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 mas...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.展开更多
In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows ar...In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.展开更多
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 gra...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.展开更多
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 ...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.展开更多
electrolyte. The properties of lithium-ion (Li-ion) battery, such as cycle life, irreversible capacity loss, self-discharge rate, electrode corrosion and safety are usually ascribed to the quality of the SEI, which ar...electrolyte. The properties of lithium-ion (Li-ion) battery, such as cycle life, irreversible capacity loss, self-discharge rate, electrode corrosion and safety are usually ascribed to the quality of the SEI, which are highly dependent on the thickness. Thus, understanding the formation mechanism and the SEI thickness is of prime interest. First, we apply dimensional analysis to obtain an explicit relation between the thickness and the number density in this study. Then the SEI thickness in the initial charge-discharge cycle is analyzed and estimated for the first time using the Cahn-Hilliard phase-field model. In addition, the SEI thickness by molecular dynamics simulation validates the theoretical results. It has been shown that the established model and the simulation in this paper estimate the SEI thickness concisely within order-of-magnitude of nanometers. Our results may help in evaluating the performance of SEI and assist the future design of Li-ion battery.展开更多
In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous c...In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids.We prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.展开更多
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...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.展开更多
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11425210,11621202 and 11672288)
文摘In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.
基金supported in part by US NSF-DMS 1016073,NSFC 11271350 and 91130019Special Research Funds for State Key Laboratories Y22612A33S+1 种基金China 863 project 2010AA012301 and 2012AA01A304China 973 project 2011CB309702.
文摘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.
基金The PhD fellowship(P.M.Dupuy)financed by the Research Council of Norway,Petromaks programme,through the project HiPGLS(169477)is gratefully appreciated.
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11372313, U1562105, and 11611130019)the Chinese Academy of Sciences (CAS) through CAS Interdisciplinary Innovation Team Project, the CAS Key Research Program of Frontier Sciences (Grant No. QYZDJ-SSW-JSC019)the CAS Strategic Priority Research Program (Grant No. XDB22040401)
文摘electrolyte. The properties of lithium-ion (Li-ion) battery, such as cycle life, irreversible capacity loss, self-discharge rate, electrode corrosion and safety are usually ascribed to the quality of the SEI, which are highly dependent on the thickness. Thus, understanding the formation mechanism and the SEI thickness is of prime interest. First, we apply dimensional analysis to obtain an explicit relation between the thickness and the number density in this study. Then the SEI thickness in the initial charge-discharge cycle is analyzed and estimated for the first time using the Cahn-Hilliard phase-field model. In addition, the SEI thickness by molecular dynamics simulation validates the theoretical results. It has been shown that the established model and the simulation in this paper estimate the SEI thickness concisely within order-of-magnitude of nanometers. Our results may help in evaluating the performance of SEI and assist the future design of Li-ion battery.
基金Supported by the NNSF of China(Grant Nos.12171438,11801133)the Natural Science Foundation of Henan Province(Grant No.152300410227)the grant from the Special Project of Basic Scientific Research Business Expenses of Zhongyuan University of Technology(Grant No.K2020TD004)。
文摘In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids.We prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.
基金supported by National Natural Science Foundation of China under grant number No.11971047supported by National Natural Science Foundation of China under grant number No.61962056.
文摘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.
