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Journal of Computational Mathematics 2017年第6期35卷 737-765页

作者： Qiujin Peng Zhonghua Qiao Shuyu Sun Institute for Mathematical Sciences Renmin University of China Beijing 100872 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Horn Hong Kong Division of Physical Sciences and Engineering King Abdullah University of Science and Technology Thuwal 23955-6900 Kingdom of Saudi Arabia

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a Diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.

关键词： Diffuse interface model Fourth order parabolic equation Energy stability,Convergence.

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

Retrieving Topological Information of Implicitly Represented diffuse interfaces with Adaptive Finite Element Discretization

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Communications in Computational Physics 2013年第5期13卷 1209-1226页

作者： Jian Zhang Qiang Du Supercomputing center Chinese Academy of SciencesBeijingP.R.China Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA State Key Laboratory of Space Weather Chinese Academy of SciencesBeijingP.R.China

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface framework.Utilizing an adaptive finite element implementation with effective gradient recovery techniques,we discuss how the Euler number can be accurately computed directly from the numerically solved phase field functions or order parameters.Numerical examples and applications to the topological analysis of point clouds are also presented.

关键词： Diffuse interface model phase field method Euler number Gauss curvature adaptive finite element gradient recovery

Multiphysic Two-Phase Flow Lattice Boltzmann:Droplets with Realistic Representation of the interface

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Communications in Computational Physics 2011年第5期9卷 1414-1430页

作者： Pablo M.Dupuy María Fernandino Hugo A.Jakobsen Hallvard F.Svendsen Department of Chemical Engineering Norwegian University of Science and TechnologyN-7491 TrondheimNorway Department of Energy and Process Engineering Norwegian University of Science and TechnologyN-7491 TrondheimNorway CSIRO-Mathematics Informatics and StatisticsMelbourneAustralia.(Current affiliation)

Free energy lattice Boltzmann methods are well suited for the simulation of two phase flow problems.The model for the interface is based on well understood physical grounds.In most cases a numerical interface is used instead of the physical one because of lattice resolution limitations.In this paper we present a framework where we can both follow the droplet behavior in a coarse scale and solve the interface in a fine scale simultaneously.We apply the method for the simulation of a droplet using an interface to diameter size ratio of 1 to 280.In a second simulation,a small droplet coalesces with a 42 times larger droplet producing on it only a small capillary wave that propagates and dissipates.

关键词： Two-phase flow Diffuse interface model multi-scale real interface