Volume 48, Issue 4
Numerical Approximations of the Spectral Discretization of Flame Front Model

Jun Zhang, Wu-Lan Li, Xin-Yue Fan & Xiao-Jun Yu

J. Math. Study, 48 (2015), pp. 345-361.

Published online: 2015-12

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  • Abstract

In this paper, we consider the numerical solution of the flame front equation, which is one of the most fundamental equations for modeling combustion theory. A schema combining a finite difference approach in the time direction and a spectral method for the space discretization is proposed. We give a detailed analysis for the proposed schema by providing some stability and error estimates in a particular case. For the general case, although we are unable to provide a rigorous proof for the stability, some numerical experiments are carried out to verify the efficiency of the schema. Our numerical results show that the stable solution manifolds have a simple structure when $\beta$ is small, while they become more complex as the bifurcation parameter $\beta$ increases. At last numerical experiments were performed to support the claim the solution of flame front equation preserves the same structure as K-S equation.

  • AMS Subject Headings

65N35, 65T50, 65L12, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zj654440@email (Jun Zhang)

liwulan@163.com (Wu-Lan Li)

fan.xinyue@163.com (Xin-Yue Fan)

xjyu-myu@163.com (Xiao-Jun Yu)

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@Article{JMS-48-345, author = {Zhang , JunLi , Wu-LanFan , Xin-Yue and Yu , Xiao-Jun}, title = {Numerical Approximations of the Spectral Discretization of Flame Front Model}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {4}, pages = {345--361}, abstract = {

In this paper, we consider the numerical solution of the flame front equation, which is one of the most fundamental equations for modeling combustion theory. A schema combining a finite difference approach in the time direction and a spectral method for the space discretization is proposed. We give a detailed analysis for the proposed schema by providing some stability and error estimates in a particular case. For the general case, although we are unable to provide a rigorous proof for the stability, some numerical experiments are carried out to verify the efficiency of the schema. Our numerical results show that the stable solution manifolds have a simple structure when $\beta$ is small, while they become more complex as the bifurcation parameter $\beta$ increases. At last numerical experiments were performed to support the claim the solution of flame front equation preserves the same structure as K-S equation.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n4.15.03}, url = {http://global-sci.org/intro/article_detail/jms/9939.html} }
TY - JOUR T1 - Numerical Approximations of the Spectral Discretization of Flame Front Model AU - Zhang , Jun AU - Li , Wu-Lan AU - Fan , Xin-Yue AU - Yu , Xiao-Jun JO - Journal of Mathematical Study VL - 4 SP - 345 EP - 361 PY - 2015 DA - 2015/12 SN - 48 DO - http://doi.org/10.4208/jms.v48n4.15.03 UR - https://global-sci.org/intro/article_detail/jms/9939.html KW - Flame front equation, Finite difference, Fourier method, Error estimates. AB -

In this paper, we consider the numerical solution of the flame front equation, which is one of the most fundamental equations for modeling combustion theory. A schema combining a finite difference approach in the time direction and a spectral method for the space discretization is proposed. We give a detailed analysis for the proposed schema by providing some stability and error estimates in a particular case. For the general case, although we are unable to provide a rigorous proof for the stability, some numerical experiments are carried out to verify the efficiency of the schema. Our numerical results show that the stable solution manifolds have a simple structure when $\beta$ is small, while they become more complex as the bifurcation parameter $\beta$ increases. At last numerical experiments were performed to support the claim the solution of flame front equation preserves the same structure as K-S equation.

Jun Zhang, Wu-Lan Li, Xin-Yue Fan & Xiao-Jun Yu. (2020). Numerical Approximations of the Spectral Discretization of Flame Front Model. Journal of Mathematical Study. 48 (4). 345-361. doi:10.4208/jms.v48n4.15.03
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