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viscous Shock Wave to an Inflow Problem for Compressible viscous Gas with Large Density Oscillations

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Acta Mathematicae Applicatae Sinica 2019年第1期35卷 129-157页

作者： Dong-fen BIAN Li-li FAN Lin HE Hui-jiang ZHAO School of Mathematics and Statistics Beijing Institute of Technology School of Mathematics and Computer Science Wuhan Polytechnic University Institute of Applied Mathematics Academy of Mathematics and Systems Science The Chinese Academy of Sciences School of Mathematics and Statistics Wuhan University Computational Science Hubei Key Laboratory Wuhan University

This paper is concerned with the inflow problem for one-dimensional compressible Navier-Stokes equations. For such a problem, Huang, Matsumura, and Shi showed in [4] that there exists viscous shock wave solution to the inflow problem and both the boundary layer solution, the viscous shock wave, and their superposition are time-asymptotically nonlinear stable provided that both the initial perturbation and the boundary velocity are assumed to be sufficiently small. The main purpose of this paper is to show that similar stability results still hold for a class of large initial perturbation which can allow the initial density to have large oscillations. The proofs are given by an elementary energy method and our main idea is to use the smallness of the strength of the viscous shock wave and the boundary velocity to control the possible growth of the solutions induced by the nonlinearity of the compressible Navier-Stokes equations and the inflow boundary *** key point in our analysis is to deduce the desired uniform positive lower and upper bounds on the density.

关键词： compressible Navier-Stokes equations inflow problem viscous shock wave large density oscillations

Three vortex motion in the slightly viscous flow

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Science China(Physics,Mechanics & Astronomy) 2010年第4期53卷 735-744页

作者： ZHU Hao & CHENG KeMing College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 1. College of Aerospace Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

The dynamics of three vortices moving in an ideal fluid in a plane can be expressed in Hamiltonian form. However, when viscosity can not be ignored, the system of point vortices has not this delicious structure. This investigation focuses on the viscosity effect on the motion of three vortices. Since the viscous diffusion of vortices is simulated by Brownian motion, the equations of intervortical distances are obtained by Ito formula. These equations show that there exist two viscosity effects on intervortical distances: stable expansion and random impulse. Furthermore, via employing the asymptotic solution to these equations, these two viscous effects have been shown to destroy the self-similar process of collapse and make it into a new configuration, which is similar to the near collapse in the ideal case.

关键词： point vortex slightly viscous flow Fokker-Planck equation collapse Ito formula

THE　ESTABLISHMENT　OF　CALCULATION　FORMULA　FOR　CASTING－ROLLING　FORCE　OF　viscous　FLUID　AND　THE　INFLUENCE　OF　TECHNOLOGICAL　FACTORS

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中国有色金属学会会刊：英文版 1995年第3期5卷 101-104页

作者： Sun, Binyu Zhang, Hong Zhang, Xiaoping Shi, Rong (Taiyuan Heavy Machinery Institute, Taiyuan 030024) Taiyuan Heavy Machinery Inst Taiyuan China

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关键词： casting-rolling force viscous fluid flow function

Existence and blow-up of the solutions to the viscous quantum magnetohydrodynamic nematic liquid crystal model

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Science China Mathematics 2019年第3期62卷 469-508页

作者： Guangwu Wang Boling Guo School of Mathematics and Information Science Guangzhou University Graduate School of China Academy of Engineering Physics Institute of Applied Physics and Computational Mathematics China Academy of Engineering Physics

In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.

关键词： viscous quantum magnetohydrodynamic equations nematic liquid crystal global weak solution singular pressure smooth solution blow-up

viscous Fingering in Correlated Site-Bond Square Lattice

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Chinese Physics Letters 2001年第4期18卷 544-546页

作者： TIAN Ju-Ping YAO Kai-Lun Department of Physics Wuhan Institute of Science and TechnologyWuhan 430073 Department of Physics Huazhong University of Science and TechnologyWuhan 430074 CCAST(World Laboratory) P.O.Box 8730Beijing 100080 International Center for Material Physics Chinese Academy of ScienceShenyang 110015

A new porous media model with correlated sites-bonds has been *** into account both the pore and throat geometries,the viscous fingering(VF)in porous media has been investigated by using the standard over-relaxed Gauss-Seidel *** simulation results show that the VF's structure varies with the correlation parameterεand the viscous ratio *** sweep efficiency E decreases along with the increase of the correlation parameterεand the lattice size *** surface fractal Ds gradually increases as the correlation parameterεincreases,whatever the viscous ratio M ***,Ds gradually increases as M increases whateverε*** mean that not only the viscosity ratio but also the topology and the geometry of the porous media have a strong effect on the displacement process,the VF's structure,the sweep efficiency and the surface pattern.

