A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field
The study of the evolution of the atmosphere requires careful consideration of multicomponent gaseous flows under gravity. The gas dynamics under an external force field is usually associated with an intrinsic multiscale nature due to large particle density variation along the direction of force. A...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/24/8/1110 |
| _version_ | 1797445599029624832 |
|---|---|
| author | Tianbai Xiao |
| author_facet | Tianbai Xiao |
| author_sort | Tianbai Xiao |
| collection | DOAJ |
| description | The study of the evolution of the atmosphere requires careful consideration of multicomponent gaseous flows under gravity. The gas dynamics under an external force field is usually associated with an intrinsic multiscale nature due to large particle density variation along the direction of force. A wonderfully diverse set of behaviors of fluids can be observed in different flow regimes. This poses a great challenge for numerical algorithms to accurately and efficiently capture the scale-dependent flow physics. In this paper, a well-balanced unified gas-kinetic scheme (UGKS) for a gas mixture is developed, which can be used for the study of cross-scale multicomponent flows under an external force field. The well-balanced scheme here indicates the capability of a numerical method to evolve a gravitational system under any initial condition to the hydrostatic equilibrium and to keep such a solution. Such a property is crucial for an accurate description of multicomponent gas evolution under an external force field, especially for long-term evolving systems such as galaxy formation. Based on the Boltzmann model equation for gas mixtures, the UGKS leverages the space–time integral solution to construct numerical flux functions and, thus, provides a self-conditioned mechanism to recover typical flow dynamics in various flow regimes. We prove the well-balanced property of the current scheme formally through theoretical analysis and numerical validations. New physical phenomena, including the decoupled transport of different gas components in the transition regime, are presented and studied. |
| first_indexed | 2024-03-09T13:29:12Z |
| format | Article |
| id | doaj.art-5f945cfc188c46789f9389d30fcf97c9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T13:29:12Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-5f945cfc188c46789f9389d30fcf97c92023-11-30T21:20:36ZengMDPI AGEntropy1099-43002022-08-01248111010.3390/e24081110A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force FieldTianbai Xiao0Department of Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, GermanyThe study of the evolution of the atmosphere requires careful consideration of multicomponent gaseous flows under gravity. The gas dynamics under an external force field is usually associated with an intrinsic multiscale nature due to large particle density variation along the direction of force. A wonderfully diverse set of behaviors of fluids can be observed in different flow regimes. This poses a great challenge for numerical algorithms to accurately and efficiently capture the scale-dependent flow physics. In this paper, a well-balanced unified gas-kinetic scheme (UGKS) for a gas mixture is developed, which can be used for the study of cross-scale multicomponent flows under an external force field. The well-balanced scheme here indicates the capability of a numerical method to evolve a gravitational system under any initial condition to the hydrostatic equilibrium and to keep such a solution. Such a property is crucial for an accurate description of multicomponent gas evolution under an external force field, especially for long-term evolving systems such as galaxy formation. Based on the Boltzmann model equation for gas mixtures, the UGKS leverages the space–time integral solution to construct numerical flux functions and, thus, provides a self-conditioned mechanism to recover typical flow dynamics in various flow regimes. We prove the well-balanced property of the current scheme formally through theoretical analysis and numerical validations. New physical phenomena, including the decoupled transport of different gas components in the transition regime, are presented and studied.https://www.mdpi.com/1099-4300/24/8/1110fluid mechanicskinetic theoryrarefied gas dynamicsmulticomponent flowswell-balanced schemes |
| spellingShingle | Tianbai Xiao A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field Entropy fluid mechanics kinetic theory rarefied gas dynamics multicomponent flows well-balanced schemes |
| title | A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field |
| title_full | A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field |
| title_fullStr | A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field |
| title_full_unstemmed | A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field |
| title_short | A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field |
| title_sort | well balanced unified gas kinetic scheme for multicomponent flows under external force field |
| topic | fluid mechanics kinetic theory rarefied gas dynamics multicomponent flows well-balanced schemes |
| url | https://www.mdpi.com/1099-4300/24/8/1110 |
| work_keys_str_mv | AT tianbaixiao awellbalancedunifiedgaskineticschemeformulticomponentflowsunderexternalforcefield AT tianbaixiao wellbalancedunifiedgaskineticschemeformulticomponentflowsunderexternalforcefield |