同位网格摄动有限体积格式求解浮力驱动方腔流

利用对流扩散方程的摄动有限体积格式，在Rayleigh数从10$^{3}$ 到10$^{8}$的范围内对浮力驱动方腔流动问题作了数值模拟. 对流扩散方程的摄动 有限体积格式具有一阶迎风格式的简洁形式，使用相同的基点，重构近似精度高，特别是两 相邻控制体中心到公共界面的距离相等或不相等，PFV格式公式相同等优点. 在数值模拟中， 无论均匀网格还是非均匀网格均获得与DSC方法、自适应有限元法、多重网格法等Benchmark 解相符较好的数值结果，证明UPFV格式对高Rayleigh数对流传热问题的适用性和有效性.

SOLVING 2-D BUOYANCY-DRIVEN CAVITY FLOW ON COLLOCATED MESHES BY PERTURBATIONAL FINITE VOLUME SCHEME

The buoyancy-driven cavity flow in the case of Ra=10~3 to Ra=10~8 is numerically simulated with the upwind type of perturbation finite volume (UPFV) scheme for the convective and diffusive equations initiated by the second author.The UPFV scheme for diffusive and convective equations takes the same concise expressions and uses the same nodes as the upwind scheme of the first order and high approximate accuracy of reconstruction can be achieved.Especially,the UPFV scheme is identical for uniform grid and non-uniform grid regardless of the distance from the CV center to the common face.The results of numerical simulations to buoyancy-driven cavity flows by UPFV are consistent with these by spectral method and finite element method and DSC in the range from Ra=10~3 to Ra=10~8 with uniform or non-uniform structured grid.It shows that the PFV scheme is valid and can be applied for the heat convection and transfer problems.