@misc{SchefflerStrehlerVargasKoch, author = {Scheffler, Robert and Strehler, Martin and Vargas Koch, Laura}, title = {Routing Games with Edge Priorities}, series = {ACM Transactions on Economics and Computation}, volume = {10}, journal = {ACM Transactions on Economics and Computation}, number = {1}, issn = {2167-8375}, doi = {10.1145/3488268}, pages = {1:1 -- 1:27}, language = {en} } @misc{BehrangStarickWheeleretal., author = {Behrang, Masoomeh and Starick, Tommy and Wheeler, Isaac and Schmidt, Heiko and Kerstein, Alan and Lignell, David}, title = {Hierarchical parcel-swapping representation of turbulent mixing : part 4 : extension to the viscous range and to mixing of scalars with non-unity Schmidt numbers}, series = {Journal of fluid mechanics}, volume = {1020}, journal = {Journal of fluid mechanics}, publisher = {Cambridge University Press}, address = {Cambridge}, issn = {0022-1120}, doi = {doi:10.1017/jfm.2025.10512}, pages = {1 -- 39}, abstract = {Hierarchical parcel swapping (HiPS) is a multiscale stochastic model of turbulent mixing based on a binary tree. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent eddies are represented by swapping subtrees. Lowest-level swaps change fluid parcel pairings, with new pairings instantly mixed. This formulation suitable for unity Schmidt number Sc is extended to non-unity Sc. For high Sc, the tree is extended to the Batchelor level, assigning the same time scale (governing the rate of swap occurrences) to the added levels as the time scale at the base of the Sc=3 tree. For low Sc, a swap at the Obukhov-Corrsin level mixes all parcels within corresponding subtrees. Well-defined model analogues of turbulent diffusivity, and mean scalar-variance production and dissipation rates are identified. Simulations idealising stationary homogeneous turbulence with an imposed scalar gradient reproduce various statistical properties of viscous-range and inertial-range pair dispersion, and of the scalar power spectrum in the inertial-advective, inertial-diffusive and viscous-advective regimes. The viscous-range probability density functions of pair separation and scalar dissipation agree with applicable theory, including the stretched-exponential tail shape associated with viscous-range scalar intermittency. Previous observation of that tail shape for Sc=1, heretofore not modelled or explained, is reproduced. Comparisons to direct numerical simulation allow evaluation of empirical coefficients, facilitating quantitative applications. Parcel-pair mixing is a common mixing treatment, e.g. in subgrid closures for coarse-grained flow simulation, so HiPS can improve model physics simply by smarter (yet nearly cost-free) selection of pairs to be mixed.}, language = {en} } @misc{BehrangStarickSchmidtetal., author = {Behrang, Masoomeh and Starick, Tommy and Schmidt, Heiko and Lignell, David O.}, title = {A C++ library for turbulent mixing simulation using Hierarchical Parcel Swapping (HiPS)}, series = {SoftwareX}, volume = {31}, journal = {SoftwareX}, publisher = {Elsevier BV}, address = {Amsterdam}, issn = {2352-7110}, doi = {10.1016/j.softx.2025.102331}, pages = {1 -- 7}, abstract = {Turbulence models are crucial for simulating flows at all scales, capturing both large-scale structures and small-scale mixing. Software libraries that implement such models should support modular integration, customization, and scalability across different simulation frameworks. This paper presents Hierarchical Parcel Swapping (HiPS), a C++ library documented with Doxygen and available on GitHub. HiPS supports both mixing and reactions and can be used as a standalone model or as a subgrid model in CFD simulations. The code includes examples for users to run it as a standalone model. Additionally, considerations for using it as a subgrid model are provided.}, language = {en} } @misc{KleinHaqueSchmidt, author = {Klein, Marten and Haque, Zubaer and Schmidt, Heiko}, title = {Map-based stochastic turbulence modeling for utilization in wind engineering}, series = {IFAC-PapersOnLine}, volume = {59}, journal = {IFAC-PapersOnLine}, number = {26}, publisher = {Elsevier BV}, address = {Amsterdam}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2025.12.046}, pages = {271 -- 276}, abstract = {Aeroelastic simulation tools provide means for modeling wind energy systems and their response to control actions, but these tools are notably limited by the representation of the atmospheric turbulence variability under changing conditions. The objective of this study is to assess the potential for more realistic fluctuation modeling by utilizing stochastic one-dimensional turbulence (ODT). As preliminary step towards control-oriented applications, wind speed fuctuations generated by ODT are compared to those from a state-of-the-art model, such as TurbSim. It is demonstrated that weak excursions are statistically similar, whereas ODT offers a broader variability range and enhanced turbulence intermittency features.}, language = {en} } @misc{YapKleinMedinaMendezetal., author = {Yap, Li Toong and Klein, Marten and Medina M{\´e}ndez, Juan A. and Schmidt, Heiko}, title = {Towards an improved wall function formulation for Reynolds-Averaged Navier-Stokes simulations of turbulent concentric coaxial pipe flows}, series = {Proceedings in applied mathematics and mechanics : special issue: 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, volume = {25}, journal = {Proceedings in applied mathematics and mechanics : special issue: 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, number = {4}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.70025}, pages = {1 -- 7}, abstract = {Concentric coaxial (annular) pipe flow is numerically investigated using a high Reynolds number (HRN) Reynolds-Averaged Navier-Stokes (RANS) approach, given direct numerical simulation (DNS) boundary conditions. Previous work has shown that traditional wall models fail in predicting bulk quantities due to insufficient representation of the inner wall. The main objective is to assess the suitability of RANS for prediction of the flowfield if a wall function that captures the effect of the inner wall spanwise curvature at small radius ratios is provided. As a starting point, the mixing length model is used as the RANS turbulence model. The results suggest that while improved mean flow statistics can potentially be obtained, an accurate wall model representation is insufficient for capturing the mean flow in terms of the location of the velocity maximum properly.}, language = {en} } @misc{JoshiKleinSchmidt, author = {Joshi, Abhishek and Klein, Marten and Schmidt, Heiko}, title = {Non-negligible influence of forcing mechanisms on turbulent mixing at low Reynolds numbers : a one-dimensional turbulence study}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {26}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {https://doi.org/10.1002/pamm.70073}, pages = {1 -- 11}, abstract = {This study presents a numerical investigation of passive scalar mixing in homogeneous isotropic turbulence (HIT). Different volumetric forcing schemes have been used in the literature, but the side effects are rarely discussed, either because these are assumed irrelevant or because it is too costly to conduct such an analysis with a high-fidelity model. In this study, we have used One-Dimensional Turbulence (ODT) model to compare forcing schemes at low Reynolds numbers. Our analysis reveals critical flaws in the linear forcing model when applied to ODT. While both schemes exhibit spectral deviations from direct numerical simulation (DNS), the stochastic forcing scheme demonstrates superior dynamic fidelity, better capturing the turbulent energy cascade. In contrast, the linear forcing scheme suffers from a non-physical energy deficit at large scales and is approximately 10 times more computationally expensive. These artefacts directly impact scalar mixing: The stochastic scheme produces classic, multi-scale intermittency, whereas linear forcing generates extreme gradients confined only at the dissipative scales. These results demonstrate that the choice of forcing is a critical modelling decision in ODT, leading to fundamentally different model-dependent artifacts in both turbulence dynamics and scalar mixing statistics, at least in low Reynolds number regimes.}, language = {en} }