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.
A proposed simplification of the adaptive local deconvolution method
S. Hickel, N.A. Adams (2006)
European Series in Applied and Industrial Mathematics 16: 66-76. doi: 10.1051/proc:2007008
The adaptive local deconvolution method (ALDM) [Hickel, Adams and Domaradzki. J. Comp. Phys., 213:413436, 2006] provides a systematic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Subject of the present paper is a modification of the numerical algorithm that allows for reducing the amount of computational operations without affecting the quality of the results.
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.
Optimization of an implict subgrid-scale model for LES
S. Hickel, S. Franz, N.A. Adams, P. Koumoutsakos (2004)
Proceedings of XXI ICTAM, 15–21 August 2004, Warsaw, Poland.
We give a summary of the derivation of an implicit subgrid-scale model for LES which is obtained from a new approach for the approximation of hyperbolic conservation laws. Adaptive local deconvolution is performed using a quasi-linear solution-adaptive combination of local interpolation polynomials. The physical flux function is substituted by a suitable numerical flux function. The truncation error has physical significance and effectively acts as subgrid-scale model. It can be determined by a modified-differential-equation analysis and is adjustable through free parameters. Computational results for Burgers equation show that the model with parameters identified by evolutionary optimization give significantly better results than other models.
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.