Development of New Numerical Methods Based on Nonlocally Exact Differencing and Numerical Investigation on Naturally Convected Heat Transfer

1)提出了一种基于非局部精确数值差分概念的数值方法。该方法的本质在于确定差分格式的系数，使得在控制体积表面插值数值通量的所得方程满足具有吸收项和源项的输运方程的解析解。在相邻三个控制体之间的四区域模型中，考虑了输运方程系数的空间分布，并在相邻两个区域的边界上施加了解的连续条件。2）采用特征多项式分析方法分析了该格式的非振动性。结果表明，该格式对具有吸收项的定常对流扩散方程具有非振动性势。通过数值实验对该格式进行了检验，结果表明，该格式具有良好的收敛性， 关于我们 对具有强空间相关系数的输运方程的数值实验表明，SDCLENS格式的解明显优于局部精确格式透镜和QUICK格式的解。采用SDCLENS格式离散动量方程和能量方程，编制了二维热工水力分析程序。用精确解对剪切驱动空腔流动进行了数值模拟，验证了上述程序的正确性。6）对高瑞利数Ra 10^5-10^9的方形空腔内自然循环流动进行了数值模拟，其中，由于多维场的热-液耦合，传统的数值方法往往遭受大的数值扩散和不稳定的解决方案。在Ra = 10^9的情况下，得到了稳定的层流解。然而，在Ra = 10^8的情况下，解不是稳定的，而是随时间变化的。对壁面施加温差后涡的形成发展及涡的混沌结构进行了数值研究。此外，作为Ra = 10^9的情况下的统计分析结果，对雷诺应力和波动能谱进行了评估。结果表明，在湍流充分发展的情况下，能谱近似为1/f谱，这与Kolmogorov的（-5/3）功率谱不同。少

1) A numerical method on the concept of nonlocally exact numerical differencing is presented. The essence of this method consists in determining the coefficients of the difference scheme such that the resulting equation interpolating numerical fluxes at the control volume surface satisfies the analytical solution of transport equations with absorption and source terms. The spatial distribution of the coefficients of transport equations is taken into consideration based on a four- region model among adjacent three control volumes, in which continuous conditions for solutions are imposed on the boundary between adjacent two regions.2) The analysis on nonoscillation properties of the present scheme was performed using the characteristic polynomial analysis method. It was found that the present scheme possesses potential of nonoscillation properties for stationary convection- diffusion equations with absorption. The present scheme is examined through numerical experiments, and shows good s … More olutions for transport equations with absorption and source terms.3) Numerical experiments for transport equations with strongly spatially dependent coefficients show that the present SDCLENS scheme gives solutions distinctly better than solutions with the locally exact scheme LENS and the QUICK scheme.4) The mass, momentum and energy equations were discretized using the SDCLENS scheme and a 2- D thermal hydraulics analysis program has been developed.5) The above computer program was validated through numerical experiments for the shear-driven cavity flow with the exact solution.6) The numerical simulation using the present computer program was performed for naturally circulating flows with high Rayleigh numbers Ra 10^5-10^9 in a square cavity, where conventional numerical methods tend to suffer from large numerical diffusions and unstable solutions because of thermohydraulically coupling in multidimensional fields. Steady laminar solutions were obtained up to Ra = 10^9. However, in case of Ra = 10^8the solutions were not steady but temporally dependent. Developing of vortex formation and the chaotic structure of vortex after the temperature difference was imposed on the walls are made numerically investigated. Further, as results of statistical analysis in case of Ra = 10^9, a Reynolds stress and a fluctuation energy spectrum were evaluated. It was shown that the energy spectrum is roughly 1/f spectrum, which is different from the Kolmogorov's (-5/3) power spectrum in case of fully developed turbulent flows. Less