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Accelerated discrete velocity method for axial-symmetric gaseous flows

机译:轴向对称气流的加速离散速度方法

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摘要

An accelerated discrete velocity method is presented for the simulation of axial-symmetric single-component gas flows in the whole range of gas rarefaction. The method relies on the Bhatnagar-Gross-Krook (BGK) kinetic equation. A diffusion-type moment equation is derived on the basis of the cylindrical kinetic one. Both equations are solved by discretizing the spatial and molecular velocity spaces in a joint iteration. The relationship between the cylindrical and the two-dimensional moment equations is shown. A stability analysis is developed to show the improved iteration performance of the accelerated method. Pressure-driven flow in a tube is simulated to study the method. The accelerated scheme is superior compared to the non-accelerated standard one at intermediate and high values of the rarefaction parameter in terms of the number of iterations required and the computational time. The flow rates and the velocity profiles are compared to the analytical discrete ordinate solution of the problems. There is a very good agreement between the results provided by the two methods.
机译:提出了一种加速离散速度方法,用于模拟整个气体稀化范围内的轴对称单组分气体流动。该方法依赖于Bhatnagar-Gross-Krook(BGK)动力学方程。在圆柱动力学方程的基础上推导了扩散型力矩方程。通过在联合迭代中离散化空间和分子速度空间,可以解决这两个方程。显示了圆柱矩和二维矩方程之间的关系。进行了稳定性分析,以显示加速方法的改进迭代性能。模拟了管中压力驱动的流动以研究该方法。就所需的迭代次数和计算时间而言,在稀疏性参数的中间值和较高值时,加速方案比非加速标准方案优越。将流速和速度曲线与问题的解析离散纵坐标解决方案进行比较。两种方法提供的结果之间有很好的一致性。

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