Volume 15, Issue 1
SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions

Adv. Appl. Math. Mech., 15 (2023), pp. 139-158.

Published online: 2022-10

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• Abstract

In this paper, the Peng-Robinson equation of state with dynamic boundary conditions is discussed, which considers the interactions with solid walls. At first, the model is introduced and the regularization method on the nonlinear term is adopted. Next, The scalar auxiliary variable (SAV) method in temporal and finite element method in spatial are used to handle the Peng-Robinson equation of state. Then, the energy dissipation law of the numerical method is obtained. Also, we acquire the convergence of the discrete SAV finite element method (FEM). Finally, a numerical example is provided to confirm the theoretical result.

35K35, 35K55, 65M12, 65M60

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@Article{AAMM-15-139, author = {Yao , ChanghuiDu , Zhaoyue and Yang , Lei}, title = {SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {1}, pages = {139--158}, abstract = {

In this paper, the Peng-Robinson equation of state with dynamic boundary conditions is discussed, which considers the interactions with solid walls. At first, the model is introduced and the regularization method on the nonlinear term is adopted. Next, The scalar auxiliary variable (SAV) method in temporal and finite element method in spatial are used to handle the Peng-Robinson equation of state. Then, the energy dissipation law of the numerical method is obtained. Also, we acquire the convergence of the discrete SAV finite element method (FEM). Finally, a numerical example is provided to confirm the theoretical result.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0216}, url = {http://global-sci.org/intro/article_detail/aamm/21129.html} }
TY - JOUR T1 - SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions AU - Yao , Changhui AU - Du , Zhaoyue AU - Yang , Lei JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 139 EP - 158 PY - 2022 DA - 2022/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0216 UR - https://global-sci.org/intro/article_detail/aamm/21129.html KW - Peng-Robinson equation of state, dynamic boundary conditions, scalar auxiliary variable, finite element method, error estimates. AB -

In this paper, the Peng-Robinson equation of state with dynamic boundary conditions is discussed, which considers the interactions with solid walls. At first, the model is introduced and the regularization method on the nonlinear term is adopted. Next, The scalar auxiliary variable (SAV) method in temporal and finite element method in spatial are used to handle the Peng-Robinson equation of state. Then, the energy dissipation law of the numerical method is obtained. Also, we acquire the convergence of the discrete SAV finite element method (FEM). Finally, a numerical example is provided to confirm the theoretical result.

Changhui Yao, Zhaoyue Du & Lei Yang. (2022). SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions. Advances in Applied Mathematics and Mechanics. 15 (1). 139-158. doi:10.4208/aamm.OA-2021-0216
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