<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <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>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>
