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SAV Finite Element Method for the peng-robinson equation of state with Dynamic Boundary Conditions

Advances in Applied Mathematics and Mechanics 2023年第1期15卷 139-158页

作者： Changhui Yao Zhaoyue Du Lei Yang School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China Faculty of Information Technology Macao University of Science and TechnologyMacao

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.

关键词： peng-robinson equation of state dynamic boundary conditions scalar auxiliary variable finite element method error estimates

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Exponential Time Differencing Schemes for the peng-robinson equation of state with Preservation of Maximum Bound Principle

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 494-527页

作者： Qiumei Huang Kun Jiang Jingwei Li College of Mathematics Faculty of ScienceBeijing University of TechnologyBeijing 100124China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Laboratory of Mathematics and Complex Systems and School of Mathematical Science Beijing Normal UniversityBeijing 100875China

The peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of ma-terials.It has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation law.Based on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efﬁcientﬁrst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with peng-Robison 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 theo-retical results.

关键词： peng-robinson equation of state diffuse interface model maximum bound principle exponential time differencing Lagrange multiplier

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Hybrid Particle Swarm-Ant Colony Algorithm to Describe the Phase Equilibrium of Systems Containing Supercritical Fluids with Ionic Liquids

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Communications in Computational Physics 2013年第6期14卷 107-125页

作者： Juan A.Lazzus Departamento de Fisica Universidad de La SerenaCasilla 554La SerenaChile

Based on biologically inspired algorithms,a thermodynamic model to describe the vapor-liquid equilibrium of binary complex mixtures containing supercritical fluids and ionic liquids,is presented.The peng-robinson equation of state with the Wong-Sandler mixing rules are used to evaluate the fugacity coefficient on the systems.Then,a hybrid particle swarm-ant colony optimization was used to minimize the difference between calculated and experimental bubble pressure,and calculate the binary interaction parameters for the excess Gibbs free energy of all systems used.Simulations are carried out in nine systems with imidazolium-based ionic liquids.The results show that the bubble pressures were correlated with low deviations between experimental and calculated values.These deviations show that the proposed hybrid algorithm is the preferable method to describe the phase equilibrium of these complex mixtures,and can be used for other similar systems.

关键词： Particle swarm optimization ant colony optimization vapor-liquid equilibrium ionic liquids supercritical fluids peng-robinson equation of state

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An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

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Petroleum Science 2021年第3期18卷 923-938页

作者： Jing-Fa Li Bo Yu Dao-Bing Wang Shu-Yu Sun Dong-Liang Sun School of Mechanical Engineering Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil and Gas DevelopmentBeijing Institute of Petrochemical TechnologyBeijing 102617China Division of Physical Science and Engineering King Abdullah University of Science and TechnologyThuwal 23955-6900Saudi Arabia

In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of peng-robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the peng-robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.

关键词： Compressible fow Porous media Multigrid method Discrete empirical interpolation method peng-robinson equation of state

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