城市交通系统的建模与仿真

本文首先通过分析建模中常用的离散事件仿真算法,根据大系统理论的递阶思想,提出了一个适合大系统仿真的新算法——递阶仿真算法.然后,建立了一个较通用的交通系统仿真模型(UTSS 模型).经过模型有效性验证,证明该模型是可行的,具有实用价值.

裂隙/孔隙型弹性介质中地震波场模拟与叠前逆时偏移

With the development of oil/gas seismic exploration, seismic survey for fracture/porosity type reservoir is becoming more and more important. As for China, since it has over 60% store of low porosity and low permeability oil/gas reservoir, it’s more urgent to validly describe fracture/porosity type oil/gas trap and proposing the related, developed seismic technique. To achieve mapping fracture/porosity region and its development status, it demands profound understanding of seismic wave propagation discipline in complex fractured/pored media. Meanwhile, it has profound scientific significance and applied worth to study forward modeling of fracture/porosity type media and pre-stacked reverse time migration. Especially, pre-stacked reverse-time migration is the lead edge technique in the field of seismology and seismic exploration. In this paper, the author has summarized the meaning, history and the present state of numerical simulation of seismic propagation in fractured/pored media and seismic exploration of fractured/pored reservoirs. Extensive Dilatancy Anisotropy (EDA) model is selected as media object in this work. As to forward modeling, due to local limitation of solving spatial partial derivative when using finite-difference and finite-element method, the author turns to pseudo-spectral method (PSM), which is based on the global characteristic of Fourier transform to simulate three-component elastic wave-field. Artifact boundary effect reduction and simulation algorithm stability are also discussed in the work. The author has completed successfully forward modeling coding of elastic wave-field and numerical simulation of two-dimensional and three-dimensional EDA models with different symmetric axis. Seismic dynamic and kinematical properties of EDA media are analyzed from time slices and seismic records of wave propagation. As to pre-stacked reverse-time migration for elastic wave-field in fractured/pored media, based on the successful experience in forward modeling results with PSM, the author has studied pre-stacked reverse-time depth-domain migration technique using PSM of elastic wave-field in two dimensional EDA media induced by preferred fracture/pore distribution. At the same time, different image conditions will bring up what kind of migration result is detailed in this paper. The author has worded out software for pre-stacked reverse-time depth-domain migration of elastic wave-field in EDA media. After migration processing of a series of seismic shot gathers, influences to migration from different isotropic and anisotropy models are described in the paper. In summary, following creative research achievements are obtained:  Realizing two-dimensional and three-dimensional elastic wave-field modeling for fractured/pored media and related software has been completed.  Proposed pre-stacked reverse-time depth-domain migration technique using PSM of elastic wave-field.  Through analysis of the seismic dynamic and kinematical properties of EDA media, the author made a conclusion that collection of multi-component seismic data can provide important data basis for locating and describing the fracture/pore regions and their magnitudes and the preferred directions.  Pre-stacked reverse-time depth-domain migration technique has the ability to reconstruct complex geological object with steep formations and tilt fracture distribution. Neglecting seismic anisotropy induced by the preferred fracture/pore distribution, will lead to the disastrous imaging results.

