SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.

N-S EQUATION CALCULATIONS ON MULTI-ELEMENT AIRFOILS WITH ZONAL PATCHED GRIDS

For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.

Direct Numerical Simulation of Interaction Between Wave and PorousBreakwater Based on N-S Equation

In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference method. The free surface is tracked by the VOF method. The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method. Finally, compared with the physical model test results of wave flume, the numerical model established in the present study is validated.

An h-adaptive Discontinuous Galerkin Method for Laminar Compressible Navier-Stokes Equations on Curved Mesh

An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.

Application of Mixed Differential Quadrature Method for Solving the Coupled Two-Dimensional Incompressible Navier-Stokes Equation and Heat Equation

The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.

Solution of N-S equations based on the quadtree cut cell method

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.

Motion Equation and Solution of Mushroom Cloud

Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.

An Extented Wave Action Equation

Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity u i and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.

光路交叠对强光传输的影响

实验中观察到高能激光束通过光程总长、气体环境等条件相同,但局部布置不同的光路后,其接收光斑峰值功率密度、波前离焦和高阶像差等光束参量有差异.对此问题,选择Z型和X型两种总长度相等的光路在相同气体环境下进行了数值研究.结果表明,产生上述差异的主要原因是由于两种光路中光束交叠区域大小和形状不同引起的气体热效应产生的附加相位有所不同.而且对不同特性的光束,该差异也不同.对高斯光束,两种光路中气体热效应对光束影响的差异较小;对平顶高斯空心光束,两种光路中气体热效应对光束影响的差异较明显.因此,为抑制气体热效应对光束的影响,在考虑其它因素的同时,应尽可能减小光路中的光束交叠区域.

FLOW CHARACTERISTIC AND HEAT TRANSFER FOR SINGLE PHASE GASEOUS IN SLIP REGIME OF MICROCHANNEL FLOW

Based on analyzing some simulation models of single phase gaseous flow in microchannels （0. 001〈 Kn〈0. 1 ）, a numerical simulation of N-S equations with the slip model is presented. In the simulation, the collocated grid and the SIMPLE scheme are used. Results show that the pressure in the inlet is changed with Knudsen number. The slip speed and the temperature creep are increased with the augment of Knudsen number. The drag force decreases and the resistance of the heat trensfer has a little increase.

Characteristic-based operator-splitting finite element method for Navier-Stokes equations

A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the temporal discretization is performed by the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective part can be discretized using the characteristic Galerkin method and solved explicitly. The driven square flow and backward-facing step flow are conducted to validate the model. It is shown that the numerical results agree well with the standard solutions or existing experimental data, and the present model has high accuracy and good stability. It provides a prospective research method for solving N-S equations.

Numerical Simulation of Wave Field near Submerged Bars by PLIC-VOF Model

Investigating the wave field near structures in coastal and offshore engineering is of increasing significance. In the present study, simulation is done of the wave profile and flow field for waves propagating over submerged bars, using PLIC-VOF （Pieeewise Linear Interface Construction） to trace the free surface of wave and finite difference method to solve vertical 2D Navier-Stokes （N-S） equations. A comparison of the numerical results for two kinds of submerged bars with the experimental ones shows that the PLIC-VOF model used in this study is effective and can compute the wave field precisely.

On the stability of contact discontinuity for Cauchy problem of compress Navier-Stokes equations with general initial data

Abstract In this paper, we study the stability of solutions of the Cauchy problem for 1-D compressible Narvier- Stokes equations with general initial data. The asymptotic limit of solution is found, under some conditions. The results in this paper imply the case that the limit function of solution as t → ee is a viscous contact wave in the sense, which approximates the contact discontinuity on any finite-time interval as the heat conduction coefficients toward zero. As a by-product, the decay rates of the solution for the fast diffusion equations are also obtained. The proofs are based on the elementary energy method and the study of asymptotic behavior of the solution to the fast diffusion equation.

