非稳态导热问题高精度数值计算方法研究  

Research on High‑Precision Numerical Calculation Methods for Unsteady Heat Conduction Problems

作　　者：谢金耀 王强[1] 闫文鑫 XIE Jinyao;WANG Qiang;YAN Wenxin(School of Energy and Power Engineering,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学能源与动力工程学院,山西太原030051

出　　处：《中北大学学报(自然科学版)》2025年第1期98-104,共7页Journal of North University of China(Natural Science Edition)

基　　金：国防科技重点实验室基金(JCKYS2019603C003)。

摘　　要：高精度数值计算非稳态导热问题拥有更准的精度和更高的效率。本文研究了二维非稳态导热问题,基于Python语言编写了数值求解程序。分别实现了Taylor级数展开差分格式和Hermite插值三点紧致差分格式的构造方法,通过结构化网格设计了边缘绝热的导热平板计算模型,并结合算例来验证方法,分析了高精度差分格式对非稳态导热问题的求解效率和精度的影响。数值仿真计算表明模拟结果与解析解拟合较好,误差精度保持在2%以下,证明了数值计算程序的有效性。通过对比同为空间五点计算方法的求解效率,发现四阶紧致差分格式和六阶紧致差分格式在二阶差分格式的基础上约有48%和65%的效率提升,证明了高精度数值计算的可靠性。随着算力的快速发展,非稳态导热问题的高精度数值计算将成为一种趋势。High precision numerical calculation of unsteady heat conduction problems possesses higher precision and higher efficiency.In this paper,the two-dimensional unsteady heat conduction problem was investigated and a numerical solution program based on Python language was written.The construction methods of Taylor series expansion difference scheme and Hermite interpolation three-point compact difference scheme were respectively realized,and the heat conduction plate computational model of edge heat insulation was designed by structured mesh,which was combined with examples to validate the method,and the effect of high-precision difference format on the efficiency and precision of the unsteady heat conduction problem was analyzed.The numerical simulation shows that the simulation results fit well with the analytical solution,and the error accuracy is kept below 2%,which proves the effectiveness of the numerical calculation program.And by comparing the solution efficiency of the same spatial five-point computation method,it is found that the fourth-order compact difference scheme and the sixth-order compact difference scheme have about 48%and 65%efficiency improvement based on the second-order difference scheme,which proves the reliability of high-precision numerical computation.With the rapid progress of arithmetic power,high-precision numerical computation of unsteady heat conduction problems will become a trend.

关 键 词：非稳态导热 有限差分 高阶精度 紧致差分格式 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]