A Novel Computational Approach to Combustion Modelling

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ABSTRACT-Paolucci CTS-9705150 Unsteady, multi-dimensional combustion processes are modeled using a newly developed wavelet technique combined with a technique to rationally reduce the relevant differential equations to lower dimensions. The focus is on problems in which there is full coupling between fluid mechanics and chemical kinetics; such problems are characterized by a multiplicity of phenomena evolving over widely disparate length and time scales. The first technique uses a multi-level wavelet collocation approximation. The multilevel structure of the algorithm facilitates the computational adaptation of the grid refinement according to the temporal evolution of the solution. The rational reduction phase of the compu- tation applies intrinsic low-dimensional manifold (ILDM) theory; those processes occurring on time scales faster than a physically motivated cutoff time scale are allowed to relax to partial equilibrium while the remaining processes are subject to time evolution. In brief, the wavelet decomposition reduces the total number of unknowns and the rational reduction then reduces the dimension of the manifold on which the system of differential equations is solved resulting in a more efficient numerical method. This project considers both general algorithmic development and application to specific combustion problems well characterized by experiment and/or independent theory. This work introduces wavelet techniques into combustion modelling and also has applicability to other large-scale numerical simulations.