配置点谱方法-人工压缩法(SCM-ACM)求解不可压缩流体流动

摘要

开发了配置点谱方法 SCM(spectral collocation method)与人工压缩法 ACM(artificial compressibility method)相结合的方法SCM-ACM,用于求解不可压缩粘性流动问题.选取典型的方腔顶盖驱动流为研究测试对象,首先建立人工压缩格式的控制方程,其次采用SCM离散控制方程的空间偏微分项,推导出矩阵形式的代数方程,最后测试了SCM-ACM代码的有效性.结果显示,SCM-ACM 能够有效求解不可压缩流动问题,并继承了谱方法的指数收敛特性,且具有ACM求解过程简单及易于实施的特点.%The combined method spectral collocation method(SCM)and the artificial compressibility method(ACM)is developed in this work for solving incompressible viscous flow problems.The classical case of lid-driven cavity flow in a square cavity is selected to test the method.First of all,artificial compressibility governing equations are given.Secondly,the spatial partial differential terms of the governing equations are discretised by the SCM,and then,the algebraic equations in matrix form are obtained.Lastly,the validation of SCM-ACM code is made.The results show that the SCM-ACM can solve the problem of incompressible flow effectively,and it inherits the exponential convergence of the spectral method and has the characteristics of being simple and easy to implement derived from the ACM.