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本文着重从两个方面研究圣·维南方程中阻力项对解决一维明渠非恒定流问题数值计算稳定性的影响。通过数值试验验证了考虑阻力影响的卡宁稳定附加条件,无论从扩散法还是从特征线法都证明了这一条件的正确性。通过以半隐式格式和引入权因子来表达阻力项,找到了这些因素变化对稳定性的影响,并得到了最稳定的格式不一定是最精确的结论。
This article focuses on two aspects to study the influence of resistance items in Sheng Weinan equation on the numerical stability of solving one-dimensional open channel unsteady flow problems. By numerical experiments, the additional Kalin ’s stability conditions considering the influence of resistance are verified. The correctness of this condition is proved both in the diffusion method and the characteristic method. By expressing the resistance terms in a semi-implicit format and introducing a weight factor, it is not necessarily the most accurate conclusion to find out the influence of these factors on the stability and obtain the most stable format.