The paper presents a new solver for the numerical solution of the Boltzmann kinetic equation with the Shakhov model collision integral (S-model) for arbitrary spatial domains. The numerical method utilizes the Tucker decomposition, which reduces the required computer memory for up to 100 times, even on a moderate velocity grid. This improvement is achieved by representing the distribution function values on a structured velocity grid as a 3D tensor in the Tucker format. The resulting numerical method makes it possible to solve complex 3D problems on modern desktop computers. Our implementation may serve as a prototype code for researchers concerned with the numerical solution of kinetic equations in 3D domains using a discrete velocity method.

Program summary

Program Title: Boltzmann-T

CPC Library link to program files: https://doi.org/10.17632/29wv8nmbgn.1

Developer’s repository link: https://github.com/chikitkin/Boltzmann-Tucker

Licensing provisions: MIT

Programming language: Python 3

External libraries: Solver is based on the customized version of the tucker3d library [1]

Nature of problem: Numerical solution of the Boltzmann kinetic equation with the S-model collision integral in an arbitrary 3D spatial domain

Solution method: Discrete velocity method utilizing tensor decomposition for memory reduction

Additional comments including restrictions and unusual features: At present, 1st order advection scheme is used, solver supports unstructured hexagonal meshes written in StarCD ASCII format

Reference tucker3d (https://github.com/rakhuba/tucker3d) library contains Python implementations of several important procedures for working with tensors in the Tucker format.

中文翻译：

---

张量分解的S型碰撞积分玻尔兹曼方程的数值解

本文提出了一种新的求解器，用于求解带有任意空间域的Shakhov模型碰撞积分（S模型）的Boltzmann动力学方程的数值解。数值方法利用了Tucker分解，即使在中等速度的网格上，它也可以将所需的计算机内存减少多达100倍。通过将结构化速度网格上的分布函数值表示为Tucker格式的3D张量来实现此改进。所得的数值方法使解决现代台式计算机上的复杂3D问题成为可能。对于使用离散速度方法在3D域中的动力学方程的数值解的研究人员来说，我们的实现可以用作原型代码。

计划摘要

节目名称： Boltzmann-T

CPC库链接到程序文件： https : //doi.org/10.17632/29wv8nmbgn.1

开发人员的资料库链接： https : //github.com/chikitkin/Boltzmann-Tucker

许可条款：麻省理工学院

编程语言： Python 3

外部库： Solver基于tucker3d库的自定义版本[1]

问题性质：在任意3D空间域中具有S模型碰撞积分的玻尔兹曼动力学方程的数值解

解决方法：利用张量分解的离散速度法进行记忆约简

其他注释，包括限制和异常功能：当前，使用一阶对流方案，求解器支持以StarCD ASCII格式编写的非结构化六角形网格

参考tucker3d（https://github.com/rakhuba/tucker3d）库包含使用Tucker格式处理张量的几个重要过程的Python实现。