Abstract: A new self-adapting grid method is presented by adding the new point atthe centre of the grid cell. Compared with the traditional method addingthe new point at the median, the new refine method is more convenient toprogram and has better geometrical feature. At last, this paper combinesthe new refined method with characterized based split method to solveN-S equation. The convective acceleration term disappear along thecharacteristic. In order to avoid the restriction on the nature of theinterpolation function, the momentum equation is solved bynon-incremental split method, which satisfies the Babuska-Brezzi(BB)condition. The variable gradient is used as the adaptive parameter. Theresult shows the combined method has goodprecision and convergence.