A new approach based on dynamical systems theory is introduced in order to study turbulent combustion. Here, instead of the conventional statistical approach to chaotic systems, a perturbation-based dynamical systems approach is used. The main focus is in the characterization of the attractor, which represents the loci of solutions given a set of initial, boundary and operating conditions. In this paper, we discuss the basic formulation, the definition of so-called Lyapunov vectors and exponents, and the numerical approach for computing these quantities. The method is applied to a canonical premixed turbulent flame in a periodic box. The algorithms are developed in the context of low-Mach number direct numerical simulation solvers, which introduces certain unique complications. Tests of numerical convergence and behavior of the Lyapunov quantities are discussed.
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