## GPU-accelerated simulations for eVTOL aerodynamic analysis

Pasquariello, V., Bunk, Y., Eberhardt, S., Huang, P.-H., Matheis, J., Ugolotti, M., Hickel, S. (2023)

AIAA Scitech paper 2023-2107. doi: 10.2514/6.2023-2107

The demand for fast, high-fidelity, scale-resolving computational fluid dynamics (CFD) simulations is continuously growing. Especially new emerging aviation technologies, such as electrical vertical take-off and landing aircraft (eVTOL), strongly rely on advanced numerical methods to retain development life-cycle costs and achieving design targets more quickly. This paper presents a cutting-edge large-eddy simulations (LES) solver developed to enable over-night turnaround times for full aircraft simulations on advanced graphics processing unit (GPU) architectures.

## An enhanced algorithm for online Proper Orthogonal Decomposition and its parallelization for unsteady simulations

Li, X., Hulshoff, S., Hickel, S. (2022)*Computers & Mathematics with Applications* 126: 43-59. doi: 10.1016/j.camwa.2022.09.007

We present an enhanced online algorithm based on incremental Singular Value Decomposition (SVD), which can be used to efficiently perform a Proper Orthogonal Decomposition (POD) analysis on the fly. The proposed enhanced algorithm for modal analysis has significantly better computational efficiency than the standard incremental SVD and good parallel scalability, such that the strong reduction of computational cost is maintained in parallel computations.

## Verification and Validation of Immersed Boundary Solvers for Hypersonic Flows with Gas-Surface Interaction

Baskaya, A.O., Capriati, M., Ninni, D., Bonelli, F., Pascazio, G., Turchi, A., Magin T., Hickel, S. (2022)*AIAA Aviation Forum, Chicago*. AIAA paper 2022-3276. doi: 10.2514/6.2022-3276

Verification and validation results of two immersed boundary solvers, INCA and CHESS, for atmospheric entry flows characterized by complex fluid thermochemistry and gas-surface interactions (GSI) are presented. Results are compared with those obtained with the body-conforming solver US3D, which is coupled to the same external thermochemistry library, Mutation++, as INCA and CHESS. In these campaigns, the INCA solver has shown an almost perfect agreement with the body-conforming reference solver and other reference results from literature.

## Adaptive reduced-order modeling for non-linear fluid-structure interaction

Thari, A., Pasquariello, V., Aage, N., Hickel, S. (2021) *Computers and Fluids* 229: 105099. doi: 10.1016/j.compfluid.2021.105099

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid–structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance equations. Upon each linearization step, the number of unknowns is strongly decreased by using modal reduction, which leads to a substantial gain in computational efficiency.

## Towards adjoint-based mesh refinement for Large Eddy Simulation using reduced-order primal solutions: Preliminary 1D Burgers study

Li, X., Hulshoff, S., Hickel, S. (2021) *Computer Methods in Applied Mechanics and Engineering* 379: 113733. doi: 10.1016/j.cma.2021.113733

Adaptive Mesh Refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). When combined with adjoint methods, which are able to localize error contributions, AMR can generate meshes that are optimal for computing a physical quantity of interest (e.g. lift or drag).

## 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.

## Rapid multi-component phase-split calculations using volume functions and reduction methods

Fathi, M., Hickel, S. (2021) *AIChE Journal *67: e17174. doi: 10.1002/aic.17174

We present a new family of fast and robust methods for the calculation of the vapor–liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy.

## Effectivity and efficiency of selective frequency damping for the computation of unstable steady-state solutions

Casacuberta, J., Groot, K.J., Tol, H.J., Hickel, S. (2018)*Journal of Computational Physics *375: 481-497. doi: 10.1016/j.jcp.2018.08.056

Selective Frequency Damping (SFD) is a popular method for the computation of globally unstable steady-state solutions in fluid dynamics. The approach has two model parameters whose selection is generally unclear. In this article, a detailed analysis of the influence of these parameters is presented, answering several open questions with regard to the effectiveness, optimum efficiency and limitations of the method.

## Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A

Matheis, J., Hickel, S. (2018) *International Journal of Multiphase Flow *99: 294-311. doi: 10.1016/j.ijmultiphaseflow.2017.11.001

We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component subcritical two-phase states via a homogeneous mixture approach.

## Multi-component vapor-liquid equilibrium model for LES and application to ECN Spray A

Matheis, J., Hickel, S. (2016)

Proceedings of the 2016 Summer Program, Center for Turbulence Research, Stanford University. (also available online on arXiv:1609.08533)

We present and evaluate a detailed multi-species two-phase thermodynamic equilibrium model for large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model can represent the coexistence of supercritical states and multi-component subcritical two-phase states.

