Splitting Based Scheme for Three-dimensional MHD with Dual Time Stepping

A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.

The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect stability.

The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect the numerical stability.

A Proper Time Integration with Split Stepping for the Explicit Free-Surface Modeling

Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.

A SINGLE STEP SCHEME WITH HIGH ACCURACY FOR PARABOLIC PROBLEM

A single step scheme with high accuracy for solving parabolic problem is proposed. It is shown that this scheme possesses good stability and fourth order accuracy with respect to both time and space variables, which are superconvergent.

A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS

In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.

ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

LARGE TIME STEP GENERALIZATION OF RANDOM CHOICE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.

GENERALIZED UPWIND SCHEME WITH FRACTIONAL STEPS FOR 3-D PROBLEM OF CONVECTION DOMINATING GROUNDWATER TRANSPORT

A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation.These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.

Computational uncertainty and optimal grid size and time step of the Lax-Friedrichs scheme for the 1D advection equation

本文对于应用Lax-Friedrichs格式数值求解一维平流方程,研究数值求解过程中产生的截断误差与舍入误差,以及两种误差逐层向高时间层传播的累积,得到新的数值解总误差上界的理论近似公式,以及最优格距和最优时间步长的理论公式.通过数值算例验证了所得公式的可靠性。然后,发现了两种不同机器精度下最优时间步长之比满足的一个仅与机器精度有关的普适关系.最后,理论验证了在网格比固定的情况下,此问题满足数值计算的不确定性原理,以及在机器有限精度下最优时间步长的必然存在。

Lagrangian model of zooplankton dispersion:numerical schemes comparisons and parameter sensitivity tests

This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion:numerical schemes and time steps.Firstly,we compared three numerical schemes using idealized circulations.Results show that the precisions of the advanced Adams-Bashfold-Moulton(ABM) method and the Runge-Kutta(RK) method were in the same order and both were much higher than that of the Euler method.Furthermore,the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption.We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm.Secondly,we performed a sensitivity test for time steps,using outputs of the hydrodynamic model,Symphonie.Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields.The method introduced by Oliveira et al.in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models,at least when only considering advection.

An Improved Scalar Costa Scheme Based on Watson Perceptual Model

An improved scalar Costa scheme (SCS) was proposed by using improved Watson perceptual model to adaptively decide quantization step size and scaling factor. The improved scheme equals to embed hiding data based on an actual image. In order to withstand amplitude scaling attack, the Watson perceptual model was redefined, and the improved scheme using the new definition can insure quantization step size in decoder that is proportional to amplitude scaling attack factor. The performance of the improved scheme outperforms that of SCS with fixed quantization step size. The improved scheme combines information theory and visual model.

High Order Padé Schemes for Nonlinear Wave Propagation Problems

Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective method,which has a spectral-like resolution and good stability nature.In particular,we propose an unconditional stable implicit Padé scheme to solve odd order nonlinear equations.Numerical results demonstrate the excellent performance of Padé schemes for high order nonlinear equations.

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

一维平流方程迎风格式的最优时空步长

在考虑舍入误差影响的情况下,研究一维平流方程迎风格式最优时空步长的选取.首先,分析每一时间层产生的离散误差和舍入误差,以及2种误差向高时间层传播的累积,得到数值解总误差的理论上界;然后推导出最优时间步长和最优空间步长的理论公式,进而得到2种不同机器精度下最优时间步长之比满足的一个仅与机器精度有关的普适关系;最后通过数值算例验证了结论的可靠性.

