Zhaowei Wang , Danxia Wang , Yanping Chen , Chenhui Zhang , Hongen Jia
{"title":"Numerical approximation for the MHD equations with variable density based on the Gauge-Uzawa method","authors":"Zhaowei Wang , Danxia Wang , Yanping Chen , Chenhui Zhang , Hongen Jia","doi":"10.1016/j.apnum.2024.09.006","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the numerical approximation of incompressible magnetohydrodynamic (MHD) system with variable density. Firstly, we provide first- and second-order time discretization schemes based on the convective form of the Gauge-Uzawa method. Secondly, we prove that the proposed schemes are unconditionally stable. We also provide error estimates through rigorous theoretical analysis. Then, we construct a fully-discrete first-order scheme with finite elements in space and provide its stability result. Finally, we present some numerical experiments to validate the effectiveness of the proposed schemes. Furthermore, we also present the conserved scheme and its numerical results.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424002435","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the numerical approximation of incompressible magnetohydrodynamic (MHD) system with variable density. Firstly, we provide first- and second-order time discretization schemes based on the convective form of the Gauge-Uzawa method. Secondly, we prove that the proposed schemes are unconditionally stable. We also provide error estimates through rigorous theoretical analysis. Then, we construct a fully-discrete first-order scheme with finite elements in space and provide its stability result. Finally, we present some numerical experiments to validate the effectiveness of the proposed schemes. Furthermore, we also present the conserved scheme and its numerical results.