ω循环型预条件矩阵及其应用

In this paper, we apply the preconditioned conjugate gradient method to the solution of positive-definite Toeplitz systems, especially we introduce a new kind of co-circulant preconditioners Pn[ca] by the use of embedding method. We have also discussed the properties of these new preconditioners and proved that many of former preconditioners can be considered as some special cases of Pn[co\. Because of the introduction of co-circulant preconditioners pn[a>], we can greatly overcome the singularity caused by circulant preconditioners. We have discussed the oo-circulant series and functions. We compare the ordinary circularity with the co-circularity, showing that the latter one can be considered as the extended form of the former one; correspondingly, many methods and theorems of the ordinary circularity can be extended. Furthermore, we present the co-circulant decompositional method. By the use of this method, we can divide any co-circulant signal into a summation of many sub-signals; especially among those sub-signals, there are many subseries of which their period is just equal to 1, which are actually the frequency elements of the original co-circulant signal. In this way, we can establish the relationship between the signal and its frequency elements, that is, the frequency elements hi the frequency domain are actually signals with the period of 1 in the spatial domain. We have also proved that the co-circulant has already existed in the traditional Fourier theory. By the use of different criteria for constructing preconditioners, we can get many different preconditioned systems. From the preconditioned systems PN[conditioned systems instead of the given Toeplitz systems to get some approximate solutions. Theoretical analysis and actually numerical experiments have already proved the effectiveness of this approximation. By combining the co-circulant with the boundary condition, we can overcome end effects efficiently. We have also presented the co-circulant boundary condition and compared it with the helix boundary condition. Furthermore, we can also get another new boundary condition: the mixed boundary condition. Numerical experiments have proved that the co-circulant boundary condition is better than the mixed one while the helix boundary condition is the worst among them.

地震偏移宽角吸收边界条件和Toeplitz矩阵反演中的边界效应研究

The content of this paper is based on the research work while the author took part in the key project of NSFC and the key project of Knowledge Innovation of CAS. The whole paper is expanded by introduction of the inevitable boundary problem during seismic migration and inversion. Boundary problem is a popular issue in seismic data processing. At the presence of artificial boundary, reflected wave which does not exist in reality comes to presence when the incident seismic wave arrives at the artificial boundary. That will interfere the propagation of seismic wave and cause alias information on the processed profile. Furthermore, the quality of the whole seismic profile will decrease and the subsequent work will fail.This paper has also made a review on the development of seismic migration, expatiated temporary seismic migration status and predicted the possible break through. Aiming at the absorbing boundary problem in migration, we have deduced the wide angle absorbing boundary condition and made a compare with the boundary effect of Toepiitz matrix fast approximate computation.During the process of fast approximate inversion computation of Toepiitz system, we have introduced the pre-conditioned conjugate gradient method employing co circulant extension to construct pre-conditioned matrix. Especially, employment of combined preconditioner will reduce the boundary effect during computation.Comparing the boundary problem in seismic migration with that in Toepiitz matrix inversion we find that the change of boundary condition will lead to the change of coefficient matrix eigenvalues and the change of coefficient matrix eigenvalues will cause boundary effect. In this paper, the author has made an qualitative analysis of the relationship between the coefficient matrix eigenvalues and the boundary effect. Quantitative analysis is worthy of further research.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Application of enthalpy method for moving boundary problem in laser surface melting

A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization. The enthalpy method was applied to solve this two-phase axisymmetrical melting problem Computational results of temperature fields were obtained, which provide useful information to practical laser treatment processing. The validity of enthalpy method in solving such problems is presented.

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma=6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at free-stream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibilty effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely to occur.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Experimental Study on Vortex-Induced Vibrations of a Pipeline Near a Plane Boundary in Steady Flow

对单向水流作用下近壁管道横向涡激振动进行了实验模拟,重点探讨了管道与壁面间隙比(e/D)对管道涡激振动幅值和涡激振动频率响应特性的影响规律.实验结果表明,管道与壁面间隙宽度对管道涡激振动特性有较明显影响.在较大间隙比(e/D＞0.66)下,管道振幅随着Vr数的增大先快速增长到最大值,然后平缓下降;在振动初期(即Vr数较小时),管道振动频率变化基本符合Strouhal规律;在振动中后期(即Vr数较大时),管道振动频率变化不符合Strouhal规律,而在管道固有频率附近缓慢增长.在较小间隙比(e/D＜0.30)下,管道振幅随Vr数的增大先平缓上升到最大值,随后较快速下降;在振动初期,管道振动频率变化不遵循Strouhal规律;在整个振动范围内,与较大间隙比情况相比,随着Vr数增加,管道振动频率增长幅度明显较大.

