An adaptive Hermite spectral method for the Boltzmann equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914051189112832 |
|---|---|
| author | Shao, Sihong Wang, Yanli Wu, Jie |
| author_facet | Shao, Sihong Wang, Yanli Wu, Jie |
| contents | We propose an adaptive Hermite spectral method for the three-dimensional velocity space of the Boltzmann equation guided by a newly developed frequency indicator. For the homogeneous problem, the indicator is defined by the contribution of high-order coefficients in the spectral expansion. For the non-homogeneous problem, a Fourier-Hermite scheme is employed, with the corresponding frequency indicator formulated based on distributions across the entire spatial domain. The adaptive Hermite method includes scaling and p-adaptive techniques to dynamically adjust the scaling factor and expansion order according to the indicator. Numerical experiments cover both homogeneous and non-homogeneous problems in up to three spatial dimensions. Results demonstrate that the scaling adaptive method substantially reduces L2 errors at negligible computational cost, and the p-adaptive method achieves time savings of up to 74%. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An adaptive Hermite spectral method for the Boltzmann equation Shao, Sihong Wang, Yanli Wu, Jie Numerical Analysis We propose an adaptive Hermite spectral method for the three-dimensional velocity space of the Boltzmann equation guided by a newly developed frequency indicator. For the homogeneous problem, the indicator is defined by the contribution of high-order coefficients in the spectral expansion. For the non-homogeneous problem, a Fourier-Hermite scheme is employed, with the corresponding frequency indicator formulated based on distributions across the entire spatial domain. The adaptive Hermite method includes scaling and p-adaptive techniques to dynamically adjust the scaling factor and expansion order according to the indicator. Numerical experiments cover both homogeneous and non-homogeneous problems in up to three spatial dimensions. Results demonstrate that the scaling adaptive method substantially reduces L2 errors at negligible computational cost, and the p-adaptive method achieves time savings of up to 74%. |
| title | An adaptive Hermite spectral method for the Boltzmann equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.17981 |