Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

doi:10.1007/s42967-023-00283-9

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1): 625-657.doi: 10.1007/s42967-023-00283-9

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Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Ruihan Guo¹, Yinhua Xia²

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, China;
2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

收稿日期:2022-07-20 修回日期:2023-01-29 发布日期:2024-04-16
通讯作者: Yinhua Xia,E-mail:yhxia@ustc.edu.cn;Ruihan Guo,E-mail:rguo@zzu.edu.cn E-mail:yhxia@ustc.edu.cn;rguo@zzu.edu.cn
基金资助:
Research of Ruihan Guo was partially supported by the NSFC Grant no. 12271492, and the Natural Science Foundation of Henan Province of China Grant no. 222300420550. Research of Yinhua Xia was partially supported by the NSFC Grant no. 12271498, and the National Key R & D Program of China Grant no. 2022YFA1005202/2022YFA1005200.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Ruihan Guo¹, Yinhua Xia²

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, China;
2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

Received:2022-07-20 Revised:2023-01-29 Published:2024-04-16
Contact: Yinhua Xia,E-mail:yhxia@ustc.edu.cn;Ruihan Guo,E-mail:rguo@zzu.edu.cn E-mail:yhxia@ustc.edu.cn;rguo@zzu.edu.cn
Supported by:
Research of Ruihan Guo was partially supported by the NSFC Grant no. 12271492, and the Natural Science Foundation of Henan Province of China Grant no. 222300420550. Research of Yinhua Xia was partially supported by the NSFC Grant no. 12271498, and the National Key R & D Program of China Grant no. 2022YFA1005202/2022YFA1005200.

摘要/Abstract

摘要： Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows, it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations. One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them. The resulting schemes are only first-order accurate in time, and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version. In this paper, we employ the spectral deferred correction method to improve the temporal accuracy, based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea. The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency. Within the framework of the spatially discretized local discontinuous Galerkin method, the resulting numerical schemes are fully decoupled, efficient, and high-order accurate in both time and space. Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

关键词: Two-phase incompressible flows, Fully-decoupled, High-order accurate, Linear implicit, Spectral deferred correction method, Local discontinuous Galerkin method

Abstract: Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows, it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations. One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them. The resulting schemes are only first-order accurate in time, and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version. In this paper, we employ the spectral deferred correction method to improve the temporal accuracy, based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea. The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency. Within the framework of the spatially discretized local discontinuous Galerkin method, the resulting numerical schemes are fully decoupled, efficient, and high-order accurate in both time and space. Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Key words: Two-phase incompressible flows, Fully-decoupled, High-order accurate, Linear implicit, Spectral deferred correction method, Local discontinuous Galerkin method

Ruihan Guo, Yinhua Xia. Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows[J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 625-657.

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Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

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