一维无源对流扩散方程的近场动力学计算格式  

Peridynamic calculation scheme of a one-dimensional passive convection-diffusion equation

作　　者：王庆[1] 李家宝 鞠磊 薛彦卓[1] 贾定睿 WANG Qing;LI Jiabao;JU Lei;XUE Yanzhuo;JIA Dingrui(College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China)

机构地区：[1]哈尔滨工程大学船舶工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2022年第1期9-16,共8页Journal of Harbin Engineering University

基　　金：国家重点研发计划(2018YFC1406000,2016YFE0202700);国家自然科学基金项目(51639004,51809061).

摘　　要：为了深入研究对流扩散问题,本文针对一维无源对流扩散方程给出了利用近场动力学理论求解方程的一般计算格式。推导出了对流项的收敛时间步长计算公式,并采用迎风格式对一维无源对流方程进行验证,证明了近场动力学可以用于求解对流项,随后引入无量纲数Pe,对对流扩散中的占优情况进行判断,最终得到同时满足对流项和扩散项收敛要求的时间步长。结果表明:利用近场动力学理论求解无源对流方程时,当安全系数ζ与近场范围系数m满足1/ζ=2m,误差可达到最小;无量纲数Pe可用于判断对流扩散中的占优情况,且经过理论值和计算值的比对,证实了近场动力学理论求解一维无源对流扩散方程的可行性及数值准确性。To examine the convection-diffusion problem in-depth,we take the one-dimensional(1D)passive convection-diffusion equation as the research object and propose a general calculation scheme for the solution.The calculation formulation for the convergence time step of the convection term is derived,and the upwind scheme is used to verify the 1D passive convection equation.The results prove that peridynamics can be used to solve the convection equation.Moreover,when the safety factorζand horizon factor m satisfy 1/ζ=2m,the error in solving the convection equation is minimal.Through the introduction of the dimensionless number Pe,the dominant situation in convective diffusion can be evaluated,and the time step that satisfies convection and diffusion is obtained.The feasibility and numerical accuracy of peridynamics in solving the 1D passive convection-diffusion equation can be proved through the comparison of theoretical and calculated values.

关 键 词：近场动力学 对流扩散 收敛时间步长 安全系数 离散格式 中心差分 无源项 数值模拟 

分 类 号：O241[理学—计算数学]