Numerical Approximations of the Spectral Discretization of Flame Front Model (Journal of Mathematical Study, 2021)
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 spectralmethod for the space discretization is proposed. We give a detailed analysis for theproposed 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 structurewhen $β$ is small, while they become more complex as the bifurcation parameter $β$ increases. At last numerical experiments were performed to support the claim thesolution of flame front equation preserves the same structure as K-S equation.
Keywords: Flame front equation; Finite difference; Fourier method; Error estimates.