非结构网格下非定常流场双时间步长的加权ENO-强紧致杂交高分辨率格式

针对三维非定常、可压缩流场的Navier-Stokes方程组,本文提出一种新的双时间步长高精度快速迭代格式。该格式在时间上具有二阶精度,在空间离散上不低于三阶。在对流项与粘性项的处理上,本格式分别采用了加权ENO-强紧致格式与紧致四阶精度格式的思想。几个典型算例的实践表明:计算结果与相关实验数据比较吻合,初步表明了该算法可以在非结构网格下具有高效率与高分辨率的特征。

A NEW WEIGHTED END-STRONGLY COMPACT DIFFERENCE SCHEMES AND DUAL-TIME METHOD FOR THE SOLUTION OF THE UNSTEADY FLOWS ON UNSTRUCTURED GRIDS

A new shock capturing finite difference dual-time method of weighted END and strongly compact difference-based finite-volume type is presented for solving three-dimensional, unsteady Navier-Stokes equations on unstructured grids. The present numerical method has the second order accuracy in time and no than the third order accuracy in space. The convective numerical flux functions of the fundamental governing equations are estimated using third order weighted END scheme and strongly compact scheme, based on an approximate Riemann solver. The viscosity items of Navier-Stokes equations are estimated using fourth order accurate strongly compact scheme. In the current paper numerical results obtained by using present method are compared to experimental data. The results indicate the present method gives good agreement with the measured values. In summary, the present method has high efficiency and high resolution to capture shock wave and contact surface.