一维周期介质中瞬态波的色散、界面和源点均质化模型

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-03-27 DOI:10.1051/m2an/2023027

Rémi Cornaggia, B. Lombard

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引用次数: 1

摘要

提出了一维微结构介质中线性波的均匀化模型。它结合了二阶渐近均匀化(以解释色散)和界面校正(用于从均匀介质传输或向均匀介质传输)。证明了二阶有效系数的新界，保证了均匀化模型在任何微观结构下的适定性。在类比已有的富连续体的基础上，将演化方程重新表述为一个色散双曲系统。通过时域数值模拟验证了该模型的有效性。对狄拉克源项进行了扩展。

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A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media

A homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model whatever the microstructure. Based on an analogy with existing enriched continua, the evolution equations are reformulated as a dispersive hyperbolic system. The efficiency of the model is illustrated via time-domain numerical simulations. An extension to Dirac source terms is also proposed.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.