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Volume 36, Issue 4
Modelling of Compressible Multi-Component Two-Phase Flow with Multi-Component Navier Boundary Condition

Junkai Wang & Qiaolin He

DOI: 10.4208/cicp.OA-2024-0313

Commun. Comput. Phys., 36 (2024), pp. 1053-1089.

Published online: 2024-10

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  • Abstract

In this paper, we derive a dimensionless model for compressible multi-component two-phase flows with Peng-Robinson equation of state (EoS), incorporated with the multi-component Navier boundary condition (MNBC). We propose three linearly decoupled and energy-stable numerical schemes for this model. These schemes are developed based on the Lagrange multiplier approach for bulk Helmholtz free energy and surface free energy. One of them is based on a component-wise approach, which requires solving a sequence of linear, separate mass balance equations and leads to an original discrete energy that unconditionally dissipates. Another numerical scheme is based on a component-separate approach, which requires solving a sequence of linear, separate mass balance equations but leads to a modified discrete energy dissipating under certain conditions. Numerical results are presented to verify the effectiveness of the proposed methods.

  • Keywords

Compressible, Helmholtz free energy, energy-stable, Lagrange multiplier, multi-component, Peng-Robinson EoS.

  • AMS Subject Headings

65N12, 76T10, 76N99, 49S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-36-1053, author = {Wang , Junkai and He , Qiaolin}, title = {Modelling of Compressible Multi-Component Two-Phase Flow with Multi-Component Navier Boundary Condition}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {4}, pages = {1053--1089}, abstract = {

In this paper, we derive a dimensionless model for compressible multi-component two-phase flows with Peng-Robinson equation of state (EoS), incorporated with the multi-component Navier boundary condition (MNBC). We propose three linearly decoupled and energy-stable numerical schemes for this model. These schemes are developed based on the Lagrange multiplier approach for bulk Helmholtz free energy and surface free energy. One of them is based on a component-wise approach, which requires solving a sequence of linear, separate mass balance equations and leads to an original discrete energy that unconditionally dissipates. Another numerical scheme is based on a component-separate approach, which requires solving a sequence of linear, separate mass balance equations but leads to a modified discrete energy dissipating under certain conditions. Numerical results are presented to verify the effectiveness of the proposed methods.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0313}, url = {http://global-sci.org/intro/article_detail/cicp/23486.html} }
TY - JOUR T1 - Modelling of Compressible Multi-Component Two-Phase Flow with Multi-Component Navier Boundary Condition AU - Wang , Junkai AU - He , Qiaolin JO - Communications in Computational Physics VL - 4 SP - 1053 EP - 1089 PY - 2024 DA - 2024/10 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2024-0313 UR - https://global-sci.org/intro/article_detail/cicp/23486.html KW - Compressible, Helmholtz free energy, energy-stable, Lagrange multiplier, multi-component, Peng-Robinson EoS. AB -

In this paper, we derive a dimensionless model for compressible multi-component two-phase flows with Peng-Robinson equation of state (EoS), incorporated with the multi-component Navier boundary condition (MNBC). We propose three linearly decoupled and energy-stable numerical schemes for this model. These schemes are developed based on the Lagrange multiplier approach for bulk Helmholtz free energy and surface free energy. One of them is based on a component-wise approach, which requires solving a sequence of linear, separate mass balance equations and leads to an original discrete energy that unconditionally dissipates. Another numerical scheme is based on a component-separate approach, which requires solving a sequence of linear, separate mass balance equations but leads to a modified discrete energy dissipating under certain conditions. Numerical results are presented to verify the effectiveness of the proposed methods.

Wang , Junkai and He , Qiaolin. (2024). Modelling of Compressible Multi-Component Two-Phase Flow with Multi-Component Navier Boundary Condition. Communications in Computational Physics. 36 (4). 1053-1089. doi:10.4208/cicp.OA-2024-0313
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