TY - GEN A1 - Klein, Marten A1 - Starick, Tommy A1 - Zenker, Christian A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Reduced order stochastic modeling of turbulent mixing based on conservative baker’s maps T2 - Proceedings of the 14th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM-14) N2 - The detailed numerical representation of turbulent mixing processes is a standing challenge for non-premixed chemically reacting flows. The full range of relevant flow scales needs to be captured and it is also necessary to distinguish turbulent advective from molecular diffusive processes in order to represent Reynolds and Schmidt number effects. These requirements are addressed here by utilizing two different map-based stochastic turbulence modeling strategies. The one-dimensional turbulence (ODT) model utilizes event-based turbulence modeling, whereas the hierarchical parcel-swapping (HiPS) model is a fully event-based mixing model. ODT provides full-scale resolution at affordable costs by dimensional model reduction based on the boundary-layer approximation to shear flow. HiPS is far less costly than ODT but currently limited to locally homogeneous isotropic turbulence. The physics-compatible modeling capabilities with respect to phase-space representation of turbulent mixing are demonstrated for two canonical cases using standalone model formulations. KW - turbulent mixing KW - one-dimensional turbulence (ODT) KW - hierarchical parcel swapping (HiPS) KW - stochastic turbulence modeling KW - round jet KW - passive scalar Y1 - 2023 UR - https://etmm.ercoftac.org/etmm/program/conference-program/ UR - https://drive.google.com/file/d/1q2BDOO5bXfqq0Y4z4HCGndiFI033bPyg/view?usp=drive_link SP - 613 EP - 618 PB - ERCOFTAC CY - Barcelona, Spain ER - TY - GEN A1 - Vallem, Rishindra A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Numerical modeling and simulation of two-phase internal flow instabilities using Smoothed Particle Hydrodynamics (SPH) T2 - STAB Jahresbericht 2023 KW - Smoothed Particle Hydrodynamics (SPH) KW - Kelvin-Helmholtz instability KW - linear stability analysis KW - two-phase flow Y1 - 2023 UR - https://www.dlr.de/as/Portaldata/5/Resources/dokumente/veranstaltungen/stab_workshop/Jahresbericht2023.pdf UR - https://www.dlr.de/as/desktopdefault.aspx/tabid-128/268_read-1678/ VL - 21/2023 SP - 158 EP - 159 PB - Deutsche Strömungsmechanische Arbeitsgemeinschaft (STAB) CY - Göttingen, Germany ER - TY - GEN A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Stochastic modeling of asymmetric turbulent boundary layers in annular pipe flow Y1 - 2023 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Tsai_2023_poster_PragueSummerSchoolX.pdf U6 - https://doi.org/10.13140/RG.2.2.18789.78567 N1 - Stochastics in Fluids Summer School and Workshop 2023, Czech Academy of Sciences Institute of Mathematics, Prague, Czech Republic ER - TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Stochastic modeling of electrohydrodynamically enhanced drag in one-way and fully coupled turbulent Poiseuille and Couette flow T2 - Technische Mechanik N2 - Joint predictive modeling of hydrodynamics and electrokinetics is a standing numerical challenge but crucial for various applications in electrochemistry and power engineering. The present lack in modeling of electrohydrodynamic (EHD) turbulent flows lies in the treatment of small-scale processes and scale interactions. To overcome these limitations, a stochastic one-dimensional turbulence (ODT) model is utilized. The model aims to resolve all scales of the flow, but only on a notional line-of-sight, modeling turbulent advection by a stochastically sampled sequence of eddy events that punctuate deterministic molecular diffusive advancement. In this study, two canonical flow configurations are investigated that address different coupling strategies and flow physics. First, EHD effects in a variable-density vertical pipe flow of an ideal gas with an inner concentric electrode are investigated with a one-way coupled model formulation. Electric fields are generated by means of a corona discharge and the corresponding effect of a fixed ionic charge density field. Second, in order to reduce physical complexity, EHD effects the turbulent boundary layers in plane Couette flow of an isothermal univalent ionic liquid are investigated with a fully coupled model formulation. Both application cases demonstrate that ODT has predictive capabilities due to multiscale resolution of transport processes. Present results suggest that more expensive fully than one-way coupling of electrokinetics is crucial when charge relaxation times are significantly larger than the