Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR DYNAMIC ANALYSES IN SATURATED PORO-ELASTO-PLASTIC MEDIUM

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.

GREEN FUNCTION ON TWO-PHASE SATURATED MEDIUM BY CONCENTRATED FORCE IN TWO-DIMENSIONAL DISPLACEMENT FIELD

The Green function on two-phase saturated medium by concentrated force has a broad and important use In seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. According to the Green function on two-phase saturated medium by concentrated force in three-dimentional displacement field obtained by Ding Bo-yang et al., it gives out the Green function in two-dimensional displacement field by infinite integral method along x(3)-direction derived by De Hoop and Manolis. The method adopted in the thesis is simpler. The result will be simplified to the boundary element method of dynamic problem.

Solutions of Green's function for Lamb's problem of a two-phase saturated medium

The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space.

Review on the plastic instability of medium -Mn steels for identifying the formation mechanisms of Lüders and Portevin -Le Chatelier bands

Plastic instability,including both the discontinuous yielding and stress serrations,has been frequently observed during the tensile deformation of medium-Mn steels(MMnS)and has been intensively studied in recent years.Unfortunately,research results are controversial,and no consensus has been achieved regarding the topic.Here,we first summarize all the possible factors that affect the yielding and flow stress serrations in MMnS,including the morphology and stability of austenite,the feature of the phase interface,and the deformation parameters.Then,we propose a universal mechanism to explain the conflicting experimental results.We conclude that the discontinuous yielding can be attributed to the lack of mobile dislocation before deformation and the rapid dislocation multiplication at the beginning of plastic deformation.Meanwhile,the results show that the stress serrations are formed due to the pinning and depinning between dislocations and interstitial atoms in austenite.Strain-induced martensitic transformation,influenced by the mechanical stability of austenite grain and deformation parameters,should not be the intrinsic cause of plastic instability.However,it can intensify or weaken the discontinuous yielding and the stress serrations by affecting the mobility and density of dislocations,as well as the interaction between the interstitial atoms and dislocations in austenite grains.

Deformation of a two-phase medium due to a long buried strike-slip fault

The aim of the present paper is to obtain the two-dimensional deformation of a two-phase elastic medium consisting of half-spaces of different ri- gidities in welded contact due to a buried long strike-slip fault. The solution is valid for arbitrary values of the fault-depth and the dip angle. The effect of fault-depth on the displacement and stress fields for different values of dip angle has been studied numerically. It is found that the displacement field varies significantly for a buried fault from the corresponding displacement field for an interface-breaking fault. The contour maps showing the stress field for various dip angles for buried and interface-breaking fault have been plotted. It has been observed that the stress field varies significantly for a buried fault from the corresponding stress field for an interface-breaking fault.

A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows

In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.

NEW STUDYING OF LATTICE BOLTZMANN METHOD FOR TWO-PHASE DRIVEN IN POROUS MEDIA

By using the interaction of particles, such as the physical principle of the same attract each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore, the method economizes on computer time, has less fluctuation on boundary surface and takes no average measure.

INTERACTION OF A SCREW DISLOCATION WITH AN INTERFACIAL EDGE CRACK IN A TWO-PHASE PIEZOELECTRIC MATERIAL

The interaction of a screw dislocation with an interracial edge crack in a two-phase piezoelectric medium is investigated.Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle.Based on the electroelastic fields derived,the stress and electric displacement intensity factors,the image force acting on the dislocation are given explicitly.We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants.In the case where one of two phases is purely elastic,the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect,the position of the dislocation and the material properties on the interaction mechanism.

Pressure/Saturation System for Immiscible Two-Phase Flow: Uniqueness Revisited

We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct 'mobilities' (or mobility-like functions) that satisfy the new condition (when the parameter is 2). For the constructed 'mobilities', we do graphical experiments that show, empirically, that this condition could be satisfied for other values of . These empirical experiments indicate that the usual smoothness condition on the fractional flow function (and on the total mobility), for uniqueness and convergence, might not be necessary. This condition is also sufficient for the convergence of a family of perturbed problems to the original pressure/saturation problem.

Development and microstructure characterization of BG110E high-strength expansion pipe

The BG110E high-strength expansion pipe was developed using medium manganese steel and subjected to a two-phase zone heat treatment process.Mechanical properties and microstructure analysis results have proven that the BG110E expansion pipe exhibits uniform elongation of more than 19%.Moreover,after undergoing expan-sion deformation,its strength,toughness,and plasticity are found to meet the stringent requirements of the P110 pipe.The microstructure of this high-strength expansion pipe,which has a strength of 110 ksi(1 ksi=6.895 MPa),consists of tempered martensite,ferrite,retained austenite,and granular bainite.The propotion of retained austenite reaches up to 12%,ensuring high plasticity and the occurrence of the transformation-induced plasticity effect during the deformation process.Consequently,it enhances the coordinated deformation ability between different phases,which significantly improves the internal yield pressure of the BG110E high-strength expansion pipe in turn.

Enhanced Oil Recovery by Injecting Oleic Acid as a Surfactant into the Porous Medium

Physico-chemical methods of improved oil recovery make it possible to increase oil production in deposits by injecting surfactants acting on various physical parameters. Oleic acid has an effect on the viscosity of the displacement fluid and the flow rate. Therefore, increasing the viscosity of the displacement fluid plays an essential role in improving the improved oil recovery. The physicochemical properties at the interface between petroleum and water are modified by oleic acid, lowering the viscosity of petroleum and increasing the viscosity of water, which facilitated the mobility of petroleum in the porous medium.

