一维平流输送问题的欧拉-泰勒-伽辽金算法及数值试验

介绍了一维常系数平流输送问题的Euler-Taylor-Galerkin(ETG)算法?为获得精确的时间导数,该算法采用了包括二阶和三阶时间导数的前向泰勒级数展开,这些导数值可从空间控制微分方程求出?由此产生一般的时间分离方程?该方程采用标准的Bubnov-Galerkin有限元方法在空间离散化?在使用线性元(帽子函数)和Euler时间差分格式时,可获得精确的Taylor-Galerkin算法?当采用2步显示步骤时,算法为计算效率很高的显式?数值实验结果显示,ETG算法的误差很小,而相误差更可忽略不计,结果令人满意 

A Euler-Taylor-Galerkin Method and Its Numerical Test for One Dimension Convective Transport Problem

In this paper, a Euler-Taylor-Galerkin algorism for constant coefficient one dimension convective problem is introduced. To obtain the accurate temporal differencing, the method employs forward-time Taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation. This yields a general time discretized equation which is successively discretized in space by means of the standard Bubnov-Galerkin finite element method. The technique is illustrated first in one dimension. With linear elements and Euler time stepping , several interesting relations with standard Galerkin and recently developed Petrov-Galerkin methods emerge and new Taylor-Galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping.