非均匀介质中压力驱动火焰传播的高度非线性模型的分析与解

IF 1.7 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Multidiscipline Modeling in Materials and Structures Pub Date : 2023-05-30 DOI:10.1108/mmms-11-2022-0247
S. Rahman, José Luis Díaz Palencia
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引用次数: 0

摘要

目的利用p-拉普拉斯算子研究非均匀介质中火焰的传播模型。这种操作符的目的是模拟在非均匀介质中可能出现的慢速和快速扩散的影响,这取决于压力驱动的条件。此外,作者还介绍了反应项的一般形式,即火焰化学动力学。设计/方法/方法为了引入控制方程,作者脱离了先前报道的火焰传播模型,但作者考虑了一种基于p-拉普拉斯算子的新建模方法。结果给出了解的正则性和唯一性的证据。然后,作者根据哈密顿量的定义,介绍了新讨论模型的平稳解的轮廓。最后,作者利用标度法将模型转化为非线性Hamilton-Jacobi方程,得到了指数曲线解。原创性/价值这个新模型在以前的文献中没有报道过。作者认为,p-拉普拉斯算子的数学性质(特别是有限传播的性质)对模拟具有缓慢或快速扩散的压力驱动火焰具有固有的兴趣。事实上,作者的方法提供了一个更适合模拟火焰传播的算子的价值。此外,作者还介绍了化学动力学的一般形式,使作者的模型进一步一般化。
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Analysis and profiles of solution for a highly nonlinear model of pressure driven flame propagation in nonhomogeneous medium
PurposeThis article aims to study a model of flame propagation in a nonhomogeneous medium with a p-Laplacian operator. The intention with such operator is to model the effects of slow and fast diffusion, that can appear in a nonhomogeneous media, depending on the pressure driven conditions. In addition, the authors introduce a general form in the reaction term, that introduces the flame chemical kinetics.Design/methodology/approachTo introduce the governing equations, the authors depart from previously reported models in flame propagation, but the authors consider a new modeling approach based on a p-Laplacian operator.FindingsThe authors provide evidences of regularity and uniqueness of solutions. Afterward, the authors introduce profiles of stationary solutions based on the definition of a Hamiltonian for the newly discussed model. Eventually, the authors obtain exponential profiles solutions with the help of a scaling, that transforms the model into a nonlinear Hamilton–Jacobi equation.Originality/valueThe new model has not been previously reported in the literature. The authors consider that the mathematical properties of a p-laplacian (in particular the property known as finite propagation) is of inherent interest to model pressure drive flames with slow or fast diffusion. Indeed, the authors’ approach has the value of providing an operator that can fit better to model flame propagation. In addition, the authors introduce a general form of chemical kinetics, to make the authors’ model further general.
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来源期刊
CiteScore
3.70
自引率
5.00%
发文量
60
期刊介绍: Multidiscipline Modeling in Materials and Structures is published by Emerald Group Publishing Limited from 2010
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