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Volume 35, Issue 6
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

J. Comp. Math., 35 (2017), pp. 737-765.

Published online: 2017-12

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  • 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

Diffuse interface model, Fourth order parabolic equation, Energy stability, Convergence.

  • AMS Subject Headings

65N06, 65B99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

pengqiujin@ruc.edu.cn (Qiujin Peng)

zqiao@polyu.edu.hk (Zhonghua Qiao)

shuyu.sun@kaust.edu.sa (Shuyu Sun)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-737, author = {Peng , QiujinQiao , Zhonghua and Sun , Shuyu}, title = {Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {6}, pages = {737--765}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1611-m2016-0623}, url = {http://global-sci.org/intro/article_detail/jcm/10492.html} }
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 JO - Journal of Computational Mathematics VL - 6 SP - 737 EP - 765 PY - 2017 DA - 2017/12 SN - 35 DO - http://doi.org/10.4208/jcm.1611-m2016-0623 UR - https://global-sci.org/intro/article_detail/jcm/10492.html KW - Diffuse interface model, Fourth order parabolic equation, Energy stability, Convergence. 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.

Qiujin Peng, Zhonghua Qiao & Shuyu Sun. (2020). Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State. Journal of Computational Mathematics. 35 (6). 737-765. doi:10.4208/jcm.1611-m2016-0623
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