摘要
本文研究一类燃烧爆炸数学模型的有限差分解法.方程的指数源项刻画了Arrhenius反应速率,常用于模拟刚性点火过程.通过引入截断函数,原问题转化为具有一致有界连续解的近似模型.当截断常数充分大时,模型的爆破解和几乎完全爆破解可以通过求解近似系统获得,且求解过程不产生数值爆炸.适当优化步长选择,爆破位置和爆破时刻的逼近效果比直接离散原问题求解更简单,计算效果更好.最后,数值实验验证了理论分析的结果和模型的物理性质.
In this paper,we study an efficient finite difference method based on the uniform mesh for a class of semilinear parabolic equation arising from combustion process.Due to the capability of exponential source on simulating Arrhenius reactive rate,the considered model may theoretically describe the rigid ignition process in combustion.By introducing an indicator,the original equation is transformed to an approximate model with globally smooth solution.When the cut-off level constant is sufficiently large,the solution of original equation can be obtained by solving the approximate model,without numerical blowup.By carefully choosing the step sizes,the blowup position and moment can be computed more simply and efficiently.Finally,numerical simulations are provided to verify the mathematical analysis and physical properties of proposed blowup-combustion model.
作者
杨红宾
徐宇锋
Yang Hongbin;Xu Yufeng(School of Mathematical Sciences,Nankai University,Tianjin 300071,China;School of Mathematics and Statistics,Central South University,Changsha 410083,China)
出处
《数学理论与应用》
2020年第3期40-53,共14页
Mathematical Theory and Applications
基金
partly supported by the Natural Science Foundation of Hunan Province(No.2019JJ50755)~~
关键词
半线性抛物型方程
有限差分法
指数源项
单调性
截断函数
Semilinear parabolic equation
Finite difference method
Exponential source
Monotonicity
Cut-off level function
作者简介
通信作者:徐宇锋(1987-),副教授,博士,从事计算数学研究,E-mail:xuyufeng@csu.edu.cn
