Boundary condition treatment in 2×2 systems of propagation equations
Boundary condition treatment in 2×2 systems of propagation equations
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DOI：
10.1002/(sici)1097-0207(19980630)42:4
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发表时间：
1998-06
影响因子：
2.9
通讯作者：
V. Guinot
中科院分区：
文献类型：
--
作者：
V. Guinot
水击现象的数值模拟涉及数值求解2×2传播方程组。在本文中，这个系统是解决使用分段抛物方法（PPM）计划，一个高阶扩展的Goddom方法。为了达到高阶离散精度，PPM格式使用空间中的六个点来求解平流方程。因此，边界条件的处理-这被证明是重要的水锤建模-是不简单的。本文提出了处理边界条件的几种选择，九种选择中只有一种组合可以提供良好的结果。这表明，如果边界条件处理不当，即使是非常精确的数值格式也可能对解决问题没有多大帮助。PPM方案给出的结果进行了比较与其他解决方案的技术（方法的特征-MOC），证明了上级的精度-效率的关系所使用的PPM超过通常的近似MOC。© 1998 John Wiley & Sons，Ltd。
Numerical modelling of the water hammer phenomenon involves solving a 2×2 system of propagation equations numerically. In the present paper, this system is solved using the Piecewise Parabolic Method (PPM) Scheme, a higher-order extension of the Godunov Method. To reach high-order discretization accuracy, the PPM scheme uses six points in space to solve the advection equation. Hence, treatment of boundary conditions—which proves to be of importance to water hammer modelling—is not straightforward. Several options for the handling of boundary conditions are presented herein, and only one combination among nine is shown to provide good results. This shows that even very accurate numerical schemes may be of poor help in problem solving if boundary conditions are not handled properly. Results given by the PPM scheme are compared with those given by other solution techniques (Method Of Characteristics—MOC), proving the superior accuracy–efficiency relations used by the PPM over the usual approximations of the MOC. © 1998 John Wiley & Sons, Ltd.