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<export-example>
  <doc>
    <id>28365</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject_noref</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2022-01-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Using Hips As a New Mixing Model to Study Differential Diffusion of Scalar Mixing in Turbulent Flows</title>
    <abstract language="eng">Mixing two or more streams is ubiquitous in chemical processes and industries involving turbulent liquid or gaseous flows. Modeling turbulent mixing flows is complicated due to a wide range of time and length scales, and non-linear processes, especially when reaction is involved. On the other hand, in turbulent reacting flows, sub-grid scales need to be resolved accurately because they involve reactive and diffusive transport processes. Transported PDF methods use mixing models to capture the interaction in the sub-grid scales. Several models have been used with varying success. In this study, we present a novel model for simulation of turbulent mixing called Hierarchical Parcel Swapping (HiPS). The HiPS model is a stochastic mixing model that resolves a full range of time and length scales with the reduction in the complexity of modeling turbulent reacting flows. This model can be used as a sub-grid mixing model in PDF transport methods, as well as a standalone model. HiPS can be applied to transported scalars with variable Schmidt numbers to capture the effect of differential diffusion which is important for modeling scalars with low diffusivity like soot. We present an overview of the HiPS model, its formulation for variable Schmidt number flows, and then present results for evaluating the turbulence properties including the scalar energy spectra, the scalar dissipation rate, and Richardson dispersion. These model developments are an important step in applying HiPS to more complex flow configurations.</abstract>
    <parentTitle language="eng">2021 AIChE Annual Meeting</parentTitle>
    <identifier type="url">https://plan.core-apps.com/aiche2021/event/002309c77cf108fff1a6a8a101a07ebd</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.source">publish</enrichment>
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    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Alan R.</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <submitter>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </submitter>
    <author>
      <firstName>David O.</firstName>
      <lastName>Lignell</lastName>
    </author>
    <author>
      <firstName>Heiko</firstName>
      <lastName>Schmidt</lastName>
    </author>
    <author>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </author>
    <author>
      <firstName>Isaac</firstName>
      <lastName>Wheeler</lastName>
    </author>
    <author>
      <firstName>Masoomeh</firstName>
      <lastName>Behrang</lastName>
    </author>
    <collection role="institutes" number="3504">FG Numerische Strömungs- und Gasdynamik</collection>
  </doc>
  <doc>
    <id>30238</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>7</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject_ref</type>
    <publisherName>Department of Fluid Mechanics, University of Technology and Economics</publisherName>
    <publisherPlace>Budapest, Hungary</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-02-03</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Turbulent mixing simulation using the Hierarchical Parcel  Swapping (HiPS) model</title>
    <parentTitle language="eng">Proceedings of the Conference on Modelling Fluid Flow (CMFF’22)</parentTitle>
    <identifier type="isbn">978-963-421-881-4</identifier>
    <identifier type="url">https://www.cmff.hu/papers/CMFF22_Final_Paper_PDF_96.pdf</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </author>
    <submitter>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </submitter>
    <author>
      <firstName>Masoomeh</firstName>
      <lastName>Behrang</lastName>
    </author>
    <author>
      <firstName>David O.</firstName>
      <lastName>Lignell</lastName>
    </author>
    <author>
      <firstName>Heiko</firstName>
      <lastName>Schmidt</lastName>
    </author>
    <author>
      <firstName>Alan R.</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>differential diffusion, hierarchical parcel swapping, HiPS, mixing model, passive scalar mixing</value>
    </subject>
    <collection role="institutes" number="3504">FG Numerische Strömungs- und Gasdynamik</collection>
  </doc>
  <doc>
    <id>34850</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject_noref</type>
    <publisherName>American Physical Society</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-12-11</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model</title>
