Volume 26, Issue 4
Linear and Unconditionally Energy Stable Schemes for the Multi-Component Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State

Chenfei Zhang, Hongwei Li, Xiaoping Zhang & Lili Ju

Commun. Comput. Phys., 26 (2019), pp. 1071-1097.

Published online: 2019-07

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  • Abstract

In this paper we consider numerical solutions of the diffuse interface model with Peng-Robinson equation of state for the multi-component two-phase fluid system, which describes real states of hydrocarbon fluids in petroleum industry. A major challenge is to develop appropriate temporal discretizations to overcome the strong nonlinearity of the source term and preserve the energy dissipation law in the discrete sense. Efficient first and second order time stepping schemes are designed based on the "Invariant Energy Quadratization" approach and the stabilized method. The resulting temporal semi-discretizations by both schemes lead to linear systems that are symmetric and positive definite at each time step, and their unconditional energy stabilities are rigorously proven. Numerical experiments are presented to demonstrate accuracy and stability of the proposed schemes.

  • Keywords

Diffuse interface model, Peng-Robinson equation of state, linear scheme, Invariant Energy Quadratization, energy stability.

  • AMS Subject Headings

65M12, 65M06, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chenfei@math.sc.edu (Chenfei Zhang)

hwli@sdnu.edu.cn (Hongwei Li)

xpzhang.math@whu.edu.cn (Xiaoping Zhang)

ju@math.sc.edu (Lili Ju)

  • BibTex
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  • TXT
@Article{CiCP-26-1071, author = {Zhang , Chenfei and Li , Hongwei and Zhang , Xiaoping and Ju , Lili }, title = {Linear and Unconditionally Energy Stable Schemes for the Multi-Component Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {4}, pages = {1071--1097}, abstract = {

In this paper we consider numerical solutions of the diffuse interface model with Peng-Robinson equation of state for the multi-component two-phase fluid system, which describes real states of hydrocarbon fluids in petroleum industry. A major challenge is to develop appropriate temporal discretizations to overcome the strong nonlinearity of the source term and preserve the energy dissipation law in the discrete sense. Efficient first and second order time stepping schemes are designed based on the "Invariant Energy Quadratization" approach and the stabilized method. The resulting temporal semi-discretizations by both schemes lead to linear systems that are symmetric and positive definite at each time step, and their unconditional energy stabilities are rigorously proven. Numerical experiments are presented to demonstrate accuracy and stability of the proposed schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0237}, url = {http://global-sci.org/intro/article_detail/cicp/13229.html} }
TY - JOUR T1 - Linear and Unconditionally Energy Stable Schemes for the Multi-Component Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State AU - Zhang , Chenfei AU - Li , Hongwei AU - Zhang , Xiaoping AU - Ju , Lili JO - Communications in Computational Physics VL - 4 SP - 1071 EP - 1097 PY - 2019 DA - 2019/07 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0237 UR - https://global-sci.org/intro/article_detail/cicp/13229.html KW - Diffuse interface model, Peng-Robinson equation of state, linear scheme, Invariant Energy Quadratization, energy stability. AB -

In this paper we consider numerical solutions of the diffuse interface model with Peng-Robinson equation of state for the multi-component two-phase fluid system, which describes real states of hydrocarbon fluids in petroleum industry. A major challenge is to develop appropriate temporal discretizations to overcome the strong nonlinearity of the source term and preserve the energy dissipation law in the discrete sense. Efficient first and second order time stepping schemes are designed based on the "Invariant Energy Quadratization" approach and the stabilized method. The resulting temporal semi-discretizations by both schemes lead to linear systems that are symmetric and positive definite at each time step, and their unconditional energy stabilities are rigorously proven. Numerical experiments are presented to demonstrate accuracy and stability of the proposed schemes.

Chenfei Zhang, Hongwei Li, Xiaoping Zhang & Lili Ju. (2019). Linear and Unconditionally Energy Stable Schemes for the Multi-Component Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. Communications in Computational Physics. 26 (4). 1071-1097. doi:10.4208/cicp.OA-2018-0237
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