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Mathematical and numerical aspects of one-dimensional laminar flame simulation. (English) Zbl 0654.65085

Summary: The aim of this paper is to solve several mathematical and numerical questions related to the simulation of stationary and nonstationary premixed flat flames. Most of the results are obtained in the general context of complex chemical and diffusion mechanisms. The main mathematical results concern: (i) the a priori positivity of the mass fractions, and (ii) the sensitivity of the flame speed to the computational domain. The numerical method proposed for solving the stationary problem is a new combination of the pseudo-nonstationary approach, the Newton iterations, and the adaptive gridding. The computation of \(H_ 2-O_ 2-N_ 2\) flames with various initial concentrations (including the chemical extinction zone) shows the efficiency of this method.

MSC:

65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
80A25 Combustion

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