Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption

We consider a convective flow in a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with suction, and internal heat generation/absorption. Using a similarity transformation the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations. We first examine a number of special cases for which we may obtain exact solutions. We then obtain analytical solutions (by the Homotopy Analysis Method) and numerical solutions (by a boundary value problem solver), in order to further study the behavior of the nonlinear differential equations, for various values of the physical parameters. Our numerical solutions are shown to agree with the available results in the literature. We then employ the numerical results to bring out the effects of the suction parameter, heat source/sink parameter, stretching parameter, porosity parameter, the Prandtl number and the free convection parameter on the flow and heat transfer characteristics. In the absence of suction and free convection, our findings are in agreement with the corresponding numerical results of Attia [H.A. Attia, On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation, Comput. Mater. Sci. 38 (2007) 741-745].     

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.     

QUASI-NEUTRAL LIMIT OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

This paper is concerned with the quasi-neutral limit of the bipolar NavierStokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible NavierStokes equations as the Debye length goes to zero. Moreover, if we let the viscous coefficients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations.     

Mass and momentum conservation of the least-squares spectral collocation method for the Navier-Stokes equations

From the literature, it is known that the Least-Squares Spectral Element Method (LSSEM) for the stationary Stokes equations performs poorly with respect to mass conservation but compensates this lack by a superior conservation of momentum. Furthermore, it is known that the Least-Squares Spectral Collocation Method (LSSCM) leads to superior conservation of mass and momentum for the stationary Stokes equations. In the present paper, we consider mass and momentum conservation of the LSSCM for time-dependent Stokes and Navier-Stokes equations. We observe that the LSSCM leads to improved conservation of mass (and momentum) for these problems. Furthermore, the LSSCM leads to the well-known time-dependent profiles for the velocity and the pressure profiles. To obtain these results, we use only a few elements, each with high polynomial degree, avoid normal equations for solving the overdetermined linear systems of equations and introduce the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero. Furthermore, we combined the transformation of Gordon and Hall (transfinite mapping) with the least-squares spectral collocation scheme to discretize the internal flow problems.     

A Nine-modes Truncation of the Plane Incompressible Navier-Stokes Equations

In this paper a nine-modes truncation of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. The stationary solutions, the existence of attractor and the global stability of the equations are firmly proved. What is more, that the force f acts on the mode ks and k7 respectively produces two systems, which lead to a much richer and varied phenomenon. Numerical simulation is given at last, which shows a stochastic behavior approached through an involved sequence of bifurcations.     

一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性

主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:其中粘性系数μ依赖于密度ρ,Φ是非牛顿位势.证明了上述问题的强解的存在性.在相容性条件下,得到了强解的唯一性.     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

A high-order upwind scheme has been developed to capture the vortex wake of a helicopter rotor in the hover based on chimera grids. In this paper, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate the higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and is compared with the monotone upwind scheme for scalar conservation laws (MUSCL). For profitably capturing the wake and enforcing the period boun...     

基于局部DQ-RBF不可压缩N-S方程的数值求解

以RBF作为DQ方法的基函数,将迎风机制引入DQ-RBF中,建立了二维不可压缩黏性N-S方程数值求解模型,采用Levenberg-Marquardt算法求解非线性方程组.求解时分析了形状参数对求解精度的影响,改进了边界速度的处理方法.对平板Couette流及有限宽台阶绕流流动问题进行了数值求解.比较了本文方法和FLUE...     

On Compressible Smooth Viscous Fluids in Slowly Expanding Balls

In[17]and[19,20],the global existence and large time behaviors of smooth compressible fluids(including inviscid gases of Euler equations,viscous gases of Navier-Stokes equations,and rarified gases of Boltzmann equation,respectively)have been established in an infinitely expanding ball with a constant expansion speed.This paper concerns with the viscous fluids in a slowly expanding ball.By involved analy-sis on the density function and the weighted energy estimates,we show that the fluid in the slowly expanding ball smoothly tends to a vacuum state and there is no appearance of vacuum in any part of the expansive ball.Our present result is a meaningful supplement to the one in[19].