同位非结构和结构网格摄动有限体积法（PFV）求解二维Navier-Stokes方程组

根据NS方程组的一阶迎风和二阶中心有限体积（UFV和CFV）格式，导出NS方程组迎风和中心摄动有限体积(UPFV和CPFV)格式．该格式通过把控制体界面质量通量摄动展开成网格间距的幂级数，并由守恒方程本身求得幂级数系数而获得．迎风和中心摄动有限体积格式使用了与一阶迎风和二阶中心格式相同的基点数和相同的表达形式，宜于计算机编程．顶盖驱动方腔流和驻点流标量输运的数值实验证明，迎风PFV格式比一阶UFV、二阶CFV格式有更高的精度，更高的分辨率．尤其是良好的鲁棒特性．对顶盖驱动方腔流，在Re数从102到104范围内，亚松弛系数可在0.3～0.8任取，收敛性能良好．

Perturbational Finite Volume Method for the Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first order upwind and second order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first order UFV and second order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness . The numerical computation to flow in a lid-driven cavity shows that the underrelaxation factor can be arbitrarily selected ranging from 0.3 to 0.8 and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.