High Accuracy Compact Schemes and Gibbs' Phenomenon
High Accuracy Compact Schemes and Gibbs' Phenomenon
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DOI：
10.1007/s10915-004-1317-2
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发表时间：
2004-12
影响因子：
2.5
通讯作者：
T. Sengupta;G. Ganerwal;A. Dipankar
中科院分区：
文献类型：
--
作者：
T. Sengupta;G. Ganerwal;A. Dipankar
紧致差分格式因其捕捉间断的能力而被研究。一个新的提议方案(Sengupta，Ganerwal和de(2003).J.Comp.物理192(2)、677。)与文献钟(1998)中的另一个作了比较.J.Comp.Phys.144,622是为高超声速过渡流而开发的，其特性与光谱分辨率和数值稳定性有关。得到了需要捕捉不连续面的线性对流方程的解。我们还研究了新格式在捕获Burgers方程间断解方面的性能。本文提出了一种非常简单但有效的方法来对瞬逝间断进行早期诊断。在不连续处，我们切换到三阶单面模板，从而保持了解的高精度。这就产生了解，极大地减少了吉布斯解的现象。还解释了吉布斯现象背后的根本原因。
Compact difference schemes have been investigated for their ability to capture discontinuities. A new proposed scheme (Sengupta, Ganerwal and De (2003).J. Comp. Phys.192(2), 677.) is compared with another from the literature Zhong (1998).J. Comp. Phys.144, 622 that was developed for hypersonic transitional flows for their property related to spectral resolution and numerical stability. Solution of the linear convection equation is obtained that requires capturing discontinuities. We have also studied the performance of the new scheme in capturing discontinuous solution for the Burgers equation. A very simple but an effective method is proposed here in early diagnosis for evanescent discontinuities. At the discontinuity, we switch to a third order one-sided stencil, thereby retaining the high accuracy of solution. This produces solution with vastly reduced Gibbs' phenomenon of the solution. The essential causes behind Gibbs' phenomenon is also explained.