A windowed Fourier pseudospectral method for hyperbolic conservation laws
A windowed Fourier pseudospectral method for hyperbolic conservation laws
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DOI：
10.1016/j.jcp.2005.09.027
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发表时间：
2006-05
期刊：
影响因子：
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通讯作者：
Yuhui Sun;Yongcheng Zhou;Shu-Guang Li;G. Wei
中科院分区：
文献类型：
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作者：
Yuhui Sun;Yongcheng Zhou;Shu-Guang Li;G. Wei
利用一类局部谱小波滤波器，离散奇异卷积（DSC）滤波器，以方便傅立叶伪谱方法的双曲守恒律系统的解决方案。DSC低通滤波器直接在傅立叶域中自适应地实现（即，窗口傅立叶伪谱方法），同时也给出了一个物理域算法，使一些特殊的边界条件的处理。通过调整DSC滤波器的有效波数区域，可以有效地消除Gibbs振荡，而谱方法的高分辨率特性可以被保留用于具有各种边界条件的广泛问题。大量的数值实验验证了该方法的实用性和有效性。所提出的方法可以在分辨率高达每波长只有五个点（PPW）的冲击和物理高频波的相互作用，这是一些最好的这类问题。这种高分辨率，再加上快速傅里叶变换（FFT）的低复杂性，赋予所提出的方法相当大的潜力，解决大规模的双曲守恒律问题。
A class of local spectral wavelet filters, discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC lowpass filters are adaptively 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, Gibbs oscillations can be removed effectively while the high resolution feature of the spectral method can be retained for a wide class of problems with various boundary conditions. The utility and effectiveness of the present approach are validated by extensive numerical experiments. The proposed method could operate at a resolution as high as only five points per wavelength (PPW) for the interaction of shocks and physical high frequency waves, which is some of the best for this class of problems. This high resolution, together with the low complexity of the fast Fourier transform (FFT), endows the proposed method considerable potential for solving large scale problems in hyperbolic conservation laws.