High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.

A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy

To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.

Prediction Model for Net Cutting Specific Energy in CNC Turning

A prediction model for net cutting specific energy in computer numerical control(CNC)turning based on turning parameters and tool wear is developed.The model can predict the net cutting energy consumption before turning.The prediction accuracy of the model is verified in AISI 1045 steel turning.The comparative experimental results show that the prediction accuracy of the model is significantly improved because the influence of tool wear is taken into account.Finally,the influences of turning parameters and tool wear on net cutting specific energy are studied.With the increase of cutting depth,the net cutting specific energy decreases.With the increase of spindle speed,the additional load loss power of spindle drive system increases,so the net cutting specific energy increases.The net cutting specific energy increases approximately linearly with tool wear.The results are helpful to formulate efficient and energy-saving CNC turning schemes and realize low‑carbon manufacturing.

Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrodinger Equation

Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.

Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method

River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

Higher-Order Numerical Solution of Two-Dimensional Coupled Burgers’ Equations

We proposed a higher-order accurate explicit finite-difference scheme for solving the two-dimensional heat equation. It has a fourth-order approximation in the space variables, and a second-order approximation in the time variable. As an application, we developed the proposed numerical scheme for solving a numerical solution of the two-dimensional coupled Burgers’ equations. The main advantages of our scheme are higher accurate accuracy and facility to implement. The good accuracy of the proposed numerical scheme is tested by comparing the approximate numerical and the exact solutions for several two-dimensional coupled Burgers’ equations.

新型管道环切机切割方案设计及进给轨迹规划

刀旋式切管机采用刀具绕固定管道外围旋转的方式进行环形切割,在需要精密切割薄壁管材的场合中得到了广泛的应用,但其进给轨迹常为直线或弧线,存在相对单一、无法实现柔性化切割等问题。为此,提出一种新型管道环切机,其核心部件为冗余驱动环切机构,可以在平面内移动以控制环切进给量,并以半圆管道包络切割为例,基于5-6-5-6-5分段高次多项式曲线进行进给轨迹规划,搭建样机平台进行仿真和实验研究。结果表明:实际轨迹与理论轨迹具有一致性,且切割过程较为柔顺,管道切口质量较好,验证了管道环切机结构设计的合理性和柔顺切割的可行性。

复杂结构的铝合金锻件高速切削加工方法研究

以支臂零件为例,展示了零件的典型结构,并对零件进行了工艺性分析。根据零件的特点,从零件的毛坯形式、工艺装备的设计、加工设备的选择以及典型的加工工序等方面出发,设计了一套适宜的加工方案。基于高速切削加工技术的特点,详细描述了零件在高速切削情况下的加工与编程方法,并通过对零件的实际加工,验证了加工方案的可行性,进而总结出复杂结构的铝合金锻件数控高速切削的加工方法及合理的切削参数。

基于“3414”试验的切花芍药氮磷钾推荐施肥量研究

针对切花芍药生长过程中盲目施肥的现状,以二年生芍药‘向天歌’为研究对象,采用“3414”试验施肥方案,结合隶属函数法,研究氮、磷、钾肥不同用量对切花芍药生长的影响,探讨切花芍药生产适宜的肥料用量。结果表明:不同施肥处理对芍药株高、茎粗、蕾径、分株数和切花数影响显著(P<0.05);氮、磷缺素区的综合隶属函数值小于无肥区,缺钾区大于无肥区,对芍药生长的影响为氮>磷>钾;N2P2K1处理的综合隶属函数值最大,为0.61,芍药植株生长最好;对各处理的综合隶属函数值和施肥量进行肥料效应函数拟合分析,一元二次、二元二次肥料效应函数方程拟合相关性均达显著水平,三元二次肥料效应方程为非典型模型,采用频率分析法计算肥料推荐量。综合分析各肥料效应函数方程的推荐用量及相应的综合隶属函数值,本试验切花芍药推荐施肥量为N 212.7 kg/hm^(2)、P_(2)O_(5)46.2 kg/hm^(2)、K_(2)O 49.9 kg/hm^(2),施肥配比为1∶0.21∶0.23,可用于本试验区切花芍药生产的施肥参考。

运营隧道防水板切割二衬的危害及整治方案研究

[目的]随着我国隧道建设步伐的加快,运营隧道中各类病害问题日益突显。尽管众多学者已对多种病害进行了深入研究,但针对防水板切割二衬的危害研究仍显不足。因此,有必要深入探究运营隧道中防水板切割二衬危害,并提出有效的整治方案。[方法]基于防水板的防水与受力作用机理,运用数值模拟技术,系统研究了运营隧道中防水板切割二衬的危害。重点分析了环向与纵向不同切割长度下,防水板拱部弯矩、衬砌Mises应力及位移等三项关键指标的变化规律。在此基础上,提出了一种新型整治设计方案,并通过对比防水板整治前后衬砌结构拱顶位移的变化,验证了该整治设计方案的合理性与优越性。[结果及结论]研究结果表明,随着防水板环向与纵向切割长度的增加,防水板拱部弯矩、衬砌应力及位移均呈现显著增长趋势。特别是防水板的纵向切割长度,对衬砌位移等三项指标的影响更为显著。通过综合分析弯矩、应力及位移的突变区域,发现防水板环向与纵向切割长度在2~3 m范围内时,对衬砌结构的受力及变形影响最为不利。

