## On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves

Muraschko, J., Fruman, M.D., Achatz, U., Hickel, S., Toledo, Y. (2015) *Quarterly Journal of the Royal Meteorological Society* 141: 676-697. doi: 10.1002/qj.2381

The dynamics of internal gravity waves is modelled using Wentzel–Kramer–Brillouin (WKB) theory in position–wave number phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and time-dependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves.

## Numerical simulation of a Richtmyer-Meshkov instability with an adaptive central-upwind 6th-order WENO scheme

Tritschler, V.K., Hu, X.Y., Hickel, S., Adams, N.A. (2013) *Physica Scripta *2013: 014016. doi: 10.1088/0031-8949/2013/T155/014016

Two-dimensional simulations of the single-mode Richtmyer–Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005).

## A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization

Rieper, F., Hickel, S., Achatz, U. (2013)*Monthly Weather Review* 141: 861-886. doi: 10.1175/MWR-D-12-00026.1

Durran’s pseudo-incompressible equations are integrated in a mass and momentum conserving way with a new implicit turbulence model. This system is soundproof, which has two major advantages over fully compressible systems: the Courant–Friedrichs–Lewy (CFL) condition for stable time advancement is no longer dictated by the speed of sound and all waves in the model are clearly gravity waves (GW).

## An innovative approach to thermo-fluid-structure interaction based on an immersed interface method and a monolithic thermo-structure interaction algorithm

Grilli, M., Hickel, S., Adams, N.A., Hammerl, G., Danowski, C., Wall, W.A. (2012) * *

*AIAA paper*2012-3267. doi: 10.2514/6.2012-3267

We present a loosely-coupled approach for the solution of the thermo-fluid-structure interaction problem, based on Dirichlet-Neumann partitioning. A cartesian grid finite volume scheme, with conservative interface method is used for the fluid and a finite-element scheme for the thermo-structure problem. Special attention is given to the transfer of forces, temperatures and to the structural positions.

## Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics

Lauer, E., Hu, X.Y., Hickel, S., Adams, N.A. (2012) *Computers and Fluids* 69: 1-19. doi: 10.1016/j.compfluid.2012.07.020

In this paper, we investigate the high-speed dynamics of symmetric and asymmetric cavitation bubble-collapse. For this purpose, a sharp-interface numerical model is employed, that includes a numerically efficient evaporation/condensation model.

## A parametrized non-equilibrium wall-model for large-eddy simulations

Hickel, S., Touber, E., Bodart, J, Larsson, J. (2012)

Proceedings of the 2012 Summer Program, Center for Turbulence Research, Stanford University.

Wall-models are essential for enabling large-eddy simulations of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall- model while still solving only wall-normal ODEs.

## Implicit Large Eddy Simulation of cavitation in micro channel flows

Hickel, S., Mihatsch, M., Schmidt S.J. (2011)

In *proceedings of the WIMRC 3rd International Cavitation Forum* ; Warwick, UK.; ISBN 978-0-9570404-1-0. arXiv: 1401.6548

We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben *et al. *(2010).

## Wall modeling for implicit large-eddy simulation and immersed-interface methods

Chen, Z.L., Hickel, S., Devesa, A., Berland, J., Adams, N.A. (2013) *Theoretical and Computational Fluid Dynamics *28: 1-21. doi: 10.1007/s00162-012-0286-6

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations.

## A conservative immersed interface method for large-eddy simulation of incompressible flows

Meyer, M., Devesa, A., Hickel, S., Hu, X.Y., Adams, N.A. (2010) *Journal of Computational Physics* 229: 6300-6317. doi: 10.1016/j.jcp.2010.04.040

We propose a conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid. The method is based on a finite-volume discretization of the incompressible Navier–Stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained.

## Assessment of implicit large-eddy simulation with a conservative immersed interface method for turbulent cylinder flow

Meyer, M., Hickel, S., Adams, N.A. (2010) *International Journal of Heat and Fluid Flow* 31: 368-377. doi: 10.1016/j.ijheatfluidflow.2010.02.026

The success of Large-Eddy Simulations (LES) of wall-bounded turbulence depends strongly on an accurate representation of the flow near the boundaries. Since in implicit LES the truncation error of the numerical discretization itself functions as SGS model, the order of accuracy of the discretization should be maintained near the boundary. In this paper, we analyze the performance of implicit LES for predicting turbulent flows along complex geometries.

## 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.

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

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

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

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

Hickel, S., Weynans, L., Adams, N.A., Cottet, G.-H. (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

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

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 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.