H(div)-conforming IPDG FEM with pointwise divergence-free velocity field for the micropolar Navier-Stokes equations

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-07-18 DOI:10.1016/j.apnum.2025.07.007

Xinran Huang, Haiyan Su, Xinlong Feng

引用次数: 0

Abstract

The mass-conservative finite element method (FEM) is considered for the micropolar Navier-Stokes equations (MNSE), which couple the Navier-Stokes equations (NSE) with the angular momentum equation. A fully divergence-free algorithm is proposed for the MNSE. The Raviart-Thomas element is employed for discretizing the velocity field, ensuring that its divergence-free property is maintained. Furthermore, the interior penalty discontinuous Galerkin (IPDG) method is utilized in order to guarantee the

H^{1}

-continuity of velocity. Some implicit-explicit treatments are used to address the convection terms. We also provide energy stability proof and pressure robust error estimation for the proposed scheme. Finally, the accuracy and effectiveness of the proposed algorithm are validated through several 2D/3D numerical experiments.

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微极Navier-Stokes方程的H（div）型无点发散速度场IPDG有限元

考虑将Navier-Stokes方程（NSE）与角动量方程耦合的微极Navier-Stokes方程（MNSE）的质量守恒有限元法。提出了一种完全无发散的MNSE算法。采用Raviart-Thomas单元对速度场进行离散，保证了速度场的无散度特性。为了保证速度的h1连续性，采用了内罚不连续伽辽金（IPDG）方法。采用隐式显式处理来处理对流项。我们还提供了能量稳定性证明和压力鲁棒误差估计。最后，通过若干2D/3D数值实验验证了该算法的准确性和有效性。

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

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.