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拟线性频谱特性分析方法,能够更加准确地给出非线性空间离散格式的频谱特性,已成为非线性格式性能评估的重要手段,但时间离散方法和计算点数等因素严重影响了该方法的预估精度和使用的方便性。为了剔除这些因素的影响,首先,通过理论推导获得了与时间离散无关的频谱表达式,解释了该式中各项的物理含义,并给出了推进时间步长对频谱计算结果的影响;其次,基于时间离散无关的拟线性频谱分析方法,分析了格式频谱特性曲线在某些点发生跳跃的主要原因是选取了不恰当的计算点数,并给出了一种计算点数选取方法,当计算点数超过某整数后,该方法可以有效地消除计算点数和初始相位变化对格式频谱特性所带来的影响。在此基础上,基于两个三阶精度WCNS格式,开展了它们的频谱特性和典型算例的数值模拟研究,结果表明,所发展的方法得到的拟线性频谱特性在定性上能够正确评价非线性空间离散格式特性,但定量上仍显不足。
Quasi-linear spectral characteristics analysis method, which can give more accurate spectral characteristics of nonlinear spatial discrete format, has become an important method for nonlinear format performance evaluation. However, the time-discrete method and the number of calculation points seriously affect the estimation of the method Accuracy and ease of use. In order to get rid of the influence of these factors, we first obtain the spectrum expression unrelated to the time dispersion by theoretical derivation, explain the physical meaning of each term in the equation, and give the effect of advancing time step on the spectrum calculation result. Based on the time-discrete quasi-linear spectral analysis method, the main reason that the spectral characteristic curve of the format jumps at some points is that the improper calculation of the number of points is selected and a method of calculating the number of points is given. When calculating the number of points After an integer is exceeded, this method can effectively eliminate the influence of the calculated points and initial phase changes on the spectral characteristics of the format. On the basis of this, the two third-order precision WCNS schemes are used to study their spectral characteristics and numerical examples. The results show that the quasi-linear spectral characteristics obtained by the developed method can qualitatively evaluate the nonlinearity Spatial discrete format features, but still insufficient quantitative.