Acoustic Emission Experiments of Rock Failure under Load Simulating the Hypocenter Condition

A series of acoustic emission (AE) experiments of rock failure have been conducted under cyclic load in tri-axial stress tests. To simulate the hypocenter condition the specimens are loaded by the combined action of a constant stress, intended to simulate

Some characteristics of low-speed streaks under sheared air-water interfaces

The characteristics of low-speed fluid streaks occurring under sheared air-water interfaces were examined by means of hydrogen bubble visualization technique. A critical shear condition under which the streaky structure first appears was determined to be u(tau) approximate to 0.19 cm/s. The mean spanwise streak spacing increases with distance from the water surface owing to merging and bursting processes, and a linear relationship describing variation of non-dimensional spacing <(+)over bar> versus y(+) was found essentially independent of shear stress on the interface. Values of <(+)over bar>, however, are remarkably smaller than their counterparts in the near-wall region of turbulent boundary layers. Though low-speed streaks occur randomly in time and space, the streak spacing exhibits a lognormal probability distribution behavior. A tentative explanation concerning the formation of streaky structure is suggested, and the fact that <(+)over bar> takes rather smaller values than that in wall turbulence is briefly discussed.

Influence of grain boundary on melting

The temperature behaviour of an Al bicrystal with surfaces consisting of (110) and (111) crystals is simulated using molecular dynamics. The result shows that the (110) crystal losses its crystalline order at 820K, whereas the disorder does not propagate through the (111) crystal at this temperature. Instead, some disordered atoms are recrystallized into the (111) crystal and the initial grain boundary changes into a stable order-disorder interface. Thus, it was discovered that at a temperature near its melting point, the (111) crystal grew and obstructed the propagation of disorder. Such an obstruction is helpful for understanding melting.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Applicability Range of Stoneys Formula and Modified Formulas for a Film/Substrate Bilayer

In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

Flow Characteristics and Its Friction Coefficient of Laminar Near-Wall Boundary Layer in Dusty Atmosphere

采用双向耦合的双流体模型,研究了大气悬浮沙尘的存在对大气边界层中层流底层流动特性及摩阻系数的影响,计算并讨论了不同沙尘含量下含尘大气相对于无尘大气摩阻系数的变化。结果表明：摩阻系数的变化取决于悬浮沙尘的初始运动状态和质量载荷率。

Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma=0.7

Direct numerical simulation (DNS) of a spatially evolving flat-plate boundary layer transition process at free stream Mach number 0.7 is performed. Tollmien-Schlichting (T-S) waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the transition process plays an important role in the laminar breakdown process.

Experimental Study on Vortex-Induced Vibrations of Submarine Pipeline Near Seabed Boundary in Ocean Currents

Unlike most previous studies on vortex- induced vibrations of a cylinder far from a boundary, this paper focuses On the influences of close proximity of a submarine pipeline to a rigid seabed boundary upon the dynamic responses of the pipeline in ocean currents. The effects of gap-to-diameter ratio and those of the stability parameter on the amplitude and frequency responses of a pipeline are investigated experimentally with a novel hydro-elastic facility. A comparison is made between the present experimental results Of the amplitude and frequency responses for the pipes with seabed boundary effects and those for wall-free cylinders given by Govardhan and Williamson (2000) and Anand ( 1985). The comparison shows that the close proximity of a pipeline to seabed has much influence on the vortex- induced vibrations of the pipeline. Both the width of the lock-in ranges in terms of V, and the dimensionless amplitude ratio A(max)/D become larger with the decrease of the gap-to-diameter ratio e/D. Moreover, the vibration of the pipeline becomes easier to occur and its amplitude response becomes more intensive with the decrease of the stability parameter, while the pipeline frequency responses are affected slightly by the stability parameter.