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首页> 外文期刊>Jorunal of computational and theoretical transport >On the Applicability of Nonoscillatory Hyperbolic Solvers to Splitting-Method Solutions of the Boltzmann Equation
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On the Applicability of Nonoscillatory Hyperbolic Solvers to Splitting-Method Solutions of the Boltzmann Equation

机译：非振荡双曲解在玻尔兹曼方程分裂方法解中的适用性

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摘要

We use various weighted essentially nonoscillatory (WENO) schemes to calculate the advection (free-transport) step of a splitting-method solver for the Boltzmann equation with hard-sphere collisions. The collision integral is calculated using a fast spectral method recently proposed by Filbet and colleagues (2006). For the advection step we consider three different WENO schemes for the purpose of spatial discretization, and use a total variation diminishing Runge-Kutta method for time-stepping. The WENO schemes differ only in terms of the underlying flux scheme (Godunov, Lax-Friedrichs, or Rusanov). We use the one-dimensional shock profile as a test problem, comparing the WENO methods among themselves, and also with a positive flux conservation (PFC) method (Filbet and Russo, 2004) and with Bird’s well-known direct simulation Monte Carlo method. Our results show that the WENO-Godunov method produces accurate and stable shock solutions in good agreement with the Monte Carlo results, whereas solutions obtained with the other two WENO methods and the PFC method display some unphysical features such as density undershoots near the shock front and excessive upstream temperature.
机译：我们使用各种加权的基本非振荡（WENO）方案来计算具有硬球碰撞的Boltzmann方程的分裂方法求解器的对流（自由运输）步骤。碰撞积分是使用Filbet及其同事（2006年）最近提出的快速光谱方法计算的。对于平流步骤，出于空间离散化的目的，我们考虑了三种不同的WENO方案，并使用总变分减小Runge-Kutta方法进行时间步进。 WENO方案仅在基础通量方案（Godunov，Lax-Friedrichs或Rusanov）方面有所不同。我们将一维冲击轮廓作为测试问题，将它们之间的WENO方法进行了比较，还采用了正通量守恒（PFC）方法（Filbet和Russo，2004年）以及Bird著名的直接模拟蒙特卡洛方法。我们的结果表明，WENO-Godunov方法产生的精确和稳定的冲击解与蒙特卡洛结果非常吻合，而其他两种WENO方法和PFC方法获得的解则表现出一些非物理特征，例如冲击前沿附近的密度下冲和上游温度过高。

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