On the design of computational experiment in combustion theory

Abstract

Combustion is a complex physicochemical pro cess, which is generally characterized by a significant nonlinearity and nonstationarity, as well as by a com bination of many factors, such as chemical and phase transformations, heat and mass transfer, etc. [1]. Accordingly, the theory of combustion contains a sig nificant number of mathematical models of the pro cesses under study [2][3][4][5][6], providing a basis for a wide spread use of modern methods of computational experiment [7][8][9][10][11].In this work, we formulate, in a compact form, the concept of planning a computational experiment in combustion theory, which generalizes the accumu lated experience in mathematical modeling of com bustion processes, including the development and qualitative and numerical analysis of mathematical models and their use in studying the problems of sta bility and control combustion processes. This report is closely related to [12], where the adequacy of the experimental and theoretical models of combustion processes is considered.Computational experiment (CE) is an effective means of modern mathematical modeling [8][9][10][11]. In the conventional cyclic sequence: Experiment → Physical Model → Mathematical model → CE → Experiment, CE occupies an important place, which, in turn, consists of several stages: CE → Model → Algorithm → Program → CE, being, generally, also a cyclic procedure. Currently, CE includes not so much the development of computational methods and its implementation on a computer [13,14], but rather planning a series of calculations with a clearly defined objective. The formulation of this goal is largely dependent on the adequacy of consideration of the theoretical model and the level of physicochemical understanding of the process.According to Academician A.G. Merzhanov [12], there are the following levels of adequacy of combus tion models:(1) basic mathematical model that qualitatively reproduce a limited set of main properties of a certain class of processes;(2) mathematical models that reflect basic charac teristic dependences upon variation of the parameters that have real physicochemical sense;(3) quantitative description of some of the experi mentally observed dependences;(4) detailed mathematical models capable of quan titatively describe all the observed data with required degree of adequacy.The whole practice of theoretical and experimental studies of combustion processes has shown that a given phenomenon can be described within the framework of various mathematical models, but the adequacy of which may be different. The physicochemical ade quacy of the model implies that it can, in principle, describe an experimentally observed property of the process. The mathematical adequacy means a quanti tative description of a specific set of experimental data in accordance with a desired criterion. Basic models of combustion theory reflect a certain level of specifica tion of the physicochemical description of a given class of processes. In passing from a base to a quantita tive model for a particular proce...