{"title":"Improved discrete unified gas-kinetic scheme for interface capturing","authors":"Kaiyu Shi, Guanqing Wang, Jiangrong Xu, Lu Wang","doi":"10.1103/physreve.110.015311","DOIUrl":null,"url":null,"abstract":"In this paper, we extend the improved discrete unified gas-kinetic scheme (DUGKS) from solving the hydrodynamic equations to addressing the phase field equations, building upon our prior work [Wang <i>et al.</i>, <span>Phys. Fluids</span> <b>35</b>, 017106 (2023)]. The conservative Allen-Cahn equation and its modified form are presented first, followed by the construction of two improved DUGKS methods for interface capturing, based on the corresponding kinetic equations. The improved DUGKS for interface capturing utilizes the node distribution function instead of the interface center distribution function for evaluating the interface flux. The improved DUGKS enhances the numerical stability of the original DUGKS, and the good stability allows the calculations to be performed using large time steps, reducing the cumulative error from which more accurate predictions can be obtained. To verify the validity of the scheme, a series of numerical experiments were further carried out, including the diagonal translation, Zalesak's disk rotation, reversed single vortex, and deformation field. The comparison with the benchmark data shows that the improved DUGKS can simply and effectively capture the sharp interface and complex deformation interface of the two-phase flow interface.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreve.110.015311","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we extend the improved discrete unified gas-kinetic scheme (DUGKS) from solving the hydrodynamic equations to addressing the phase field equations, building upon our prior work [Wang et al., Phys. Fluids35, 017106 (2023)]. The conservative Allen-Cahn equation and its modified form are presented first, followed by the construction of two improved DUGKS methods for interface capturing, based on the corresponding kinetic equations. The improved DUGKS for interface capturing utilizes the node distribution function instead of the interface center distribution function for evaluating the interface flux. The improved DUGKS enhances the numerical stability of the original DUGKS, and the good stability allows the calculations to be performed using large time steps, reducing the cumulative error from which more accurate predictions can be obtained. To verify the validity of the scheme, a series of numerical experiments were further carried out, including the diagonal translation, Zalesak's disk rotation, reversed single vortex, and deformation field. The comparison with the benchmark data shows that the improved DUGKS can simply and effectively capture the sharp interface and complex deformation interface of the two-phase flow interface.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.