应用数学和力学2026，Vol.47Issue(2)：219-229,11.DOI:10.21656/1000-0887.460061
有限差分法计算热传导方程的几何诱导误差
Geometrically-Induced Errors in the Finite Difference Method for Solving Heat Conduction Equations
刘君 1刘光英 2徐春光2
作者信息
- 1. 宁波大学 机械工程与力学学院,浙江 宁波 315211
- 2. 中山大学 航空航天学院,广州 510275
- 折叠
摘要
Abstract
Firstly,as an example,the unstructured finite difference method(UFDM)based on discrete equiva-lent equations was proposed,to enhance the geometric adaptability of the finite difference method.During the solution of the heat conduction equations with the finite difference method in the curvilinear coordinate system,the coordinate transformation will lead to geometric-induced errors.This phenomenon was illustrated by means of the central difference scheme to solve the temperature field equation.Based on the precision definition of the truncation errors of the difference scheme,the geometry-induced error was theoretically demonstrated to inevi-tably leads to a reduction in order.Secondly,a linear preservation assessment model was built to verify the 1st-order accuracy,and the difference scheme was proved to be difficult to guarantee the 1st-order accuracy of the assessment model on non-uniform grids.On this basis,a linear preservation algorithm based on gradient recon-struction was proposed.Numerical calculations show that,for structured grids with any shape to calculate line-arly distributed temperature fields,numerical solutions with errors at the machine precision level of 0 can be obtained.This study provides a theoretical and practical foundation for developing fully automatic temperature field calculation software.关键词
有限差分法/热传导方程/贴体坐标系/精度评估/验证与确认Key words
finite difference method/heat conduction equation/body-fitted coordinate system/accuracy as-sessment/verification and validation分类
数理科学引用本文复制引用
刘君,刘光英,徐春光..有限差分法计算热传导方程的几何诱导误差[J].应用数学和力学,2026,47(2):219-229,11.
