Random vortex and expansion-rate model for Oberbeck-Boussinesq fluid flows
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912057300877312 |
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| author | Guo, Zihao Qian, Zhongmin Shen, Zihao |
| author_facet | Guo, Zihao Qian, Zhongmin Shen, Zihao |
| contents | By using a formulation of a class of compressible viscous flows with a heat source via vorticity and expansion-rate, we study the Oberbeck-Boussinesq flows. To this end we establish a new integral representation for solutions of parabolic equations subject to certain boundary condition, which allows us to develop a random vortex method for certain compressible flows and to compute numerically solutions of their dynamical models. Numerical experiments are carried out, which not only capture detailed Bénard convection but also are capable of providing additional information on the fluid density and the dynamics of expansion-rate of the flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random vortex and expansion-rate model for Oberbeck-Boussinesq fluid flows Guo, Zihao Qian, Zhongmin Shen, Zihao Analysis of PDEs Numerical Analysis Probability Fluid Dynamics 76M35, 76M23, 60H30, 65C05, 68Q10 By using a formulation of a class of compressible viscous flows with a heat source via vorticity and expansion-rate, we study the Oberbeck-Boussinesq flows. To this end we establish a new integral representation for solutions of parabolic equations subject to certain boundary condition, which allows us to develop a random vortex method for certain compressible flows and to compute numerically solutions of their dynamical models. Numerical experiments are carried out, which not only capture detailed Bénard convection but also are capable of providing additional information on the fluid density and the dynamics of expansion-rate of the flow. |
| title | Random vortex and expansion-rate model for Oberbeck-Boussinesq fluid flows |
| topic | Analysis of PDEs Numerical Analysis Probability Fluid Dynamics 76M35, 76M23, 60H30, 65C05, 68Q10 |
| url | https://arxiv.org/abs/2410.02923 |