基于连续-非连续分析理论的隧道围岩破坏区判识方法研究

准确分析隧道挖破坏区的范围对合理确定支护参数有着重要的指导作用和工程意义,主要围绕连续介质分析方法和以有限元-离散元耦合方法(finite element-discrete element coupling method,简称FDEM)为代表的连续-非连续方法开展了隧道围岩破坏区判识方法研究。研究了连续介质分析方法与FDEM识别围岩破坏的判别标准;将岩体划分为弹性的岩石单元和弹塑性的界面单元,基于等效连续模型的思想,推导了界面单元力学参数与岩石单元及岩体单元力学参数的关系表达式,首次建立这两种方法参数取值的联系,解决了连续-非连续方法取值难的问题;对比了两种方法模拟不同岩性、断面铁路隧道开挖过程中围岩破坏区范围。基于规范中各级围岩的力学参数取值范围,给出了各级围岩下以FDEM中罚参数和断裂能等围岩主要破坏参数的取值范围;FLAC3D为代表的连续介质方法和FDEM两种方法对不同岩性、断面铁路隧道开挖过程模拟结果表明,连续介质方法得出的塑性区和以塑性极限应变得出的破坏区域和连续-非连续方法得出的裂纹扩展区和破坏区在分布范围、形态及破坏形式上基本一致,验证了提出的FDEM围岩破坏参数取值方法是合理可行的。

MULTI-MODE NETWORK ANALYSIS FOR DISCONTINUITIES IN PARALLEL-PLATE WAVEGUIDES PARTIALLY FILLED WITH MULTI CHIRAL RODS

The reflection and transmission characteristics of the guided modes in parallel-plate waveguides partially filled with one or multi chiral rods have been investigated by a method, which combines the multi- mode network theory with a rigorous mode matching procedure. The formulas of the reflection and transmis- sion coefficient matrix are derived. The numerical results for different cases are presented and have indicated that the chirality parameters and the geometrical dimensions of the chiral rods have significant influence on the reflection and transmission characteristics of the guided modes.

On the Vortex Sheets of Compressible Flows

This paper provides a review of the recent results on the stability of vortex sheets in compressible flows.Vortex sheets are contact discontinuities of the underlying flows.The vortex sheet problem is a free boundary problem with a characteristic boundary and is challenging in analysis.The formulation of the vortex sheet problem will be introduced.The linear stability and nonlinear stability for both the two-dimensional two-phase compressible flows and the two-dimensional elastic flows are summarized.The linear stability of vortex sheets for the three-dimensional elastic flows is also presented.The difficulties of the vortex sheet problems and the ideas of proofs are discussed.

SOLUTION OF RELATIVE PERMEABILITY OF TWO-PHASE FLOW IN POROUS MEDIUM

In view of the resolution of relative Permeability curves of unconsolidated core containing heavy petroleum, a set of equations governing the oil/water coreflood are obtained based on porous medium flow theory, numerical analysis, optimum theory and error analysis.The optimum problems are solved by means of constraint variable metric method. The sensitivity of results to initial data is eliminated. Several examples are included to illustrate the reliability and usefulness of this method.

深埋地下洞室柱状节理围岩变形特征分析

【目的】金沙江白鹤滩水电站输水系统中的尾水调压室规模巨大,洞室埋深大,穹顶柱状节理玄武岩发育,地质条件复杂,为了降低围岩变形破坏的风险,保证工程安全,节约生产成本,需对深埋地下洞室柱状节理围岩变形特征进行分析。【方法】依托右岸深埋地下洞室8#尾水调压室,结合现场工程地质资料及施工过程,运用非连续介质力学的数值计算方法,得出无支护条件下穹顶在柱状节理岩体及完整岩体两种情况下围岩的应力应变分布,继而分析评价两种情况下围岩可能出现的变形特征。【结果】结果表明,柱状节理的发育使穹顶开挖面附近浅层围岩强度降低、应力集中区与开挖面的距离增大,围岩塑性区深度显著增大;受初始最大主应力方向及柱状节理各向异性影响,穹顶S侧翼围岩变形值及N/S两侧翼变形值的差异均有所增大,层间错动带C5在N侧法向应力有所减弱,在S侧的松弛变形有所增大。【结论】分析方法及结果符合地下工程设计施工的一般规律,为围岩稳定、设计方案和支护安全评价提供了有力支撑,具有可靠的工程指导价值。

离散元法用于块石土强夯过程模拟

针对深厚松散块石土中强夯加固机理问题，引入离散元法，采用一定级配条件下的平面圆盘模型，模拟了夯击作用下松散块石层的变形过程，反映出夯击能量在地基土中的传播特征。数值分析成果与实测资料比较，结果令人满意。

横向荷载下桩-土相互作用的无网格分析

基于新型的岩土工程数值分析方法——无网格Galerkin法,利用移动最小二乘法所具备的局部化技术,引入不同材料介质之间材料不连续问题的无网格求解方法,对横向荷载作用下桩-土相互作用特性进行了无单元数值模拟分析,并采用MATLAB语言编制出相应的计算程序,由此对不同荷载作用大小、桩周土性质及桩-土刚度比等因素对桩身受力变形特性的影响进行了对比分析,获得了一些定性的结论。工程实例应用结果表明,这一方法在精度和后处理方面比传统的有限元等数值方法更具优势,且计算结果与通用有限元软件ANSYS计算结果吻合良好。