Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust
Collisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evoluti...
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| Format: | Article |
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MDPI AG
2020-09-01
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| Series: | Journal of Imaging |
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| Online Access: | https://www.mdpi.com/2313-433X/6/9/98 |
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| author | Mikhail A. Bezborodov Mikhail A. Eremin Vitaly V. Korolev Ilya G. Kovalenko Elena V. Zhukova |
| author_facet | Mikhail A. Bezborodov Mikhail A. Eremin Vitaly V. Korolev Ilya G. Kovalenko Elena V. Zhukova |
| author_sort | Mikhail A. Bezborodov |
| collection | DOAJ |
| description | Collisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evolution in such media occurs in phase space, i.e., in a space of greater dimensions than the usual coordinate space. As a consequence, the process of the formation of features in collisionless media (clustering or vice versa, a loss of continuity) can occur primarily in the velocity space, which, in contrast to the features in the coordinate space (folds, caustics, or voids), is poorly observed directly. To identify such features, it is necessary to use visualization methods that allow us to consider, in detail, the evolution of the medium in the velocity space. This article is devoted to the development of techniques that allow visualizing the degree of anisotropy of the velocity fields of collisionless interpenetrating media. Simultaneously tracking the behavior of different fractions in such media is important, as their behavior can be significantly different. We propose three different techniques for visualizing the anisotropy of velocity fields using the example of two- and three-continuum dispersed media models. We proposed the construction of spatial distributions of eccentricity fields (scalar fields), or fields of principal directions of the velocity dispersion tensor (tensor fields). In the first case, we used some simple eccentricity functions for dispersion tensors for two fractions simultaneously, which we call surrogate entropy. In the second case, to visualize the anisotropy of the velocity fields of three fractions simultaneously, we used an ordered array (3-vector) of eccentricities for the color representation through decomposition in three basic colors. In the case of a multi-stream flow, we used cluster analysis methods to identify sections of a multi-stream flow (beams) and used glyphs to visualize the entire set of beams (vector-tensor fields). |
| first_indexed | 2024-03-10T16:16:05Z |
| format | Article |
| id | doaj.art-e5346ff880364d97ad6ee30c3a3c2a6d |
| institution | Directory Open Access Journal |
| issn | 2313-433X |
| language | English |
| last_indexed | 2024-03-10T16:16:05Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Imaging |
| spelling | doaj.art-e5346ff880364d97ad6ee30c3a3c2a6d2023-11-20T14:06:56ZengMDPI AGJournal of Imaging2313-433X2020-09-01699810.3390/jimaging6090098Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse DustMikhail A. Bezborodov0Mikhail A. Eremin1Vitaly V. Korolev2Ilya G. Kovalenko3Elena V. Zhukova4Institute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, RussiaInstitute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, RussiaInstitute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, RussiaInstitute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, RussiaInstitute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, RussiaCollisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evolution in such media occurs in phase space, i.e., in a space of greater dimensions than the usual coordinate space. As a consequence, the process of the formation of features in collisionless media (clustering or vice versa, a loss of continuity) can occur primarily in the velocity space, which, in contrast to the features in the coordinate space (folds, caustics, or voids), is poorly observed directly. To identify such features, it is necessary to use visualization methods that allow us to consider, in detail, the evolution of the medium in the velocity space. This article is devoted to the development of techniques that allow visualizing the degree of anisotropy of the velocity fields of collisionless interpenetrating media. Simultaneously tracking the behavior of different fractions in such media is important, as their behavior can be significantly different. We propose three different techniques for visualizing the anisotropy of velocity fields using the example of two- and three-continuum dispersed media models. We proposed the construction of spatial distributions of eccentricity fields (scalar fields), or fields of principal directions of the velocity dispersion tensor (tensor fields). In the first case, we used some simple eccentricity functions for dispersion tensors for two fractions simultaneously, which we call surrogate entropy. In the second case, to visualize the anisotropy of the velocity fields of three fractions simultaneously, we used an ordered array (3-vector) of eccentricities for the color representation through decomposition in three basic colors. In the case of a multi-stream flow, we used cluster analysis methods to identify sections of a multi-stream flow (beams) and used glyphs to visualize the entire set of beams (vector-tensor fields).https://www.mdpi.com/2313-433X/6/9/98hydrodynamic modelingmultiphase flowpolydisperse dustvisualization of flowcomputational color sciencecluster analysis |
| spellingShingle | Mikhail A. Bezborodov Mikhail A. Eremin Vitaly V. Korolev Ilya G. Kovalenko Elena V. Zhukova Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust Journal of Imaging hydrodynamic modeling multiphase flow polydisperse dust visualization of flow computational color science cluster analysis |
| title | Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust |
| title_full | Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust |
| title_fullStr | Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust |
| title_full_unstemmed | Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust |
| title_short | Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust |
| title_sort | visualization of the anisotropy of the velocity dispersion and characteristics of the multi velocity continuum in the regions of multi stream flows of gas dust media with polydisperse dust |
| topic | hydrodynamic modeling multiphase flow polydisperse dust visualization of flow computational color science cluster analysis |
| url | https://www.mdpi.com/2313-433X/6/9/98 |
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