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.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

On the Behavior of Combination High-Order Compact Approximations with Preconditioned Methods in the Diffusion-Convection Equation

In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the time and space derivatives by compact finite-difference approximations. The system of resulting nonlinear finite difference equations are solved by preconditioned Krylov subspace methods. Numerical results are given to verify the behavior of high-order compact approximations in combination preconditioned methods for stability, convergence. Also, the accuracy and efficiency of the proposed scheme are considered.

Efficient high-order immersed interface methods for heat equations with interfaces

An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.

High-Order Iterative Methods Repeating Roots a Constructive Recapitulation

This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of initially known and unknown multiplicity. Efficient methods are presented in this note for the evaluation of the multiplicity index of the root being sought. Also reviewed here are super-linear and super-cubic methods that converge contrarily or alternatingly, enabling us, not only to approach the root briskly and confidently but also to actually bound and bracket it as we progress.

变容积密集烤房的CFD分析与试验研究

为保障密集烤房装烟密度,降低烘烤的能源消耗,研发一套适用于密集烤房的变容积系统。在完成变容积装置的设计后,基于CFD方法模拟分析装置与烟叶的不同距离对烤房内部气体分布均匀性的影响。通过烘烤试验获取实际烘烤数据,对模拟值加以验证。试验结果表明:当隔板与烟叶距离为0 cm时,流速不均匀系数Kv为0.40,温度不均匀系数Kt为0.41,距离为10 cm时,Kv=0.41,Kt=0.43;距离为20 cm时,Kv=0.42,Kt=0.49。装烟区9个测量点的温度模拟值与实测值基本吻合,误差在6%以内。变容积烤房在装烟量为一半时,相比常规烤房的燃料消耗可节约13.4%。研究结果表明:当隔板与烟叶距离为0 cm时烤房内部的气体分布最均匀;CFD模型与数值模拟结果具有可靠性;变容积装置具有较好的保温效果,可保证装烟密度,降低烤烟能耗。

混凝土搅拌筒CFD-DEM多相流数值模拟与分析

为研究混凝土运输车搅拌筒内的混凝土与骨料颗粒的真实运动情况,采用CFD-DEM耦合的方法,考虑混凝土的非牛顿流体特性及骨料颗粒间的相互作用,对混凝土进料、搅拌、出料过程的混凝土及颗粒运动规律进行数值模拟。通过将出料时间和出料速率数值仿真结果与实验对比,验证了CFD-DEM耦合方法的可行性。将计算流体动力学(Computational Fluid Dynamics,CFD)和离散元(Discrete Element Method,DEM)仿真结果导入ABAQUS中对叶片结构强度进行了分析,结果表明:叶片所受应力远小于材料的许用应力,最大节点位移满足刚度设计要求。最后对叶片的磨损情况进行了分析。

基于CFD-DEM耦合的梯级溜槽的设计与分析

针对传统物料转运过程中溜槽和输送带磨损严重、出口处粉尘浓度过高的问题,建立含臂架的梯级溜槽几何模型,采用基于计算流体力学与离散单元法(CFD-DEM)耦合的数值模拟方法,分析了臂架对转运溜槽的磨损以及对其出口处粉尘排放浓度的影响。仿真结果表明:含臂架的梯级溜槽可以有效控制物料流的速度和方向,降低对溜槽内表面的冲击磨损,降低出口处的粉尘量。

基于“一维系统+三维CFD”耦合方法的快堆非能动余热排出系统自然循环特性的数值模拟

池式快堆采用了新型非能动堆内直接余热排出(DRACS)方式,提升了快堆的安全性。目前针对池式快堆自然循环开展的数值模拟研究中,系统程序难以准确预测池内复杂自然循环路径,难以准确模拟池内三维热工水力现象,如果采用三维CFD计算建模及网格划分难度较高,且所需计算资源较大。为此本文开发了“一维系统+三维CFD”耦合方法,用于快堆非能动余热排出系统自然循环特性计算分析。利用日本大型钠回路实验台架(PLANDTL)DRACS自然循环模式对该耦合方法进行验证,稳态工况关键位置参数相对误差小于3%,瞬态工况关键位置参数与实验值变化趋势吻合较好,相对误差小于10%,验证了该耦合方法的适用性和准确性。利用该耦合方法,开展了中国实验快堆(CEFR)自然循环及余热排出特性计算分析,识别了池内自然循环流动路径,揭示了池内温度分层以及盒间流现象。本文方法可为大型钠冷快堆自然循环三维瞬态特性分析提供重要数值方法。

HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM

The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.

