Numerical simulation of intermediate phase growth in Ti/Al alternate foils

To investigate the diffusion reaction between Ti/Al solid diffusion couple, Ti/Al alternate foils formed by hot pressing were annealed at 525, 550, 575 and 600 °C for time ranging from 1 to 40 h. The experimental results show that TiAl3 was the only observed phase at Ti/Al interface. The interface thermodynamics favored the preferential formation of TiAl3 in Ti/Al couple. The growth of TiAl3 layer occurred mainly towards Al foil side and exhibited a parabolic law. Using the interdiffusion coefficients calculated based on the contribution of grain boundary diffusion, the growth of TiAl3 was simulated numerically with the finite difference method, and the simulated results were in good agreement with the experimental ones.

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Seismic wavefield modeling in media with fluid-filled fractures and surface topography

We present a finite difference （FD） method for the simulation of seismic wave fields in fractured medium with an irregular （non-fiat） free surface which is beneficial for interpreting exploration data acquired in mountainous regions. Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded. To implement surface topography, we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one. We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations （in a curvilinear coordinate system） in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry （HTI）. Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration. The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography. The scattered waves provoked by the topography are re-scattered by the fractures, especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.

Application of the double absorbing boundary condition in seismic modeling

We apply the newly proposed double absorbing boundary condition（DABC）（Hagstrom et al., 2014） to solve the boundary reflection problem in seismic finite-difference（FD） modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer（PML）, the complexity decreases, and the stability and fl exibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton–Engquist boundary condition and nearly the same as that in the PML.

Modeling and Simulation Study on Reverse Swirl of Secondary Air in Large Tangentially Fired Boiler

Based on the porosity method and the improved non uniform QUICK scheme, this paper describes a three dimensional computer simulation to predict the flow characteristics in a tangentially fired boiler. The model is applied to a 600?MW boiler modeling under different operating conditions of reverse swirl of secondary air. The numerical results achieve reasonable agreement with experimental data. The calculated results of flow field, the pressure distribution, the relative diameter of tangential circle, angular momentum flux in furnace and the velocity distribution index in horizontal gas pass are analyzed in detail. And then the effects of the reverse swirl of secondary air on flue gas imbalance are discussed. Finally a reasonable operating condition of the reverse swirl of secondary air is presented.

Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media

To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.

True-amplitude wavefield separation using staggered-grid interpolation in the wavenumber domain

Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave＇s dynamic properties.

Rough interfaces and ultrasonic imaging logging behind casing

Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the early- arrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.

Numerical simulation and experimental study of the hydrodynamics of a modeled reef located within a current

The hydrodynamic forces and flow field of artificial reef models in steady flow were numerically investigated using the RNG κ-ε turbulent model. The numerical simulation results are consistent with results observed by experimental means. A comparative study indicates that the corresponding errors of forces between calculated values and values observed in the experiment vary in the range of2.3%-11.2% and that the corresponding errors of velocities vary in the range of 1.3%-15.8%. The flow field numerical results show that upstream and vortices exist when the current passes over and through the surface of the reef model. This study suggests that the numerical simulation method can be applied to predict the forces and flow field associated with artificial reefs.

A Numerical Study on the Density Driven Circulation in the Yellow Sea Cold Water Mass

The circulation of Yellow Sea Cold Water Mass （YSCWM） in the Southern Yellow Sea is investigated using a diagnostic 2D MITgcm model. The resolution of the computational grid is 900 m in the horizontal and 2 m in the vertical where an initial tem- perature distribution corresponding to a typical measured Yellow Sea Cold Water Mass was applied. The existence of YSCWM that causes fluid density difference, is shown to produce counter-rotating cyclonic horizontal eddies in the surface layer： the inner one is anti-cyclonic （clockwise） and relatively weaker （8-10cms-1） while the outer one is cyclonic （anti-clockwise） and much stronger （15-20cms-~）. This result is consistent with the surface pattern observed by Pang et al. （2004）, who has shown that a mesoscale anti-cyclonic eddy （clockwise） exists in the upper layer of central southern Yellow Sea, and a basin-scale cyclonic （anticlockwise） gyre lies outside of the anti-cyclonic eddy, based on the trajectories and drifting velocities of 23 drifters. Below the thermocline, there is an anti-cyclonic （clockwise） circulation. This complex current eddy system is considered to be capable of trapping suspended sediments and depositing them near the front between YSCWM and the coastal waters off the Subei coast, providing an explanation on the sediment depth and size distribution of mud patches in the Southern Yellow Sea. Moreover, sensitive test scenarios indicate that variations of bottom friction do not substantially change the main features of the circulation structure, but will reduce the bottom current velocity, increase the surface current velocity and weaken the upwelling around the frontal area.

Unknown parameter’s variance-covariance propagation and calculation in generalized nonlinear least squares problem

The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.

Study on fast calibration of a ULA's gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.

Arrangement Strategy of Ground Heat Exchanger with Groundwater

The orientation strategy of side pipe and the heat transfer performance of six ground heat exchangers(GHEs) were optimized by numerical simulation,with soil being treated as a porous medium.An experiment on the heat transfer of four GHEs was carried out in 2010.Results indicate that the velocity field is disturbed by GHEs.The optimal orientation strategy of side pipe is that the upward pipe is located upstream and the downward pipe downstream.The space between GHEs should be appropriately adjusted,depending on the direction and flow velocity.Groups of GHEs should be installed perpendicular to the mainstream in a single row,but if the acreage does not meet the requirements,GHEs should be installed in staggered multiple rows.Fewer GHEs parallel to the mainstream strengthen the heat transfer.Moreover,numerical results agree well with the test data,with the maximum relative error being less than 7.7%.

Improved Cotes Formula and Error Analysis

The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.

The Effect of Error Growth and Propagation on the Predictability of Quantitative Precipitation in a Cloud-Resolving Model

Limitations in the predictability of quantitative precipitation forecasting (QPF) that arise from initial errors of small amplitude and scale are investigated by means of real-case high-resolution (cloud-resolving) numerical weather prediction (NWP) integrations. The case considered is the hail and wind disaster that occurred in Sichuan on 8 April 2005. A total of three distinct perturbation methods are used. The results suggest that a tiny initial error in the temperature field can amplify and influence the weather in a large domain, changing the 12-h forecasted rainfall by as much as one-third of the original magnitude. Furthermore, the comparison of the perturbation methods indicates that all of the methods pinpoint the same region (the heavy rainfall areas in the control experiment) as suffering from limitations in predictability. This result reveals the important role of nonlinearity in severe convective events.

氧化还原反应方程式配平的新方法探讨

本文讨论了氧化还原反应配平的几个问题 。

Temporal and spatial differences and imbalance of China's urbanization development during 1950-2006

A better understanding of the regional disparity and imbalance characteristics of China's urbanization development is the important premise for constituting correct policy and strategy and promoting the healthy and sustainable development of urbanization in the 21st century. The regional differences of China's urbanization level have close relations with natural conditions of landform and climate etc.,the urbanization level reduces with the eleva-tion of topography and decrease of precipitation. According to the statistical data set of ur-banization in 1950-2006,the temporal change course of inter-provincial disparity of Chinese urbanization level since the founding of New China in 1949 was studied,and then the inter-regional and intra-regional disparities of urbanization development were analyzed by the Theil index and its nested decomposition method,to grasp the dynamic change of spatial disparities of China's urbanization level on the whole. Using the imbalance index model,the imbalance status of urban population distribution relative to total population,grain output,total agricultural output value,gross output value of industry,tertiary industrial output value as well as gross regional product was discussed,to hold the balance characteristics of urbanization development relative to the regional development conditions from the macroscopic scales.

GIS-based Numerical Modelling of Debris Flow Motion across Three-dimensional Terrain

The objective of this study is to incorporate a numerical model with GIS to simulate the movement, erosion and deposition of debris flow across the three dimensional complex terrain. In light of the importance of erosion and deposition processes during debris flow movement, no entrainment assumption is unreasonable. The numerical model considering these processes is used for simulating debris flow. Raster grid networks of a digital elevation model in GIS provide a uniform grid system to describe complex topography. As the raster grid can be used as the finite difference mesh, the numerical model is solved numerically using the Leap-frog finite difference method. Finally, the simulation results can be displayed by GIS easily and used to debris flow evaluation. To illustrate this approach, the proposed methodology is applied to the Yohutagawa debris flow that occurred on 2oth October 2010, in Amami- Oshima area, Japan. The simulation results that reproduced the movement, erosion and deposition are in good agreement with the field investigation. The effectiveness of the dam in this real-ease is also verified by this approach. Comparison with the results were simulated by other models, shows that the present coupled model is more rational and effective.