An adaptive three-dimensional mesh refinement method based on the law of mass conservation

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 used to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. Users can choose how many times refinements they want to perform on the initial mesh. The more times the 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 equal 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.