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Volume 14, Issue 2
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle

Qiumei Huang, Kun Jiang & Jingwei Li

Adv. Appl. Math. Mech., 14 (2022), pp. 494-527.

Published online: 2022-01

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  • Abstract

The Peng-Robinson equation of state, one of the most extensively applied equations of state in the petroleum industry and chemical engineering, has an excellent appearance in predicting the thermodynamic properties of a wide variety of materials. It has been a great challenge on how to design numerical schemes with preservation of mass conservation and energy dissipation law. Based on the exponential time difference combined with the stabilizing technique and added Lagrange multiplier enforcing the mass conservation, we develop the efficient first- and second-order numerical schemes with preservation of maximum bound principle (MBP) to solve the single-component two-phase diffuse interface model with Peng-Robinson equation of state. Convergence analyses as well as energy stability are also proven. Several two-dimensional and three-dimensional experiments are performed to verify these theoretical results.

  • Keywords

Peng-Robinson equation of state, diffuse interface model, maximum bound principle, exponential time differencing, Lagrange multiplier.

  • AMS Subject Headings

35B50, 35K55, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-494, author = {Qiumei and Huang and and 22068 and and Qiumei Huang and Kun and Jiang and and 22069 and and Kun Jiang and Jingwei and Li and and 22070 and and Jingwei Li}, title = {Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {494--527}, abstract = {

The Peng-Robinson equation of state, one of the most extensively applied equations of state in the petroleum industry and chemical engineering, has an excellent appearance in predicting the thermodynamic properties of a wide variety of materials. It has been a great challenge on how to design numerical schemes with preservation of mass conservation and energy dissipation law. Based on the exponential time difference combined with the stabilizing technique and added Lagrange multiplier enforcing the mass conservation, we develop the efficient first- and second-order numerical schemes with preservation of maximum bound principle (MBP) to solve the single-component two-phase diffuse interface model with Peng-Robinson equation of state. Convergence analyses as well as energy stability are also proven. Several two-dimensional and three-dimensional experiments are performed to verify these theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0008}, url = {http://global-sci.org/intro/article_detail/aamm/20207.html} }
TY - JOUR T1 - Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle AU - Huang , Qiumei AU - Jiang , Kun AU - Li , Jingwei JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 494 EP - 527 PY - 2022 DA - 2022/01 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0008 UR - https://global-sci.org/intro/article_detail/aamm/20207.html KW - Peng-Robinson equation of state, diffuse interface model, maximum bound principle, exponential time differencing, Lagrange multiplier. AB -

The Peng-Robinson equation of state, one of the most extensively applied equations of state in the petroleum industry and chemical engineering, has an excellent appearance in predicting the thermodynamic properties of a wide variety of materials. It has been a great challenge on how to design numerical schemes with preservation of mass conservation and energy dissipation law. Based on the exponential time difference combined with the stabilizing technique and added Lagrange multiplier enforcing the mass conservation, we develop the efficient first- and second-order numerical schemes with preservation of maximum bound principle (MBP) to solve the single-component two-phase diffuse interface model with Peng-Robinson equation of state. Convergence analyses as well as energy stability are also proven. Several two-dimensional and three-dimensional experiments are performed to verify these theoretical results.

Qiumei Huang, Kun Jiang & Jingwei Li. (2022). Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle. Advances in Applied Mathematics and Mechanics. 14 (2). 494-527. doi:10.4208/aamm.OA-2021-0008
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