Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

Qiujin Peng; Zhonghua Qiao; Shuyu Sun

doi:10.4208/jcm.1611-m2016-0623

Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

Qiujin Peng
, Zhonghua Qiao
, Shuyu Sun

Research output: Journal article publication › Journal article › Academic research › peer-review

11 Citations (Scopus)

Abstract

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L^∞ convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

Original language	English
Pages (from-to)	737-765
Number of pages	29
Journal	Journal of Computational Mathematics
Volume	35
Issue number	6
DOIs	https://doi.org/10.4208/jcm.1611-m2016-0623
Publication status	E-pub ahead of print - 2017

Keywords

Convergence
Diffuse interface model
Energy stability
Fourth order parabolic equation

ASJC Scopus subject areas

Computational Mathematics

More information

10.4208/jcm.1611-m2016-0623

http://hdl.handle.net/10397/76478

Cite this

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title = "Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State",

abstract = "In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L∞ convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.",

keywords = "Convergence, Diffuse interface model, Energy stability, Fourth order parabolic equation",

author = "Qiujin Peng and Zhonghua Qiao and Shuyu Sun",

note = "Funding Information: Acknowledgments. We are grateful to Prof. Zhizhong Sun of Department of Mathematics of Southeast University and Prof. Hehu Xie of Institute of Computational Mathematics of Chinese Academy of Sciences for providing useful suggestions and many helpful discussions. The research of Zhonghua Qiao is partially supported by the Hong Kong Research Grant Council GRF grant 15302214, NSFC/RGC Joint Research Scheme N HKBU204/12 and the Hong Kong Polytechnic University internal grant 1-ZE33. Shuyu Sun gratefully acknowledges that the research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). Publisher Copyright: {\textcopyright} 2017 Global Science Press. All rights reserved.",

year = "2017",

doi = "10.4208/jcm.1611-m2016-0623",

language = "English",

volume = "35",

pages = "737--765",

journal = "Journal of Computational Mathematics",

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TY - JOUR

T1 - Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

AU - Peng, Qiujin

AU - Qiao, Zhonghua

AU - Sun, Shuyu

N1 - Funding Information: Acknowledgments. We are grateful to Prof. Zhizhong Sun of Department of Mathematics of Southeast University and Prof. Hehu Xie of Institute of Computational Mathematics of Chinese Academy of Sciences for providing useful suggestions and many helpful discussions. The research of Zhonghua Qiao is partially supported by the Hong Kong Research Grant Council GRF grant 15302214, NSFC/RGC Joint Research Scheme N HKBU204/12 and the Hong Kong Polytechnic University internal grant 1-ZE33. Shuyu Sun gratefully acknowledges that the research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). Publisher Copyright: © 2017 Global Science Press. All rights reserved.

PY - 2017

Y1 - 2017

N2 - In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L∞ convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

AB - In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L∞ convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

KW - Convergence

KW - Diffuse interface model

KW - Energy stability

KW - Fourth order parabolic equation

UR - https://www.scopus.com/pages/publications/85051479254

U2 - 10.4208/jcm.1611-m2016-0623

DO - 10.4208/jcm.1611-m2016-0623

M3 - Journal article

AN - SCOPUS:85051479254

SN - 0254-9409

VL - 35

SP - 737

EP - 765

JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

IS - 6

ER -

Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

Abstract

Keywords

ASJC Scopus subject areas

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