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，提出了对流项的一种新的数值格式LENS，通过确定差分系数，使差分方程满足具有节点处吸收项和源项的输运方程的精确解。2)改进了LENS方案，在控制体的双区域模型基础上考虑了输运方程中系数的空间分布。3)数值稳定性分析表明，在任何输运速度和吸收值下，LENS格式的解都不受数值振荡的影响。4)采用LENS格式对质量、动量和能量方程进行离散化，编制了二维热工分析程序。5)通过平面泊泽维尔流和卡门涡脱落的数值实验验证了上述计算机程序。(6)利用本程序对方形腔内高瑞利数Ra=10^8-10^<10>的自然循环流动进行了数值模拟，在这种情况下，由于多维场的强热压耦合，传统的数值方法容易产生大的数值扩散和不稳定的解。当Ra=10^8时，得到稳定解，但当Ra=10^<10>时，得到的解不是稳定的，而是时间相关的。对壁面施加温差后涡的形成发展和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.