土石混合体细观结构力学及其边坡稳定性研究

Soil-rock mixture (S-RM) refers to one extremely uneven loose rock and soil materials system with certain stone content. Its formation has started since Quaternary and it is composed of block stone, fine grained soil and pore with certain project scale and high strength. S-RM has extensive distribution in nature, especially in southwest China where the geotectonic background is complicated, the fracture activity is developed and the geomorphological characteristics of high mountain and steep gorge area are protuberant. This kind of complicated geologic body has developed wider in these areas. S-RM has obvious difference with the general soil or rock (rock mass) in physical and mechanical properties because its two components-“soil” and “rock-block” has extreme differences in physical and mechanical properties. The proposition of S-RM and its deep research are needed in the modern engineering construction. It is also the necessity in the modern development of rock and soil mechanics. The dissertation starts from the meso-structural characteristics of soil-rock and takes a systematic research on its meso-structural mechanics, deformation and failure mechanism and the stability of S-RM slope. In summary, it achieves the following innovative results and conclusions. There are various views on the conception of S-RM and its classification system. Based on the large number of field tests, the dissertation makes the conception and classification of S-RM more systematic. It systematically proposed the conception of meso-structural mechanics of S-RM. Thus the dissertation has laid a foundation for its deep study. With the fast development of the computer technology and digital image processing theory, digital image processing technology has been successfully applied in many fields and provided reliable technology support for the quantitative description of the structural characteristics of S-RM. Based on the digital image processing technology, the dissertation systematically proposes and developed the quantitative analysis method and quantitative index for the meso-structure of S-RM. The results indicate that the meso-structure such as its internal soil-rock granularity composition, the soil-rock shape and the orientability has obvious self-organization in the macro statistical level. The dissertation makes a systematic research on the physical mechanical properties, deformation and failure mechanism of S-RM based on large field test. It proposes the field test for the underwater S-RM and deduces the 3D data analysis method of in-situ horizontal push-shear test. The result indicates that S-RM has significant phenomenon of shear dilatancy in the shearing process, and its dilatancy will be more obvious with the increased proportion of rock or the decreased confining pressure. The proportion of rock has great effect on the strength of S-RM and rock-block, especially the spatial position of particles with comparatively big size has great effect on the shape and spatial position of the sample shear zone. The dissertation makes some improvements in the single ring infiltration test equipment and its application on the permeability of S-RM. The results indicate that the increasing of rock-block would make it more difficult for the soil to fill in the vacuity between the rock-block and the proportion would increase which would result in the increased permeability coefficient. The dissertation builds the real meso-structural model of S-RM based on the digital image processing technology. By using geometric reconstruction technology, it transfers the structural mode represented by Binary image into CAD format, which makes it possible to introduce the present finite element analysis software to take research on numerical experimental investigation. It systematically realizes leaping research from the image，geometric mode, to meso-structural mechanics numerical experiment. By using this method, the dissertation takes large scale numerical direct-shear test on the section of S-RM. From the mesoscopic perspective, it reveals three extended modes about the shear failure plane of S-RM. Based on the real meso-structural model and by using the numerical simulation test, the character and mechanics of seepage failure of S-RM are studied. At the same time, it builds the real structural mode of the slope based on the analysis about the slope crosssection of S-RM. By using the strength reduction method, it takes the research on the stability of S-RM and gets great achievements. The three dimensional geometric reconstruction technology of rock block is proposed, which provides technical support for the reconstruction of the 3D meso-structural model of S-RM. For the first time, the dissertation builds the stochastic structure model of two-dimensional and three-dimensional polygons or polyhedron based on the stochastic simulation technique of monte carlo method. It breaks the traditional research which restricted to the random generation method of regular polygon and develops the relevant software system (R-SRM2D/3D) which has great effect on meso-structural mechanics of S-RM. Based on the R-SRM software system which randomly generates the meso-structural mode of S-RM according to the different meso-structural characteristics, the dissertation takes a series of research on numerical test of dual axis and real three-axis, systematically analyses the meso destroy system, the effects of meso-structural characteristics such as on the stone content, size composition and block directionality on the macro mechanical behavior and macro-permeability. Then it proposes the expression of the upper and lower limit for the macro-permeability coefficient of the inhomogeneous geomaterials, such as S-RM. By using the strength reduction FEM, the dissertation takes the research on the stability of the slope structural mode of the randomly formed S-RM. The results indicate that generally, the stability coefficient of S-RM slope increases with the increasing of stone content; on the condition of the same stone content, the stability coefficient of slope will be different with different size composition and the space position of large block at the internal slop has great effect on the stability. It suggests that meso-structural characteristics, especially the space position of large block should be considered when analyzing the stability of this kind of slope and strengthening design. Taking Xiazanri S-RM slope as an example, the dissertation proposes the fine modeling of complicated geologic body based on reverse engineering and the generation method of FLAC3D mode. It resolves the bottleneck problem about building the fine structural mode of three-dimensional geological body. By using FLAC3D, the dissertation takes research on the seepage field and the displacement field of Xiazanri S-RM slope in the process of reservoir water level rising and decreasing. By using strength reduction method, it analyses the three-dimension stability in the process of reservoir water level rising and decreasing. The results indicate that the slope stability firstly show downward trend in the process of reservoir water level rising and then rebound to increase; the sudden drawdown of reservoir water level has great effect on the slope stability and this effect will increase with the sudden drawdown amplitude rising. Based on the result of the rock block size analysis of S-RM, and using R-SRM2D the stochastic structure model of Xiazanri S-RM slope is built. By using strength reduction method, the stability of the stochastic structure model is analysis, the results shows that the stability factor increases significantly after considering the block.

