High-precision Numerical Calculation Method And Its Application

For applications involving shocks, second order schemes such as TVD schemes are usually adequate if only relatively simple structures are present in the smooth part of the solution. However, High order shock capturing schemes(order of at least three) are more efficient than low order schemes when a problem contains rich structures as well as schocks. In this paper, we analyzed and discussed the basic principle of the recently developed high order accuracy finite difference schemes ?ENO schemes and WENO schemes. Based on 2nd order NND schemes, we introduced a 3rd order WNND scheme with Jiang and Shu's "weighted" idea and a TVD Runge-Kutta time discretization method. We practically applied the WNND scheme to solve scalar conservation laws and Euler system in one dimension and N-S equations in two and three dimensions. The numerical results of WNND schemes indicated good shock transitions without any noticeable oscillations and uniformly high accuracy in smooth regions. The WNND scheme could catch the detail of the flow field more particularly. Taking accuracy, robust and computational efficiency into consideration, we expect a far-ranging application in computational fluid dynamics scopes in the future.