Abstract: The study by H.X.Zhang shows that in order to suppress the spurious oscillation at both upstream and downstream of the shock, the coefficient of the third-order derivative on the right hand side of the modified equation of the difference scheme must be positive upstream and negative downstream of the shock. According to this principle, a new non-oscillatory, containing no free parameters and dissipative difference scheme of second-order both in time and space is proposed. It is proved that this scheme possesses TVD property and is generalized Gudunov scheme of second-order. In the presence of the shock wave in the flow field, this scheme is the generalization and improvement of the Lax-Wendroff scheme. Several numerical examples are given which demonstrate that the proposed scheme is non-oscillatory of high order accuracy and high resolution. It also has the advantages of compact form, greater maximum allowable Courant number and convenient to use.

Key words: new NND difference scheme, Euler equation