TY - JOUR
T1 - A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
AU - Hu, Jingwei
AU - Qi, Kunlun
PY - 2020/12/15
Y1 - 2020/12/15
N2 - 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.
AB - 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.
KW - Boltzmann equation
KW - Non-cutoff collision kernel
KW - Singularity
KW - Fractional Laplacian
KW - Fourier spectral method
KW - Fast fourier transform
UR - http://www.scopus.com/inward/record.url?scp=85091782218&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85091782218&origin=recordpage
U2 - 10.1016/j.jcp.2020.109806
DO - 10.1016/j.jcp.2020.109806
M3 - 21_Publication in refereed journal
VL - 423
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 109806
ER -