基于车速平稳过渡的高速公路出口限速方案

研究能够满足出口车速平稳过渡的逐级限速方案,对出口区域车辆平稳运行及安全提升有重要意义。利用无人机采集高速公路出口车辆运行参数,分析出口车辆运行特征,考虑驾驶员对相邻限速标志的认知反应,构建了连续限速标志设置间距计算模型,建立了高速公路出口不同级别的限速方案,利用驾驶模拟试验对设计的不同限速方案进行分析及评价。模型的计算结果显示,二级限速方案中,限速值为60-40 km/h的限速标志间距为160 m;三级限速方案中,限速值为80-60-40 km/h的限速标志间距分别为300 m和80 m,限速值为90-60-40 km/h的限速标志间距分别为300 m和85 m;四级限速方案中,限速值为100-80-60-40 km/h的限速标志间距分别为295、160、80 m。利用驾驶模拟器对模型结果进行验证,试验结果表明:随着限速级数增加,车辆离散幅度显著降低,表明逐级限速方案对出口车辆运行速度有明显管控效果;逐级限速方案的平均减速度指标小于1.3 m/s^(2),均在驾驶舒适性阈值内;四级限速方案可使在分流鼻端车速标准差、平均减速度、分流鼻运行速度V85分别控制在5.23 km/h、0.52 m/s^(2)、54 km/h左右,极大满足了车速平稳过渡要求。可见,借助模型定量优化的逐级限速方案可以显著提高出口车速过渡的平稳性和安全性。

基于同步ADMM算法含P2G-CCS的多园区综合能源系统优化调度

多园区综合能源微电网系统交互需要解决每个微电网之间的协调优化调度的问题,文中通过引入交互耦合功率变量解耦的方法,来求解园区内微电网之间交互的电功率,将集中求解的复杂问题转换为各微电网之间相互合作而且可以内部管理的优化问题,于是文中考虑采用同步式交替向乘子法(alternating direction method of multipliers,ADMM)分布式求解方法来实现各个园区微电网系统的成本关系分配,系统只需要求解分布式优化方案所需的信息,可以最大限度地降低运行成本,同时为了保证多园区微电网系统的低碳运行和降低环境成本,在考虑单个电热冷综合能源微电网系统的基础上,采用碳捕集设备和电转气装置以及配合阶梯碳交易机制的方法,更进一步降低系统碳排放;最后,通过仿真算例来验证所提方法和模型的有效性。

无人机折叠翼分步展开机构设计及动力学分析

小型巡飞无人机折叠翼的展开方案对于无人机飞行模式切换具有重要影响。针对无人机折叠翼折叠特点与展开需求,提出同步展开和分步展开2种方案。采用拉格朗日法建立折叠翼展开动力学模型,应用气动力仿真软件计算折叠翼在展开过程中所受空气阻力,得出折叠翼采用不同展开方案时所需驱动力矩,以驱动力矩作为评判标准,选取折叠翼最优展开方案。仿真计算结果表明,折叠翼分步展开方案可在保证展开到位的情况下,以小力矩在短时间内完成展开运动。针对折叠翼分步展开方案设计折叠翼分步展开机构,并进行结构静强度分析,验证结构方案的可行性。

三维TTI介质qP波透射立体层析方法研究

致力于研究三维TTI介质下的qP波立体层析反演算法.将射线扰动理论应用于三维具有倾斜对称轴的横向各向同性(TTI)介质拟声波程函方程,导出立体层析所需的三维TTI介质qP波数据空间与三维TTI介质模型空间之间的所有Frechét导数.在通过灵敏度测试验证了相应Frechét导数对于三个各向异性THOMSEN参数的正确性之后,使用两步法反演策略——即先使用坐标分量和射线参数水平分量(不包括走时)实施初始反演而后再使用所有数据空间分量进行反演,在三维qP波TTI介质情形下针对三个各向异性THOMSEN参数可以获得理想的反演结果,为三维qP波TTI介质下透射立体层析的应用做好了理论准备.用一个典型的理论数据算例证实了上述观点.

150 m超长管幕支护下隧道施工力学特性研究

依托某浅埋下穿高速公路的铁路隧道工程,通过有限元数值模拟,分析超长管幕、超前小导管两种支护体系下隧道施工时支护结构的受力及变形规律。结果表明:管幕支护拱顶最大沉降量3.55 mm,初支结构峰值拉应力2.19 MPa,围岩压力最大值2.06 MPa,围岩与支护结构稳定性满足施工安全要求,各支护结构变形量及受力状态均处于稳定状态;相较于超前小导管支护措施,管幕支护体系抵抗地表及周边围岩变形作用明显。