mean advection time scale. KW - turbulent drag enhancement KW - electrohydrodynamic turbulence KW - high Schmidt number KW - multiphysical boundary layers KW - one-dimensional turbulence Y1 - 2023 U6 - https://doi.org/10.24352/UB.OVGU-2023-049 SN - 0232-3869 N1 - This article is part of the "Special Issue for CMFF’22". VL - 43 IS - 1 SP - 111 EP - 127 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Capturing features of turbulent Ekman–Stokes boundary layers with a stochastic modeling approach T2 - Advances in Science and Research N2 - Atmospheric boundary layers (ABLs) exhibit transient processes on various time scales that range from a few days down to seconds, with a scale separation of the large-scale forcing and the small-scale turbulent response. One of the standing challenges in modeling and simulation of ABLs is a physically based representation of complex multiscale boundary layer dynamics. In this study, an idealized time-dependent ABL, the so-called Ekman–Stokes boundary layer (ESBL), is considered as a simple model for the near-surface flow in the mid latitudes and polar regions. The ESBL is driven by a prescribed temporal modulation of the bulk–surface velocity difference. A stochastic one-dimensional turbulence (ODT) model is applied to the ESBL as standalone tool that aims to resolve all relevant scales of the flow along a representative vertical coordinate. It is demonstrated by comparison with reference data that ODT is able to capture relevant features of the time-dependent boundary layer flow. The model predicts a parametric enhancement of the bulk–surface coupling in the event of a boundary layer resonance when the flow is forced with the local Coriolis frequency. The latter reproduces leading order effects of the critical latitudes. The model results suggest that the bulk flow decouples from the surface for high forcing frequencies due to a relative increase in detached residual turbulence. KW - turbulent boundary layer KW - stochastic modeling KW - periodic forcing KW - one-dimensional turbulence KW - rotating flow Y1 - 2023 UR - https://asr.copernicus.org/articles/20/55/2023/ U6 - https://doi.org/10.5194/asr-20-55-2023 SN - 1992-0636 SN - 1992-0628 N1 - This article is part of the special issue “EMS Annual Meeting: European Conference for Applied Meteorology and Climatology 2022”. N1 - This research is supported by the German Federal Government, the Federal Ministry of Education and Research and the State of Brandenburg within the framework of the joint project EIZ: Energy Innovation Center with funds from the Structural Development Act (Strukturstärkungsgesetz) for coal-mining regions. VL - 20 SP - 55 EP - 64 ER - TY - GEN A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Schöps, Mark Simon A1 - Schmidt, Heiko T1 - Predicting volatile wind energy: Stochastic forward modeling and machine learning T2 - 86. Jahrestagung der DPG (86th Annual Conference of the DPG), DPG-Frühjahrstagung 2023, (DPG Spring Meeting 2023 of the Matter and Cosmos Section (SMuK), 20-24 March 2023, Technische Universität Dresden Y1 - 2023 UR - https://smuk23.dpg-tagungen.de/programm/assets/verhandlungen-smuk23.pdf UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_dpg23.pdf SN - 2751-0522 SP - S. 343 PB - Deutsche Physikalische Gesellschaft CY - Bad Honnef ER - TY - GEN A1 - Tsai, Pei‐Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Stochastic modeling and theoretical analysis of weakly heated concentric coaxial pipe flows at low prandtl number T2 - Proceedings in Applied Mathematics and Mechanics N2 - Heated concentric coaxial (annular) pipe flows are numerically investigated by a stochastic one‐dimensional turbulence (ODT) model. The main objective of this work is to more accurately predict the heat transfer in tubular heat exchangers at low Prandtl numbers by extending the analysis for weak temperature fluctuations as recently introduced in Tsai et al., Proceedings in Applied Mathematics and Mechanics, 23:e202300167, 2023. The ODT model offers the required predictive capabilities at affordable cost by providing full‐scale resolution of viscous, conductive, and turbulent advective transport processes along a representative radial coordinate. The Prandtl numbers and are considered for which the radius ratio of the annular pipe and the Reynolds number are varied. Numerical results demonstrate that the geometry (radius ratio) has a significant influence on the thermal boundary layer that emerges over the inner and outer curved wall, respectively. Application of boundary layer theory and mixing length arguments yield an analytical expression that includes both Reynolds number