配置点谱方法-人工压缩法(SCM-ACM)求解同心圆筒内流体流动

Spectral collocation method-Artificial compressibility method(SCM-ACM)for solving the fluid flow in concentric cylinder

发展了配置点谱方法SCM(Spectral collocation method)和人工压缩法ACM(Artificial compressibility method)相结合的SCM-ACM数值方法,计算了柱坐标系下稳态不可压缩流动N-S方程组。选取典型的同心圆筒间旋转流动Taylor-Couette流作为测试对象,首先,采用人工压缩法获得人工压缩格式的非稳态可压缩流动控制方程;再将控制方程中的空间偏微分项用配置点谱方法进行离散,得到矩阵形式的代数方程;编写了SCM-ACM求解不可压缩流动问题的程序;最后,通过与公开发表的Taylor-Couette流的计算结果对比,验证了求解程序的有效性。结果证明,本文发展的SCM-ACM数值方法能够用于求解圆筒内不可压缩流体流动问题,该方法既保留了谱方法指数收敛的特性,也具有ACM形式简单和易于实施的特点。本文发展的SCM-ACM数值方法为求解柱坐标下不可压缩流体流动问题提供了一种新的选择。

The SCM-ACM numerical method is developed by combing the spectral collocation method(SCM)and the artificial compressibility method(ACM)in this work.The incompressible flow N-S equations in the cylindrical coordinate system are solved.The Taylor-Couette flow which is a typical concentric cylinder-rotating flow is selected as the test object.Firstly,the artificial compressibility method is used to obtain the unsteady compressible flow governing equations with the artificial compressibility format,and then the spatial partial differential terms in the governing equations are discretized by the spectral collocation method.The algebraic equations in matrix form are obtained.The computer codes of SCM-ACM are developed to solve the incompressible flow problem.The validity of the solver is confirmed by comparing with the published results of Taylor-Couette flow.The results show that the SCM-ACM numerical method developed in this paper can be used to solve the problem of incompressible fluid flow in a cylinder,which not only retains the exponential convergence characteristics of the spectral method,but also has the characteristics of simplicity and implementablity of ACM.The SCM-ACM numerical method developed in this paper provides a new choice for solving the problem of incompressible fluid flow in the cylindrical coordinate system.