偏微分方程差分格式算法的适用性研究

The Research on the Applicability of the Difference Algorithms to Solve the Partial Differential Equation

针对CAE仿真技术中偏微分方程数值模型求解的稳定性、准确性以及步长参数设置问题,采用CAE技术中常用的一阶迎风格式、Lax-Wendroff格式以及隐式中心格式分别对双曲偏微分方程数值模型进行计算分析.结果表明:Lax-Wendroff格式具有较高的求解精度,而隐式中心格式属于无条件稳定,其求解易于收敛;在满足差分计算稳定性的条件下,随着时间步长τ的减小,差分数值解的结果误差逐渐降低,但是其求解精度主要依赖合适的差分格式.

The first-order upwind, the Lax-Wendroff format and implicit center formats of the usual difference algorithms in the CAE technology are analyzed to study the stability, accuracy and the parameter settings of numeri- cal solution of the hyperbolic partial differential equation. The results show that the Lax-Wendroff format has high accuracy, and the implicit central format is unconditional stable and easy to reach convergence; then, on the condition of the difference calculation stability, the error of the solution difference numerical solution is gradually reduced with the reducing of time step, but its accuracy is mainly dependent on the appropriate differential format.