中北大学学报（自然科学版）2025，Vol.46Issue(1)：98-104,7.DOI:10.62756/jnuc.issn.1673-3193.2023.08.0021
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
摘要
Abstract
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 differ-ence 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 con-duction 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 com-pact difference scheme have about 48%and 65%efficiency improvement based on the second-order differ-ence scheme,which proves the reliability of high-precision numerical computation.With the rapid prog-ress 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Key words
unsteady heat conduction/finite difference/high-order precision/compact difference scheme分类
信息技术与安全科学引用本文复制引用
谢金耀,王强,闫文鑫..非稳态导热问题高精度数值计算方法研究[J].中北大学学报（自然科学版）,2025,46(1):98-104,7.基金项目
国防科技重点实验室基金(JCKYS2019603C003) （JCKYS2019603C003）
