Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport
Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport
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DOI：
10.1016/j.jmaa.2018.10.074
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发表时间：
2018-07
影响因子：
1.3
通讯作者：
M. Brun;E. Ahmed;J. Nordbotten;F. Radu
中科院分区：
文献类型：
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作者：
M. Brun;E. Ahmed;J. Nordbotten;F. Radu
本文讨论了准静态热-孔隙弹性模型的分析问题。该模型是非线性的，包括与经典的准静态多孔弹性模型（也称为毕奥模型）相比的热效应。它由动量平衡方程、质量平衡方程和能量平衡方程组成，由于能量平衡方程中的对流输运项而完全耦合和非线性。本文的目的是调查，在混合配方的背景下，弱解的存在性和唯一性，这个模型问题。这些公式中的主要变量是流体压力、温度和弹性位移以及达西通量、热通量和总应力。首先通过使用Galerkin方法和suitablea priorestimates解决线性化制剂的适定性。这是接下来用来研究适定性的迭代求解程序的完整的非线性问题。然后，通过使用适当的范数压缩迭代的连续差函数来推导该算法的收敛性证明。
This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists of a momentum balance equation, a mass balance equation, and an energy balance equation, fully coupled and nonlinear due to a convective transport term in the energy balance equation. The aim of this article is to investigate, in the context of mixed formulations, the existence and uniqueness of a weak solution to this model problem. The primary variables in these formulations are the fluid pressure, temperature and elastic displacement as well as the Darcy flux, heat flux and total stress. The well-posedness of a linearized formulation is addressed first through the use of a Galerkin method and suitablea prioriestimates. This is used next to study the well-posedness of an iterative solution procedure for the full nonlinear problem. A convergence proof for this algorithm is then inferred by a contraction of successive difference functions of the iterates using suitable norms.