CAJ | 학술논문

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.
침대CAE방진기술중편미분방정수치모형구해적은정성、준학성이급보장삼수설치문제,채용CAE기술중상용적일계영풍격식、Lax-Wendroff격식이급은식중심격식분별대쌍곡편미분방정수치모형진행계산분석.결과표명：Lax-Wendroff격식구유교고적구해정도,이은식중심격식속우무조건은정,기구해역우수렴；재만족차분계산은정성적조건하,수착시간보장τ적감소,차분수치해적결과오차축점강저,단시기구해정도주요의뢰합괄적차분격식.
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.