A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 109806 |
Journal / Publication | Journal of Computational Physics |
Volume | 423 |
Online published | 31 Aug 2020 |
Publication status | Published - 15 Dec 2020 |
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Abstract
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in the deviation angle which arise in a wide range of interaction potentials (e.g., the inverse power law potentials). Albeit more physical, the non-cutoff kernels bring a lot of difficulties in both analysis and numerics, hence are often cut off in most studies (the well-known Grad's angular cutoff assumption). We demonstrate that the general framework of the fast Fourier spectral method developed in [9], [14] can be extended to handle the non-cutoff kernels, achieving the accuracy/efficiency comparable to the cutoff case. We also show through several numerical examples that the solution to the non-cutoff Boltzmann equation enjoys the smoothing effect, a striking property absent in the cutoff case.
Research Area(s)
- Boltzmann equation, Non-cutoff collision kernel, Singularity, Fractional Laplacian, Fourier spectral method, Fast fourier transform
Citation Format(s)
A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels. / Hu, Jingwei; Qi, Kunlun.
In: Journal of Computational Physics, Vol. 423, 109806, 15.12.2020.
In: Journal of Computational Physics, Vol. 423, 109806, 15.12.2020.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review