准静态孔弹性模型的新型多物理场有限元方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-11-13 DOI:10.1016/j.apnum.2024.11.002

Zhihao Ge , Yanan He

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引用次数: 0

摘要

本文针对准静态孔弹性模型提出了一种新的多物理场有限元方法。首先，为了克服位移锁定现象和压力振荡，我们通过引入新变量--广义非局部斯托克斯方程和扩散方程，将原模型重新表述为流体-流体耦合问题，这是一个全新的模型。然后，我们为重构模型设计了一种完全离散的多物理场有限元方法，即空间变量（u,ξ,η）的线性有限元对和时间离散的后向欧拉法。我们证明了所提出的方法是稳定的，没有任何稳定项，对许多参数都是鲁棒的，并且具有最佳收敛阶数。最后，我们展示了一些数值检验来验证理论结果。

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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A new multiphysics finite element method for a quasi-static poroelasticity model

In this paper, we propose a new multiphysics finite element method for a quasi-static poroelasticity model. Firstly, to overcome the displacement locking phenomenon and pressure oscillation, we reformulate the original model into a fluid-fluid coupling problem by introducing new variables-the generalized nonlocal Stokes equations and a diffusion equation, which is a completely new model. Then, we design a fully discrete multiphysics finite element method for the reformulated model-linear finite element pairs for the spatial variables

(u, ξ, η)

and backward Euler method for time discretization. And we prove that the proposed method is stable without any stabilized term and robust for many parameters and it has the optimal convergence order. Finally, we show some numerical tests to verify the theoretical results.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.