and curvature effects. Unknown closure coefficients are estimated with ODT, providing a physically based correlation for the Nusselt number. KW - Turbulent pipe flow KW - Coaxial heat exchanger KW - Low Prandtl number KW - Boundary layer theory KW - Mixing-length theory Y1 - 2025 U6 - https://doi.org/10.1002/pamm.70006 SN - 1617-7061 VL - 25 IS - 1 SP - 1 EP - 7 PB - Wiley CY - Weinheim ER - TY - GEN A1 - Marinković, Pavle A1 - Medina, Juan A. A1 - Schöps, Mark Simon A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Experiences from the bottom‐up development of an object‐oriented CFD solver with prospective hybrid turbulence model applications T2 - Proceedings in Applied Mathematics and Mechanics N2 - In this work, we discuss recent experiences related to the development and enhancement of a hybrid stochastic computational fluid dynamics (CFD) solver, the C++ version of the Implicit/Explicit (IMEX) time‐advancement algorithm used in the one‐dimensional turbulence‐based (ODT) large eddy simulation (LES) model, abbreviated as ODTLES. After being ported from Fortran 90, the current capabilities of the C++ code are restricted to the reproducibility of turbulent channel flow simulations with respect to the former Fortran code version that was able to achieve reasonable agreement with available reference direct numerical simulation (DNS) for low to moderate Reynolds number turbulent channel flows. This is far from satisfactory so that current efforts are centered on improving the solver code structure through comprehensive refactoring, robust unit testing, and strict adherence to code style guides, following the principles of Clean Code. We focus the discussion on a methodology to balance unit, regression, and integration testing, here for the LES component of the code. The objective is to frame a starting point that is relevant also for other CFD codes, irrespective of whether they utilize conventional or novel discretization or flow modeling approaches. KW - Computational fluid dynamics (CFD) KW - Solver development KW - Software maintainabilit KW - Software dependability KW - Large-eddy simulation (LES) KW - Stochastic subgrid scale modeling Y1 - 2025 U6 - https://doi.org/10.1002/pamm.202400190 SN - 1617-7061 VL - 25 IS - 1 PB - Wiley ER - TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Simulating Volatile Wind Energy: Stochastic Forward Modeling and Machine Learning N2 - The transformation of the energy sector is based on the integration of various renewable sources, such as wind and solar energy. One of the key challenges for the integration of these sources into the existing power grid is their erratic and sometimes discontinuous availability (volatility). Wind energy is one of the most relevant sources of CO2 neutral electric energy, but volatile due to fluctuating wind fields on multiple scales. This has already been realized so that senors provide real-time information on the scale of individual wind turbines. However, fore- casting remains an unresolved problem since numerical weather prediction models cannot provide the necessary level of detail. New modeling strategies are required that integrate turbine-scale and meso-scale information for accurate site-specific short-term prediction. Present and forthcoming research aims to incorporate fluctuations on multiple levels of fidelity, depending on the abstraction layer KW - AI transfer KW - AI teaching KW - stochastic modeling KW - machine learning KW - wind energy KW - volatility modeling and prediction Y1 - 2022 UR - https://ai-science-atlas.innohub13.de/files/pdf/NSGSimulatingVolatileWindEnergyBTUpdf.pdf UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_KI-Atlas22.pdf PB - Innovation Hub 13, TH Wildau CY - Wildau ER - TY - GEN A1 - Li, Hanchen A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Simulation of radiatively driven mixing in a smoke cloud using "one-dimensional turbulence" N2 - Large-eddy simulations (LESs) are known to significantly overestimate entrainment in cloud-topped boundary layers, negatively impacting predictions on cloud mass and cover. This overestimation stems from coarse model resolutions that lead to numerical broadening of the entrainment layer. While it has been shown in direct numerical simulations (DNSs) that down-to-centimetre-scale resolutions can mitigate this issue, such high resolutions are not viable for most applications in the atmospheric sciences. The one-dimensional turbulence model (ODT), introduced by Kerstein [1], offers a computationally efficient alternative that provides full-scale resolution along a 1-D vertical domain. Molecular diffusion is explicitly resolved, while