应用谱理论研究压力脉动的湍流模式

本文应用谱分析理论研究了剪切湍流场中的压力脉动,包括功率谱、均方值等.通过对压力脉动Possion方程的Fourier变换,首先将压力脉动谱表示成速度脉动谱的形式.利用Navier-Stokes方程的形式解及准正态分布假设,可以进一步将压力脉动功率谱表达式中所包含的速度脉动的三阶相关与四阶相关表示成速度脉动的二阶相关（功率谱）.最后,引入高雷诺数流的速度脉动功率谱模型,导出了由湍动e₀,耗散ε,雷诺应力-iu_j>及时均速度梯度表示的压力脉动均方值的湍流模式,并同现有数据进行了比较.     

DAE的Runge-Kutta方法在不可压NS方程求解中的应用

1．引言自然界中的流场通常是非定常复杂流场，要正确模拟和跟踪复杂流场的变化，计算格式的时间精度极为重要．对于常微分方程（＊＊q，一般采用＊K方法及线性多步法来提高格式的时间精度．前者是单步法，在计算过程中可以改变步长，可找到稳定性较好的高精度格式：近年来在发展到偏微分方程的数倩水解中也有很多应用．原始变量的INS方程（二维）为：其中u，v分别是x，y方向速度分量，r是压力，连续方程（1．幻可视为约束条件．从［1］，［2］可见，经空间差分化后（固定空间网格），它可看作带约束的微分方程组，即微分代数方程（DAE－…     

On the Potential Flow of an Ideal Incompressible Fluid through a Porous Boundary

The potential flow of an incompressible fluid is considered.The fluid is supposed to be ideal except on the porous boundarywhere the normal velocity is proportional to the pressure. Thisleads to the Laplace equation with the square of the gradientin the boundary condition. The linearized problem (small velocities)is trivially solvable by the variational method in the usualenergy space. The nonlinearity of the boundary condition beingtoo strong for that space, the stationary problem is treatedin some Banach algebras of functions defined on the boundaryof . The existence and uniqueness of the solution are provedfor small flows or for large boundary resistances.     

Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity–stress–pressure formulation

In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity–stress–pressure formulation) in six equations and six unknowns together with Riemann–Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H¹ product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L²-norm and in the H¹-norm. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Adaptive stabilized mixed finite volume methods for the incompressible flow

In this article, we study adaptive stabilized mixed finite volume methods for the incompressible flows approximated using the lower order elements. A residual type of a posteriori error estimator is designed and studied with the derivation of upper and lower bounds between the exact solution and the finite volume solution. A discrete local lower bound between two successive finite volume solutions is also obtained. Also, convergence of the adaptive stabilized mixed finite volume methods is established. The presented methods have three prominent features. First, it is of practical convenience in real applications with the same partitions for velocity and pressure. Second, less computational time is required by easily applying both the lower order elements and the local grid refinement necessary for the elements of interest. Third, compared with the standard finite element method, its analysis of H¹‐norm and L²‐norm for the velocity and pressure are usually derived without any high order regularity conditions on the exact solution. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1424–1443, 2015     

Global strong solutions for nonhomogeneous heat conducting Navier‐Stokes equations

We study the Cauchy problem of the 3‐dimensional nonhomogeneous heat conducting Navier‐Stokes equations with nonnegative density. First of all, we show that for the initial density allowing vacuum, the strong solution to the problem exists globally if the velocity satisfies the Serrin's condition. Then, under some smallness condition, we prove that there is a unique global strong solution to the 3D viscous nonhomogeneous heat conducting Navier‐Stokes flows. Our method relies upon the delicate energy estimates.     

Velocity field and pressure analysis of equatorial flows beneath solitary water waves

In this paper, we investigate steady equatorial flows beneath solitary water waves subject to the Coriolis effect, which propagate over a flat bed. In particular, we focus on irrotational flows and present some properties of velocity field, behavior of the pressure and the extrema of the dynamic pressure. In addition, we provide some estimates for the elevation of wave from pressure measurements at an arbitrary intermediate depth. The analysis is based on the maximum principles.     

The Motion of Small Particles and Droplets in Quadratic Flows

We consider the low-Reynolds-number motion of small particles and droplets in the most general unbounded quadratic flows. The fluid velocity and pressure fields are obtained by means of a vectorial formulation of Lamb's general solution, providing a compact representation for the requisite flow field. The leading-order deformation of the droplet from its initial spherical shape is also calculated.     

Unsteady flows of fluids with pressure dependent viscosity in unbounded domains

In order to describe the behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the Cauchy stress and the velocity gradient these models are consistent with standard procedures of continuum mechanics. Understanding the mathematical properties of the governing equations is connected with various types of idealizations, some of them lead to studies in unbounded domains. In this paper, we first bring up several characteristic features concerning fluids with pressure dependent viscosity. Then we study the three-dimensional flows of a class of fluids with the viscosity depending on the pressure and the shear rate. By means of higher differentiability methods we establish the large data existence of a weak solution for the Cauchy problem. This seems to be a first result that analyzes flows of considered fluids in unbounded domains. Even in the context of purely shear rate dependent fluids of a power-law type the result presented here improves some of the earlier works.     