## Large-eddy simulation of nitrogen injection at trans- and supercritical conditions

Müller, H., Niedermeier, C., Matheis, J., Pfitzner, M., Hickel, S. (2016) *Physics of Fluids* 28: 015102. doi: 10.1063/1.4937948

Large-eddy simulations (LES) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of different SGS models — the Smagorinsky model, the Vreman model, and the adaptive local deconvolution method — shows that the representation of turbulence on the resolved scales has a notable effect on the location of jet break-up, whereas the particular modeling of unresolved scales is less important for the overall mean flow field evolution. More important are the models for the fluid’s thermodynamic state.

## Efficient implicit LES method for the simulation of turbulent cavitating flows

Egerer, C.P., Schmidt, S.J., Hickel, S., Adams, N.A. (2016) *Journal of Computational Physics* 316: 453-469. doi: 10.1017/10.1016/j.jcp.2016.04.021

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells).

## A cut-cell finite volume-finite element coupling approach for fluid-structure interaction in compressible flow

Pasquariello, V., Hammerl, G., Örley, F., Hickel, S., Danowski, C., Popp, A., Wall, W.A., Adams, N.A. (2016) *Journal of Computational Physics* 307: 670-695. doi: 10.1016/j.jcp.2015.12.013

We present a loosely coupled approach for the solution of fluid–structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet–Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface.

## Volume translation methods for real-gas computational fluid dynamics simulations

Matheis, J., Müller, H., Lenz, C., Pfitzner, M., Hickel, S. (2016) *Journal of Supercritical Fluids* 107: 422-432.
doi: 10.1016/j.supflu.2015.10.004

We report on recent developments within the field of real gas thermodynamics models with particular emphasis on volume translation methods for cubic equations of state. On the basis of the generalized form of a cubic equation of state, a mathematical framework for applying volume translations is provided, allowing for an unified and thermodynamically consistent formulation in the context of computational fluid dynamics simulations.

## Assessing the numerical dissipation rate and viscosity in numerical simulations of fluid flows

Schranner, F., Domaradzki, J.A., Hickel, S., Adams, N.A. (2015) *Computers and Fluids* 114: 84-97. doi:10.1016/j.compfluid.2015.02.011

We propose a method for quantifying the effective numerical dissipation rate and effective numerical viscosity in Computational Fluid Dynamics (CFD) simulations. Different from previous approaches that were formulated in spectral space, the proposed method is developed in a physical-space representation and allows for determining numerical dissipation rates and viscosities locally, that is, at the individual cell level, or for arbitrary subdomains of the computational domain.

## Finite-volume models with implicit subgrid-scale parameterization for the differentially heated rotating annulus

Borchert, S., Achatz, U., Remmler, S., Hickel, S., Harlander, U., Vincze, M., Alexandrov, K.D., Rieper, F., Heppelmann, T., Dolaptchiev, S.I. (2014) *Meteorologische Zeitschrift* 23: 561-580. doi: 10.1127/metz/2014/0548

The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment, measured at the BTU Cottbus-Senftenberg, are used to validate two numerical finite-volume models (INCA and cylFloit) which differ basically in their grid structure.

## Cut-element based immersed boundary method for moving geometries in compressible liquid flows with cavitation

Örley, F., Pasquariello, V., Hickel, S., Adams, N.A. (2015) *Journal of Computational Physics* 283: 1-22. doi: 10.1016/j.jcp.2014.11.028

The conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on Cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries. We demonstrate that an approximation of moving interfaces by a level-set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water. By introducing an exact reconstruction of the cut-cell properties directly based on a surface triangulation of the immersed boundary, we are able to recover the correct flow evolution free of numerical artifacts.

## Subgrid-scale modeling for implicit Large Eddy Simulation of compressible flows and shock turbulence interaction

Hickel, S., Egerer, C.P., Larsson, J. (2014)*Physics of Fluids* 26: 106101. doi: 10.1063/1.4898641

## On the Richtmyer-Meshkov instability evolving from a deterministic multimode planar interface

Tritschler, V., Olson, B., Lele, S., Hickel, S., Hu, X.Y., Adams, N.A. (2014)*Journal of Fluid Mechanics *755, 429-462. doi: 10.1017/jfm.2014.436

We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer–Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma = 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Well-resolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour.

## 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.