ENERGY ESTIMATES FOR DISCRETIZATION ERRORS IN WATER HAMMER PROBLEMS
ENERGY ESTIMATES FOR DISCRETIZATION ERRORS IN WATER HAMMER PROBLEMS
复制标题
水锤问题中离散化误差的能量估计
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
D. McInnis
中科院分区：
文献类型：
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作者：
M. Ghidaoui;B. Karney;D. McInnis
采用固定网格法的特征线法，建立了求解管道暂态问题的综合能量法。目标是了解与常见内插方案相关的离散化误差是如何产生的，以及如何控制这些误差。具体来说，新的解析能量表达式表明，时间线和空间线内插都衰减了系统的总能量；相反，波速调节方法保留了总能量，但扭曲了动能和内能的分配。通过对多个串联管系的数值研究，验证了分析结果的正确性。数值实验和数学表达式都表明，只要系统中的工作是连续和实质性的，离散化误差就很小，可以忽略不计。然而，当功很小或可以忽略时，需要一个接近1的Courant数Cr值来控制数值耗散。
An integrated energy approach is developed for transient problems in pipelines using the fixed-grid method of characteristics. The goal is to understand how discretization errors associated with common interpolation schemes arise and how these errors can be controlled. Specifically, new analytical energy expressions demonstrate that both time-line and space-line interpolation attenuate the total energy of the system; in contrast, the wave-speed adjustment approach preserves the total energy but distorts the partitioning between kinetic and internal energy. The analytic results are confirmed through numerical studies of several series pipe systems. Both the numerical experiments and the mathematical expressions show that the discretization errors are small and can be ignored as long as the work in the system is continuous and substantial. When the work is small or negligible, however, a Courant number Cr value close to 1 is required to control the numerical dissipation.