Mesh generation is one of key issues in Computational Fluid Dynamics. This paper presents an adaptive three-dimensional mesh refinement method based on the law of mass conservation. The method can be applied to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. Users can choose how many refinements they want to perform on the initial mesh. The more the number of refinements, the less the error of calculations is. The refined meshes can identify the accurate locations of asymptotes, the points at which one, two, or all components of velocity fields are equal to zero, and draw accurate closed streamlines if the number of refinements is big enough and the initial mesh is fine enough. We show three examples that demonstrate the claims.
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