Accurate and reliable numerical simulations of combustion phenomena using complex models

Some reasonable simplifications of the combustion model are made, and a system of partial differential-algebraic equations is derived that is suitable for numerical computations.;To develop an efficient algorithm, fourth-order finite-differences are used for the spatial discretization. A spectral deferred correction method is used in time integration to achieve higher order accuracy in time. The overall order of the algorithm currently implemented is four. While the spectral deferred correction method has good stability properties, an efficient preconditioner is also utilized to enhance the stability of the method. Because of the steep fronts in the solution, adaptive grid generation based on the equi-distribution of the gradient and curvature of the important variable, temperature, is used to resolve the large gradients. An adaptive time step based on an error estimate for the numerical solution is also incorporated in the algorithm to increase the time integration efficiency.;The numerical algorithm solves a complex chemistry model that, for example, includes 13 species for the hydrogen-oxygen-nitrogen gas mixture. It is implemented both in serial and in parallel. The SCALapack software is used in the parallel implementation to solve the linear systems of equations.;Computational results on a hydrogen-air system show that the algorithm is accurate, stable and efficient. The algorithm is then applied to the ignition problem and combustion bomb problem to compute the minimum ignition energy and the burning velocity of some gas mixtures.