An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids
•A linear, totally decoupled, and second-order scheme for the ternary CAC fluids.•The proposed scheme is highly efficient and is very easy to implement.•The discrete energy dissipation law of the numerical scheme is proven. Based on a time-dependent auxiliary variable approach, we propose linear, to...
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| Vydáno v: | Applied mathematics and computation Ročník 438; s. 127599 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.02.2023
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | •A linear, totally decoupled, and second-order scheme for the ternary CAC fluids.•The proposed scheme is highly efficient and is very easy to implement.•The discrete energy dissipation law of the numerical scheme is proven.
Based on a time-dependent auxiliary variable approach, we propose linear, totally decoupled, and energy dissipative methods for the three-phase conservative Allen–Cahn (CAC) fluid system. The three-phase CAC equation has been extensively applied in the simulation of multi-component fluid flows because of the following advantages: (i) Total mass is conserved, (ii) Topological change of the interface can be implicitly captured. Compared with the ternary Cahn–Hilliard (CH) model, the CAC-type model is simple to solve. When we solve the CAC model by using the classical scalar auxiliary variable (SAV) approach, extra computational time is needed because we must decouple the local and non-local variables. The variant of SAV approach considered in the present study not only leads to linear and energy stable schemes, but also achieves highly efficient computation. Linear and decoupled equations need to be updated at each time step. We adopt the linear multigrid algorithm to speed up the convergence. Extensive numerical experiments with and without fluid flows are conducted to validate the temporal accuracy, mass conservation, and energy law. |
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| AbstractList | •A linear, totally decoupled, and second-order scheme for the ternary CAC fluids.•The proposed scheme is highly efficient and is very easy to implement.•The discrete energy dissipation law of the numerical scheme is proven.
Based on a time-dependent auxiliary variable approach, we propose linear, totally decoupled, and energy dissipative methods for the three-phase conservative Allen–Cahn (CAC) fluid system. The three-phase CAC equation has been extensively applied in the simulation of multi-component fluid flows because of the following advantages: (i) Total mass is conserved, (ii) Topological change of the interface can be implicitly captured. Compared with the ternary Cahn–Hilliard (CH) model, the CAC-type model is simple to solve. When we solve the CAC model by using the classical scalar auxiliary variable (SAV) approach, extra computational time is needed because we must decouple the local and non-local variables. The variant of SAV approach considered in the present study not only leads to linear and energy stable schemes, but also achieves highly efficient computation. Linear and decoupled equations need to be updated at each time step. We adopt the linear multigrid algorithm to speed up the convergence. Extensive numerical experiments with and without fluid flows are conducted to validate the temporal accuracy, mass conservation, and energy law. |
| ArticleNumber | 127599 |
| Author | Kim, Junseok Chen, Jianjun Yang, Junxiang Tan, Zhijun |
| Author_xml | – sequence: 1 givenname: Zhijun surname: Tan fullname: Tan, Zhijun organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China – sequence: 2 givenname: Junxiang surname: Yang fullname: Yang, Junxiang organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China – sequence: 3 givenname: Jianjun orcidid: 0000-0001-7503-1889 surname: Chen fullname: Chen, Jianjun organization: School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China – sequence: 4 givenname: Junseok orcidid: 0000-0002-0484-9189 surname: Kim fullname: Kim, Junseok email: cfdkim@korea.ac.kr organization: Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea |
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| Cites_doi | 10.1016/j.cma.2021.113987 10.1155/2016/9532608 10.1016/j.cma.2020.113382 10.1063/5.0049971 10.1090/mcom/3578 10.4208/cicp.OA-2019-0175 10.1016/j.jcp.2020.109718 10.1016/j.euromechflu.2014.08.001 10.1051/m2an:2006028 10.1051/m2an/2010072 10.1016/j.cma.2021.113918 10.1007/s11075-019-00804-9 10.1016/j.compfluid.2017.07.009 10.1016/j.cnsns.2021.105923 10.1017/jfm.2018.702 10.1016/j.camwa.2018.09.021 10.1063/5.0018391 10.1103/PhysRevE.89.053320 10.1016/j.jcp.2021.110703 10.1016/j.jcp.2021.110536 10.1016/j.jcp.2021.110909 10.1016/j.cma.2019.112743 10.1016/j.cam.2021.113778 10.1007/s10665-011-9504-2 10.1007/s10915-018-0690-1 10.1016/j.ijmecsci.2022.107342 10.3390/math8010097 10.1016/j.cam.2018.05.039 10.1016/j.compfluid.2018.08.023 10.1007/s10915-021-01564-2 |
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| Keywords | Three-phase conservative allen–Cahn fluids Multigrid algorithm Finite difference method Dissipation law |
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| SubjectTerms | Dissipation law Finite difference method Multigrid algorithm Three-phase conservative allen–Cahn fluids |
| Title | An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids |
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