一种新的无矩阵运算的高效差分格式

A NEW KIND OF HIGH EFFICIENT NON-MATRIX CALCULATION DIFFERENTIAL SCHEME

本文提出了一种新的显、隐两步差分格式。该格式在构造显式和隐式差分步时，采用即时修正的思想，充分利用了ｎ＋１时刻点的信息值，从而可以加速边界信息在计算区域的传播速度；同时，在隐式步计算中，结合谱半径思想，简化了格式，完全避免了矩阵运算。通过对一维缩放喷管算例的计算表明，新格式可以减少 ３／４～１／２的计算时间，是一种高效的差分格式。

A new kind of explicit-implicit differential scheme is developed in this paper. The process of the boundary information propagation is accelerated with the immediate update method in which the information of the n+1 time step is applied. Meanwhile, the form of the implicit part is simplified and the matrix calculation is avoided. An example on a quasi-one dimensional flow in a Layal Nozzle is provided, which testifies the efficiency of the new scheme with the result of saving about three quarter to half of the calculation time compared with the old scheme.