南海张裂大陆边缘数值模拟研究

The South China Sea (SCS) is one of the largest marginal seas in the western Pacific, which is located at the junction of Eurasian plate, Pacific plate and Indian-Australian plate. It was formed by continent breakup and sea-floor spreading in Cenozoic. The complicated interaction among the three major plates made tectonic movement complex and geological phenomena very rich in this area. The SCS is an ideal place to study the formation and evolution of rifted continental margin and sea-floor spreading since it is old enough to have experienced the major stages of the basin evolution but still young enough to have preserved its original nature. As the demand for energy grows day by day in our country, the deep water region of the northern continental margin in the SCS has become a focus of oil and gas exploration because of its huge hydrocarbon potential. Therefore, to study the rifted continental margin of the SCS not only can improve our understanding of the formation and evolution processes of rifted continental margin, but also can provide theoretical support for hydrocarbon exploration in rifted continental margin. This dissertation mainly includes five topics as follows: (1) Various classic lithosphere stretching models are reviewed, and the continuous non-uniform stretching model is modified to make it suitable for the case where the extension of lithopheric mantle exceeds that of the crust. Then simple/pure shear flexural cantilever model is applied to model the basement geometries of SO49-18 profile in the northern continental margin of the SCS. By fitting the basements obtained by using 2DMove software with modeling results, it is found that the reasonable effective elastic thickness is less than 5km in this region. According to this result, it is assumed that there is weak lower crust in the northern continental margin in the SCS. (2) We research on the methods for stretching factor estimation based on various lithosphere stretching models, and apply the method based on multiple finite rifting model to estimate the stretching factors of several wells and profiles in the northern continental margin of the SCS. (3) We improve one-dimension strain rate inversion method with conjugate gradient method, and apply it to invert the strain rate of several wells in the northern continental margin of the SCS. Two-dimension strain rate forward modeling is carried out, and the modeling results show that effective elastic thickness is a key parameter to control basin’s geometry. (4) We simulate divergent upwelling mantle flow model using finite difference method, and apply this newly developed model to examine the formation mechanism of the northwest and central sub-basin in the SCS. (5) We inverse plate thickness and basal temperature of oceanic lithosphere using sea-floor ages and bathymetries of the North Pacific and the North Atlantic based on varied-parameters plate model, in which the heat conductivity, heat capacity and coefficient of thermal expansion depend on temperature or depth. A new empirical formula is put forward based the inversed parameters, which depicts the relation among sea-floor age, bathymetry and heat flow. Then various similar empirical formulae, including the newly developed one, are applied to examine the sea-floor spread issue in the SCS based on the heat flow and bathymetry data of the abyssal sub-basin.

各向同性与各向异性介质中地震波旅行时正演模拟与反演成像

By seismic tomography, interesting results have been achieved not only in the research of the geosphere with a large scale but also in the exploration of resources and projects with a small scale since 80'. Compared with traditional inversion methods, seismic tomography can offer more and detailed information about subsurface and has been being paid attention by more and more geophysicists. Since inversion based on forward modeling, we have studied and improved the methods to calculate seismic traveltimes and raypaths in isotropic and anisotropic media, and applied the improved forward methods to traveltime tomography. There are three main kinds of methods to calculate seismic traveltime field and its ray path distribution, which are ray-tracing theory, eikonal equation by the finite-difference and minimum traveltime tree algorithm. In ray tracing, five methods are introduced in the paper, including analytic ray tracing, ray shooting, ray bending, grid ray tracing and rectangle grid ray perturbation with three points. Finite-difference solution of eikonal equation is very efficient in calculation of seismic first-break, but is awkward in calculation of reflection traveltimes. We have put forward a idea to calculate traveltimes of reflected waves using a combining way of eikonal equation method and other one in order to improve its capability of dealing with reflection waves. The minimum traveltime tree algorithm has been studied with emphases. Three improved algorithms are put forward on the basis of basic algorithm of the minimum traveltime tree. The first improved algorithm is called raypath tracing backward minimum traveltime algorithm, in which not only wavelets from the current source but also wavelets from upper source points are all calculated. The algorithm can obviously improve the speed of calculating traveltimes and raypaths in layered or blocked homogeneous media and keep good accuracy. The second improved algorithm is raypath key point minimum traveltime algorithm in which traveltimes and raypaths are calculated with a view of key points of raypaths (key points of raypths mean the pivotal points which determine raypaths). The raypath key point method is developed on the basis of the first improved algorithm, and has better applicability. For example, it is very efficient even for inhomogeneous media. Another improved algorithm, double grid minimum traveltime tree algorithm, bases upon raypath key point scheme, in which a model is divided with two kinds of grids so that the unnecessary calculation can be left out. Violent undulation of curved interface often results in the phenomenon that there are no reflection points on some parts of interfaces where there should be. One efficacious scheme that curved interfaces are divided into segments, and these segments are treated respectively is presented to solve the problem. In addition, the approximation to interfaces with discrete grids leads to large errors in calculation of traveltimes and raypaths. Noting the point, we have thought a new method to remove the negative effect of mesh and to improve calculation accuracy by correcting the traveltimes with a little of additional calculation, and obtained better results.

