## An adaptive local deconvolution model for compressible turbulence

S. Hickel, J. Larsson (2008)

Proceedings of the 2008 Summer Program, Center for Turbulence Research, Stanford University.

The objective of this project was the analysis and the control of local truncation errors in large eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a non-linear discretization method is developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model which accurately represents the effects of unresolved turbulence.

## Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence

S. Hickel, N.A. Adams (2008)*International Journal of Heat and Fluid Flow* 29: 626-639. doi: 10.1016/j.ijheatfluidflow.2008.03.008

Well resolved large-eddy simulations (LES) of a fully turbulent flat-plate boundary-layer flow subjected to a constant adverse pressure gradient are conducted. Flow parameters are adapted to an available experiment. The Reynolds number based on the local free-stream velocity and momentum thickness is 670 at the inflow and 5100 at the separation point. Clauser’s pressure-gradient parameter increases monotonically from 0 up to approximately 100 since a constant pressure gradient is prescribed. The adverse pressure gradient leads to a highly unsteady and massive separation of the boundary layer. The numerical predictions agree well with theory and experimental data.

## Analysis of truncation errors and design of physically optimized discretizations

S. Hickel, N.A. Adams (2008) *Quality and Reliability of Large-Eddy Simulations*, Springer. doi: 10.1007/978-1-4020-8578-9_4

Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. In this paper, we explore how implicit SGS models can be derived systematically and propose a procedure for design, analysis, and optimization of nonlinear discretizations.

## On implicit subgrid-scale modeling in wall-bounded flows

S. Hickel, N.A. Adams (2007) *Physics of Fluids* 19: 105106. doi: 10.1063/1.2773765

Approaches to large eddy simulation where subgrid-scale model and numerical discretization are fully merged are called implicit large eddy simulation (ILES). Recently, we have proposed a systematic framework for development, analysis, and optimization of nonlinear discretization schemes for ILES [Hickel *et al.*, J. Comput. Phys. 213, 413(2006)]. The resulting adaptive local deconvolution method (ALDM) provides a truncation error which acts as a subgrid-scale model consistent with asymptotic turbulence theory. In the present paper ALDM is applied to incompressible, turbulent channel flow to analyze the implicit model for wall-bounded turbulence.

## Implicit subgrid-scale modeling for large-eddy simulation of passive-scalar mixing

S. Hickel, N.A. Adams, N.N. Mansour (2007)*Physics of Fluids* 19: 095102. doi: 10.1063/1.2770522

Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The name “implicit LES” is used for approaches that merge the SGS model and numerical discretization.

## Towards implicit subgrid-scale modeling by particle methods

S. Hickel, L. Weynans, N.A. Adams, G.-H. Cottet (2007) *European Series in Applied and Industrial Mathematics* 16: 77-88. doi: 10.1051/proc:2007014

The numerical truncation error of vortex-in-cell methods is analyzed a-posteriori through the effective spectral numerical viscosity for simulations of three-dimensional isotropic turbulence. The interpolation kernels used for velocity-smoothing and re-meshing are identified as the most relevant components affecting the shape of the spectral numerical viscosity as a function of wave number.

## An adaptive local deconvolution method for implicit LES

S. Hickel, N.A. Adams, J.A. Domaradzki (2006) *Journal of Computational Physics* 213: 413-436. doi: 10.1016/j.jcp.2005.08.017

The adaptive local deconvolution method (ALDM) is proposed as a new nonlinear discretization scheme designed for implicit large-eddy simulation (ILES) of turbulent flows. In ILES the truncation error of the discretization of the convective terms functions as a subgrid-scale model. Therefore, the model is implicitly contained within the discretization, and an explicit computation of model terms becomes unnecessary.

## Implicit subgrid-scale modeling by adaptive deconvolution

N.A. Adams, S. Hickel, S. Franz (2004)*Journal of Computational Physics* 200: 412-431. doi: 10.1016/j.jcp.2004.04.010

A new approach for the construction of implicit subgrid-scale models for large-eddy simulation based on adaptive local deconvolution is proposed. An approximation of the unfiltered solution is obtained from a quasi-linear combination of local interpolation polynomials. The physical flux function is modeled by a suitable numerical flux function. The effective subgrid-scale model can be determined by a modified-differential equation analysis.

## Implicit subgrid-scale modeling by adaptive local deconvolution

S. Hickel, N.A. Adams (2004) *Proceedings in Applied Mathematics and Mechanics* 4: 460-461. doi: 10.1002/pamm.200410211

A class of implicit Subgrid-Scale (SGS) models for Large-Eddy Simulation (LES) is obtained from a new approach for the finite-volume discretization of hyperbolic conservation laws. The extension of a standard deconvolution operator and the choice of a suitable numerical flux function result in a truncation error that can be forced to act as a physical turbulence model.