turbulent advection is modelled through a stochastically sampled sequence of spatial mappings, known as eddy events. Physically plausible eddy events are selected based on their current kinetic and potential energy. This allows an accurate representation of local turbulence properties and their dynamical complexity by evolving instantaneous property profiles. This study applies ODT to investigate cloud-top turbulent mixing processes driven by radiative cooling in a smoke cloud, benchmarking the results against DNS. Building on the preliminary findings by Meiselbach [2], we demonstrate improvements in mean profiles and turbulent fluxes of buoyancy and smoke concentration, showing ODT's ability to reproduce salient features observed in DNSs. In addition, we explore convective boundary layer scalings at extended Reynolds and Richardson numbers beyond those accessible in DNS studies. References: [1] A. R. Kerstein, Journal of Fluid Mechanics 392, 277334 (1999). [2] F. T. Meiselbach, Application of ODT to Turbulent Flow Problems, doctoral thesis, BTU Cottbus-Senftenberg (2015). Y1 - 2025 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Li_2025_poster_EGU.pdf U6 - https://doi.org/10.5194/egusphere-egu25-9491 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Investigating cutoff scales in turbulent Ekman flow with a map-based stochastic modeling approach N2 - The Ozmidov scale marks the cutoff scale above which overturning fluid motions in stably stratified shear flows are energetically prohibited. A recent study of a turbulent shear layer demonstrates that the Corrsin scale provides an intrinsic cutoff scale when stratification is absent [1]. For the neutral boundary layer, it is proposed by analogy to the mixing layer that the cutoff scale is linked to the Corrsin scale rather than the unbounded Ozmidov scale. The claim is numerically investigated for turbulent Ekman flow with the aid of Kerstein’s one-dimensional turbulence (ODT) model [2], utilizing the case setup described in [3]. ODT offers full-scale resolution along a vertical coordinate by autonomously evolving the instantaneous property profiles. Molecular diffusion is directly resolved, whereas turbulent advection is modeled by a stochastic process that is formulated with the aid of spatial mapping events, which are sampled based on the local available energy. In this model formulation, a cutoff scale is economically prescribed by limiting the sampling range of turbulent scales. Model results in terms of low-order and detailed turbulence statistics will be presented and compared to available reference data and theoretical analysis. References [1] F. G. Jacobitz and K. Schneider. Phys. Rev. Fluids 9:044602, 2024. [2] A. R. Kerstein and S. Wunsch. Bound.-Lay. Meteorol. 118:325–356, 2006. [3] M. Klein and H. Schmidt. Adv. Sci. Res. 19:117–136, 2022. Y1 - 2025 UR - https://presentations.copernicus.org/EGU25/EGU25-13495_presentation-h326475.pdf U6 - https://doi.org/10.5194/egusphere-egu25-13495 PB - Copernicus GmbH CY - Göttingen ER - TY - GEN A1 - Marinkovic, Pavle A1 - Medina, Juan A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Application of extended large-eddy simualtion (XLES) to turbulent channel flow T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - Extended large-eddy simulation (XLES) offers a promising middle ground between computational efficiency and predictive accuracy in turbulent flow simulations. By integrating the one-dimensional turbulence model as a stochastic subgrid-scale approach, XLES autonomously resolves turbulent microscales in a dimensionally reduced setting. Our implementation employs a coarse grid solely for pressure calculations, while three specialized high-resolution grids handle the turbulence dynamics. This multi-scale architecture reduces computational requirements by approximately two orders of magnitude compared to direct numerical simulation while maintaining comparable accuracy. Our results for turbulent channel flow at Reynolds number 395 demonstrate that XLES with a base resolution of just cells closely matches DNS reference data, vastly outperforming implicit LES using identical resolution and discretization schemes. This updated implementation of XLES, though still under active development, demonstrates significant potential for accurately simulating wall-bounded turbulent flows while substantially reducing computational requirements compared to traditional high-fidelity approaches. Y1 - 2025 U6 - https://doi.org/10.1002/pamm.70010 SN - 1617-7061 VL - 25 : special issue : 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) IS - 2 SP - 1 EP - 7 PB - Wiley CY - Weinheim ER -