高阶特征线性及其与semi-Lagrangian方法的比较

A High Order Characteristic Method and Comparison with the Semi-Lagrangian Method

特征线性与semi-Lagrangian方法都是处理流体方程时间离散的两种有效的方法。它们比经典的半隐格式,如Backward-Euler/adams-Bashforth方法有更好的稳定性。本文提出一种基于高阶空间离散的特征线法,通过稳定性,精度和计算复杂性与semi-Lagrangian方法进行比较,分析了高阶特征线法的有效性和适用性,并从数值试验上对分析结果进行验证。

The characteristic method and semi-Lagrangian method are efficient ways to deal with the time-discretization of fluids equations > which have better stability properties as compared with the classical semi-implicit Backward-Euler/Adames-Bashforth method. In this paper we introduce a characteristic method based on high order space discretization and compare it with the semi-Lagrangian method in term of stability, accuracy and computational complexity- Lastly, we show some numerical results.