角点区域上椭圆问题的有限体方法

使用基于 (h ,γ ,L)型三角网格剖分的有限体方法求解具有角点奇性的二阶椭圆边值问题 .经过详细分析 ,证明了在此种三角网格剖分下H1范数的收敛阶数仍是最优的 .

控制体有限元方法中质量加权迎风格式的迁延修正

控制体有限元方法对于处理流动问题提供了一种较好的数值模拟方法，但对于大Ｒｅｙｎｏｌｄｓ数的回流流动问题，该方法在采用各种迎风格式时仍存在着严重的假扩散．为此，对二维质量加权迎风格式，给出了一种由插值单元及其一个与插值点最靠近的相邻单元所确定的多项式插值格式迁延修正的形式．通过对Ｒｅ＝４００、１０００、５０００三种情形的二维空穴流问题的计算，表明该格式可有效地减少控制体有限元方法对回流问题数值模拟的假扩散．

复杂介质中地震波传播的数值模拟

提出了复杂介质中地震波传播数值模拟的有限体方法,有限体方法具有与有限元方法相同的网格剖分的灵活性,但计算工作量和存储量少得多。数值结果表明了算法的有效性。

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation（capillary pressure）.So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.

The Finite Element Solutions to the Semiconductor Equations

In this paper, the approximation of stationary equations of the semiconductor devices with mixed boundary conditions is considered. Two schemes are proposed for the system. One is Glerkin discrete scheme, the other is hybrid variable discrete scheme. A convergence analysis is also given.

半圆域上自然对流的数值模拟

对半圆域上的自然对流采用控制体有限元方法进行数值模拟 .采用非结构三角形网格与质量加权迎风格式对计算域及控制方程进行离散 ,对压力离散方程采用波前法求解 ,保证了对所有Ra≤ 10

Computational modeling of free-surface slurry flow problems using particle simulation method

The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles.Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods,the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained.The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system.For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems,three examples involving slurry flow on three different types of river beds have been considered.The related particle simulation results obtained from these three examples have demonstrated that:1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields;2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed.

Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes

In this study,the cylindrical finite-volume method(FVM)is advanced for the efficient and high-precision simulation of the logging while drilling(LWD)orthogonal azimuth electromagnetic tool(OAEMT)response in a three-dimensional(3 D)anisotropic formation.To overcome the ill-condition and convergence problems arising from the low induction number,Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system.The electrical fi eld continuation method is applied to approximate the perfectly electrical conducting(PEC)boundary condition,to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels.On the base,the 3 D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries.The equivalent conductivity in a non-uniform element is determined by a standardization technique.The direct solver,PARDISO,is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem.To reduce the number of calls to PARDISO,the whole computational domain is divided into small windows that contain multiple measuring points.The electromagnetic(EM)solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix,relevant to all the transmitters in the same window,is changed.Finally,the 3 D FVM is validated against the numerical mode matching method(NMM),and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.

Numerical investigation on flow and heat transfer characteristics of corrugated tubes with non-uniform corrugation in turbulent flow

Based on finite volume method, the pressure drop and heat transfer characteristics of one smooth tube and ten different axisymmetric corrugated tubes, including two with uniform corrugation and eight with non-uniform corrugation, have been studied. A physical model of the corrugated tube was built, then the numerical simulation of the model was carried out and the numerical simulation results were compared with the empirical formula.The results show that: the friction factor decreases with the increase of Reynolds number ranging from 6000 to 57000, the value of which in the corrugated tubes with non-uniform corrugation(tube 03–10) are smaller than those with uniform corrugation(tube 01–02). The geometry parameters of tube(01) have advantages on the heat transfer enhancement in low Reynolds number flow region(from 6000 to 13000) and tube(07–08)have advantages on the heat transfer enhancement in high Reynolds number flow region(from 13000 to 57000). The vortex, existed in each area between two adjacent corrugations called second flow region, is the root of the enhancement on heat transfer in the corrugated tubes. The effectiveness factor decreases with the increasing of Reynolds number and the performances of the corrugated tubes with pitch of 12.5 mm have advantages than these of 10 mm under the same corrugation geometric parameter.

An Essential Solution of Water Entry Problems and its Engineering Applications

For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh.In this approach, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method.Then artificial compressibility method, dual time-stepping technique and Roe's approximate Riemann solver are adopted in the numerical scheme.Finally, some application cases are designed to show the ability of the current method to cope with water entry problems in ocean engineering.

Creating Technology and Numerical Analysis of Warm Plastic Forming for Non-symmetrical Axostyle

A creating technology of the part forming was discussed and finite volume method(FVM)was used to simulate the forming process of the non-symmetrical axostyle spring core-bar.The results show that the no-even radial flange on the top part of the eccentric peachy surface can remarkably block the metal flow and the eccentric peachy can be filled contentedly.Increasing the radius of punch near the inner pocket,the head bulge also can be filled contentedly.The temperature distribution in the part and the forming force,which helps to decide the forming temperature and to select the equipment,was also analyzed.The comparison between the simulation and the experiment result shows that they are accordant.

FEM Analysis of Tube Preforming and Hydroforming Process for an Automotive Part

The tube hydroforming technology is used today in the mass production of lightweight components for the automotive industries due to its advantages over conventional stamping methods. A typical tube hydroforming process is usually a multiple forming operation process. The tube preforming and hydroforming process of an automobile subframe were analyzed by finite element method (FEM), and a parametric study was also carried out to obtain the effect of the forming parameters such as the die closing, the internal pressure and the axial feeding. The simulation results were also compared with industrial products in respect to the thickness distribution of some typical and key cross-sections. The study indicates that the internal pressure and the axial feeding should be set correctly and the multiple forming operations of tube hydroforming process can be simulated well by using the explicit code Ls-Dyna.

