Junxiang Yang , Huan Han , Shuhong Liu , Zhigang Zuo
{"title":"针对不可压缩三元流体问题的高效且能量稳定的 L2- 相场方法","authors":"Junxiang Yang , Huan Han , Shuhong Liu , Zhigang Zuo","doi":"10.1016/j.physd.2024.134346","DOIUrl":null,"url":null,"abstract":"<div><p>Ternary incompressible fluid flows extensively exist in atmospheric science, chemical engineering, and energy and power engineering, etc. The phase-field method is popular in multi-phase fluid modeling thanks to its efficient ability of interface capturing. This work aims to develop an energy dissipation law-preserving and temporally second-order accurate algorithm for a ternary phase-field fluid system. To establish a simple energy estimation, an adapted auxiliary variable approach is used to transform the original model into its equivalent form. Later, a second-order backward difference strategy is used to design the fully decoupled and linear time-marching scheme. To improve the consistency between original and modified discrete energy functionals, a practical energy correction technique is presented. We analytically prove the discrete energy dissipation property and show that the energy estimation can be easily established without considering the complex treatments of nonlinear and coupling terms. To facilitate the interested readers, we briefly describe the numerical implementation in each time step. The numerical tests indicate that the proposed method not only has desired accuracy, but also satisfies the energy stability even if a larger time step is used. Moreover, the proposed method can well simulate various ternary fluid phenomena, such as the liquid lens, phase separation, droplet dynamics, Kelvin–Helmholtz instability, and billowing cloud.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134346"},"PeriodicalIF":2.7000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Efficiently and consistently energy-stable L2-phase-field method for the incompressible ternary fluid problems\",\"authors\":\"Junxiang Yang , Huan Han , Shuhong Liu , Zhigang Zuo\",\"doi\":\"10.1016/j.physd.2024.134346\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Ternary incompressible fluid flows extensively exist in atmospheric science, chemical engineering, and energy and power engineering, etc. The phase-field method is popular in multi-phase fluid modeling thanks to its efficient ability of interface capturing. This work aims to develop an energy dissipation law-preserving and temporally second-order accurate algorithm for a ternary phase-field fluid system. To establish a simple energy estimation, an adapted auxiliary variable approach is used to transform the original model into its equivalent form. Later, a second-order backward difference strategy is used to design the fully decoupled and linear time-marching scheme. To improve the consistency between original and modified discrete energy functionals, a practical energy correction technique is presented. We analytically prove the discrete energy dissipation property and show that the energy estimation can be easily established without considering the complex treatments of nonlinear and coupling terms. To facilitate the interested readers, we briefly describe the numerical implementation in each time step. The numerical tests indicate that the proposed method not only has desired accuracy, but also satisfies the energy stability even if a larger time step is used. Moreover, the proposed method can well simulate various ternary fluid phenomena, such as the liquid lens, phase separation, droplet dynamics, Kelvin–Helmholtz instability, and billowing cloud.</p></div>\",\"PeriodicalId\":20050,\"journal\":{\"name\":\"Physica D: Nonlinear Phenomena\",\"volume\":\"470 \",\"pages\":\"Article 134346\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica D: Nonlinear Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278924002975\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924002975","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Efficiently and consistently energy-stable L2-phase-field method for the incompressible ternary fluid problems
Ternary incompressible fluid flows extensively exist in atmospheric science, chemical engineering, and energy and power engineering, etc. The phase-field method is popular in multi-phase fluid modeling thanks to its efficient ability of interface capturing. This work aims to develop an energy dissipation law-preserving and temporally second-order accurate algorithm for a ternary phase-field fluid system. To establish a simple energy estimation, an adapted auxiliary variable approach is used to transform the original model into its equivalent form. Later, a second-order backward difference strategy is used to design the fully decoupled and linear time-marching scheme. To improve the consistency between original and modified discrete energy functionals, a practical energy correction technique is presented. We analytically prove the discrete energy dissipation property and show that the energy estimation can be easily established without considering the complex treatments of nonlinear and coupling terms. To facilitate the interested readers, we briefly describe the numerical implementation in each time step. The numerical tests indicate that the proposed method not only has desired accuracy, but also satisfies the energy stability even if a larger time step is used. Moreover, the proposed method can well simulate various ternary fluid phenomena, such as the liquid lens, phase separation, droplet dynamics, Kelvin–Helmholtz instability, and billowing cloud.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.