An Adaptive-Mesh Finite-Difference Solution Method for the Navier-Stokes Equations

A variable-spacing grid system for finite-difference calculations is presented. The system allows single points to be added to or deleted from the mesh independently of each other, while maintaining each point at the center of a symmetrical cross formed with four other mesh points. The single finite-difference form of the steady, incompressible Navier-Stokes equations necessary for use with this system is written in a suitable form insuring stability, and the addition-deletion procedure is easily automated and transformed into a self-adjusting algorithm capable of recognizing the high-gradient regions of the solution field and selectively refining the mesh in those regions. It also determines the best-suited number of points for the calculation. The method is finally applied to two test cases to show its performance.