非结构网格上新型的 NND 有限元格式

A New NND Finite Element Scheme on Unstructed Grid

张涵信［１］发展的ＮＮＤ差分格式是由中心差分格式、二阶迎风格式和一阶迎风格式混合组成的杂交型格式。众所周知，和中心差分格式相对应的是Ｇａｌｅｒｋｉｎ有限元格式。通过对中心型有限元格式加修正项的方法本文成功地构造出二阶迎风型有限元格式和一阶迎风型有限元格式。通过在非结构网格上实现导数的单侧有限元计算，使得判断间断前后和实现二阶迎风型有限元格式成为可能。本文将这些格式组合起来，首次得到了非结构网格上的无波动无自由参数耗散性的有限元格式，即ＮＮＤ有限元格式。通过若干个典型的二维跨声速和超声速可压缩无粘流动的算例证明这确是一个高精度的，对激波具有高分辨率的无波动的新型有限元格式。特别是，与网格自适应相结合，可得到十分满意的结果。

The NND finite element scheme developed by Zhang Hanxin is a mixed scheme containing central difference scheme,second order upwind scheme and first order upwind scheme.Adding a corrected term to the central finite element scheme,the second order and first order finite element schemes are constructed.The one side finite element calculation of the derivative on the unstructed scheme makes the judgement of the upstream regions and downstream regions possible.Combining these schemes,a new non oscillatory,containing no free parameter and dissipative scheme,i.e.NND finite element scheme is constructed at first time on unstructed grid.Several numerical results of typical examples for two dimensional inviscid compressible transonic and supersonic steady flow demonstrate that this is a new finite element scheme with high accuracy and high resolution for shock wave.Especially,intergrating with the adaptive remeshing technique,the satisfactory results can be obtained by this scheme.