The flow due to rotating surfaces in a cylindrical enclosure is commonly used in many applications such as rheometry, electronic cooling, and turbomachinery, and has drawn scientists' attention for many years. The main objective of this study is to solve the problem with a robust and efficient code. It is achieved by using the 'Portable, Extensible Toolkit for Scientific computation' (PETSc), which is a computational tool for the parallel solution of scientific problems. By keeping the Newton's method as the non-linear solver, different linear solvers, preconditioning techniques, and numbers of processors are tested for the performance. In addition to computational parameters such as the performance of the linear solver, performance of the preconditioner, parallel performance, and grid dependence, the effects of some physical parameters such as the Reynolds number, aspect ratio, and altering of the rotating surface are investigated. The results indicate that the core of the circulation moves towards the stationary boundaries and the boundary layers become thinner with the increasing Reynolds number. Furthermore, decreasing the aspect ratio makes diffusion harder and lowers the maximum velocities. Some of the results are compared with data in the literature.
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