Numerical Analysis of Fluid-Hammer Waves by the Method of Characteristics
Numerical Analysis of Fluid-Hammer Waves by the Method of Characteristics
复制标题
液锤波的特征值法数值分析
DOI：
10.1016/0021-9991(76)90066-8
复制
发表时间：
1976
影响因子：
4.1
通讯作者：
R. Valentin
中科院分区：
文献类型：
--
作者：
Y. Shin;R. Valentin
本文将二维平面或轴对称系统中流体冲击现象的准线性双曲型微分方程表示为沿着双特征线和流线的积分。一个逐步的解决方案的过程中构造的替代积分的近似公式。通过线性组合剩余的差分关系，消除了因变量在特征锥外方向上的导数，得到了显式解。对由这两个近似公式得到的两种解的稳定性进行了检验，并对平面声波从90°尖角衍射进行了数值计算，与解析解和实验结果进行了比较。数值结果进一步得到一个简单的问题，涉及突然膨胀和收缩，并与一维声学解决方案的结果进行了比较。
The quasi-linear hyperbolic differential equations governing fluid-hammer phenomena in a two-dimensional plane or axisymmetric system are written as integrals along bi-characteristics and a streamline. A stepwise solution procedure is constructed by replacing the integrals by approximation formulas. Derivatives of dependent variables in directions outside the characteristic cone are eliminated and explicit solutions are obtained by linearly combining the remaining difference relations. Two solution schemes resulting from the two approximation formulas are examined for their numerical stability.Numerical calculations are carried out for a plane acoustic wave diffracting from a 90° sharp corner, and the result is compared with analytical solutions and experiment. Numerical results are further obtained for a simple problem involving a sudden expansion and contraction and the results are compared with one-dimensional acoustic solutions.