三角洲储层孔隙结构模型与剩余油分布研究——以临南油田沙河街组储层为例

The study of pore structure in reservoir was paid attention to in the early reservoir research and now a systematic research methodology is set up. On the limits of tools and conditions, methodologies and technologies on formation condition and distribution laws of pore structure and the relationship between remaining oil distribution and pore structure are uncertain and some knownage about it is also uncertain. As the development of petroleum industry, the characterization of pore structure and the prediction of remaining oil are the hot spot and difficult point in the research of oil development. The author pays a close attention to this subject and has done much research on it. In a case study in Linnan oilfield Huimin sag Jiyang Depression Bohai Bay basin by using a new method, named varied scale comprehensive modeling of pore structure, the author builds pore structure models for delta reservoir, reveals the remaining oil distribution laws in delta facies, and predicts the distribution of remaining oil in Linnan oilfield. By the application of stratigraphy, sedimentology and structure geology. the author reveals the genetic types of sandbody and its distribution laws, builds the reservoir geological models for delta sandstone reservoir in Shahejie group in Linnan oilfield and points out the geological Factors that control the development of pores and throats. Combining petrology and the reservoir sensitive analysis, the author builds the rock matrix models. It is the first time to state that rocks in different sentimental micro facies have different sensitive .response to fluid pressed into the rocks. Normally. the reservoirs in the delta front have weaker sensitivity to fluid than the reservoirs in delta plain, In same subfacies, the microfacies that have fine grain, such as bank and crevasse splay, have stronger reservoir sensitivity than the microfacies that have coarse grains, such as under-water branched channel and debauch bar. By the application of advanced testing, such as imagine analysis, scan electronic microscope, and morphology method, the author classifies the pore structure and set up the distribution models of pore, throat and pore structure. By the application of advanced theory in well-logging geology, the author finds the relationship between microscope pore structure and macroscopic percolation characteristics, and then builds the well-logging interpretation formulae for calculating pore structure parameters. By using the geostatistics methods, the author reveals the spatial correlative characteristics of pore structure. By application of conditional stochastic simulation methods, the author builds the 3D models of pore structure in delta reservoir. It is the base of predicting remaining oil distribution. By a great deal of experiments and theoretical deduction, The author expounds the laws of percolation flow in different pore structures, and the laws by which the pore structure controls the micro distribution of remaining oil, and then, states the micro mechanism of remaining oil distribution. There are two types of remaining oil. They are by-pass flow caused by micro-fingering and truncation caused by non-piston movement. By new method, the author states the different pore structure has different replacement efficiency, reveals the formation condition and distribution laws of remaining oil. predicts the remaining oil distribution in Linnan oil field, and put forward some idea about how to adjust the oil production. The study yielded good results in the production in Linnan oilfield.

