Effects of resolution inhomogeneity in large-eddy simulation

Large Eddy Simulation (LES) of turbulence in complex geometries is often conducted using discretizations with highly inhomogeneous resolution. The issues associated with resolution inhomogeneity are related to the noncommutativity of the filtering and differentiation operators, which introduces a commutation term into the governing equations. Neglect of this commutation term gives rise to commutation error. While the commutation error is well recognized, it is often ignored in practice. Moreover, the commutation error related to the implicit filter (i.e., projection onto the underlying discretization) has not been well investigated. Modeling of the commutation term that arises from the noncommutativity between numerical projection and differentiation is crucial for correcting errors induced by resolution inhomogeneity in practical LES settings, which typically rely solely on implicit filtering. Here, we investigate how this implicit commutation error manifests in simulation and demonstrate its impact on the convection of a packet of homogeneous isotropic turbulence through an inhomogeneous grid. A connection is made between the implicit commutation error and the propagation properties of the underlying numerics. We also introduce a statistical description of the commutation term that can be used in situ to determine the importance of the commutator relative to the subgrid stress term. A model is proposed for the correction of these issues in the case considered here, which highlights several important characteristics of commutation modeling for LES and the importance of considering numerical properties during the formulation of LES models in general. Several insights are discussed that could also be applied to other issues in LES, such as discretization error.

[1]  L. Margolin,et al.  Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics , 2011 .

[2]  S. Ghosal.  An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence , 1996 .

[3]  John Thuburn,et al.  Numerical wave propagation on non-uniform one-dimensional staggered grids , 2011, J. Comput. Phys..

[4]  Robert Vichnevetsky,et al.  Propagation through numerical mesh refinement for hyperbolic equations , 1981 .

[5]  Parviz Moin,et al.  Grid-independent large-eddy simulation using explicit filtering , 2008 .

[6]  T. Hughes,et al.  Large Eddy Simulation and the variational multiscale method , 2000 .

[7]  T. Lund.  The use of explicit filters in large eddy simulation , 2003 .

[8]  C. Fureby,et al.  Mathematical and Physical Constraints on Large-Eddy Simulations , 1997 .

[9]  P. Moin,et al.  A further study of numerical errors in large-eddy simulations , 2003 .

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

[11]  R. Moser,et al.  Two-Dimensional Mesh Embedding for B-spline Methods , 1998 .

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

[13]  D. Tordella,et al.  Variable scale filtered Navier–Stokes equations: A new procedure to deal with the associated commutation error , 2003, 1211.6680.

[14]  Fotini K Atopodes.  The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering , 2003 .

[15]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[16]  R. Moser,et al.  Optimal LES formulations for isotropic turbulence , 1999, Journal of Fluid Mechanics.

[17]  Nikolaus A. Adams,et al.  Direct modelling of subgrid scales of turbulence in large eddy simulations , 2002 .

[18]  Group velocity and reflection phenomena in numerical approximations of hyperbolic equations , 1983 .

[19]  Robert Vichnevetsky,et al.  Energy and group velocity in semi discretizations of hyperbolic equations , 1981 .

[20]  Jason Frank,et al.  On spurious reflections, nonuniform grids and finite difference discretizations of wave equations , 2004 .

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

[22]  Sharath S. Girimaji,et al.  Closure modeling in bridging regions of variable-resolution (VR) turbulence computations , 2013 .

[23]  Robert Vichnevetsky,et al.  Wave propagation and reflection in irregular grids for hyperbolic equations , 1987 .

[24]  Javier Jiménez,et al.  A critical evaluation of the resolution properties of B-Spline and compact finite difference methods , 2001 .

[25]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[26]  H. V. D. Ven.  A family of large eddy simulation (LES) filters with nonuniform filter widths , 1995 .

[27]  F. Grinstein,et al.  Large Eddy simulation of high-Reynolds-number free and wall-bounded flows , 2002 .

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

[29]  Alison L. Marsden,et al.  Construction of commutative filters for LES on unstructured meshes , 2000 .

[30]  J. Sochacki,et al.  On Taylor-series expansions of residual stress , 2001 .

[31]  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.

[32]  Parviz Moin,et al.  B-Spline Method and Zonal Grids for Simulations of Complex Turbulent Flows , 1997 .

[33]  Robert Vichnevetsky,et al.  Wave propagation analysis of difference schemes for hyperbolic equations: A review , 1987 .

[34]  Andrew W. Cook,et al.  Short Note: Hyperviscosity for shock-turbulence interactions , 2005 .

[35]  U. Ascher,et al.  Multisymplectic box schemes and the Korteweg{de Vries equation , 2004 .

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

[37]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[38]  F. Hamba.  Analysis of filtered Navier–Stokes equation for hybrid RANS/LES simulation , 2011 .

[39]  S. Haering.  Anisotropic hybrid turbulence modeling with specific application to the simulation of pulse-actuated dynamic stall control , 2015 .

[40]  P. Moin,et al.  The basic equations for the large eddy simulation of turbulent flows in complex geometry , 1995 .

[41]  R. Moser,et al.  Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions , 1991 .

[42]  L. Trefethen.  Group velocity in finite difference schemes , 1981 .

[43]  The nonlocal nature of internal reflection in computational fluid dynamics with spectral methods , 1991 .