地震波场模拟及叠前深度偏移的李群方法

The processes of seismic wave propagation in phase space and one way wave extrapolation in frequency-space domain, if without dissipation, are essentially transformation under the action of one parameter Lie groups. Consequently, the numerical calculation methods of the propagation ought to be Lie group transformation too, which is known as Lie group method. After a fruitful study on the fast methods in matrix inversion, some of the Lie group methods in seismic numerical modeling and depth migration are presented here. Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method. Under the frame of Hamiltonian, the propagation of seismic wave is a symplectic group transformation with one parameter and consequently, the numerical calculation methods of the propagation ought to be symplectic method. After discrete the wave field in time and phase space, many explicit, implicit and leap-frog symplectic schemes are deduced for numerical modeling. Compared to symplectic schemes, Finite difference (FD) method is an approximate of symplectic method. Consequently, explicit, implicit and leap-frog symplectic schemes and FD method are applied in the same conditions to get a wave field in constant velocity model, a synthetic model and Marmousi model. The result illustrates the potential power of the symplectic methods. As an application, symplectic method is employed to give synthetic seismic record of Qinghai foothills model. Another application is the development of Ray+symplectic reverse-time migration method. To make a reasonable balance between the computational efficiency and accuracy, we combine the multi-valued wave field & Green function algorithm with symplectic reverse time migration and thus develop a new ray+wave equation prestack depth migration method. Marmousi model data and Qinghai foothills model data are processed here. The result shows that our method is a better alternative to ray migration for complex structure imaging. Similarly, the extrapolation of one way wave in frequency-space domain is a Lie group transformation with one parameter Z and consequently, the numerical calculation methods of the extrapolation ought to be Lie group methods. After discrete the wave field in depth and space, the Lie group transformation has the form of matrix exponential and each approximation of it gives a Lie group algorithm. Though Pade symmetrical series approximation of matrix exponential gives a extrapolation method which is traditionally regarded as implicit FD migration, it benefits the theoretic and applying study of seismic imaging for it represent the depth extrapolation and migration method in a entirely different way. While, the technique of coordinates of second kind for the approximation of the matrix exponential begins a new way to develop migration operator. The inversion of matrix plays a vital role in the numerical migration method given by Pade symmetrical series approximation. The matrix has a Toepelitz structure with a helical boundary condition and is easy to inverse with LU decomposition. A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix. The major merit of LU decomposition with spectral factorization (SF Decomposition) is its efficiency in dealing with a large number of matrixes. After the setup of a table of the spectral factorization results of each array of matrix, the SF decomposition can give the lower triangular matrix by reading the table. However, the relationship among arrays is ignored in this method, which brings errors in decomposition method. Especially for numerical calculation in complex model, the errors is fatal. Direct elimination method can give the exact LU decomposition But even it is simplified in our case, the large number of decomposition cost unendurable computer time. A hybrid method is proposed here, which combines spectral factorization with direct elimination. Its decomposition errors is 10 times little than that of spectral factorization, and its decomposition speed is quite faster than that of direct elimination, especially in dealing with a large number of matrix. With the hybrid method, the 3D implicit migration can be expected to apply on real seismic data. Finally, the impulse response of 3D implicit migration operator is presented.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

