论文标题
蒙特卡洛随机盖尔金方法，用于不确定性的玻尔兹曼方程
Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case
论文作者
论文摘要
在本文中，我们提出了一种具有不确定性的玻尔兹曼方程的新型数值方法。该方法结合了相位空间中经典的直接模拟蒙特卡洛（DSMC）方案的效率，以及随机空间中随机Galerkin（SG）方法的准确性。这种混合制剂使得可以构建保留溶液的主要物理特性的方法以及随机空间中的光谱精度。在空间均匀问题的情况下，这些方案是开发和分析的，因为这些方案包含主要数值困难。在麦克斯韦和可变硬球（VHS）框架中报告了几个测试用例，并确认新方法的属性和性能。
In this paper we propose a novel numerical approach for the Boltzmann equation with uncertainties. The method combines the efficiency of classical direct simulation Monte Carlo (DSMC) schemes in the phase space together with the accuracy of stochastic Galerkin (sG) methods in the random space. This hybrid formulation makes it possible to construct methods that preserve the main physical properties of the solution along with spectral accuracy in the random space. The schemes are developed and analyzed in the case of space homogeneous problems as these contain the main numerical difficulties. Several test cases are reported, both in the Maxwell and in the variable hard sphere (VHS) framework, and confirm the properties and performance of the new methods.
