A Novel Computational Approach to Combustion Modelling

摘要：采用新发展的小波技术，结合相应的微分方程合理降维技术，对非定常、多维燃烧过程进行建模。重点是流体力学和化学动力学完全耦合的问题；这类问题的特点是在广泛不同的长度和时间尺度上演变的多种现象。第一种技术使用多级小波搭配近似。该算法的多层结构便于根据解的时间演化对网格细化进行计算适应。计算的理性约简阶段采用本征低维流形理论；那些在时间尺度上发生的过程比物理驱动的截止时间尺度快，允许放松到部分平衡，而其余的过程受制于时间演变。简而言之，小波分解减少了未知量的总数，而理性约简则减少了求解微分方程组的流形的维数，从而产生了更有效的数值方法。该项目考虑了通用算法的开发和应用于具体的燃烧问题，并通过实验和/或独立的理论来表征。这项工作将小波技术引入到燃烧模拟中，也适用于其他大规模数值模拟。

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.