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

1)提出了非局部精确数值差分概念的一种数值方法。这种方法的实质在于确定差分格式的系数，使得在控制体积面上插值数值通量的方程满足具有吸收项和源项的输运方程的解析解。基于相邻三个控制体之间的四区域模型考虑了输运方程系数的空间分布，其中在相邻两个区域的边界上施加了解的连续条件。2)利用特征多项式分析方法分析了该格式的非振荡特性。结果表明，对于具有吸收项的定常对流扩散方程，本格式具有潜在的非振动性。通过数值实验对该格式进行了检验，结果表明S格式具有较好的…3)对具有强空间相关系数的输运方程进行了数值实验，结果表明，SDCLENS格式的解明显优于局部精确格式LENS和QUICK格式。4)采用SDCLENS格式对质量、动量和能量方程进行离散，编制了二维热工水力分析程序。5)对剪切驱动空腔流动进行了数值实验验证，得到了精确解。6)对方腔内瑞利数Ra为10^5-10^9的自然循环流动进行了数值模拟。由于多维场中的热液耦合，传统的数值方法往往会受到大的数值扩散和不稳定解的影响。当Ra=10^9时，得到了稳定的层流解，而当Ra=10^8时，解不是稳定的，而是随时间变化的。数值研究了壁面温差作用后旋涡形成的发展过程和旋涡的混沌结构。此外，在Ra=109的情况下，作为统计分析的结果，评估了雷诺应力和涨落能谱。结果表明，在湍流充分发展的情况下，能量谱大致为1/f谱，不同于Kolmogorov(-5/3)功率谱。较少

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