可压缩Navier-Stokes方程三阶精度的求解

Solution of third order accuracy of compressible Navier-Stokes equation

为提高可压缩Navier-Stokes方程求解精度,提出基于双线性奇异摄动特征分析的可压缩Navier-Stokes方程三阶精度的求解方法。构建方程的三阶统计特征量解析模型,通过参数奇异摄动抑制方法分解方程三阶特征,提取方程的边值特征分量,结合边界层校正项信息融合度解析方法实现可压缩Navier-Stokes方程三阶融合和自相关特征分析。通过模板匹配寻优方法,实现方程的三阶非线性时滞奇摄动控制,完成可压缩Navier-Stokes方程三阶精度求解。结果表明,所提方法的收敛性较好,稳定性较高。

In order to improve the solution accuracy of compressible Navier-Stokes equations,a method for solving the third order accuracy of compressible Navier-Stokes equations was proposed based on bilinear singular perturbation feature analysis.The third-order statistical eigenvalue analytical model of the equation was constructed,and the third-order features of the equation were decomposed by the parameter singular perturbation suppression method,and the boundary value eigencomponents of the equation were extracted.The third-order fusion and autocorrelation analysis of the compressible Navier-Stokes equation were achieved by combining the boundary layer correction information fusion degree analytical method.And the third-order nonlinear singular perturbation control of the equation is realized through the template matching optimization method,and the third-order precision solution of the compressible Navier-Stokes equation is completed.The analysis shows that the proposed method has good convergence and high stability.