对流-扩散方程精细积分法与差分法比较

可用单内点子域精细积分 ,求解对流 -扩散方程初值问题 .当单内点精细积分中的传递函数 ,即指数函数用 Taylor展开式的一阶近似来替代时 ,精细积分转化为差分方程 .文中研究了这一对应关系 .各种常见差分格式均找到了对应的单点精细积分格式 。

关于流体问题的混合有限元方法

本文对流体力学中解偏微分方程的混合有限元方法进行研讨．并考虑位势流体方程和不可压粘性流体方程为例．提出其理论结果与误差。

Modeling of Bubble Motion in Two Dimensional Space

The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, acting vertically downwards. The non-linear equations of motion obtained are solved numerically for different values of the various parameters of the problem. The path traced by the centre of the bubble and velocity of the centre, the change of radius R with time, and the influence of the buoyancy force, which is experienced by the expanding bubble for different values of the gravitational acceleration on these quantities, are investigated. The radius R（t） of the bubble is found to vary periodically with time when the acceleration due to gravity is small. But when the acceleration due to gravity increases, this periodicity in the value of R（t） with t is lost. The influence of viscosity in determining the periodicity of the bubble motion is also investigated.

Thick Domain Walls in Lyra Geometry with Bulk Viscosity

In this paper, we evaluate the general solutions for plane-symmetric thick domain walls in Lyra geometry in presence of bulk viscous fluid. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.

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.

Investigation on Expanded Boundary Layer Equation

In this paper, the two approximate hypotheses in boundary layer theory p/y=0,2u/x2=0, are reinvestigated and analyzed, while a new approximate hypothesis, p/y =μ2v/y2, is suggested to establish a new expanded boundary layer equation. Its formula of equilibrium of force coincides basically with that of Navier-Stokes equations on the boundary while the applicable range of the boundary layer expansion equation can be extended to the leading edge region. Theoretical analysis and discussion are presented.

Three-Dimensional Viscous Numerical Simulation of Tip Clearance Flow in Axial-Flow Pump

The blade tip clearance flow in axial-flow pump is simulated based on three-dimensional N-S equations, RNG k -e turbulence model, and SIMPLEC algorithm. It shows that numerical results agree well with experiment data measured by 5-hole probe through validation. Flow fields at the blade tip and velocity distribution at the exit of rotor are analyzed in detail. The numerical results show that the increase in tip clearance reduces hydro-head, especially at small flow rate. Experiment equipment is also introduced.

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.

On Regularity of Incompressible Fluid with Shear Dependent Viscosity

The authors consider a non-Newtonian fluid governed by equations with p-structure in a cubic domain.A fluid is said to be shear thinning(or pseudo-plastic) if 1 < p < 2,and shear thickening(or dilatant) if p > 2.The case p > 2 is considered in this paper.To improve the regularity results obtained by Crispo,it is shown that the secondorder derivatives of the velocity and the first-order derivative of the pressure belong to suitable spaces,by appealing to anisotropic Sobolev embeddings.

Impact of Internal Heat Source on Mixed Convective Transverse Transport of Viscoplastic Material under Viscosity Variation

This communication addresses the impact of heat source/sink along with mixed convection on oblique flow of Casson fluid having variable viscosity. Similarity analysis has been utilized to model governing equations, which are simplified to set of nonlinear differential equations. Computational procedure of shooting algorithm along with 4 th order Range-Kutta-Fehlberg scheme is opted to attain the velocity and temperature distributions. Impact of imperative parameters on Casson fluid flow, temperature, significant physical quantities such as skin friction, local heat flux and streamlines are displayed via graphs.