the Clark model , 1996 .

[5]  J. Bentham,et al.  Microscale modelling of air flow and pollutant dispersion in the urban environment , 2004 .

[6]  P. Roache.  Code Verification by the Method of Manufactured Solutions , 2002 .

[7]  Fernando Porté-Agel,et al.  Dynamic subgrid‐scale models for momentum and scalar fluxes in large‐eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain , 2006 .

[8]  M. Germano.  Differential filters of elliptic type , 1986 .

[9]  J. Deardorff.  A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[10]  C.R.E. de Oliveira,et al.  Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations , 2001 .

[11]  Christer Fureby,et al.  Large-Eddy Simulation: Current Capabilities, Recommended Practices, and Future Research , 2009 .

[12]  H. ApSimon,et al.  Synthetic-Eddy Method for Urban Atmospheric Flow Modelling , 2010 .

[13]  Knut Akselvoll,et al.  Large Eddy Simulation of a Backward Facing Step Flow , 1993 .

[14]  Kenneth E. Jansen,et al.  Spatial test filters for dynamic model large‐eddy simulation with finite elements , 2002 .

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

[16]  P. Moin,et al.  A dynamic localization model for large-eddy simulation of turbulent flows , 1995, Journal of Fluid Mechanics.

[17]  Large Eddy Simulation of Backward Facing Step Flow , 2009 .

[18]  Christopher C. Pain,et al.  A new computational framework for multi‐scale ocean modelling based on adapting unstructured meshes , 2008 .

[19]  M. Germano.  Differential filters for the large eddy numerical simulation of turbulent flows , 1986 .

[20]  Hervé Jeanmart,et al.  Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynami , 2001 .

[21]  J. Fröhlich,et al.  Hybrid LES/RANS methods for the simulation of turbulent flows , 2008 .

[22]  Charles Meneveau,et al.  Generalized Smagorinsky model for anisotropic grids , 1993 .

[23]  Pierre Sagaut,et al.  Multiscale And Multiresolution Approaches In Turbulence , 2006 .

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

[25]  Parviz Moin,et al.  Erratum: ‘‘A dynamic subgrid‐scale eddy viscosity model’’ [Phys. Fluids A 3, 1760 (1991)] , 1991 .

[26]  P. Moin,et al.  Direct numerical simulation of turbulent flow over a backward-facing step , 1997, Journal of Fluid Mechanics.

[27]  S. Benhamadouche,et al.  LES, coarse LES, and transient RANS comparisons on the flow across a tube bundle , 2003 .

[28]  Christer Fureby,et al.  Large-Eddy Simulation: Current Capabilities, Recommended Practices, and Future Research , 2009 .

[29]  Alain Dervieux,et al.  Large‐eddy simulation of a bluff‐body flow on unstructured grids , 2002 .

[30]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[31]  Stephen B. Pope,et al.  Large-Eddy Simulation Using Projection onto Local Basis Functions , 2001 .

[32]  K. Jansen,et al.  A dynamic Smagorinsky model with dynamic determination of the filter width ratio , 2004 .

[33]  C. Meneveau,et al.  On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet , 1994, Journal of Fluid Mechanics.

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

[35]  M. Kopera.  Direct numerical simulation of turbulent flow over a backward-facing step , 2011 .

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

[37]  D. Carati,et al.  On the self-similarity assumption in dynamic models for large eddy simulations , 1997 .

[38]  Julia S. Mullen,et al.  Filtering techniques for complex geometry fluid flows , 1999 .