关键词： viscous porous bonds

viscous Fingering Patterns and Fractal Nature in Two-Dimensional Porous Media

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Chinese Physics Letters 2001年第10期18卷 1371-1373页

作者： TIAN Ju-Ping YAO Kai-Lun Department of Physics Wuhan Institute of Science and TechnologyWuhan 430073 Department of Physics:Huazhong University of Science and Technology Wuhan 430074 COAST(World Laboratory) P.O.Box 8730Beijing 100080 International Center for Material Physics Chinese Academy of SciencesShenyang 110015

A new computer model of viscous fingering (VF) in a porous medium is presented. The simulation results show that the VF pattern is in agreement with the experimental results. The simulation on the sweep efficiency als... 详细信息

关键词： viscous Porous fractal

Effects of the number of particles and coordination number on viscous-flow agglomerate sintering

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Particuology 2019年第2期17卷 76-83页

作者： Mohammadmahdi Kamyabi Khashayar Saleh Rahmat Sotudeh-Gharebagh Reza Zarghami Multiphase Systems Research Laboratory School of Chemical Engineering College of Engineering University of Tehran Tehran 11155/4563 Iran Sorbonne University/Compiegne University of Technology EA 4297 Transformations Integrees de la Matiere renouvelable France

The process of sinteri ng of several particles in con tact via a viscous flow mecha nism was studied numerically using computational fluid dynamics. The volume of fluid technique within a finite volume method was used to simulate bridge formation between particles, as well as densification at different configurational states of the particles. The method was validated by comparing results for two-particle coalescence with the *** effect of the numberof particles on agglomerati on kin etics was studied by comparing bridge growth rate for systems having different numbers of particles in a chain. Although increasing the number of particles led to a decrease in the local bridge growth rate and to slower equilibration, there were no marked differences, when the overall volume of the system was considered. The effect of coordination number on the densification rate was directly studied by changing the number of particles in contact with a central *** the coordination nurnbec caused the overall rate of densificatio n to in crease, but delayed equilibration, analogous to steric effects. These findi ngs describe the con figurational state of agglomerates, typical of mesoscale caking. In a multi-scale study, they can be used to characterize caking at a bulk scale to partly address the lack of experimental data in this field.

关键词： Caking Agglomeration Sintering viscous flow mechanism Volume of fluid Coordination number

Computer Simulation of Radial viscous Fingering in Two-Dimension Porous Media

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Chinese Physics Letters 1998年第8期15卷 577-578页

作者： TIAN Ju-ping YAO Kai-lun Department of Physics Huazhong University of Science and TechnologyWuhan 430074 Department of Basic Science Jianghan Petroleum InstituteJingzhou 434102 CCAST(World Laboratory) P.O.Box 8730Beijing 100080 International Center for Material Physics Chinese Academy of SciencesShenyang 110015

A computer model of capillary and viscous fingering in a porous medium is presented which treats the medium as a square lattice connected with randomly chosen *** fractal properties of the model are studied for circular shell-shell aggregation by a Monte Carlo *** simulation results show that the dimension D increases with decrease of the viscous ratio M and increase of the throat *** is found that the displacement process is stable when M=1,and viscous fingering pattern of porous media in the limit M→∞is similar to the diffusion-limited aggregation pattern in a uniform *** larger viscous ratio M and smaller positive integer k,the fluid is situated in the co-existence region of viscous and capillary fingering.

关键词： viscous capillary aggregation

The Strong Solution for the viscous Polytropic Fluids with Non-Newtonian Potential

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Chinese Annals of Mathematics,Series B 2019年第2期40卷 237-250页

作者： Qiu MENG Hongjun YUAN Institute of Mathematics and Statistics Beihua University Institute of Mathematics Jilin University

The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.

关键词： Compressible Navier-Stokes equations viscous polytropic fluids Vacuum Poincare type inequality Non-Newtonian potential