Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications
In recent years, the fast growth of computational power has allowed the application of computational fluid dynamics (CFD) in a wide range of areas of interest, such as gas–solid unit operations. In this context, the multiphase particle-in-cell (MP-PIC) method appears as an option to represent fluid–...
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2024-11-01
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| author | Luis Henríquez-Vargas Pablo Donoso-García Lawrence Lackey Mauricio Bravo-Gutiérrez Benjamín Cajas Alejandro Reyes Nicolás Pailahueque Isaac Díaz-Aburto Valeri Bubnovich |
| author_facet | Luis Henríquez-Vargas Pablo Donoso-García Lawrence Lackey Mauricio Bravo-Gutiérrez Benjamín Cajas Alejandro Reyes Nicolás Pailahueque Isaac Díaz-Aburto Valeri Bubnovich |
| author_sort | Luis Henríquez-Vargas |
| collection | DOAJ |
| description | In recent years, the fast growth of computational power has allowed the application of computational fluid dynamics (CFD) in a wide range of areas of interest, such as gas–solid unit operations. In this context, the multiphase particle-in-cell (MP-PIC) method appears as an option to represent fluid–particle and particle–particle interactions, avoiding the complexity of tracking each particle and the high computational cost derived from this. The MP-PIC method can represent the particles as a group with the same characteristics, allowing the simulation of gas–solid systems at different scales. To achieve this, the particle–particle interactions are simplified using the solid stress tensor to represent them; this does not require explicit expressions. This approach has a low computational cost, allowing the simulation of industrial cases using just workstations. This paper provides a review of the literature on the solid stress tensor and its commercial and non-commercial applications, including its historical and mathematical development in the description of particle–particle interactions. In addition, to consolidate the knowledge and advancing understanding in this crucial aspect of multiphase flow simulations, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor. In addition, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor. |
| format | Article |
| id | doaj-art-ee0b23f2211b4153af4b08364de8b2ff |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-ee0b23f2211b4153af4b08364de8b2ff2025-08-20T02:38:41ZengMDPI AGMathematics2227-73902024-11-011223370010.3390/math12233700Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and ApplicationsLuis Henríquez-Vargas0Pablo Donoso-García1Lawrence Lackey2Mauricio Bravo-Gutiérrez3Benjamín Cajas4Alejandro Reyes5Nicolás Pailahueque6Isaac Díaz-Aburto7Valeri Bubnovich8Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileDepartamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, ChileIn recent years, the fast growth of computational power has allowed the application of computational fluid dynamics (CFD) in a wide range of areas of interest, such as gas–solid unit operations. In this context, the multiphase particle-in-cell (MP-PIC) method appears as an option to represent fluid–particle and particle–particle interactions, avoiding the complexity of tracking each particle and the high computational cost derived from this. The MP-PIC method can represent the particles as a group with the same characteristics, allowing the simulation of gas–solid systems at different scales. To achieve this, the particle–particle interactions are simplified using the solid stress tensor to represent them; this does not require explicit expressions. This approach has a low computational cost, allowing the simulation of industrial cases using just workstations. This paper provides a review of the literature on the solid stress tensor and its commercial and non-commercial applications, including its historical and mathematical development in the description of particle–particle interactions. In addition, to consolidate the knowledge and advancing understanding in this crucial aspect of multiphase flow simulations, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor. In addition, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor.https://www.mdpi.com/2227-7390/12/23/3700multiphase modelingparticle in cellfluidizationsolid stress model |
| spellingShingle | Luis Henríquez-Vargas Pablo Donoso-García Lawrence Lackey Mauricio Bravo-Gutiérrez Benjamín Cajas Alejandro Reyes Nicolás Pailahueque Isaac Díaz-Aburto Valeri Bubnovich Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications Mathematics multiphase modeling particle in cell fluidization solid stress model |
| title | Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications |
| title_full | Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications |
| title_fullStr | Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications |
| title_full_unstemmed | Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications |
| title_short | Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications |
| title_sort | modeling of the solid stress tensor in the mp pic method a review of methods and applications |
| topic | multiphase modeling particle in cell fluidization solid stress model |
| url | https://www.mdpi.com/2227-7390/12/23/3700 |
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