Numerical Calculations of Aerodynamic and Acoustic Characteristics for Scissor Tail-Rotor in Forward Flight

The aerodynamic and aeroacoustic characteristics of a scissor tail-rotor in a forward flight are numerically calculated.A novel computational fluid dynamics(CFD)model based on Navier-Stokes(N-S)equations is presented to simulate the unsteady flowfield and the aerodynamic characteristics of a scissor tail-rotor in the forward flight.Then the Farassat Formulation 1 Aderived from the FW-H equation is coupled into the CFD model in order to compute the aeroacoustic characteristics of the scissor tail-rotor.In addition,two different scissor tail-rotor configurations,i.e.,the L-and U-configuration,are analyzed in details and compared with a conventional one.The influence of scissor angles on the aerodynamic and aeroacoustic characteristics of the scissor tail-rotor is also investigated.The simulation results demonstrate that the flowfield,aerodynamic force and aeroacoustic characteristics of a scissor tail-rotor are significantly different from the conventional one,and the aerodynamic interaction decreases with the increase of scissor angle,which leads to a reduction of amplitude variation of the tail-rotor thrust in the forward flight.The scissor angle has an important effect on the aerodynamics and aeroacoustics of the scissor tail-rotor.

LATTICE-BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GASES

We present an adaptive lattice Boltzmann model to simulate super- sonic flows.The particle velocities are determined by the mean velocity and internal energy.The adaptive nature of particle velocities permits the mean flow to have high Mach number.A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio.The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As preliminary tests,two kinds of simulations have been performed on hexagonal lattices.One is the one-dimensional simulation for sinusoidal velocity distributions. The velocity distributions are compared with the analytical solution and the mea- sured viscosity is compared with the theoretical values.The agreements are basically good.However,the discretion error may cause some non-isotropic effects.The other simulation is the 29 degree shock reflection.

NUMERICAL SIMULATION OF SUPERSONIC REACTING MIXING LAYER

In this paper, the supersonic chemically reacting mixing layer is simulated with the third order ENN scheme, based on the Navier-Stokes equations, containing transport equations of all species. The numerical results show that the thickness of mixing layer increases gradually along the flow direction, and that the Kelvin-Helmholtz, instabilities may not exist in mixing layer flows.

NUMERICAL COMPUTATION OF THE FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE-BY-SIDE

The numerical method is used to calculate the flow around two square cylinders arranged side-by-side and the mean and fluctuating aerodynamic forces, and Strouhal numbers and power spectrum of lift force and drag force are obtained. An improved MAC method proposed by Chen Suqin et al.,which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side-by-side. Results show that the interference characteristic of two square cylinders arranged side-by-side is completely different with the different spacing ratio. When the spacing ratio is smaller than a certain critical value, the gap flow between two cylinders is biased to one side in a stable or unstable manner.

COMPUTATION OF SUPERSONIC TURBULENT FLOWFIELD WITH TRANSVERSE INJECTION

Three dimensional steady flowfield generated by transverse sonic injection Into a supersonic flow was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory (WENO) schemes and Jones-Launder k-epsilon model. Results indicate that in the upstream of the square injection there exist two main recirculation regions and the primary vortex induces the horseshoe vortex region. In the downstream there is a low pressure region which conduces a pair of helical vortex.

2－D SIMULATION OF OPEN CHANNEL TURBULENT FLOW WITH HIGH REYNOLDS NUMBER BY EMPLOYING N－S EQUATIONS AND IEM

Since 1986, we have been studying the topic of simulating open channel turbulent flow, especially the back flow in extended section, by directly employing N-S equations. Now a breakthrough may be obtained. The simulated turbulent flow pattern is realistic and lively, and has a good agreement with physical model test results.

Low Dissipation Simulation for Vortex Flowfield of Rotor in Hover Based upon Discontinuous Galerkin Method

The discontinuous Galerkin(DG) method is established and innovatively conducted on accurately simulating the evolution of blade-tip vortex and the aerodynamic characteristics of helicopter rotor. Firstly,the Reynolds-Averaged Navier-Stokes(RANS)equations in rotating reference frame are employed,and the embedded grid system is developed with the finite volume method(FVM)and the DG method conducted on the blade grid and background grid respectively. Besides,the Harten-Lax-Van Leer contact(HLLC)scheme with high-resolution and low-dissipation is employed for spatial discretization,and the explicit third-order Runge-Kutta scheme is used to accomplish the temporal discretization. Secondly,the aerodynamic characteristics and the evolution of blade-tip vortex for Caradonna-Tung rotor are simulated by the established CFD method,and the numerical results are in good agreement with experimental data,which well validates the accuracy of the DG method and shows the advantages of DG method on capturing the detailed blade-tip vortex compared with the FVM method. Finally,the evolution of tip vortex at different blade tip Mach numbers and collective pitches is discussed.