A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions
A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions
复制标题
DOI：
10.3934/krm.2020023
复制
发表时间：
2020
影响因子：
1
通讯作者：
Jingwei Hu;Jie Shen;Yingwei Wang
中科院分区：
文献类型：
--
作者：
Jingwei Hu;Jie Shen;Yingwei Wang
本文发展了一维非弹性Boltzmann方程的Petrov-Galerkin谱方法。这类方程的解在速度空间中通常表现为重尾，因此区域截断或傅立叶近似将遭受较大的截断误差。我们的方法是基于无界区域上的映射切比雪夫函数，因此不需要截断区域。此外，为了获得期望的收敛和守恒性质，我们仔细地选择了测试函数空间和尝试函数空间。通过一系列算例，我们证明了该方法比傅立叶谱方法具有更好的性能，并且得到了高精度的结果。
We develop in this paper a Petrov-Galerkin spectral method for the inelastic Boltzmann equation in one dimension. Solutions to such equations typically exhibit heavy tails in the velocity space so that domain truncation or Fourier approximation would suffer from large truncation errors. Our method is based on the mapped Chebyshev functions on unbounded domains, hence requires no domain truncation. Furthermore, the test and trial function spaces are carefully chosen to obtain desired convergence and conservation properties. Through a series of examples, we demonstrate that the proposed method performs better than the Fourier spectral method and yields highly accurate results.