The RKDG method, proposed by Cockburn & Shu (1988), is developed into solution of N-S equation, and the results are compared with exact solution of Burger equation with viscousity. The result of 2D problem has been also compared with the one obtained by solving Euler equation.

A technique to generate unstructured grids in arbitrary 2D region is presented depending upon the new idea to smooth the grid scale,which gives new explanation of filtered Laplace operator.Choosing appropriate relaxation factor,the iterative number in smooth process max be reduced greatly.The automatic refine of grid is developed and it can be used in adaptive process.The numerical examples show efficients of the present methods.

The basic principl of LES and SGS modelling is described. This method is used to simulate the fully-developed turbulent flow in a curved square duct numerically. Its results are compared with other numerical prediction. The structures in turbulent flow are disccused.

The detailed formulae of Navier-Stokes equations in the orthogonal curved coordinate system, the numerical methods for the integration of the momentum equations and the solution of Polisson equation of pressure are described. The fully developed laminar flow in acurved duct of rectangular cross-section is simulated numerically and the results are compared with other results.

The marching-iterative method(MIM) is extended to solve the N-S equation of the steady incompressble viscous flow. The general formula in arbitrary curved coordination are also given.The MIM sis used to calculate the flows in a cavity and around a cylinder.The reults show that the speed of convergency of this method is rapid and the satisfactory results can be obtained from this method.