An Adaptive Streamline Tracking Method for Three-Dimensional CFD Velocity Fields Based on the Law of Mass Conservation

This paper proposes an adaptive streamline tracking method for three-dimensional CFD velocity fields. We assume that the multiplication of an unknown scalar function and the linear interpolation of a CFD velocity field satisfies the law of mass conservation and then derive the expressions of the scalar function. The adaptive streamline tracking method subdivides a hexahedron of hexahedral meshes into smaller hexahedra when there are points in the hexahedron at which the scalar function equals to infinity and then seeks more data of the CFD velocity fields at the vertices of the smaller hexahedra if the values of the CFD velocity field are unknown. The subdivision can be an infinity process. We introduce a threshold number to measure how many times we will subdivide the hexahedra in the initial mesh. The accuracy of computation depends on the initial mesh and the threshold number. Exact tangent curves for linear vector fields are used to draw streamline segments in tetrahedra that are obtained from subdividing hexahedra. Examples in the last section show that the adaptive streamline tracking method can be used to draw more accurate streamlines if we choose a larger threshold number.