各向异性与非线性介质中弹性波场传播特征研究

The topic of this study is about the propagation features of elastic waves in the anisotropic and nonlinear media by numerical methods with high accuracy and stability. The main achievements of this paper are as followings: Firstly, basing on the third order elastic energy formula, principle of energy conservation and circumvolved matrix method, we firstly reported the equations of non-linear elastic waves with two dimensions and three components in VTI media. Secondly, several conclusions about some numerical methods have been obtained in this paper. Namely, the minimum suitable sample stepth in space is about 1/8-1/12 of the main wavelength in order to distinctly reduce the numerical dispersion resulted from the numerical mehtod, at the same time, the higher order conventional finite difference (CFD) schemes will give little contribution to avoid the numerical solutions error accumulating with time. To get the similar accuracy with the fourth order center finite difference method, the half truncation length of SFFT should be no less than 7. The FDFCT method can present with the numerical solutions without obvious dispersion when the paprameters of FCT is suitable (we think they should be in the scope from 0.0001 to 0.07). Fortunately, the NADM method not only can reported us with the higher order accuracy solutions (higher than that of the fourth order finite difference method and lower than that of the sixth order finite difference method), but also can distinctly reduce the numerical dispersion. Thirdly, basing on the numerial and theoretical analysis, we reported such nonlinear response accumulating with time as waveform aberration, harmonic generation and resonant peak shift shown by the propagation of one- and two-dimensional non-linear elasticwaves in this paper. And then, we drew the conclusion that these nonlinear responses are controlled by the product between nonlinear strength (SN) and the amplitude of the source. At last, the modified FDFCT numerical method presented by this paper is used to model the two-dimensional non-linear elastic waves propagating in VTI media. Subsequently, the wavelet analysis and polarization are adopted to investigate and understand the numerical results. And then, we found the following principles (attention: the nonlinear strength presented by this paper is weak, the thickness of the -nonlinear media is thin (200m), the initial energy of the source is weak and the anisotropy of the media is weak too): The non-linear response shown by the elastic waves in VTI media is anisotropic too; The instantaneous main frequency sections of seismic records resulted from the media with a non-linear layer have about 1/4 to 1/2 changes of the initial main frequency of source with that resulted from the media without non-linear layer; The responses shown by the elasic waves about the anisotropy and nonlinearity have obvious mutual reformation, namely, the non-linear response will be stronger in some directions because of the anisotropy and the anisotropic strength shown by the elastic waves will be stronger when the media is nonlinear.

基于结构分析地震资料去噪方法研究

With the development of oil and gas exploration, the exploration of the continental oil and gas turns into the exploration of the subtle oil and gas reservoirs from the structural oil and gas reservoirs in China. The reserves of the found subtle oil and gas reservoirs account for more than 60 percent of the in the discovered oil and gas reserves. Exploration of the subtle oil and gas reservoirs is becoming more and more important and can be taken as the main orientation for the increase of the oil and gas reserves. The characteristics of the continental sedimentary facies determine the complexities of the lithological exploration. Most of the continental rift basins in East China have entered exploration stages of medium and high maturity. Although the quality of the seismic data is relatively good, this areas have the characteristics of the thin sand thickness, small faults, small range of the stratum. It requests that the seismic data have high resolution. It is a important task how to improve the signal/noise ratio of the high frequency of seismic data. In West China, there are the complex landforms, the deep embedding the targets of the prospecting, the complex geological constructs, many ruptures, small range of the traps, the low rock properties, many high pressure stratums and difficulties of boring well. Those represent low signal/noise ratio and complex kinds of noise in the seismic records. This needs to develop the method and technique of the noise attenuation in the data acquisition and processing. So that, oil and gas explorations need the high resolution technique of the geophysics in order to solve the implementation of the oil resources strategy for keep oil production and reserves stable in Ease China and developing the crude production and reserves in West China. High signal/noise ratio of seismic data is the basis. It is impossible to realize for the high resolution and high fidelity without the high signal/noise ratio. We play emphasis on many researches based on the structure analysis for improving signal/noise ratio of the complex areas. Several methods are put forward for noise attenuation to truly reflect the geological features. Those can reflect the geological structures, keep the edges of geological construction and improve the identifications of the oil and gas traps. The ideas of emphasize the foundation, give prominence to innovate, and pay attention to application runs through the paper. The dip-scanning method as the center of the scanned point inevitably blurs the edges of geological features, such as fault and fractures. We develop the new dip scanning method in the shap of end with two sides scanning to solve this problem. We bring forward the methods of signal estimation with the coherence, seismic wave characteristc with coherence, the most homogeneous dip-sanning for the noise attenuation using the new dip-scanning method. They can keep the geological characters, suppress the random noise and improve the s/n ratio and resolution. The rutine dip-scanning is in the time-space domain. Anew method of dip-scanning in the frequency-wavenumber domain for the noise attenuation is put forward. It use the quality of distinguishing between different dip events of the reflection in f-k domain. It can reduce the noise and gain the dip information. We describe a methodology for studying and developing filtering methods based on differential equations. It transforms the filtering equations in the frequency domain or the f-k domain into time or time-space domains, and uses a finite-difference algorithm to solve these equations. This method does not require that seismic data be stationary, so their parameters can vary at every temporal and spatial point. That enhances the adaptability of the filter. It is computationally efficient. We put forward a method of matching pursuits for the noise suppression. This method decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. It can extract the effective signal from the noisy signal and reduce the noise. We introduce the beamforming filtering method for the noise elimination. Real seismic data processing shows that it is effective in attenuating multiples and internal multiples. The s/n ratio and resolution are improved. The effective signals have the high fidelity. Through calculating in the theoretic model and applying it to the real seismic data processing, it is proved that the methods in this paper can effectively suppress the random noise, eliminate the cohence noise, and improve the resolution of the seismic data. Their practicability is very better. And the effect is very obvious.