    <abstract language="eng">Hierarchical Parcel Swapping (HiPS) is a stochastic model of turbulent mixing. HiPS is based on a binary tree structure consisting of nodes emanating from the top of the tree and terminating in parcels at the base of the tree containing fluid properties. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent mixing is modeled by swapping subtrees at different tree levels. Swaps involving single parcels result in micromixing that changes scalar states. Swaps are implemented as a Poisson process at rates corresponding to level time scales. HiPS is extended to simulation of multiple scalars with arbitrary diffusivities, considering transport in the inertial, viscous-advective, and inertial-diffusive ranges. Fundamental analysis of particle dispersion is presented with comparisons to theoretical results and DNS data in the inertial and viscous ranges. Scalar energy spectra are analysed in the three ranges and reproduce known scaling exponents. Scalar dissipation statistics are analysed and reproduce the experimental and theoretical lognormal distribution with negative skewness represented by a stretched-exponential function. DNS data are used to evaluate empirical coefficients, facilitating quantitative applications. The physical fidelity demonstrated with HiPS suggests its use as a low-cost subgrid model for coarse-grained flow simulation, for which parcel-pair mixing is a common treatment.</abstract>
    <parentTitle language="eng">77th Annual Meeting of the Division of Fluid Dynamics, November 24–26, 2024; Salt Lake City, Utah</parentTitle>
    <identifier type="url">https://meetings.aps.org/Meeting/DFD24/Session/X39.11</identifier>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="Artikelnummer">X39.00011</enrichment>
    <enrichment key="Publikationsweg">Open Access</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>David O.</firstName>
      <lastName>Lignell</lastName>
    </author>
    <submitter>
      <firstName>Marten</firstName>
      <lastName>Klein</lastName>
    </submitter>
    <author>
      <firstName>Masoomeh</firstName>
      <lastName>Behrang</lastName>
    </author>
    <author>
      <firstName>Alan R.</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <author>
      <firstName>Isaac</firstName>
      <lastName>Wheeler</lastName>
    </author>
    <author>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </author>
    <author>
      <firstName>Heiko</firstName>
      <lastName>Schmidt</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>turbulent mixing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>variable Schmidt number</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic modeling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hierarchical parcel swapping</value>
    </subject>
    <collection role="institutes" number="3504">FG Numerische Strömungs- und Gasdynamik</collection>
    <collection role="institutes" number="7006">Energie-Innovationszentrum / Scientific Computing Lab</collection>
  </doc>
  <doc>
    <id>30361</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>49</pageFirst>
    <pageLast>58</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>43</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-02-20</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Turbulent mixing simulation using the Hierarchical Parcel-Swapping (HiPS) model</title>
    <abstract language="eng">Turbulent mixing is an omnipresent phenomenon that permanently affects our everyday life. Mixing processes also plays an important role in many industrial applications. The full resolution of all relevant flow scales often poses a major challenge to the numerical simulation and requires a modeling of the small-scale effects. In transported Probability Density Function (PDF) methods, the simplified modeling of the molecular mixing is a known weak point. At this place, the Hierarchical Parcel-Swapping (HiPS) model developed by A.R. Kerstein [J. Stat. Phys. 153, 142-161 (2013)] represents a computationally efficient and novel turbulent mixing model. HiPS simulates the effects of turbulence on time-evolving, diffusive scalar fields. The interpretation of the diffusive scalar fields or a state space as a binary tree structure is an alternative approach compared to existing mixing models. The characteristic feature of HiPS is that every level of the tree corresponds to a specific length and time scale, which&#13;
is based on turbulence inertial range scaling. The state variables only reside at the base of the tree and are understood as fluid&#13;
parcels. The effects of turbulent advection are represented by stochastic swaps of sub-trees at rates determined by turbulent time&#13;
scales associated with the sub-trees. The mixing of adjacent fluid parcels is done at rates consistent with the prevailing diffusion&#13;
time scales. In this work, a standalone HiPS model formulation for the simulation of passive scalar mixing is detailed first. The&#13;
generated scalar power spectra with forced turbulence shows the known scaling law of Kolmogorov turbulence. Furthermore, results for the PDF of the passive scalar, mean square displacement and scalar dissipation rate are shown and reveal a reasonable agreement with experimental findings. The described possibility to account for variable Schmidt number effects is an important next development step for the HiPS formulation. This enables the incorporation of differential diffusion, which represents an immense advantage compared to the established mixing models. Using a binary structure allows HiPS to satisfy a large number of criteria for a good mixing model. Considering the reduced order and associated computational efficiency, HiPS is an attractive&#13;
