Efficient implementation of weighted ENO schemes
Efficient implementation of weighted ENO schemes
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DOI：
10.1006/jcph.1996.0130
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发表时间：
1996-06-01
影响因子：
4.1
通讯作者：
Shu, CW
中科院分区：
文献类型：
--
作者：
Jiang, GS;Shu, CW
本文进一步分析、检验、修正和改进了Liu，Osher和Chan的高阶韦诺（Weighted Essentially Non-Oscillating）有限差分格式，Liu等人证明了由r阶（L（1）范数）ENO格式构造的韦诺格式具有r + 1阶精度.我们提出了一种新的测量数值解光滑性的方法，模仿最小化近似的总变差的思想，从而在r = 3的情况下得到了一个五阶韦诺格式，而不是Liu等人的四阶WENO格式。这个五阶韦诺格式与Liu等人的四阶韦诺格式一样快。这两种格式在Vector超级计算机上的计算速度大约是四阶ENO格式的两倍，在串行和并行计算机上的计算速度也差不多。对于Euler方程组，我们建议用压力和熵代替特征值来计算权系数，以简化代价很大的特征计算过程。所得的韦诺格式比用特征分解计算权系数的韦诺格式快一倍左右，并且对于不含强激波或强反射波的问题也能很好地工作。我们还证明了，对于具有光滑解的守恒律方程组，所有韦诺格式都是收敛的。通过对一维定常喷管流场和二维激波熵波干扰问题的数值试验，证明了韦诺格式的优良性能，特别是采用新的光滑性度量的韦诺格式在求解复杂激波和流场结构方面的应用，我们还将Yang的人工压缩方法应用于韦诺格式，以锐化接触间断。(C)出版社：Academic Press，Inc.
In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher, and Chan, it was shown by Liu et al. that WENO schemes constructed from the rth order (in L(1) norm) ENO schemes are (r + 1)th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of The approximation, which results in a fifth-order WENO scheme for the case r = 3, instead of the fourth-order with the original smoothness measurement by Liu et al. This fifth-order WENO scheme is as fast as the fourth-order WENO scheme of Liu et al, and both schemes are about twice as fast as the fourth-order ENO schemes on Vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest computing the weights from pressure and entropy instead of the characteristic values to simplify the costly characteristic procedure, The resulting WENO schemes are about twice as fast as the WENO schemes using the characteristic decompositions to compute weights and work well for problems which do not contain strong shocks or strong reflected waves, We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent, Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy wave interaction problem, are presented to demonstrate the remarkable capability of the WENO schemes, especially the WENO scheme using the new smoothness measurement in resolving complicated shock and flow structures, We have also applied Yang's artificial compression method to the WENO schemes to sharpen contact discontinuities. (C) 1996 Academic Press, Inc.