塔里木盆地轮南地区三叠系油气地质模型及油气预测研究

As an important measure to understand oil and gas accumulation during petroleum exploration and development, Petroleum geological model is an integrated system of theories and methods, which includes sedimentology, reservoir geology, structural geology, petroleum geology and other geological theories, and is used to describe or predict the distribution of oil and gas. Progressive exploration and development for oil and gas is commonly used in terrestrial sedimentary basin in China for the oil and gas generation, accumulation and exploitation are very intricate. It is necessary to establish petroleum geological model, adaptive to different periods of progressive exploration and development practice. Meanwhile there is lack of an integrated system of theories and methods of petroleum geological model suitable for different exploration and development stages for oil and gas, because the current different models are intercrossed, which emphasize their different aspects. According to the characteristics of exploration and development for the Triassic oil and gas pool in Lunnan area, Tarim Basin, the Lunnan horst belt was selected as the major study object of this paper. On the basis of the study of petroleum geological model system, the petroleum geological models for different exploration and development stages are established, which could be applied to predict the distribution of oil and gas distribution. The main results are as follows. (1) The generation-accumulation and exploration-development of hydrocarbon are taken as an integrated system during the course of time, so petroleum exploration and development are closely combined. Under the guidance of some philosophical views that the whole world could be understood, the present writer realizes that any one kind of petroleum geological models can be used to predict and guide petroleum exploration and development practice. The writer do not recognize that any one kind of petroleum geological models can be viewed as sole model for guiding the petroleum exploration and development in the world. Based on the differences of extents and details of research work during various stage of exploration and development for oil and gas, the system of classification for petroleum geological models is established, which can be regarded as theoretical basis for progressive petroleum exploration and development. (2) A petroleum geological model was established based on detailed researches on the Triassic stratigraphy, structure, sedimentology and reservoir rocks in the Lunnan area, northern Tarim Basin. Some sub-belt of hydrocarbon accumulation in the Lunnan area are divided and the predominate controlling factors for oil and gas distribution in the Lunnan area are given out. (3) Geological models for Lunnan and Jiefangqudong oil fields were rebuilt by the combinations of seismology and geology, exploration and development, dynamic and static behavior, thus finding out the distribution of potential zones for oil and gas accumulations. Meanwhile Oil and gas accumulations were considered as the important unit in progressive exploration and development, and the classification was made for Lunnan Triassic pools. Petroleum geological model was created through 3D seismic fine interpretation and detailed description of characteristics of reservoir rocks and the distribution of oil and gas, especially for LN3 and LN26 well zones. The possible distribution of Triassic oil traps and their efficiency in the Lunnan area has been forecasted, and quantitative analysis for original oil(water) saturation in oil pools was performed. (4) The concept of oil cell is proposed by the writer for the first time. It represents the relatively oil-rich zones in oil pool, which were formed by the differences of fluid flows during the middle stage of reservoir development. The classification of oil cells is also given out in this paper. After the studies of physical and numerical modeling, the dominant controlling factors for the formation of various oil cells are analyzed. Oil cells are considered as the most important hydrocarbon potential zones after first recovery, which are main object of progressive development adjustment and improvement oil recovery. An example as main target of analysis was made for various oil cells of Triassic reservoir in the LN2 well area. (5) It is important and necessary that the classification of flow unit and the establishment of geological model of flow unit based on analysis of forecast for inter-well reservoir parameters connected with the statistical analysis of reservoir character of horizontal wells. With the help of self-adaptive interpolation and stochastic simulation, the geological model of flow units was built on the basis of division and correlation of flow units, with which the residual oil distribution in TIII reservoir in the LN2 well area after water flooding can be established.

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.

