液压管道脉动流问题的激波计算

Computation of Shock Wave of Impulsive Flow Problem in A Hydraulic Pipe

本文将管道脉动流撞击液压问题作为一维非定常可压缩流,其激波在数学上即是两个自变量的一阶拟线性双曲型偏微分方程组的初边值问题的间断解。我们给出了其间断解应满足的连结条件和稳定性条件,并讨论了其激波计算,指出了所采用的一阶偏心四点差分格式的统一性和稳定性及矩阵追赶法的稳定性和迭代过程的收敛性的条件。

In this paper the shock wave solution of impulsive flow in a hydraulic pipe due to impact is analysed as one dimensional non-stationary compressible flow. The connection condition and the stability condition for a discontinuous solution are given mathematically as an initial-boundary value problem for first order quasilinear hyperbolic systems of partial differential equations with two variables. The computation of the shock wave is discussed. The conditions of unity and stability of the first-order four-point eccentric difference scheme, the stability of the matrix pursuing method and the convergence of the iterative process are pointed out.