双曲守恒律系统的分段边界层函数方法(PBLM)

本文提出了一个新的高阶Godunov格式。此格式放弃了9]、10]中关于参数在格子中满足多项式分布近似及在格子边界上存在间断的假设,直接引入了一个分段边界层型函数分布假设。由于引入的分布函数是单调可微的,因此PBLM格式无需进行如同MUSCL、PPM等格式中的单调性校核。该格式由于不进行单调性修正,在PPM格式中需进行修正而精度降阶的点上仍保持原有精度。对一维激波管的计算表明PBLM格式对激波的展开比PPM格式还要小,计算时间相当。同PPM格式一样,PBLM格式在激波后存在有2%~4%的皮后伪振荡,应加上适当的人工粘性。

THE PIECE-WISE BOUNDARY-LAYER DISTRIBUTION METHOD FOR HYPERBOLIC CONSERVATIVE LAW SYSTEM

A new kind of high-order Godunovian scheme is suggested here, inwhich the hyperthesis of piece-wise linear or parabolic interpolation polynomial9],10]to construct the distribution with the discontinuity on net boundary is improved in this paper by introducing a piece-wise boundarylayer distribution. This kind of distribution is piece-wise montone and differentiable,so it is unneseccery to check the monotonuity like in PPM and MUSCL schemes.The new scheme called PBLM has hihg-order accuracy the same as PPM scheme, even on the points on which the accuracy only has 1-order in PPM scheme. The results of l-dimmensional shock tube show that the spread of shock in PBLM is thiner than that in PPM and the computational time is equivalent. Just as PPM,for PBLM scheme about 2%-4% oscillations occur behind the shock. The additional dissipation should be added.