Boltzmann等式的数值解决方案,与S型碰撞结合,使用高压分解法 (Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions)

Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce required computer memory for up to 30 times even on a moderate velocity mesh. This improvement is achieved by representing values of distribution function on the structured velocity mesh as a 3D tensor in Tensor-Train 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 numerical solution of the kinetic equations in 3D domains by the discrete velocity method.

翻译：文档为任意空间域的 Shakhov 模型碰撞集成( S- 型号) 碰撞模型( S- 型号) 的波尔兹曼动能方程式的数字解决方案提供了一个新的解决方案。数字方法使用Tensor- Train 分解法, 即使在中速网格上也可以将所需的计算机内存减少30倍。实现这一改进的方法是在Tensor- Train 格式中将结构速度网格的分布功能值作为 3D 感应器格式。由此产生的数字方法使得能够解决现代台式计算机上复杂的三维问题。我们的实施可以作为一个原型代码, 用于研究人员使用离散速度法对三维域动能方程式进行数字解算。