A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods

In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation

In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.

Distributed wide field electromagnetic method based on high-order 2^(n) sequence pseudo random signal

To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this method,only one set of high-order pseudo-random waveforms,which contains all target frequencies,is needed.Based on high-order sequence pseudo-random signal construction algorithm,the waveform can be customized according to different exploration tasks.And the receivers are independent with each other and dynamically adjust the acquisition parameters according to different requirements.A field test in the deep iron ore of Qihe−Yucheng showed that the distributed WFEM based on high-order pseudo-random signal realizes the high-efficiency acquisition of massive electromagnetic data in quite a short time.Compared with traditional controlled-source electromagnetic methods,the distributed WFEM is much more efficient.Distributed WFEM can be applied to the large scale and high-resolution exploration for deep resources and minerals.

A high-order accurate wavelet method for solving Schrdinger equations with general nonlinearity

A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.

High-order discontinuous Galerkin method for applications to multicomponent and chemically reacting flows

This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.

The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq-Burgers equation

This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.

基于CFD-DEM方法的饱和砂土场地液化模拟研究

砂土液化是常见的地震灾害,目前应用于研究砂土液化动力特性的室内试验以及模型试验还不能全面反映土体液化全过程。计算流体动力学(computational fluid dynamics,CFD)与离散元法(discrete element method,DEM)耦合模拟方法能够准确地模拟各类水土耦合问题。通过二次开发的CFD-DEM流固耦合模块实现离散元软件PFC3D与计算流体力学软件OpenFOAM之间的力学信息交互,利用颗粒水下自由沉降验证该方法的可行性。利用PFC3D软件模拟室内循环三轴试验标定出具有真实饱和砂土动力特性的数值砂样。根据已有的参数信息以及耦合模拟方法建立了饱和砂土的场地液化模型。模拟结果表明,离散元法能够复现室内砂土液化试验,标定参数可应用于场地液化模拟;单颗粒沉降速度与理论解一致验证了CFD-DEM耦合方法的准确性;峰值加速度0.25g下不同深度处土体均会发生液化,液化时超孔压比无法达到1,超孔压累计值由浅层往深层递增;液化后土体强度自下而上逐渐恢复,再固结的场地土体结构呈现均匀化发展趋势。

调谐液柱阻尼器-结构系统风致振动响应的CFD/CSD耦合分析方法

针对调谐液柱阻尼器(tuned liquid column damper, TLCD)难以建立其精确的非线性理论分析模型,且其力学性能试验成本高和耗时长等问题,首先采用计算流体动力学(CFD)数值模拟方法,对TLCD系统的力学性能和动力特征进行仿真模拟,在此基础上进一步提出了基于计算流体动力学/计算结构动力学(CFD/CSD)耦合分析方法,求解带TLCD系统的高层建筑结构的风致动力响应。通过开展某一TLCD系统在特定底部激励下的力学性能和动力特性试验,得到其内液体晃荡的自由液面波高和晃动力时程,验证了CFD数值模拟方法可以准确地分析TLCD水箱内液体的非线性晃动特征。随后对风工程领域广泛采用的76层建筑结构振动控制Benchmark模型,假设其顶部设置TLCD系统时主体结构在三种风速重现期(10、50和100年)风速对应的横风向动力风荷载激励下的风致控制效率,采用提出的CFD/CSD耦合分析方法,进行了数值仿真模拟分析。耦合分析结果表明,TLCD系统对Benchmark模型的风致加速度、速度和位移响应均有一定的控制效果,对加速度响应的控制效果要优于对位移响应的控制效果。该研究方法可为复杂TLCD系统对高层建筑的风振控制分析提供有效的参考。

HIGH-ORDER NYSTRM METHOD FOR THE EFIE OF EM SCATTERING PROBLEMS

Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic scattering problems. The numerical solutions of two examples are correct compared with Method Of Moment(MOM).

A force control high-order single-step-β method (HSM) for substructure pseudo-dynamic testing

This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.