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，其中差值系数的确定使得所得到的差分方程满足具有节点处的吸收项和源项的输运方程的精确解。2)改进了透镜格式，使得基于控制体的两区域模型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，对于输运速度和吸收的任何值，采用透镜格式的解都不受数值振荡。4)质量，采用Lens格式离散动量方程和能量方程，编制了二维热工水力学分析程序。5)对平面Poiseuille流和卡门旋涡脱落进行了数值试验验证。6)对高瑞利数Ra=10^8~10^&lt的自然循环流动进行了数值模拟；在方腔中，由于多维场中的热工耦合作用，传统的数值方法往往存在大的数值扩散和不稳定的解。当Ra=10^8时，得到了稳定解，而在Ra=10^&lt；10&gt；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。

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.