泥饼的压缩性方程

本文在考虑了泥饼具有压缩性这一条件下,推导建立了泥饼的压缩性方程。它比较反映泥饼在形成的过程中静态和动态失水情况,以便失水的控制。

采用拟可压缩性方程对混流式水轮机转轮的紊流模拟

通过拟可压缩性方程,采用有限差分的隐式格式和K-ε两方程紊流模式对混流式水轮机转轮进行三维纳维斯托克斯数值算法已经研究开发出来。旋转流场中的粘性流动可以很好地得到模拟,它既可用于流场的设计运行工况,又可适用于转轮进口边附近引起流动分离产生强烈旋涡的非设计工况。由于该算法采用了隐式算法和靠近壁面采用了壁面函数,CPU时间不需要太长,因此,它可用于象桌面工作站一样的小型计算机,并能充当设计工具,曾一度用于可压缩性流体的这种算法已被证实可用于模拟透平机械行业中复杂的不可压流动。

New algorithm for solving 3D incompressible viscous equations based on projection method

A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.

Numerical Simulation of Interaction Between Laminar Flow and Elastic Sheet

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.

Exponential Stability for the Compressible Navier-Stokes Equations

We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.

Compacton, Peakon, and Foldon Structures in the （2＋1）-DimensionalNizhnik-Novikov-Veselov Equation

By the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equation is transformed into three equations of linear,bilinear,and tri-linear forms,respectively.From the above three equations,a rather general variable separation solution of the model is obtained.Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.

A Note on Unification of Translational Shape Invariant Potential and Scaling Shape Invariant Potential

This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.

Blow-up of Solution for the Nonlinear Sobolev-Galpern Equation

In this paper,the initial boundary value problems of the nonlinear Sobolev-Galpern equation are studied.The existence,uniqueness of local solution for the problem are obtained by means of a special Green's function and the contraction mapping principle.Finally,the blow-up of solution in finite time under some assumed conditions is proved with the aid of Jensen's inequality.

Analysis on effective stress formula and consolidation of gassy muddy clay

In order to found an applicable equation of consolidation for gassy muddy clay, an effective stress formula of gas-charged nearly-saturated soils was introduced. And then, a consolidation equation was derived. Subsequently, supposing soils were under tangential loading, the expressions of pore water pressure were presented. The analytic solution of pore water pressure was attempted to be validated by the measured values in a real embankment. The parameters in the expressions of pore water pressure were gotten by the method of trial. The result shows that the consolidation model is rational and the analytic solution of pore water pressure is correct. The following conclusions can be made: 1) the influence of bubbles on the compressibility of pore fluid should be considered; 2) the effective stress would be influenced by bubbles, and the consolidation would depend on the compressibility of soil skeleton: the softer the soils are, the more distinct the influence of bubbles is; for normal clay, the influence of bubbles on the effective stress may be commonly neglected.

Fe(Ⅲ)对海藻酸钙凝胶层过滤特性的影响

为考察饮用水处理膜工艺中Fe(Ⅲ)对多糖污染层过滤特性的影响,本研究以海藻酸钠为模型多糖污染物,分析海藻酸钙在有Fe(Ⅲ)及无Fe(Ⅲ)存在时形成污染层的过滤特性,并用压缩性方程及渗透性方程对凝胶层的过滤特性进行定量描述.研究结果表明,Ca2+的存在会使海藻酸钠分子间结合,形成内部结合紧密的凝胶层,产生较大的过滤阻力;往海藻酸钙溶液中进一步加入Fe(Ⅲ)后,由于可溶性Fe(Ⅲ)较易水解,加入Fe Cl3后溶液中铁离子和铁的氧化物/氢氧化物颗粒同时存在,少量Fe(Ⅲ)对海藻酸钙凝胶层的过滤特性影响不大,较多量Fe(Ⅲ)会形成铁的氧化物/氢氧化物颗粒,一定程度上改变了凝胶层的结构,使过滤性能变好.

Nonlinear instability for nonhomogeneous incompressible viscous fluids

We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,including a Rayleigh-Taylor steady-state solution with heavier density with increasing height(referred to the Rayleigh-Taylor instability).We first analyze the equations obtained from linearization around the steady density profile solution.Then we construct solutions to the linearized problem that grow in time in the Sobolev space H k,thus leading to a global instability result for the linearized problem.With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations,we can then demonstrate the instability of the nonlinear problem in some sense.Our analysis shows that the third component of the velocity already induces the instability,which is different from the previous known results.

A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries

A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.

A unified theory for gas dynamics and aeroacoustics in viscous compressible flows.PartⅡ.Sources on solid boundary

This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.

Weak Continuity and Compactness for Nonlinear Partial Differential Equations

This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.

Numerical Simulation of Flow Characteristics in Micro Shock Tubes

Recently micro shock tubes have been widely used in many engineering and industrial fields, but the characteristics of unsteady flow are not well known to date in micro shock tubes. Compared to conventional shock tubes with macro scales, flows related to shock waves in micro shock tubes are highly complicated. Stronger viscous and dissipative interactions make shock wave dynamic behaviors significantly different from theoretical predictions. In the present study, a CFD work was applied to the unsteady compressible Navier-Stokes equations which were solved using a fully implicit finite volume scheme. The diaphragm pressure ratio and shock tube diameter were varied to investigate their effects on micro shock tube flows. Different wall boundary conditions were also performed to observe shock wave and contact surface propagation with no slip and slip walls. Detailed flow characteristics at the foot of shock wave and contact surface propagation were known from the present numerical simulations.

Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.

The Asymptotic Behavior and the Quasineutral Limit for the Bipolar Euler-Poisson System with Boundary Efects and a Vacuum

In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy＇s law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → ＋∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.

Global Solutions of Shock Reflection by Wedges for the Nonlinear Wave Equation

When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. In this paper, shock reflection by large-angle wedges for compressible flow modeled by the nonlinear wave equation is studied and a global theory of existence, stability and regularity is established. Moreover, C^0,1 is the optimal regularity for the solutions across the degenerate sonic boundary.

Asymptotic limit of the Gross-Pitaevskii equation with general initial data

This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.