Numerical Approximations of the Spectral Discretization of Flame Front Model

Numerical Approximations of the Spectral Discretization of Flame Front Model

Year:    2015

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

Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v48n4.15.03

Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 345–361

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Flame front equation Finite difference Fourier method Error estimates.

Author Details

Jun Zhang

Wu-Lan Li

Xin-Yue Fan

Xiao-Jun Yu