A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-06-01 DOI:10.1515/rnam-2022-0014

A. Lozovskiy, M. Olshanskii, Y. Vassilevski

引用次数: 2

Abstract

Abstract A finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound for the finite element solution.

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Navier-Stokes /Biot耦合问题数值解的有限元格式

摘要考虑了流体-多孔结构相互作用问题的整体拟拉格朗日公式的有限元方法，该问题在流体-结构界面上具有校正的应力平衡。弹性介质的变形不一定很小，而是使用Saint-Venant–Kirchhoff（SVK）本构关系进行建模。用有限元解的能量界形式证明了该方法的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Numerical Analysis and Mathematical Modelling 数学-工程：综合

CiteScore

1.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest. Topics: -numerical analysis- numerical linear algebra- finite element methods for PDEs- iterative methods- Monte-Carlo methods- mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.