mixing model, which can contribute to an improved representation of the molecular mixing in transported PDF methods.</abstract>
    <parentTitle language="deu">Technische Mechanik</parentTitle>
    <identifier type="doi">10.24352/UB.OVGU-2023-044</identifier>
    <identifier type="issn">0232-3869</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Publikationsweg">Open Access</enrichment>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </author>
    <submitter>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </submitter>
    <author>
      <firstName>Masoomeh</firstName>
      <lastName>Behrang</lastName>
    </author>
    <author>
      <firstName>David O.</firstName>
      <lastName>Lignell</lastName>
    </author>
    <author>
      <firstName>Heiko</firstName>
      <lastName>Schmidt</lastName>
    </author>
    <author>
      <firstName>Alan R.</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>differential diffusion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hierarchical parcel-swapping</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>HiPS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mixing model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>scalar mixing</value>
    </subject>
    <collection role="institutes" number="3504">FG Numerische Strömungs- und Gasdynamik</collection>
    <collection role="institutes" number="7006">Energie-Innovationszentrum / Scientific Computing Lab</collection>
  </doc>
  <doc>
    <id>36963</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>39</pageLast>
    <pageNumber>39</pageNumber>
    <edition/>
    <issue/>
    <volume>1020</volume>
    <type>articler</type>
    <publisherName>Cambridge University Press</publisherName>
    <publisherPlace>Cambridge</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-12-08</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hierarchical parcel-swapping representation of turbulent mixing : part 4 : extension to the viscous range and to mixing of scalars with non-unity Schmidt numbers</title>
    <abstract language="eng">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.</abstract>
    <parentTitle language="eng">Journal of fluid mechanics</parentTitle>
    <identifier type="doi">doi:10.1017/jfm.2025.10512</identifier>
    <identifier type="issn">0022-1120</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="RelationnotEU">85056897 and 03SF0693A</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>
      <firstName>Masoomeh</firstName>
      <lastName>Behrang</lastName>
    </author>
    <submitter>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </submitter>
    <author>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </author>
    <author>
      <firstName>Isaac</firstName>
      <lastName>Wheeler</lastName>
    </author>
    <author>
      <firstName>Heiko</firstName>
      <lastName>Schmidt</lastName>
    </author>
    <author>
      <firstName>Alan</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <author>
      <firstName>David</firstName>
      <lastName>Lignell</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Turbulence modelling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Coupled diffusion and flow</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dispersion</value>
    </subject>
    <collection role="institutes" number="3504">FG Numerische Strömungs- und Gasdynamik</collection>
    <collection role="institutes" number="7006">Energie-Innovationszentrum / Scientific Computing Lab</collection>
  </doc>
  <doc>
    <id>36962</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>7</pageLast>
    <pageNumber>7</pageNumber>
    <edition/>
    <issue/>
    <volume>31</volume>
    <type>articler</type>
    <publisherName>Elsevier BV</publisherName>
    <publisherPlace>Amsterdam</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-12-08</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A C++ library for turbulent mixing simulation using Hierarchical Parcel Swapping (HiPS)</title>
    <abstract language="eng">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.</abstract>
    <parentTitle language="eng">SoftwareX</parentTitle>
    <identifier type="issn">2352-7110</identifier>
    <identifier type="doi">10.1016/j.softx.2025.102331</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="Publikationsweg">Open Access</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <licence>Creative Commons - CC BY-NC - Namensnennung - Nicht kommerziell 4.0 International</licence>
    <author>
      <firstName>Masoomeh</firstName>
      <lastName>Behrang</lastName>
    </author>
    <submitter>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </submitter>
    <author>
      <firstName>Tommy</firstName>
      <lastName>Starick</lastName>
    </author>
    <author>
      <firstName>Heiko</firstName>
      <lastName>Schmidt</lastName>
    </author>
    <author>
      <firstName>David O.</firstName>
      <lastName>Lignell</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Reaction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Turbulence</value>
    </subject>
    <collection role="institutes" number="3504">FG Numerische Strömungs- und Gasdynamik</collection>
    <collection role="institutes" number="7006">Energie-Innovationszentrum / Scientific Computing Lab</collection>
  </doc>
</export-example>