单（多）井抽灌对浅部地温场的影响研究

The technique of energy extraction using groundwater source heat pumps, as a sustainable way of low-grade thermal energy utilization, has widely been used since mid-1990's. Based on the basic theories of groundwater flow and heat transfer and by employing two analytic models, the relationship of the thermal breakthrough time for a production well with the effect factors involved is analyzed and the impact of heat transfer by means of conduction and convection, under different groundwater velocity conditions, on geo-temperature field is discussed.A mathematical model, coupling the equations for groundwater flow with those for heat transfer, was developed. The impact of energy mining using a single well system of supplying and returning water on geo-temperature field under different hydrogeological conditions, well structures, withdraw-and-reinjection rates, and natural groundwater flow velocities was quantitatively simulated using the finite difference simulator HST3D. Theoretical analyses of the simulated results were also made. The simulated results of the single well system indicate that neither the permeability nor the porosity of a homogeneous aquifer has significant effect on the temperature of the production segment provided that the production and injection capability of each well in the aquifers involved can meet the designed value. If there exists a lower permeable interlayer, compared with the main aquifer, between the production and injection segments, the temperature changes of the production segment will decrease. The thicker the interlayer and the lower the interlayer permeability, the longer the thermal breakthrough time of the production segment and the smaller the temperature changes of the production segment. According to the above modeling, it can also be found that with the increase of the aquifer thickness, the distance between the production and injection screens, and/or the regional groundwater flow velocity, and/or the decrease of the production-and-reinjection rate, the temperature changes of the production segment decline. For an aquifer of a constant thickness, continuously increase the screen lengths of production and injection segments may lead to the decrease of the distance between the production and injection screens, and the temperature changes of the production segment will increase, consequently.According to the simulation results of the single well system, the parameters, that can cause significant influence on heat transfer as well as geo-temperature field, were chosen for doublet system simulation. It is indicated that the temperature changes of the pumping well will decrease as the aquifer thickness, the distance between the well pair and/or the screen lengths of the doublet increase. In the case of a low permeable interlayer embedding in the main aquifer, if the screens of the pumping and the injection wells are installed respectively below and above the interlayer, the temperature changes of the pumping well will be smaller than that without the interlay. The lower the permeability of the interlayer, the smaller the temperature changes. The simulation results also indicate that the lower the pumping-and-reinjection rate, the greater the temperature changes of the pumping well. It can also be found that if the producer and the injector are chosen reasonably, the temperature changes of the pumping well will decline as the regional groundwater flow velocity increases. Compared with the case that the groundwater flow direction is perpendicular to the well pair, if the regional flow is directed from the pumping well to the injection well, the temperature changes of the pumping well is relatively smaller.Based on the above simulation study, a case history was conducted using the data from an operating system in Beijing. By means of the conceptual model and the mathematical model, a 3-D simulation model was developed and the hydrogeological parameters and the thermal properties were calibrated. The calibrated model was used to predict the evolution of the geo-temperature field for the next five years. The simulation results indicate that the calibrated model can represent the hydrogeological conditions and the nature of the aquifers. It can also be found that the temperature fronts in high permeable aquifers move very fast and the radiuses of temperature influence are large. Comparatively, the temperature changes in clay layers are smaller and there is an obvious lag of the temperature changes. According to the current energy mining load, the temperature of the pumping wells will increase by 0.7°C at the end of the next five years. The above case study may provide reliable base for the scientific management of the operating system studied.

Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel

Numerical analysis of fully developed laminar slip flow and heat transfer in trapezoidal micro-channels has been studied with uniform wall heat flux boundary conditions. Through coordinate transformation, the governing equations are transformed from physical plane to computational domain, and the resulting equations are solved by a finite-difference scheme. The influences of velocity slip and temperature jump on friction coefficient and Nusselt number are investigated in detail. The calculation also shows that the aspect ratio and base angle have significant effect on flow and heat transfer in trapezoidal micro-channel. (c) 2005 Elsevier Ltd. All rights reserved.

High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

Hybrid Finite Compact-WENO Schemes for Shock Calculation

Hybrid finite compact (FC)-WENO schemes are proposed for shock calculations. The two sub-schemes (finite compact difference scheme and WENO scheme) are hybridized by means of the similar treatment as in ENO schemes. The hybrid schemes have the advantages of FC and WENO schemes. One is that they possess the merit of the finite compact difference scheme, which requires only bi-diagonal matrix inversion and can apply the known high-resolution flux to obtain high-performance numerical flux function; another is that they have the high-resolution property of WENO scheme for shock capturing. The numerical results show that FC-WENO schemes have better resolution properties than both FC-ENO schemes and WENO schemes. In addition, some comparisons of FC-ENO and artificial compression method (ACM) filter scheme of Yee et al. are also given.

Three-dimensional finite element analysis of composites with coated spherical inclusions

A three-dimensional finite element analysis has been used to determine the internal stresses in a three-phase composite. The stresses have been determined for a variety of interphase properties, the thicknesses of the interphase and the volume fractions of particles. Young's modulus has been calculated from a knowledge of these stresses and the applied deformation. The calculations show that stress distributions in the matrix and the mechanical properties are sensitive to the interphase property in the three-phase composites. The interfacial stresses in the three-dimensional analysis are in agreement with results obtained by an axisymmetric analysis. The predicted bulk modulus in three-dimensional analysis agrees well with the theoretical solution obtained by Qui and Weng, but it presents a great divergence from that in axisymmetric analyses. An investigation indicates that this divergence may be caused by the difference in the unit cell structure between two models. A comparison of the numerically predicted bulk and shear modulus for two-phase composites with the theoretical results indicates that the three-dimensional analysis gives quite satisfactory results.

High Order Multi-Moment Constrained Finite Volume Method. Part I: Basic Formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

Stress analysis of silica-based arrayed waveguide grating by a finite element method

The stress distribution in silica optical waveguides on silicon is calculated by using finite element method (FEM). The waveguides are mainly subjected to compressive stress along the x direction and the z direction, and it is accumulated near the interfaces between the core and cladding layers. The shift of central wavelength of silica arrayed waveguide grating (AWG) on silicon-substrate with the designed wavelength and the polarization dependence are caused by the stress in the silica waveguides.

U-transformation-finite element method in 3-dimensional analysis of orthotropic laminates

For an orthotropic laminate, an equivalent system with doubly cyclic periodicity is introduced. Then a 3-dimensional finite element model for the equivalent system is transformed into the unitary space, where the large finite element matrix equation is decoupled into some small matrix equations. Such a decoupling very efficiently reduces the computational effort. For an orthotropic laminate with four clamped edges, no exact elasticity solution is available, and the deflection values predicted by different methods have a considerable difference each other for a small length-to-thickness ratio. The present predictions are the largest because the present method is a full 3-dimensional finite element analysis without superfluous constraints. Illustrative numerical examples are presented to observe the distributions of stresses through the thickness of the laminates. (C) 2010 Elsevier Ltd. All rights reserved.