A fully-decoupled energy stable scheme for the phase-field model of non-Newtonian two-phase flows

Wei Li; Guangying Lv; Wei Li; Guangying Lv

doi:10.3934/math.2024944

AIMS Mathematics

2024, Volume 9, Issue 7: 19385-19396. doi: 10.3934/math.2024944

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A fully-decoupled energy stable scheme for the phase-field model of non-Newtonian two-phase flows

Wei Li ¹,
Guangying Lv ^{1,2
,
,}

1.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
School of Mathematics and Computational Sciences, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China

Received: 16 April 2024 Revised: 14 May 2024 Accepted: 23 May 2024 Published: 12 June 2024
MSC : 65M06, 65M12, 82C26

In this paper, we first propose a novel fully-decoupled, linear and second-order time accurate scheme to solve the phase-field model of non-Newtonian two-phase flows; the developed scheme is based on a stabilized Scalar Auxiliary Variable (SAV) approach. We strictly prove the unconditional energy stability of the scheme and conduct a numerical simulation to show the accuracy and stability of the proposed scheme. Moreover, we can observe that the parameter $ r $ in non-Newtonian fluids can affect spatial patterns during phase transitions, which directly enables us to design and perform optimal control experiments in engineering processes.
- phase-field model,
- non-Newtonian two-phase flows,
- stabilized-SAV approach,
- unconditionally energy-stable scheme
Citation: Wei Li, Guangying Lv. A fully-decoupled energy stable scheme for the phase-field model of non-Newtonian two-phase flows[J]. AIMS Mathematics, 2024, 9(7): 19385-19396. doi: 10.3934/math.2024944

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Abstract

In this paper, we first propose a novel fully-decoupled, linear and second-order time accurate scheme to solve the phase-field model of non-Newtonian two-phase flows; the developed scheme is based on a stabilized Scalar Auxiliary Variable (SAV) approach. We strictly prove the unconditional energy stability of the scheme and conduct a numerical simulation to show the accuracy and stability of the proposed scheme. Moreover, we can observe that the parameter $ r $ in non-Newtonian fluids can affect spatial patterns during phase transitions, which directly enables us to design and perform optimal control experiments in engineering processes.

References

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