A high-order spatiotemporal precision-matching Taylor-Li scheme for time-dependent problems
A high-order spatiotemporal precision-matching Taylor-Li scheme for time-dependent problems
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解决瞬态问题的高阶时空精度匹配 Taylor-Li 方案
DOI：
10.1007/s00376-017-7018-1
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发表时间：
2017-12-01
影响因子：
5.8
通讯作者：
Wang，Pengfei
中科院分区：
文献类型：
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作者：
Wang，Pengfei
基于Taylor级数方法和Li空间微分方法，提出了一种高阶混合Taylor-Li格式。线性平流方程的结果表明，使用方波类型的初始值，与三阶精度的结果发生。然而，使用与高斯函数类型相关联的初始值，会出现具有非常高精度的结果。研究表明，当时间积分的阶数大于3时，相应的最优空间差分阶数可以大于6。结果表明，空间差分阶数大于6时，计算结果没有明显改善的原因是采用的时间积分格式不够高。作者还提出了一种递归微分方法来提高Taylor-Li格式的计算速度。采用了比直接计算高阶空间微分项更快速、精度更高的程序，大大提高了计算速度。基于一个多精度库，超高阶Taylor-Li格式可以用来求解对流方程和Burgers方程。
Based on the Taylor series method and Li’s spatial differential method, a high-order hybrid Taylor–Li scheme is proposed. The results of a linear advection equation indicate that, using the initial values of the square-wave type, a result with third-order accuracy occurs. However, using initial values associated with the Gaussian function type, a result with very high precision appears. The study demonstrates that, when the order of the time integral is more than three, the corresponding optimal spatial difference order could be higher than six. The results indicate that the reason for why there is no improvement related to an order of spatial difference above six is the use of a time integral scheme that is not high enough. The author also proposes a recursive differential method to improve the Taylor–Li scheme’s computation speed. A more rapid and high-precision program than direct computation of the high-order space differential item is employed, and the computation speed is dramatically boosted. Based on a multiple-precision library, the ultrahigh-order Taylor–Li scheme can be used to solve the advection equation and Burgers’ equation.