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

基于局部精确差分的新数值方法的发展和自然对流传热的数值研究

• 批准号: 05680420
• 负责人: SAKAI Katsuhiro
• 金额: $ 1.28万
• 依托单位: Saitama Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05680420/
• 关键词: finite difference method; numerical analysis; transport equation; high-order numerical scheme; numerical oscillations; natural convection; cavity flow; naturally convected heat transfer

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.

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。

项目成果

K.Sakai: "Numerical Stability Analysis of Locally Exact Numerical Scheme LENS" J.Satitama Institute of Tecnology. 5. 51-57 (1996)

K.Sakai：“局部精确数值方案 LENS 的数值稳定性分析”J.Satitama 技术研究所。

K.Sakai: "An Optimized Locally Exact Numerical Scheme Based on A Finite Variable Difference Method and Characteristic Polynomial Method" The 5th CHD Sympojyum. C-3. 9-9 (1994)

K.Sakai：“基于有限变量差分法和特征多项式法的优化局部精确数值方案”第五届 CHD Sympojyum。

K.Sakai: "Extension of Finite Variable Difference Method with Application to UICK Scheme" The 6th CHD Sympojyum. C-1. 7-7 (1995)

K.Sakai：“有限变量差分法的扩展及其在 UICK 方案中的应用”第六届 CHD Sympojyum。

酒井勝弘: "特性根が極をもつというクライテリヤに基づく新差分スキーム" 1995年日本原子力学会年会A44. (発表予定). (1995)

Katsuhiro Sakai：“基于特征根有极点准则的新差分方案”1995 年日本原子能学会年会 A44（待提交）。

Katsuhiro Sakai: "A New Finite Variable Difference Method with Application to Locally Exact Numerical Scheme LENS" J. Comput. Physics. 124. (1996)

Katsuhiro Sakai：“一种新的有限变量差分方法，应用于局部精确数值方案 LENS”J. Comput。