TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID

In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.

Research on relationship between leakage of incompressible fluid and pressure change in pipeline

In practical engineering,only pressure sensors are allowed to install to detect leakage in most of oil transportation pipelines,while flowmeters are only installed at the toll ports.For incompressible fluid,the leakage rate and amount cannot be accurately calculated through critical pressure conditions.In this paper,a micro-element body of the pipeline was intercepted for calculation.The relationship between radial displacement and pressure of pipe wall was studied based on the stress-strain equation.Then,the strain response of pipeline volume with pipeline pressure was obtained.The change in volume expansion of pipeline was used to characterize leakage of incompressible fluid.Finally,the calculation model of leakage amount of incompressible fluid was obtained.To verify the above theory,the pipeline expansion model under pressure was established by COMSOL software for simulation.Both simulation results and deduction equations show that the volumetric change has a quadratic parabolic relationship with the change of pipeline pressure.However,the relationship between them can be approximately linear when the pressure change is not too large.In addition,the leakage of incompressible fluid under the pressure of 0 MPa-0.8 MPa was obtained by experiments.The experimental results verify the linear relationship between leakage of incompressible fluid and the change of pipeline pressure.The theoretical and experimental results provide a basis for the calculation of leakage of incompressible fluid in the pipeline.

STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE

In this article, we are concerned with the strong solutions for the incompress- ible fluid models of Korteweg type in a bounded domain Ω СR^3. We prove the existence and uniqueness of local strong solutions to the initial boundary value problem. We point out that in this article we allow the existence of initial vacuum provided initial data satisfy a compatibility condition.

UNIFIED COMPUTATION OF FLOW WITH COMPRESSIBLE AND INCOMPRESSIBLE FLUID BASED ON ROE'S SCHEME

A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe＇s type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe＇s scheme.

Similarity Solutions of Unsteady Mixed Convective Boundary Layer Flow of Viscous Incompressible Fluid along Isothermal Horizontal Plate

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

Unsteady Flow of Shear-Thinning non-Newtonian Incompressible Fluid Through a Twin-Screw Extruder

The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed bound- ary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it con- tains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

ON VORTEX ALIGNMENT AND THE BOUNDEDNESS OF THE Lq-NORM OF VORTICITY IN INCOMPRESSIBLE VISCOUS FLUIDS

We show that the spatial L q-norm(q>5/3)of the vorticity of an incompressible viscous fluid in R^3 remains bounded uniformly in time,provided that the direction of vorticity is Hölder continuous in space,and that the space-time L q-norm of vorticity is finite.The Hölder index depends only on q.This serves as a variant of the classical result by Constantin-Fefferman(Direction of vorticity and the problem of global regularity for the Navier-Stokes equations,Indiana Univ.J.Math.42(1993),775-789),and the related work by Grujić-Ruzmaikina(Interpolation between algebraic and geometric conditions for smoothness of the vorticity in the 3D NSE,Indiana Univ.J.Math.53(2004),1073-1080).

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

In this paper, the Clarkson-Kruskal direct approach is employed to investigate the exact solutions of the 2-dimensionai rotationai Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is＇of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh（ kt /2 ） and sech （kt/2） due to the rotational parameter k ≠ O. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth＇s rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.

An Energy Stable SPH Method for Incompressible Fluid Flow

In this paper,a novel unconditionally energy stable Smoothed Particle Hydrodynamics(SPH)method is proposed and implemented for incompressible fluid flows.In this method,we apply operator splitting to break the momentum equation into equations involving the non-pressure term and pressure term separately.The idea behind the splitting is to simplify the calculation while still maintaining energy stability,and the resulted algorithm,a type of improved pressure correction scheme,is both efficient and energy stable.We show in detail that energy stability is preserved at each full-time step,ensuring unconditionally numerical stability.Numerical examples are presented and compared to the analytical solutions,suggesting that the proposed method has better accuracy and stability.Moreover,we observe that if we are interested in steady-state solutions only,our method has good performance as it can achieve the steady-state solutions rapidly and accurately.

ERROR ESTIMATION OF PREDICTION-CORRECTION LEGENDRE SPECTRAL APPROXIMATION TO INCOMPRESSIBLE FLUID FLOW

The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It is strictly proved that the numerical solution possesses the accuracy of second-order in time and higher order in space.

UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.

On the pressure and stress singularities induced by steady flows of incompressible viscous fluids

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

On the pressure and stress singularities induced by steady flows of a pair of nonmiscible,incompressible,viscous fluids in contact with a wall

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid： Here the asymptotic approach is extended to apply to a configuration entailing two such fluids, For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.

WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

ENERGY CONSERVATION FOR SOLUTIONS OF INCOMPRESSIBLE VISCOELASTIC FLUIDS

Some sufficient conditions of the energy conservation for weak solutions of incompressible viscoelastic flows are given in this paper.First,for a periodic domain in R^(3),and the coefficient of viscosity μ=0,energy conservation is proved for u and F in certain Besovs paces.Furthermore,in the whole space R^(3),it is shown that the conditions on the velocity u and the deformation tensor F can be relaxed,that is,u∈B_(3,c(N))^(1/3),and F∈B_(3,∞)^(1/3).Finally,when μ>0,in a periodic domain in R^(d) again,a result independent of the spacial dimension is established.More precisely,it is shown that the energy is conserved for u∈L^(T)(0,T;L^(n)(Ω))for any 1/r+1/s≤1/2,with s≥4,and F∈L^(m)(0,T;L^(n)(Ω))for any 1/m+1/n≤1/2,with n≥4.

Preconditioners for Incompressible Navier-Stokes Solvers

In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation

The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation.The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for p≥11/5.The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function.The advantage of the new formulation is to control the external force term G=-∫Rd(u-v)fdc(d=2,3).The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques.We further prove the uniqueness of weak solutions to the considered system.

The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation

Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.

Numerical simulation of viscous liquid sloshing by moving-particle semi-implicit method

A meshless numerical simulation method, the moving-particle semi-implicit method （MPS） is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses particles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of particles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method （ICCG）, the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.