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Meshing plays an important role on the accuracy and convergence of CFD solvers. The accuracy includes quantitative measures such as discretization and truncation errors and qualitative measures such as drawing closed streamline, identifying singular points, asymptotic lines/planes, and (symmetry) axis. The current study builds on previous work by further demonstrating the accuracy of the three-dimensional adaptive mesh refinement method by comparing the accuracy measures between the ones derived from analytical velocity fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is proposed based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The performance of the adaptive mesh refinement method is analysed using three-dimensional analytic velocity fields of four examples. The results provide evidence for the accuracy of the mesh refinement method in identifying the singular points, axes, and asymptote planes of the analytical velocity fields.

adaptive mesh refinement, Navier-Stokes equations, Computational fluid dynamics