Abstract

In this article, we study the influence of certain parameters on the stability conditions of the reaction front in a liquid medium. The mathematical model consists of the heat equation, the concentration equation and the Navier–Stockes equation under the Boussinesq approximation. An asymptotic analysis was performed using the approximation proposed by Zeldovich and Frank–Kamentskii to obtain the interface problem. A stability analysis was carried out to obtain a linearized problem which will be solved numerically using a multiquadric radial basis function method to find the convective threshold. This will allow us to conclude the effect of each parameter on the stability of the front, in particular the amplitude and the resonance frequency.

中文翻译：

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聚合前沿的稳定性分析

摘要

在本文中，我们研究了某些参数对液体介质中反应前沿稳定性条件的影响。数学模型由热方程、浓度方程和Boussinesq近似下的Navier-Stockes方程组成。使用 Zeldovich 和 Frank-Kamentskii 提出的近似进行渐近分析以获得界面问题。进行了稳定性分析以获得线性化问题，该问题将使用多重二次径向基函数方法进行数值求解，以找到对流阈值。这将使我们能够得出每个参数对前端稳定性的影响，特别是幅度和谐振频率。