The explicit and implicit methods are employed in the numerical simulation of unsteady transonic NACA10012 airfoil flow,and comparison analyses have been made in the respects of computational results,efficiency,and sensitivity to grid quality.

An implicit difference scheme solving Euler equations is developed based on NND ideas. Numerical test of diaphragm rupture in one-dimensional shock tube is carried out. The results are compared with those of implicit flux vector fractorization and explicit NND scheme. Extended to axisymmetric Euler equations, this scheme can be used to calculate the transonic flow near M_∞=1 for sphere cylinder.

A class of second-order explicit and implicit symmetric total variation diminishing (TVD) schemes is constructed for the computation of weak solutions of hyperbolic conservation laws.The resulting scheme can be viewed as a limited anti-diffusive flux, that is centered weighted flux, to add to a first-order GCIR scheme. Numerical experiments for solving the Euler equations for capturing shock waves show that the symmetric TVD schemes are quite robust and accurate.