Boosting the convergence of low-variance DSMC by GSIS
Abstract The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we re...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Advances in Aerodynamics |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s42774-023-00138-0 |
| _version_ | 1797773862168952832 |
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| author | Liyan Luo Qi Li Lei Wu |
| author_facet | Liyan Luo Qi Li Lei Wu |
| author_sort | Liyan Luo |
| collection | DOAJ |
| description | Abstract The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model. First, macroscopic synthetic equations are derived exactly from the kinetic equation, which not only contain the Navier-Stokes-Fourier constitutive relation, but also encompass the higher-order terms describing the rarefaction effects. Then, the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC. Finally, the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties. As a result, the convergence to steady state is greatly accelerated, and the restrictions on cell size and the time step are removed. We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS: when the Knudsen number is lower than 0.1, it can use the grid size about 10 times larger than that in traditional DSMC, and it can reduce the computational cost by two orders of magnitude in the flow regime. |
| first_indexed | 2024-03-12T22:12:35Z |
| format | Article |
| id | doaj.art-0d78c44e1e10497694ea608fb8c9a66c |
| institution | Directory Open Access Journal |
| issn | 2524-6992 |
| language | English |
| last_indexed | 2024-03-12T22:12:35Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Aerodynamics |
| spelling | doaj.art-0d78c44e1e10497694ea608fb8c9a66c2023-07-23T11:27:40ZengSpringerOpenAdvances in Aerodynamics2524-69922023-03-015112610.1186/s42774-023-00138-0Boosting the convergence of low-variance DSMC by GSISLiyan Luo0Qi Li1Lei Wu2Department of Mechanics and Aerospace Engineering, Southern University of Science and TechnologyDepartment of Mechanics and Aerospace Engineering, Southern University of Science and TechnologyDepartment of Mechanics and Aerospace Engineering, Southern University of Science and TechnologyAbstract The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model. First, macroscopic synthetic equations are derived exactly from the kinetic equation, which not only contain the Navier-Stokes-Fourier constitutive relation, but also encompass the higher-order terms describing the rarefaction effects. Then, the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC. Finally, the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties. As a result, the convergence to steady state is greatly accelerated, and the restrictions on cell size and the time step are removed. We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS: when the Knudsen number is lower than 0.1, it can use the grid size about 10 times larger than that in traditional DSMC, and it can reduce the computational cost by two orders of magnitude in the flow regime.https://doi.org/10.1186/s42774-023-00138-0Rarefied gas dynamicsDirect simulation Monte CarloGeneral synthetic iterative schemeMultiscale simulation |
| spellingShingle | Liyan Luo Qi Li Lei Wu Boosting the convergence of low-variance DSMC by GSIS Advances in Aerodynamics Rarefied gas dynamics Direct simulation Monte Carlo General synthetic iterative scheme Multiscale simulation |
| title | Boosting the convergence of low-variance DSMC by GSIS |
| title_full | Boosting the convergence of low-variance DSMC by GSIS |
| title_fullStr | Boosting the convergence of low-variance DSMC by GSIS |
| title_full_unstemmed | Boosting the convergence of low-variance DSMC by GSIS |
| title_short | Boosting the convergence of low-variance DSMC by GSIS |
| title_sort | boosting the convergence of low variance dsmc by gsis |
| topic | Rarefied gas dynamics Direct simulation Monte Carlo General synthetic iterative scheme Multiscale simulation |
| url | https://doi.org/10.1186/s42774-023-00138-0 |
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