基于固体速度的多维沉降模型的耦合混合有限元和有限体积法

IF 1.9 3区 数学 Q2 Mathematics
J. Careaga, Gabriel Nibaldo Gatica
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引用次数: 0

摘要

本文介绍并分析了一种基于固体速度公式的沉降模型。速度场是非散度的这一事实给出了控制方程的一个特殊特征。我们引入了额外的变量,如与速度梯度和压力相关的伪应力张量,从而导致由两个通过源项耦合的方程组组成的混合变分公式。利用Babuška-Brezzi理论和Banach定理,利用不动点策略证明了解的存在唯一性。此外,我们采用合适的有限维子空间,通过相关的混合有限元方法来近似这两个方程组。所得到的耦合格式的适定性也通过不动点方法处理,因此,类似于连续情况,导出了存在唯一性结果的离散版本。然后将上述方法与有限体积法结合起来求解输运方程。最后,给出了几个数值结果,说明了所提出的模型和完整的数值格式的性能,并证实了理论收敛速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Coupled mixed finite element and finite volume methods for a solid velocity-based model of multidimensional sedimentation
In this paper we introduce and analyze a model of sedimentation based on a solid velocity formulation. A particular feature of the governing equations is given by the fact that the velocity field is non-divergence free. We introduce extra variables such as the pseudostress tensor relating the velocity gradient with the pressure, thus leading to a mixed variational formulation consisting of two systems of equations coupled through their source terms. A result of existence and uniqueness of solutions is shown by means of a fixed-point strategy and the help of the Babuška-Brezzi theory and Banach theorem. Additionally, we employ suitable finite dimensional subspaces to approximate both systems of equations via associated mixed finite element methods. The well-posedness of the resulting coupled scheme is also treated via a fixed-point approach, and hence the discrete version of the existence and uniqueness result is derived analogously to the continuous case. The above is then combined with a finite volume method for the transport equation. Finally, several numerical results illustrating the performance of the proposed model and the full numerical scheme, and confirming the theoretical rates of convergence, are presented.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
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.
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