任意流场中稀疏颗粒运动方程的数值解法及其应用

任意流场中稀疏颗粒运动方程是一非线性的微分积分方程，极难获得解析解。本文首先对方程中Ｂａｓｓｅｔ力项构造了适当的计算格式，然后详细研究了颗粒运动方程的数值计算方法并提出称之为Ｐ（ＥＣ）＾ｋ多步法的差分格式，简要分析了该格式的收敛性和代数精度，给出了时域离散长长必满足的条件。

On Numerical Method of Resolving Discrete Solid Particles' Motion Equation and Its Applications

Since the motion equation of dilute particles in arbitrary flow field is a nonlinear differential and integral equation, it is very hard to get its analytical solution. In this paper, for a computing scheme the Basset force term is constructed and then the numerical method for solving the motion equation of dilute particles is carefully researched for which a difference scheme called P(EC) k multi step method is presented. The convergence and algorithm accuracy of the numerical method are briefly analyzed, and a constraint relation which discrete time step length must satisfy is presented. Finally, the P(EC) k numerical method is applied to calculating the motion of dilute particles in uniform flow and in the 2 D vertical jet stagnant zone towards an unbounded plate, leading to some meaningful conclusions. By comparison of numerical results in the case of uniform flow with the corresponding analytical solutions, one can find they are in good agreement, which proves the high accuracy of the numerical method has very high accuracy.