Pütz, M. ; Pollack, M. ; Hasse, C. ; Oevermann, M. (2022)
A Gauss/anti-Gauss quadrature method of moments applied to population balance equations with turbulence-induced nonlinear phase-space diffusion.
In: Journal of Computational Physics, 466
doi: 10.1016/j.jcp.2022.111363
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
Many particulate systems occurring in nature and technology are adequately described by a number density function (NDF). The numerical solution of the corresponding population balance equation (PBE) is typically accompanied by high computational costs. Quadrature-based moment methods are an approach to reduce the computational complexity by solving only for a set of moments associated with the NDF employing Gaussian quadrature rules to close the moment equations derived from the PBE. The evolution of a population of inertial particles dispersed in a turbulent fluid is governed by a PBE with a phase-space diffusion term as a result of random microscale fluctuations. Considerations on the microscopic behavior concerning the momentum exchange between fluid and dispersed particles suggest that this diffusion term is nonlinear and nonsmooth. The resulting integral terms in the derived moment equations entail large approximation errors when using Gaussian quadrature rules for closure. In this work, we propose a modification of the quadrature method of moments (QMOM), namely the Gauss/anti-Gauss-QMOM (GaG-QMOM), making use of anti-Gaussian quadrature formulae to reduce the large errors due to this particular form of diffusion. This new method is investigated in a series of simple one-dimensional test cases with analytical reference solutions. Moreover, we propose a realizability-preserving variation of the strong-stability preserving Runge-Kutta (RKSSP) schemes that is suited to problems involving phase-space diffusion. Besides the observation that the modified second-order RKSSP scheme can serve as a realizability-preserving alternative to the standard RKSSP scheme of the same order, the numerical results reveal that, compared to the standard QMOM, the GaG-QMOM can reduce the large errors by one to two orders of magnitude.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Pütz, M. ; Pollack, M. ; Hasse, C. ; Oevermann, M. |
| Art des Eintrags: | Bibliographie |
| Titel: | A Gauss/anti-Gauss quadrature method of moments applied to population balance equations with turbulence-induced nonlinear phase-space diffusion |
| Sprache: | Englisch |
| Publikationsjahr: | 2022 |
| Verlag: | Elsevier |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Computational Physics |
| Jahrgang/Volume einer Zeitschrift: | 466 |
| DOI: | 10.1016/j.jcp.2022.111363 |
| URL / URN: | https://www.sciencedirect.com/science/article/pii/S002199912... |
| Kurzbeschreibung (Abstract): | Many particulate systems occurring in nature and technology are adequately described by a number density function (NDF). The numerical solution of the corresponding population balance equation (PBE) is typically accompanied by high computational costs. Quadrature-based moment methods are an approach to reduce the computational complexity by solving only for a set of moments associated with the NDF employing Gaussian quadrature rules to close the moment equations derived from the PBE. The evolution of a population of inertial particles dispersed in a turbulent fluid is governed by a PBE with a phase-space diffusion term as a result of random microscale fluctuations. Considerations on the microscopic behavior concerning the momentum exchange between fluid and dispersed particles suggest that this diffusion term is nonlinear and nonsmooth. The resulting integral terms in the derived moment equations entail large approximation errors when using Gaussian quadrature rules for closure. In this work, we propose a modification of the quadrature method of moments (QMOM), namely the Gauss/anti-Gauss-QMOM (GaG-QMOM), making use of anti-Gaussian quadrature formulae to reduce the large errors due to this particular form of diffusion. This new method is investigated in a series of simple one-dimensional test cases with analytical reference solutions. Moreover, we propose a realizability-preserving variation of the strong-stability preserving Runge-Kutta (RKSSP) schemes that is suited to problems involving phase-space diffusion. Besides the observation that the modified second-order RKSSP scheme can serve as a realizability-preserving alternative to the standard RKSSP scheme of the same order, the numerical results reveal that, compared to the standard QMOM, the GaG-QMOM can reduce the large errors by one to two orders of magnitude. |
| Freie Schlagworte: | Quadrature-based moment methods, Population balance equation, Anti-Gaussian quadrature, Fokker-Planck equation, Turbulence modeling |
| Zusätzliche Informationen: | Artikel-ID: 111363 |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet Simulation reaktiver Thermo-Fluid Systeme (STFS) |
| Hinterlegungsdatum: | 18 Jul 2022 05:17 |
| Letzte Änderung: | 06 Okt 2022 08:45 |
| PPN: | 497137542 |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum