非轴对称套管井中声场的并行有限差分模拟

本文提出了一种用于模拟非轴对称套管井中扇区水泥胶结测井100 kHz 3维瞬态声场的并行算法.采用时域有限差分方法,以及非裂化的完全匹配层吸收边界条件,基于信息传递接口(MPI)并行环境,在计算机集群上实现并行计算.对内边界上的差分方程进行参数平均处理,提高了计算稳定性.通过在轴对称情况下将有限差分模拟结果与实轴积分法计算结果对比,验证了方法的正确性.使用并行有限差分算法,模拟了水泥环有不同大小和在不同方位缺失时非轴对称套管井中8扇区的扇区水泥胶结测井仪的测井波形,并分析了套管波幅度随水泥缺失-换能器夹角的变化.根据模拟和分析结果,得到了非轴对称套管井中新的声场传播规律,并建议了一种用于反演水泥缺失大小和方位的方法.     

Bénard convection in a rotating fluid

Abstract

The steady nonlinear regime of Bénard convection in a uniformly rotating fluid is treated using a two-dimensional primitive-equation numerical model with rigid boundaries. Quantitative comparisons with laboratory heat transport data for water are made in the parameter ranges for which the experimental flows are approximately two-dimensional and steady. When an experimentally realistic spatial periodicity is imposed upon the numerical solution, the model simulates the experimental determinations of Nusselt number fairly accurately. In particular, it predicts the observed non-monotonic dependence on Taylor number. When spatial periodicities corresponding to those of the linear stability problem are specified, however, the accuracy of the simulation is less and the Taylor number dependence is monotonic.     

基于有限体积法的二维大地电磁各向异性数值模拟

为了计算带任意地形的各向异性介质中二维大地电磁响应,本文在非结构化网格的基础上,采用有限体积法,开发了二维大地电磁各向异性正演模拟的新算法.首先,从Maxwell方程出发,推导二维各向异性介质中大地电磁场的边值问题;然后,采用三角网格自动生成技术对求解区域进行非结构化网格剖分,进而构建节点中心控制体积单元,利用有限体积方法,得到求解边值问题的大型稀疏线性方程组;最后,利用Pardiso精确地计算了大地电磁响应值.三个各向异性模型的计算结果表明,本文开发的有限体积算法,不仅能够高精度求解带任意地形的大地电磁电导率各向异性问题,而且对于同一模型,该方法的计算消耗和精度都与有限单元法相当.因此,有限体积法是处理电磁法各向异性问题的一种有效方法.     

An accurate time integration method for simplified overland flow models

An accurate time integration method for the diffusion-wave and kinematic-wave approximated models for the overland flow is proposed. The discretization of the first- and second-order spatial derivatives in the basic equation is obtained by using the second-order Lax–Wendroff and the three-point centred finite difference schemes, respectively. For the solution in time, the system of ordinary differential equations, obtained by the linearization of the celerity and of the hydraulic diffusivity by Taylor series expansions, is integrated analytically. The stability and the numerical dissipation and dispersion are investigated by the Fourier analysis. A proper Courant number, and the corresponding time step for the numerical simulations can be established. In addition, the proposed diffusion-wave and kinematic-wave models are straightforwardly extended to the two-dimensional flow. Test cases for both one- and two-dimensional problems, compare the solutions of the diffusion-wave and kinematic-wave models with analytical solutions, with experimental results and with numerical solutions obtained by the Saint–Venant equations. These simulations show that the proposed numerical–analytical models accurately predict the overland flow for several situations, in particular for unsteady rainfall rate and for spatial variations of the surface roughness.     

Effects of obstacles on Rayleigh wave dispersion obtained from the SASW test

This study investigates the effects of underground obstacles on a Rayleigh Wave dispersion curve obtained by spectral analysis of surface waves (SASW) testing. The SASW test is simulated by a transient response analysis of an axisymmetric finite element method. Both rigid obstacles and cavities with a variety of shapes and embedment depths are considered. Results show strong fluctuations in the dispersion curve obtained from the signals recorded by receivers in the vicinity of an obstacle. The fluctuations are primarily a result of wave reflections from the near and far faces of an obstacle. Results obtained from a finite element model are explained through a comparison with a simple theoretical model and experimental results are published. Fluctuations shown in the dispersion curve can result in misinterpretation of the shear wave velocity profile. Wherever obstacles are known to exist, an SASW test should be performed in a way that minimizes these effects. The parameters that will reduce or aggravate these effects were studied and are discussed.     

基于滞回曲线以及结构动力方程的混凝土结构抗震稳定性分析

为准确全面地量化分析研究土木工程建筑中混凝土结构抗震稳定性,提出基于滞回曲线以及结构动力方程的混凝土结构抗震稳定性分析方法。首先采用滞回曲线描述混凝土结构在地震作用下的损伤情况,对滞回曲线模型拐点进行有效操作,确保动力方程对混凝土结构抗震稳定性进行有效分析。其次采用基于混凝土结构动力方程的抗震稳定性分析方法,对地震地面运动模型以及结构分析模型来分析混凝土结构的随机地震反应情况,得到混凝土结构随机反应的汇总量,在此基础上通过双参数的结构破坏模型,基于结构稳定性原理,获取运算混凝土结构抗震稳定性的概率表达式,再基于该表达式分析混凝土结构的抗震稳定性情况。实验结果说明,所提方法能够对土木工程建筑中不同类型混凝土构件抗震稳定性进行有效分析,分析结果准确且全面。     

Accuracy of finite difference representations for the transient response analysis of shells

The frequency versus wave number characteristics of four O(ΔS₂) finite difference formulations for one-dimensional linear shell (ring and axisymmetric) equations are investigated and compared with the exact continuum characteristics. It is found that three of the formulations give virtually identical results. These are half-spacing techniques with equilibrium in terms of displacements or resultants and whole-spacing with equilibrium in terms of displacements. The formulation based on whole-spacing with equilibrium in terms of resultants produces some dramatically different results. These discrepancies partially explain some late time instability problems and critical time step behaviour that have been reported by other investigators.     

Nonlinear interaction of axisymmetric circulation and nonaxisymmetric disturbances in hurricanes

The nonlinear interaction of axisymmetric circulation and nonaxisymmetric disturbances in hurricanes is numerically studied with a quasigeostrophic barotropic model of a higher resolution. It is pointed out that the interaction may be divided into two categories. In the first category, nonaxisymmetric disturbances decay, the coordinate locus of maximum.relative vortic-ity (?)max is seemingly unordered, and the central pressure of hurricane rises; while in the second one, nonaxisymmetric disturbances develop, the locus of (?)max shows an ordered limit cycle pattern, and the central pressure falls remarkably. A succinct criterion is given to judge which category the interaction belongs to, i.e. the vortex beta Rossby number at the initial time Rβ< 1 belongs to the decaying category and Rβ> 1 to the developing one. Finally, practical applications of theoretical results of the rotational adaptation process presented by Zeng and numerical results in this paper to the hurricane intensity prediction in China     

Generation of magnetic fields by convection in a rotating sphere,I

The magnetohydrodynamic dynamo problem is solved for an electrically conducting spherical fluid shell with spherically symmetric distributions of gravity and heat sources. The dynamics of motions generated by thermal buoyancy are dominated by the effects of rotation of the fluid shell. Dynamos are found for low and intermediate values of the Taylor number, T ? 10⁵, if the scale of the nonaxisymmetric component of the velocity field is sufficiently small. The generation of magnetic fields of quadrupolar symmetry is preferred at Rayleigh numbers close to the critical value R_c for onset of convection. As the Rayleigh number increases, the generation of dipolar magnetic fields becomes preferred.     

Three-dimensional analysis of rows of piles as passive barriers for ground vibration isolation

This paper presents a theoretical study on the ground vibration isolation efficiency by multi-rows of piles as passive barrier in a three-dimensional context. Integral equations governing Rayleigh wave scattering are derived according to the Green's solution of Lamb problem. The integral equations are solved accurately and efficiently with an iteration technique. They are used to predict the complicated Rayleigh wave field that is generated by a number of irregular scatterers embedded in an elastic half-space solid. The method is verified with a numerical solution available in the literature for a simplified Rayleigh wave scattering problem. Passive isolation effectiveness of ground vibration with two or three rows of small piles is further studied in detail. Effects of relevant parameters on the effectiveness of vibration isolation are analyzed and presented.     

Hot springs mediate spatial exchange of heat and mass in the enclosed sediment domain: A stability perspective

In many natural environments, such as in underwater hot springs and hydrothermal vents, thermal gradients are accompanied with changes in the concentration of chemical compounds transported to the seawater, causing the so-called double-diffusive, mixed convection. To study the physical scenarios in such systems, a vertical channel filled with a porous medium saturated with saline water is considered. The motion in the sediment-filled channel is induced by two buoyancy forces and an external pressure gradient, similar to the situation in a vent with an upward flow direction. The fluid flow has been modeled by an extended Darcy model, and the flow instability mechanisms have been studied numerically. The linear stability analysis is performed considering a wide range of Darcy number (Da = 10⁻⁵ -10⁻⁸). The instability boundary curve showed three distinct dynamic regimes: (i) Rayleigh-Taylor (R-T), (ii) log-log non-linear variation, and (iii) log-log linear variation. The domain of different regimes were sensitive to external pressure gradient as well as permeability. Similar to cross-diffusive natural convection in pure viscous fluids, a linear relationship between logarithmic absolute values of critical thermal Rayleigh number (∣Ra_T∣) and solute Rayleigh number (Ra_C) is found in the third regime. Based on the permeability, for any solute Rayleigh number (Ra_C), there existed a minimum value of Reynolds number (Re), below which R-T type of instability appeared. Above this minimum value, the instability was due to two buoyancy forces, known as buoyant instability. Simulations of secondary flow via energy analysis demonstrated the development of complex dynamics at the critical state in all three regimes characterized by transition of multi to uni-cellular structures and vice verse.     

Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

Convection in rotating annular channels heated from below. Part 3: Experimental boundary conditions

Results are presented from both linear stability analysis and numerical simulations of three-dimensional nonlinear convection in a Boussinesq fluid in an annular channel, under experimental boundary conditions, rotating about a vertical axis uniformly heated from below. The focus is placed on the Prandtl number Pr = 7.0, representing liquid water at room temperature. The linear analysis shows that, when the aspect ratio is sufficiently small, there exists only one stationary mode that occupies the whole fluid container. When the aspect ratio is moderate or large, however, there exist three different linear solutions: (i) the outer sidewall-localized traveling wave propagating against the sense of rotation; (ii) the inner sidewall-localized traveling wave propagating in the same sense as rotation; and (iii) both the counter-traveling waves occurring simultaneously. Guided by the result of the linear stability analysis, fully three-dimensional simulations are then performed for a channel with a moderate aspect ratio. It is found that neither the prograde nor the retrograde mode is physically realizable near threshold and beyond. The dynamics of nonlinear convection in a rotating channel are chiefly characterized by the interaction between the sidewall-localized waves and the interior convection cells/rolls, producing an interesting and unusual nonlinear phenomenon. In order to compare with the classical Rayleigh–Bénard problem without vertical sidewalls, we also study linear and nonlinear convection at exactly the same parameters but in an infinitely extended layer with periodic horizontal conditions. This reveals that both the linear instability and nonlinear convection in a rotating channel are characteristically different from those in a rotating layer with periodic horizontal conditions.     

Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth-to-width ratio of the alluvial valley on surface ground motion are finally illustrated.     

Stability condition of finite difference solution for viscoelastic wave equations

The stability problem is a very important aspect in seismic wave numerical modeling. Based on the theory of seismic waves and constitutive equations of viscoelastic models, the stability problems of finite difference scheme for KelvinVoigt and Maxwell models with rectangular grids are analyzed. Expressions of stability conditions with arbitrary spatial accuracies for two viscoelastic models are derived. With approximation of quality factor Q≥?5, simplified expressions are developed and some numerical models are given to verify the validity of the corresponding theoretical results. Then this paper summarizes the influences of seismic wave velocity, frequency, size of grid and difference coefficients, as well as quality factor on stability condition. Finally the prerequisite conditions of the simplified stability equations are given with error analysis.     

Convective instability when the temperature gradient and rotation vector are oblique to gravity. II. Real fluids with effects of diffusion

Abstract

The linear stability analysis of Hathaway, Gilman and Toomre (1979) (hereafter referred to as Paper I) is repeated for Boussinesq fluids with viscous and thermal diffusion. As in Paper I the fluid is confined between plane parallel boundaries and the rotation vector is oblique to gravity. This tilted rotation vector introduces a preference for roll-like disturbances whose axes are oriented north-south; the preference is particularly strong in the equatorial region. The presence of a latitudinal temperature gradient produces a thermal wind shear which favors axisymmetric convective rolls if the gradient exceeds some critical value. For vanishingly small diffusivities the value of this transition temperature gradient approaches the inviscid value found in Paper I. For larger diffusivities larger gradients are required particularly in the high latitudes. These results are largely independent of the Prandtl number. Diffusion tends to stabilize the large wavenumber rolls with the result that a unique wavenumber can be found at which the growth rate is maximized. These preferred rolls have widths comparable to the depth of the layer and tend to be broader near the equator. The axisymmetric rolls are similar in many respects to the cloud bands on Jupiter provided they extend to a depth of about 15,000 km.     

A positivity preserving method for simulation of steam injection for NAPL site remediation

Numerical modelling of steam injection methods for cleanup of non-aqueous phase liquid (NAPL) contamination of groundwater requires consideration of multiphase, multicomponent convective and dispersive transport. Standard techniques do not ensure that the solution of the discrete equations has positive mole fractions, for finite mesh sizes. Negative mole fractions may cause the simulation to abort due to failure of the Newton iteration. A method for alleviating this problem is described. This method ensures that the mole fractions are positive, and results in an error that is the same size as the usual finite element discretization error. Example computations are presented for cartesian and axisymmetric two-dimensional geometries.     

Meridional circulation in the sun and stars

Mean-field hydrodynamics advanced to clear explanations for the origin and properties of the global meridional flow in stellar convection zones. Qualitative arguments and analysis of basic equations both show that the meridional circulation is driven by non-conservative centrifugal and buoyancy forces and results from a slight disbalance between these two drivers. The deviations from the thermal wind balance are relatively large near the boundaries of convection zones. Accordingly, the meridional flow attains its largest velocities in the boundary layers and decreases inside the convection zone. This picture, however, is neither supported nor dismissed by the conflicting results of recent helioseismic soundings or 3D numerical experiments. The relevant physics of the differential temperature and its possible relation to the solar oblateness are briefly discussed.     

一阶弹性波方程数值模拟中的混合吸收边界条件

Liu和Sen（2010和2012）在地震波场数值模拟中提出一种混合吸收边界条件. 该方法具有计算量小、容易实现及吸收效果好等优点. 但现有的混合吸收边界条件是针对二阶位移-应力方程设计的,存在稳定性问题. 本文首先推导了两种速度-应力单程波方程：二阶Higdon单程波方程和一阶Higdon单程波方程. 进而提出基于一阶弹性波方程的混合吸收边界条件方法. 在内部区域和边界之间引入一个过渡区域,通过单程波与双程波方程平滑过渡来消除人工边界反射. 为了改善混合吸收边界条件的吸收效果和稳定性,我们采用了能同时吸收纵、横波反射的一阶单程波方程和与变量位置有关的加权系数. 为了验证混合吸收边界条件的有效性,将其与常规分裂完全匹配层（PML）方法进行了比较. 数值模拟结果表明,与PML边界条件相比,混合吸收边界条件在耗用更小计算时间和存储量的前提下,可以获得更好的吸收效果. 另外,本文提出的两种混合吸收边界条件中,混合一阶Higdon吸收边界条件具有更好的稳定性.     

Anti-plane （SH） waves diffraction by cavity： analytical an underground semi-circular solution

Diffraction of a two-dimensional (2D) semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called “improved cosine halfrange expansion” algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.