A spectral element discretization for quasi-static magnetohydrodynamic flows

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-07-19 DOI:10.1002/fld.5321

Mattias Brynjell-Rahkola

{"title":"A spectral element discretization for quasi-static magnetohydrodynamic flows","authors":"Mattias Brynjell-Rahkola","doi":"10.1002/fld.5321","DOIUrl":null,"url":null,"abstract":"<p>The classical staggered <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mi>ℙ</mi>\n </mrow>\n <mrow>\n <mi>N</mi>\n </mrow>\n </msub>\n <mi>-</mi>\n <msub>\n <mrow>\n <mi>ℙ</mi>\n </mrow>\n <mrow>\n <mi>N</mi>\n <mo>−</mo>\n <mn>2</mn>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ {\\mathbb{P}}_N\\hbox{-} {\\mathbb{P}}_{N-2} $$</annotation>\n </semantics></math> spectral element method (SEM) is revisited and extended to quasi-static magnetohydrodynamic (MHD) flows. In this realm, which is valid in the limit of vanishing magnetic Reynolds number, the evaluation of the Lorentz force in the momentum equation requires the electric current density, governed by Ohm's law and a charge conservation condition derived from Ampère's law, to be determined. Once discretized with the SEM, this translates into solving one additional problem for the electric potential involving the so-called consistent Poisson operator. The method is well suited for fully three-dimensional flows in complex geometries. Changes in resolution requirements aside, consideration of the electromagnetic quantities is estimated to increase the computational cost associated with MHD by about 40% relative to hydrodynamics. The accuracy and the capabilities of the scheme is demonstrated on a set of common flows from the MHD literature. Exponential convergence with polynomial order is confirmed for the electric current density.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 11","pages":"1795-1812"},"PeriodicalIF":1.7000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5321","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Fluids","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/fld.5321","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

The classical staggered $ℙ_{N} - ℙ_{N - 2}$ spectral element method (SEM) is revisited and extended to quasi-static magnetohydrodynamic (MHD) flows. In this realm, which is valid in the limit of vanishing magnetic Reynolds number, the evaluation of the Lorentz force in the momentum equation requires the electric current density, governed by Ohm's law and a charge conservation condition derived from Ampère's law, to be determined. Once discretized with the SEM, this translates into solving one additional problem for the electric potential involving the so-called consistent Poisson operator. The method is well suited for fully three-dimensional flows in complex geometries. Changes in resolution requirements aside, consideration of the electromagnetic quantities is estimated to increase the computational cost associated with MHD by about 40% relative to hydrodynamics. The accuracy and the capabilities of the scheme is demonstrated on a set of common flows from the MHD literature. Exponential convergence with polynomial order is confirmed for the electric current density.

Abstract Image

查看原文本刊更多论文

准静态磁流体动力学流的谱元离散法

经典交错谱元法（SEM）被重新审视并扩展到准静态磁流体动力学（MHD）流。在磁雷诺数消失的极限条件下，动量方程中洛伦兹力的评估需要确定受欧姆定律和安培定则电荷守恒条件支配的电流密度。一旦使用 SEM 进行离散化，这就转化为解决涉及所谓一致泊松算子的电动势的额外问题。该方法非常适合复杂几何结构中的全三维流动。除了分辨率要求的变化之外，考虑电磁量估计会使 MHD 的相关计算成本比流体力学增加约 40%。该方案的准确性和功能已在 MHD 文献中的一组常见流体上得到验证。电流密度的多项式阶指数收敛得到了证实。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.