In this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

中文翻译：

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解高维对流方程的高阶紧凑型LOD方法

本文采用局部一维（LOD）方法，对截断误差余数中的三阶导数进行泰勒级数展开和校正，建立了两种高阶紧凑型LOD方案来求解二维和三维对流等式。它们在时间和空间上都具有四阶精度。通过冯·诺依曼分析方法，表明这两种方案都是无条件稳定的。此外，还证明了它们的一致性和收敛性。最后，通过数值实验证实了该方案的准确性和有效性。