基于Taylor展开的分步有限元格式

A Fractional Step Finite Element Method Based on Taylor Expansion -Stability and Accuracy Analysis

描述了一种基于Taylor展开的分步有限元数值格式 ,该法在时间上进行分步计算 ,在空间上采用标准的Galerkin有限元格式 .对该数值格式的稳定性分析表明 ,该法在时间和空间上均具有三阶精度 ,数值稳定性好 ,在库朗数 0～ 1的范围内均收敛 .相比于Taylor Galerkin法 ,本有限元法不包含高阶微分项 ,适用于非线性多维问题及具有复杂边界形状的流动 .该法具有计算简便、精度高、数值稳定性好等优点 .

A fractional step finite element method based on Taylor expansion theory is proposed for unsteady flows, by which time discretization is carried out in 3 steps and spatial discretization is done by the conventional Galerkin method. The stability and accuracy analysis for one dimensional and multi-dimensional pure convection problem is made. The results show that the present method is of third order accuracy and is stable for Courant Number 0～1. Compared with the Taylor-Galerkin method, the present method has no higher order derivative terms and is suitable for nonlinear multi-dimensional flow problems.