时间空间均为二阶的新型NND差分格式

张涵信的研究表明,为了避免激波前后差分解的波动,在差分格式的改型方程中三阶导数的系数在激波上游必须是正的,而在激波下游则必须是负的.据此提出了一种新型的无波动、无自由参数耗散性的差分格式,它对时间和空间都是二阶的.证明了此格式是TVD的,而且是推广的二阶Годунов格式.在处理有激波的流场时,此格式是Lax-Wendroff格式的改进和推广.给出了若干算例,计算结果表明,此格式不仅无波动,而且具有形式紧凑、应用方便、分辨率高、稳定性准则中的Courant数较大的优点.

A New NND Difference Scheme of Second Order in Time and Space

The study by Zhang Hanxin 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.