基于FLAC3D的多级路堑高边坡桩锚支护效果研究——以云南某滑坡为例

为探明公路路堑高边坡桩锚支护机理,以云南邓家村某路堑边坡的滑坡处治为例展开了系统的研究。通过现场地质调查及多元数据分析,查明了滑坡工程地质条件及成因;采用FLAC3D数值模拟研究了无支护下高边坡的稳定性,对比分析了挡土墙和桩锚支护2种方案;以预应力为400 kN、桩间距为4 m、桩直径为1 m为基本方案,通过单因素分析法分析了路堑高边坡中桩锚参数对桩锚受力性能和边坡安全系数的影响规律。研究结果表明:挡土墙虽然可以有效阻止边坡底部的滑移,但其对坡体中部和上部的稳固效果不佳;桩锚支护结构对整个滑坡体都有一个良好的加固作用,桩的位移呈现“上部大而下部趋于0”的特点,其受到的剪力、弯矩存在多个极值点,并且大多数存在于滑动面上方;随着桩直径的增大或者桩间距的减小,边坡安全系数增加,而锚索预应力对安全系数的影响很小。

煤巷快速掘进改进工艺研究

针对古城煤矿现有掘进切割工艺,介绍了1种煤巷快速掘进改进工艺设计方案。该方案以原掘进切割工艺的具体情况为基础,结合煤矿领域现有掘进技术水平,设计出了多种不同的掘进切割方案,然后利用有限元分析软件分别对各种方案在实际中的应用效果进行模拟分析,并通过对比模拟分析结果,以此确定出最终的掘进切割方案。应用该改进工艺,不仅可以提升煤巷掘进速度,而且还可以提高井下作业的安全性,具有一定的应用价值。

铝合金薄壁角片数控加工方案分析与论证

对小型铝合金薄壁角片零件的结构与材料进行了工艺性分析,设计出两种数控加工工艺方案。通过对两种加工方案所采用的加工方法进行整体论证,对比得出一种高质量的适合批量生产的加工方案,并总结出最优的数控铣切的切削参数。

半圆锥形薄壁零件车削装夹方案与切削参数优化

某半圆锥形薄壁零件具有刚性差、装夹困难、在机加工时间长等特点,零件加工后易产生壁厚不均、尺寸超差的问题。针对该零件的结构特点,提出三种装夹方案,通过有限元仿真计算零件的加工变形,得到变形最小的加工方案。在满足切削变形的前提下,以切削时间为优化目标,得出最优的切削参数组合,并通过切削实验验证了优化后装夹方案及切削参数的可行性。

基于锥切割理论的系统故障状态优化调整方法研究

为了在系统故障演化过程中控制系统故障状态,提出了一种系统故障状态优化调整方法。其主要根据锥切割理论,以及非优理论和Hat投影建立方法的数学模型,设置了分析系统并给出了分析步骤。首先论述了相关理论的基本思想;其次研究了系统故障状态优化调整的基础和关键,描述了需要研究的问题;再次建立了系统故障状态优化调整方法模型及分析步骤;最后通过实例展示了方法流程,得到了定量结果和优化调整最优方案。结果表明:系统故障状态的优化调整可通过影响因素实现;通过比较原系统故障状态和新系统故障状态与目标系统故障状态的内积,基于非优理论选择需要实施的优化调整措施。当措施是优化调整措施时计算继续;是非优化调整措施时计算停止,这时得到的按照实施顺序组成的措施集合即为优化调整最优方案。最后论述了方法的先进性和有待研究的问题。

大采高工作面切顶卸压沿空留巷技术研究及工程实践

针对山西凯嘉能源集团义棠煤业大采高工作面沿空留巷,基于数值计算分析了不同切顶高度覆岩运移及巷道围岩稳定性的影响,进一步对沿空留巷关键技术参数进行了选取,确定了切缝深度20 m,切顶角度15°,设计采用恒阻大变形锚索对巷道顶板进行加固的支护方式,并设计了合理的巷道围岩支护方案及挡矸工艺。现场实践表明,巷道变形控制在允许变形的范围内,完全可以满足工作面的正常使用。

母管制热电联产机组闭式循环冷却水系统节能改造

针对某母管制热电联产机组闭式循环冷却水系统运行中存在的泵选型偏大、能耗高等问题,对闭式循环冷却水泵叶轮优化改造,保持额定流量不变,减小了扬程。将单元制的闭式循环冷却水系统改造为“大母管制”。经过长时间运行测试,在非夏季工况闭式循环冷却水系统可减少1台水泵运行,电功率减少约166kW,每年可节约52万元,获得了较大的经济效益。