Computational simulation of convective flow in the Earth crust under consideration of dynamic crust-mantle interactions

The finite element method was used to solve fluid dynamic interaction problems between the crust and mantle of the Earth. To consider different mechanical behaviours, the lithosphere consisting of the crust and upper mantle was simulated as fluid-saturated porous rocks, while the upper aesthenospheric part of the mantle was simulated as viscous fluids. Since the whole lithosphere was computationally simulated, the dynamic interaction between the crust and the upper mantle was appropriately considered. In particular, the mixing of mantle fluids and crustal fluids was simulated in the corresponding computational model. The related computational simulation results from an example problem demonstrate that the mantle fluids can flow into the crust and mix with the crustal fluids due to the resulting convective flows in the crust-mantle system. Likewise, the crustal fluids can also flow into the upper mantle and mix with the mantle fluids. This kind of fluids mixing and exchange is very important to the better understanding of the governing processes that control the ore body formation and mineralization in the upper crust of the Earth.

COMPUTATION OF TURBULENCE FLOW ON HYBRID GRIDS USING k-ω TURBULENCE MODEL AND OSHER SCHEME

An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-ω model) is also developed for hybrid grids to compute the turbulence flow. The turbulence flow past NACA0012 airfoil and the double ellipsolids are computed, and the numerical results show that the above methods are very efficient.

Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization

Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems,porous bearings,porous layer insulation,biomechanics,geomechanics etc.Motivated by such applications,in this article,a numerical study of entropy generation impacts on the heat and momentum transfer in time-dependent laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly heated vertical cylinder embedded in a porous medium is presented.Darcy’s law is used to simulate bulk drag effects at low Reynolds number for an isotropic,homogenous porous medium.Heat line visualization is also included.The mathematical model is derived and normalized using appropriate transformation variables.The resulting non-linear time-dependent coupled governing equations with associated boundary conditions are solved via an implicit finite difference method which is efficient and unconditionally stable.The outcomes show that entropy generation and Bejan number are both elevated with increasing values of Darcy number,Casson fluid parameter,group parameter and Grashof number.To analyze the heat transfer process in a two-dimensional domain,plotting heat lines provides an excellent approach in addition to streamlines and isotherms.It is remarked that as the Darcy number increases,the deviations of heat lines from the hot wall are reduced.

Numerical investigation of water-entry of flatted-bottom seafloor mining tool in ocean waves

A numerical wave load model based on two-phase(water-air) Reynolds-Averaged Navier Stokes(RANS) type equations is used to evaluate hydrodynamic forces exerted on flatted-bottom seafloor mining tool during its entering ocean waves of deploying process.The discretization of the RANS equations is achieved by a finite volume approach(FV).The volume of fluid method(VOF) is employed to track the complicated free surface.A numerical wave tank is built to generate the ocean waves which are suitable for deploying seafloor mining tool.A typical deploying condition is employed to reflect the process of flatted-bottom body impacting with waves,and the pressure distribution of bottom is also presented.Four different lowering velocities are applied to obtain the time histories of maximum pressure of bottom,and it can be concluded that the pressure coefficient decreases with water velocity increasing,which is similar with ordinary water entry case.The numerical results clearly demonstrate the characteristics of flatted-bottom body entering ocean waves.

Parametric analysis of steel plated shear structures

Due to outstanding ductility and high strength,the steel plate shear wall(SPSW)is recognized as a good lateral system for building structures; particularly as it interacts with earthquake resistant design.This study aims to reveal the dynamic and cyclic behavior of steel plated shear wall.Finite element method of analysis was implemented in order to simulate the behavior of such a wall structure.To determine the dynamic behavior of un-stiffened plate shear wall,two different analytical models were implemented.The post buckling strength of steel plate subjected to lateral loading was also employed.The story shear-drift diagrams of steel shear wall system were presented.The strength and ductility of the system obtained from the analysis were compared with those of steel shear wall tests reported before.The pertinent parameters of the steel shear wall system such as plate thickness,column and beam stiffness and the plate aspect ratio were recognized and their effects were recorded.The effect of stiffeners on the behavior of the SPSW was also investigated.

Influence of crystallographic orientation on growth behavior of spherical voids

The influence of crystallographic orientation on the void growth in FCC crystals was numerically simulated with 3D crystal plasticity finite element by using a 3D unit cell including a spherical void, and the rate-dependent crystal plasticity theory was implemented as a user material subroutine. The results of the simulations show that crystallographic orientation has significant influence on the growth behavior of the void. Different active slip systems of the regions around the void cause the discontinuity in lattice rotation around the void, and the corner-like region is formed. In the case of the void located at grain boundary, large heterogeneous deformation occurs between the two grains, and the equivalent plastic deformation along grain boundary near the void in the case of θ=45^o （θ is the angle between grain boundary direction and X-axis） is larger than the others. Large difference of orientation factor of the two grains leads to large equivalent plastic deformation along grain boundary, and the unit cell is more likely to fail by intergranular fracture.

Experimental and Numerical Investigations on Vibration Characteristics of a Loaded Ship Model

In this paper, the vibration characteristics of the structure in the finite fluid domain are analyzed using a coupled finite element method. The added mass matrix is calculated with finite element method （FEM） by 8-node acoustic fluid elements. The vibration characteristics of the structure in the finite fluid domain are calculated combining structure FEM mass matrix. By writing relevant programs, the numerical analysis on vibration characteristics of a submerged cantilever rectangular plate in finite fluid domain and loaded ship model is performed. A modal identification experiment for the loaded ship model in air and in water is conducted and the experiment results verify the reliability of the numerical analysis. The numerical method can be used for further research on vibration characteristics and acoustic radiation problems of the structure in the finite fluid domain.