During the last decades, tabulated chemistry approaches, like manifold-based concepts to implement model reduction, have become a widespread, promising and accurate method to take chemical reactions into account in computing reacting flows. However, there is a number of crucial issues concerning the generation and implementation of the tabulated chemistry approaches. These concern the way manifolds of the arbitrary dimension are generated, parametrised (i.e. tabulated) preserving fast/slow decomposition and implemented rigorously by the formulation of a reduced model in a coordinate independent manner. This study discusses these problems in detail and suggests generic solutions based on the Reaction–Diffusion Manifolds (REDIM) method. A REDIM tabulated chemistry concept obtained by using the hierarchical nature of the invariant slow system manifolds is presented. Numerical aspects of the implementation are in the focus of the paper. It is shown how the concept is implemented to overcome most problems without a-priori knowledge of the considered system behaviour. As a basic example for discussion and illustration synthesis, gas/air combustion in premixed, freely propagating flames is used.

中文翻译：

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基于流形的模型约简的实现问题及其通用解决方案

在过去的几十年里，表格化学方法，如基于流形的概念来实现模型简化，已经成为一种广泛、有前途和准确的方法，可以在计算反应流时考虑化学反应。但是，关于列表化学方法的生成和实施存在许多关键问题。这些涉及生成任意维度的流形的方式，参数化（即列表）保持快速/慢速分解，并通过以坐标无关的方式制定简化模型来严格实施。本研究详细讨论了这些问题，并提出了基于反应扩散流形 (REDIM) 方法的通用解决方案。提出了通过使用不变慢系统流形的分层性质获得的 REDIM 列表化学概念。实现的数值方面是本文的重点。展示了如何实施该概念以克服大多数问题，而无需预先了解所考虑的系统行为。作为讨论和说明合成的基本示例，使用了预混、自由传播火焰中的气体/空气燃烧。