摘要
构建一种三阶精度的有限体积格式,数值求解考虑转动非平衡影响的Boltzmann-Rykov模型方程.针对模型方程的速度空间离散得到各个离散速度坐标点上彼此独立的控制方程组,运用高阶精度的半离散化有限体积格式在位置空间对离散控制方程进行数值求解,时间项采用三阶Runge-Kutta方法推进,方程右端二体碰撞项采用中心近似技术.该有限体积格式在气体分子对流运动项上具有三阶精度,同时保证了分布函数的正定性和流通量守恒.计算结果与有限差分方法数值模拟结果和连续流区非定常激波管问题的Riemann精确解均吻合较好,说明基于有限体积法的Boltzmann-Rykov模型方程数值求解过程是正确的.
A three order precision finite volume scheme was formulated to numerically solve the Boltzmann-Rykov model equation in which rotational energy was considered. This model e- quation was discretized into a series of equations at each discrete velocity point, and then a high order half-discretization finite volume scheme was used to compute these equations. Three order Runge-Kutta method was introduced for time marching, and central value in each cell was taken to approximate the average collision term. This finite volume scheme was of three order precision in convection term, while positive defmiteness of the distribution functions and flux conservation were ensured. Results were compared with those of finite difference method and Riemann exact solution in continuum regime. The good coincidence shows validity of the sol- ving process for the model equation by finite volume method.
出处
《应用数学和力学》
CSCD
北大核心
2014年第2期121-129,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金(91016027)
国家重点基础研究发展计划(973计划)(2014CB744100)~~
关键词
Rykov模型方程
统一算法
有限体积方法
Rykov model equation
gas kinetic unified algorithm
finite volume method
