在不规则四边形网格上逼近扩散算子的五点及九点差分格式的测试

在Lagrange坐标下使用四边形网格进行二维辐射流体力学数值计算的难点之一是需要构造在不规则四边形网格上仍能较好地逼近扩散算子的差分格式。本文就五点差分格式和目前常用的九点差分格式进行了比较全面的数值测试和理论分析。结果表明五点格式仅在均匀矩形网格上具有二阶逼近精度，九点格式仅在均匀平行四边形网格上具有二阶逼近精度，这两种格式在一般的不规则四边形网格上通常都是不相容的。尽管九点格式优于五点格式，但它对不规则网格的适应性远不如人们以前所想象的那么好。由此可见，为了进一步改进二维辐射流体力学的数值计算，构造真正能在比较一般的不规则四边形网格上逼近扩散算子的更为优越的差分格式是一件迫在眉睫的事。

Numerical Experiments for FivePoint and Nine-Point Difference Approximation of Adiffusion Operator on Irregular Quadrilateral Grids

One of the difficulties for the numerical solution of two-dimensional Lagrangian radiation hydrodynamic equations is to construct good difference schemes over irregular mesh. In this paper, a series of numerical experiments and some theoretical analysis have been done carefully for the well known difference schemes of five-point and nine-point which provide approximations to the diffusion operator in the two-dimensional energy equation with three-temperature. The results obtained show that the five-point scheme and nine-point scheme are consistent of order two over uniform rectangle mesh and uniform parallelogram mesh respectively, however, which are in general not consistent over irregular quadrilateral mesh. Although nine-point scheme is superior to five-point scheme, yet its efficiency is not as good as that we have been thought, and therefore in order to improve numerical calculation of radiation hydrodynamics, it is emergent to construct new difference scheme which really approximates to the diffusion operator over general irregular quadrilateral mesh.