Abstract:

According to the mesh-free method based on local Cartesian frame proposed by the author, partial derivatives at every node and natural boundary conditions are constructed by using the total directional derivative formulas. No mesh element is needed at all. Therefore it is very simple both theoretically and computationally. The method is tested with a numerical example of fluid flow. A reliable solution is obtained with high accuracy and efficiency.

Key words:  mesh-free method; total directional derivative; second type of boundary conditions