Implicit Large-Eddy Simulation: Theory and Application

Large-Eddy Simulation has been recognized as one of the major tools for the numerical simulation of complex turbulent flows, in events when more accessible alternative approaches, such as statistically averaged Navier-Stokes equations (Reynolds-averaged Navier-Stokes equations - RANS), fail. This is in particular the case, when complex flow phenomena (reaction, fluid-structure interaction, interfaces, shocks) introduce additional non-turbulent temporal or spatial scales. It is known since quite some time that the nonlinear truncation error of some classes of discretization schemes for the Navier-Stokes equations not only interferes with explicitly added subgrid-scale (SGS) models but also can provide some SGS closure when no model is added at all. More recent analyses of such schemes have outlined the way to a more systematic procedure for such no-model approaches, leading to what is called now implicit LES (ILES). With ILES no subgrid-scale model is added to the discretized Navier- Stokes equations, and SGS modeling is left solely to the numerical truncation error. In this contribution we will outline a theory of ILES which allows for physically motivated modeling of the nonlinear truncation error, called adaptive local deconvolution method (ALDM), and demonstrate its feasibility for reliable LES of a wide range of turbulent flow configurations.

[1]  L. Margolin,et al.  MPDATA: A Finite-Difference Solver for Geophysical Flows , 1998 .

[2]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[3]  Nikolaus A. Adams,et al.  Implicit subgrid-scale modeling for large-eddy simulation of passive-scalar mixing , 2007 .

[4]  P. Woodward,et al.  Inertial range structures in decaying compressible turbulent flows , 1998 .

[5]  Christer Fureby,et al.  From canonical to complex flows: Recent progress on monotonically integrated LES , 2004, Computing in Science & Engineering.

[6]  K. Kuwahara,et al.  Computation of high Reynolds number flow around a circular cylinder with surface roughness , 1984 .

[7]  P. Smolarkiewicz,et al.  Effective eddy viscosities in implicit large eddy simulations of turbulent flows , 2003 .

[8]  Nikolaus A. Adams,et al.  Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence , 2008 .

[9]  Piotr K. Smolarkiewicz,et al.  Multidimensional positive definite advection transport algorithm: an overview , 2006 .

[10]  P. Smolarkiewicz.  A Fully Multidimensional Positive Definite Advection Transport Algorithm with Small Implicit Diffusion , 1984 .

[11]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[12]  P. Sagaut,et al.  On the Use of Shock-Capturing Schemes for Large-Eddy Simulation , 1999 .

[13]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[14]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[15]  N. Adams,et al.  Implicit subgrid-scale modeling by adaptive deconvolution , 2004 .

[16]  P. Smolarkiewicz.  A Simple Positive Definite Advection Scheme with Small Implicit Diffusion , 1983 .

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

[18]  Robert D. Moser,et al.  Finite-volume optimal large-eddy simulation of isotropic turbulence , 2004 .

[19]  J. Larsson,et al.  An adaptive local deconvolution model for compressible turbulence , 2008 .

[20]  Nikolaus A. Adams,et al.  An adaptive local deconvolution method for implicit LES , 2005, J. Comput. Phys..

[21]  Nikolaus A. Adams,et al.  On implicit subgrid-scale modeling in wall-bounded flows , 2007 .

[22]  Nikolaus A. Adams,et al.  Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions , 2008 .

[23]  U. Schumann.  Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli , 1975 .