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**Spectral collocation method-artificial compressibility method (SCM-ACM) for solving the fluid flow in concentric cylinder.**
*(Chinese.
English summary)*
Zbl 1463.76037

Summary: 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 implementability 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.

### MSC:

76M22 | Spectral methods applied to problems in fluid mechanics |