三点强紧致加权高分辨率高阶格式及其应用

THREE POINT STRONGLY COMPACT WEIGHTING HIGH RESOLUTION HIGH ORDER SCHEME AND ITS APPLICATION

本文分别给出了采用有限体积计算时采用高阶格式遇到的网格单元体界面上三阶、四阶与五阶格式精度下的数值通量表达式,并且给出了确定权函数过程中所遇到的光滑因子表达式．文中首先对模型方程进行了格式分辨率方面的检验,然后将格式用于某涡轮级的实际流场计算．数值结果表明:所给出的高分辨率、高阶格式具有较高的激波分辨率并且具有较高的数值精度,在计算流场时,它可以用较少网格点去取代普通低阶精度格式下所采用的较密网格．

Three-order, four-order and five order accurate numerical flux expressions in grid cell interface which were used in finite volume method with high order and high resolution scheme are present. The expressions of smooth factor which used in confirming the scheme of the weighting function are also be given in the paper. At first, the resolution of the scheme of the model equation is examined, then the scheme is used in calculating the flow field of one turbine stage. The numerical result shows that the high-resolution and high-order scheme presented in the paper has higher resolution on shock-wave problems and higher numerical accuracy. Comparing with common low-order-accurate scheme, fewer grid points are needed in the schemes in computing flow fields.