Discretization of the Navier‐Stokes equations with slip boundary condition

We propose and analyze a two‐level method of discretizing the nonlinear Navier‐Stokes equations with slip boundary condition. The slip boundary condition is appropriate for problems that involve free boundaries, flows past chemically reacting walls, and other examples where the usual no‐slip condition u = 0 is not valid. The two‐level algorithm consists of solving a small nonlinear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh. The two‐level method exploits the quadratic nonlinearity in the Navier‐Stokes equations. Our error estimates show that it has optimal order accuracy, provided that the best approximation to the true solution in the velocity and pressure spaces is bounded above by the data. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 26–42, 2001     

储层岩石周期性电渗流特性的微观机制

以双电层电位理论和电渗流动的动量方程为基础,结合储层岩石平行毛管束模型,推导出岩石孔隙内周期性电渗流的解析式,揭示了储层中电渗效应的微观机制,分析了非密闭储层岩石中宏观电渗Darcy速度及密闭储层中电渗压力系数频散特性的影响因素．数学模拟结果表明:储层岩石孔隙中,周期性电渗流速度剖面在频率较高时呈“波浪”状;孔隙度越大,电渗Darcy速度模值越大,其相位也越大,而电渗压力系数数值越小．储层岩石的溶液浓度越小或阳离子交换量越大,电渗Darcy速度模值和电渗压力系数数值越大,但对电渗Darcy速度的相位没有影响．     

The spectral simulation of axisymmetric non-Newtonian flows using time splitting techniques

Algorithms for the transient simulation of axisymmetric non-Newtonian flows using spectral methods are described for the primitive variable formulation of the governing equations. A modification of the method of Ku et al. (Comput. Fluids 15, pp. 195–214 (1987)) and the construction of an optimal approximation space for the pressure ensures that the velocity field is globally divergence free at the end of each time step. The application of these techniques to some fundamental non-Newtonian flow problems is described.     

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.     

Planar flows of incompressible heat-conducting shear-thinning fluids—Existence analysis

We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called L ^∞-truncation method, used to obtain the strong convergence of the velocity gradient. The important point of the approach consists in the choice of an appropriate form of the balance of energy.     

Numerical scheme for multilayer shallow-water model in the low-Froude number regime

The aim of this note is to present a multi-dimensional numerical scheme approximating the solutions to the multilayer shallow-water model in the low-Froude-number regime. The proposed strategy is based on a regularized model where the advection velocity is modified with a pressure gradient in both mass and momentum equations. The numerical solution satisfies the dissipation of energy, which acts for mathematical entropy, and the main physical properties required for simulations within oceanic flows.     

Numerical study of spherical Couette flows for certain zenith-angle-dependent rotations of boundary spheres at low Reynolds numbers

The numerical method with splitting of boundary conditions developed previously by the first and third authors for solving the stationary Dirichlet boundary value problem for the Navier-Stokes equations in spherical layers in the axisymmetric case at low Reynolds numbers and a corresponding software package were used to study viscous incompressible steady flows between two con-centric spheres. Flow regimes depending on the zenith angle ?? of coaxially rotating boundary spheres (admitting discontinuities in their angular velocities) were investigated. The orders of accuracy with respect to the mesh size of the numerical solutions (for velocity, pressure, and stream function in a meridional plane) in the max and L ₂ norms were studied in the case when the velocity boundary data have jump discontinuities and when some procedures are used to smooth the latter. The capabilities of the Richardson extrapolation procedure used to improve the order of accuracy of the method were investigated. Error estimates were obtained. Due to the high accuracy of the numerical solutions, flow features were carefully analyzed that were not studied previously. A number of interesting phenomena in viscous incompressible flows were discovered in the cases under study.     

Harnack estimate for curvature flows depending on mean curvature

The maximum principle is applied to prove the Harnack estimate of curvature flows of hypersurfaces in Rn＋1,where the normal velocity is given by a smooth function f depending only on the mean curvature.By use of the estimate,some corollaries are obtained including the integral Harnack inequality.In particular,the conditions are given with which the solution to the flows is a translation soliton or an expanding soliton.     

A Method for Determining Linear Solutions in Magnetohydrodynamics

Given any two-dimensional and incompressible flow describedby a set of linear partial differential equations, a methodis presented for determining the solution for the dependentvariables (velocity, pressure, etc.). The method is then usedto investigate the following magnetohydrodynamic flows. (a) The flow of an irrotational and inviscid fluid. (b) The flow of a viscous fluid. (c) The flow of an electrically conducting, inviscid fluid inthe presence of a magnetic field aligned with the flow at infinity. (d) The flow of an electrically conducting, viscous fluid inthe presence of a magnetic field having arbitrary direction.     

Steady motions of a continuous medium, resonances and Lagrangian turbulence

A method which enables one to establish a non-regularity property of the motion of fluid particles (known as chaotic advection or Lagrangian turbulence) for typical steady flows is developed. The method is based on expanding solutions of the equations of motion of a continuous medium in powers of a small parameter and using the conditions for the destruction of invariant resonant tori when perturbations are added. It is shown that the velocity field, defined as the solution of the Burgers equations, generates a generally non-regular dynamical system. For an ideal barotropic fluid in an irrotational force field, the method proposed yields a well-known necessary condition for chaotization: the velocity field is collinear with its curl. Special attention is given to investigating the chaotization of typical steady flows of a heat-conducting perfect gas.     

Stokes流和理想流体轴对称问题的解析函数法

本文利用流函数解的完备性和共轭势函数的概念,导出了轴对称Stokes流和理想流体完备的速度和压力的解析函数表达式解.作为它的应用,我们求出关于球的缓慢绕流问题的解.