大港油田孔南地区孔一段储层流动单元研究

The main reservoir type in the south of Dagang Oilfield is alluvial reservoir. In this paper, the reservoir structure model and the distribution of connected body and flow barrier were built on base of the study of high-resolution sequential stratigraphic skeleton and fine sedimentary microfacies on level of single sandbody. Utilizing the static and dynamic data synthetically and carrying out the comparision of the classification method for reservoir flow unit in different reservoir, the criterion, which can be used to classify the flow unit in first section of Kongdian formation of Kongnan area, was defined. The qualitative method of well-to-well correlation and the quantitative method of conditional simulation using multiple data are adopted to disclose the oil and water moving regulation in different flow unit and the distribution rule of remaining oil by physical simulation measure. A set of flow unit study method was formed that is suit for the Dagang Oilfield on account of the remaining oil production according to the flow unit. Several outstanding progresses was obtained in the following aspects:It is considered that the reservoir structure of Zao V iow oil group- Zao Vup4 layerand are jigsaw-puzzled reservoir, while ZaoVup3-ZaoVupi layers are labyrinth reservoir,which are studied on base of high-resolution sequential stratigraphic skeleton on the levelof single sandbody in first section of Kongdian formation of Kongnan area and accordingto the study of fine sedimentary microfacies and fault sealeing.When classifying the flow unit, only permeability is the basic parameter using thestatic and dynamic data and, and also different parameters should be chose or deleted, suchas porosity, effective thickness, fluid viscosity and so on, because of the weak or stronginterlayer heterogeneous and the difference of interlayer crude oil character.The method of building predicting-model of flow unit was proposed. This methodis according to the theories of reservoir sedimentology and high-resolution sequencestratigraphic and adopts the quantitative method of well-to well correlation and the quantitative method of stochastic simulation using integrateddense well data. Finally the 3-D predicting-model of flow unit and the interlay er distribution model in flow unit were built which are for alluvial fan and fan delta fades in first section of Kongdian formation of Kongnan area, and nine genetic model of flow unit of alluvial environment that spread in the space were proposed.(4) Difference of reservoir microscopic pore configuration in various flow units and difference of flow capability and oil displacement effect were demonstrated through the physical experiments such as nuclear magnetic resonance (NMR), constant rate mercury penetration, flow simulation and so on. The distribution of remaining oil in this area was predicted combining the dynamic data and numerical modeling based on the flow unit. Remaining oil production measure was brought up by the clue of flow unit during the medium and late course of the oilfield development.

An algorithm for coarse particle sedimentation simulation by Stokesian dynamics

Coarse Particle sedimentation is studied by using an algorithm with no adjustable parameters based on stokesian dynamics. Only inter-particle interactions of hydrodynamic force and gravity are considered. The sedimentation of a simple cubic array of spheres is used to verify the computational results. The scaling and parallelism with OpenMP of the method are presented. Random suspension sedimentation is investigated with Mont Carlo simulation. The computational results are shown in good agreement with experimental fitting at the lower computational cost of O(N In N).

Exploring consensus mRNA secondary (folding) structure units by stochastic sampling and folding simulation

It is extremely difficult to explore mRNA folding structure by biological experiments. In this report, we use stochastic sampling and folding simulation to test the existence of the stable secondary structural units of-mRNA, look for the folding units, and explore the probabilistic stabilization of the units. Using this method, We made simulations for all possible local optimum secondary structures of a single strand mRNA within a certain range, and searched for the common parts of the secondary structures. The consensus secondary structure units (CSSUs) extracted from the above method are mainly hairpins, with a few single strands. These CSSUs suggest that the mRNA folding units could be relatively stable and could perform specific biological function. The significance of these observations for the mRNA folding problem in general is also discussed. (c) 2004 Elsevier B.V. All rights reserved.

stochastic process algebra based software process simulation modeling

Chinese Acad Sci, ISCAS Lab Internet Software Technologies

Simulations and Experiments of Stochastic Characteristics for Collective Short Fatigue Cracks in Steels

Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.

Computer Simulation Of Random Sphere Packing In An Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4 similar to 0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.

Numerical Simulation of R-M Instability

In order to capture shock waves and contact discontinuities in the field and easy to program with parallel computation a new algorithm is developed to solve the N-S equations for simulation of R-M instability problems. The method with group velocity control is used to suppress numerical oscillations, and an adaptive non-uniform mesh is used to get fine resolution. Numerical results for cylindrical shock-cylindrical interface interaction with a shock Mach number Ms=1.2 and Atwood number A=0.818, 0.961, 0.980 (the interior density of the interface/outer density p(1)/p(2) = 10, 50, 100, respectively), and for the planar shock-spherical interface interaction with Ms=1.2 and p(1)/p(2) = 14.28are presented. The effect of Atwood number and multi-mode initial perturbation on the R-M instability are studied. Multi-collisions of the reflected shock with the interface is a main reason of nonlinear development of the interface instability and formation of the spike-bubble structures In simulation with double mode perturbation vortex merging and second instability are found. After second instability the small vortex structures near the interface produced. It is important factor for turbulent mixing.