## Customized data-driven RANS closures for bi-fidelity LES–RANS optimization

Zhang, Y., Dwight, R.P., Schmelzer, M., Gómez, J.F., Han, Z.-H., Hickel, S. (2021)*Journal of Computational Physics* 432: 110153. doi: 10.1016/j.jcp.2021.110153

Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework.

## An adaptive local deconvolution model for compressible turbulence

Hickel, S., Larsson, J. (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 large-eddy simulation applied to turbulent channel flow with periodic constrictions

Hickel, S., Kempe, T., Adams, N.A. (2008)*Theoretical and Computational Fluid Dynamics* 22: 227-242. doi: 10.1007/s00162-007-0069-7

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES).

## An adaptive local deconvolution method for implicit LES

Hickel, S., Adams, N.A., Domaradzki, J.A. (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

Adams, N.A., Hickel, S., Franz, S. (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

Hickel, S., Franz, S., Adams, N.A., Koumoutsakos, P. (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

Hickel, S., Adams, N.A. (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.