双曲守恒律的一种实用谱方法
A practical spectral method for hyperbolic conservation laws
AI总结：
本文提出利用离散奇异卷积滤波器改进傅里叶伪谱方法，通过调整有效波数区域去除吉布斯振荡并保留高分辨率，数值实验验证了其有效性。
摘要：
本文利用一类高阶低通滤波器，即离散奇异卷积（DSC）滤波器，来促进傅里叶伪谱方法求解双曲守恒律系统。DSC滤波器直接在傅里叶域中实现（即加窗傅里叶伪谱方法），同时给出物理域算法以处理某些特殊边界条件。通过调整DSC滤波器的有效波数区域，可以有效去除吉布斯振荡，同时保留谱方法的高分辨率特性。大量数值实验验证了该方法的实用性和有效性。
英文摘要：
A class of high-order lowpass filters, the discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC filters are implemented directly in the Fourier domain (i.e., windowed Fourier pseudospectral method), while a physical domain algorithm is also given to enable the treatment of some special boundary conditions. By adjusting the effective wavenumber region of the DSC filter, the Gibbs oscillations can be removed effectively while the high resolution feature of the spectral method can be retained. The utility and effectiveness of the present approach is validated by extensive numerical experiments.
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