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

1)在局部精确数值差分的基础上发展了一种新的对流项数值格式透镜，其中确定差分系数，使得所得差分方程满足在节点处具有吸收项和源项的输运方程的精确解。2）对透镜格式进行了改进，使输运方程中系数的空间分布得到考虑，3）数值稳定性分析表明，透镜格式的解对于任何输运速度和吸收值都没有数值振荡。4）质量，采用透镜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。通过对平面Poillille流动和卡门涡脱落的数值试验，验证了上述程序的正确性。6）对高Rayleigh数Ra=10 ~ 15的自然循环流动进行了数值模拟。8-10^<10>中的方腔，其中常规的数值方法往往遭受大的数值扩散和不稳定的解决方案，因为强大的热工水力耦合在多维领域。在Ra= 10 ^8的情况下得到了稳定解，但是在Ra=10^的情况下<10>，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。

1) A new umerical scheme LENS for the convection term was developed on a base of locally exact numerical differencing, in which difference coefficients are determined such that the resulting diffcrence equation satisfies the exact solution of transport equations with the absorption and source terms at nodal points.2) The LENS scheme was improved so that the spatial distribution of the coefficients in the transport equations is taken into consideration based on a two-region model in a control volume.3) Numerical stability analysis showed that solutions with the LENS scheme are free from numerical oscillations for any value of transporting velocities and absorption.4) The mass, momentum and energy equations were discretized using the LENS scheme and a 2-D thermal hydraulics analysis program was developed.5) The above computer program was validated through numerical experiments for the plane Poiseuille flow and the Karman vortex shedding.6) The numerical simulation using the present computer program was performed for naturally circulating flows with high Rayleigh numbers Ra=10^8-10^<10> in a square cavity, where conventional numerical methods tend to suffer from large numerical diffusions and unstable solutions because of strong thermohydraulics coupling in multidimensional fields. Steady solutions were obtained in case of Ra=10^8 However, in case of Ra=10^<10> the 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 were made numerically investigated.