Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

Er∶YAG激光SWEEPS双脉冲模式激活荡洗在自由水域中的气泡动力学观测

目的:探究Er∶YAG激光光子增强的光声流(SWEEPS)技术在不同脉冲间隔参数条件下的蒸汽气泡动力学效应。方法:Er∶YAG激光手具连接工作尖放置于自由水域模型中,设置SWEEPS模式,150~600μs脉冲间隔激活。高速摄像机(200 000 Hz)摄录Er∶YAG激光激活荡洗引起空穴效应的过程,matlab逐帧分析蒸汽气泡间的相互作用关系,及蒸汽气泡消失时刻气泡残余与激光工作尖之间的距离。实验数据经SPSS 19.0统计软件进行统计分析。结果:在自由水域中,Er∶YAG激光SWEEPS模式下,脉冲间隔设置的改变会引起两次脉冲激发的蒸汽气泡形成不同的相互作用关系,包括双气泡融合、双气泡撞击及双气泡脱离。其中,脉冲间隔设置为360~440μs时,双气泡撞击现象会使蒸汽气泡消失时气泡残余与激光工作尖之间达到最远距离。结论:在自由水域中,Er∶YAG激光双脉冲SWEEPS模式在不同的脉冲间隔设置下引起双气泡间形成不同的作用关系,该现象可能可以增强Er∶YAG激光空穴效应,强化激光激活荡洗的临床应用效果。

Numerical Investigation of Flow Separation Control over an NACA0018 Airfoil Using Sweeping Jet Actuator

As an active flow control technology and with the advantages of no moving components, the Sweeping jet actuator has become a hotspot in the field of flow control. However, the linear relationship between oscillation frequency and momentum coefficient in a sweeping jet actuator makes it difficult to determine the dominant factors that affect control effectiveness. Decoupling the oscillation frequency and momentum coefficient, as well as determining the control mechanism, is the focus of studying the sweeping jet actuator. In this study, a novel sweeping jet actuator is designed using synthetic jets instead of feedback channels and applied to the flow separation control of NACA0018 airfoil. This article studies the control effect under three oscillation frequencies of F+ = f × c/U∞ = 1, 10, 100 and three momentum coefficients of Cμ = 0.45%, 0.625%, 0.9%. The numerical results indicate that all three oscillation frequencies have good control effects on flow separation, and the control effect is best when F+ = 1, with the maximum lift coefficient increasing by approximately 14% compared to the other two cases. And the sweeping jet actuator has a better ability to control flow separation as the momentum coefficient increases. By decoupling the characteristics of the sweeping jet actuator and conducting numerical analysis of the flow control effect, it will promote its better engineering application in the field of flow control. .

A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

胶束毛细管电泳Sweeping法检测畜肉中残留氟嗪酸

建立胶束毛细管电泳在线Sweeping富集法检测畜肉中残留的痕量氟嗪酸。讨论了缓冲液pH、SDS浓度、进样时间、运行电压、进样压力对富集效果的影响;考察了不同有机溶剂对蛋白的沉淀效果。结果:选择20mmol/L硼砂+80mmol/L十二烷基硫酸钠(SDS,pH=9.6)为缓冲液,电压18kV,进样时间为200s,进样压力15mbar,三氯乙酸为沉淀剂。氟嗪酸富集倍数达500倍,检测限为0.016mg/L,相对标准偏差RSD(n=3)为2.41%。胶束毛细管电泳在线Sweeping富集法可用于畜肉中残留痕量兽药的检测。

模糊需求VRP的一种Sweeping启发式算法

在对具有模糊需求的车辆路径问题(VRPFD)进行简单描述的基础上,结合模糊机会约束规划的基本:给出了解决该问题的基本思路,构建了其数学规划模型,并设计了解决该问题的一种Sweeping启发式算法.埽在最小化车辆总行驶距离的目标下,通过随机模拟方法研究了决策者的主观偏好P*对最终决策目标的影响作并给出了P*的合理取值范围.

胶束电动色谱在线Sweeping技术测定化妆品中水杨酸

采用在线富集Sweeping技术建立了胶束电动色谱法测定化妆品中水杨酸含量的方法,考察了缓冲溶液pH值、SDS浓度、进样时间和样品基体组成对富集效果的影响。结果表明,在电泳缓冲溶液为15mmoL/L磷酸盐+30mmoL/L十二烷基硫酸钠(PH=7.00),紫外检测波长214nm,分离电压18KV时,富集倍数可达700倍以上。本方法不需复杂的样品预处理,操作简单,快速,成本低,在快速分离与检测方面有很好的应用前景。

Sweeping体的离散化原理

本文主要介绍FSMTS中所采用的Sweeping体素的离散化原理。首先讨论了体素离散化的“拓扑有效性”和精度要求,并在此基础上提出了依据主曲率控制离散点密度的方法。其次研究了离散化过程中的三种活动标架,提出了在扫动过程中如何描述截面变化规律的各种策略。最后推导出Sweeping体的合法性检验判据。

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 at angle of attack 40℃ are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio （AR） of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing （forewing）, hawkmoth and dragon- fly （forewing）, respectively （AR of these wings varies greatly, from 2.84 to 5.45）. The following facts are shown. （1） The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex （LEV）. （2） The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r2 （the radius of the second ：moment of wing area） is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. （3） The effects of AR are remarkably small： whenAR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.

LARGE AERODYNAMIC FORCES ON A SWEEPING WING AT LOW REYNOLDS NUMBER

The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically.After an initial start from rest,the wing is made to execute an azimuthal rotation(sweeping)at a large angle of attack and constant angular velocity.The Reynolds number(Re)considered in the present note is 480(Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root).During the constant-speed sweeping motion,the stall is absent and large and approximately constant lift and drag coefficients can be maintained.The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows.Soon after the initial start,a vortex ring,which consists of the leading-edge vortex(LEV),the starting vortex,and the two wing-tip vortices,is formed in the wake of the wing.During the subsequent motion of the wing,a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength.This prevents the LEV from shedding.As a result, the size of the vortex ring increases approximately linearly with time,resulting in an approximately constant time rate of the first moment of vorticity,or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wing- span.The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force.

Determination of triazine herbicide residues in water samples by on-line sweeping concentration in micellar electrokinetic chromatography

A new method for the determination of atrazine, simazine and prometryn in water samples by on-line sweeping concentration technique in micellar electrokinetic chromatography （MEKC） was developed. Various parameters affecting sample enrichment and separation efficiency were systematically studied. Compared with the conventional MEKC method, up to 60-200-fold improvement in concentration sensitivity was achieved in terms of peak height by using this sweeping injection technique. The compound strychnine was used as the internal standard for the improvement of the experimental reproducibility. The limits of detection （S/ N = 3：1） for atrazine, simazine and prometryn were 9, 10 and 0.5 ng mL-1, respectively. This method has been successfully applied to the analysis of atrazine, simazine and prometryn in lake, steam and ground water.

On-line Sweeping Sample Concentration in Micellar Electrokinetic Chromatography with Enhanced Sensitivity for the Deter-mination of Carbamazepine in Human Serum

A sensitive and simple micellar electrokinetic chromatography （MEKC） method was developed for the determination of antiepileptic drug, carbamazepine （CBZ）, using sweeping on-line concentration method with photodiode array detection. Under the optimal conditions, the calibration curve was linear over a range of 0.5-40μg·mL^-1 for CBZ with a correlation coefficient of 0.998. The detection limit （S/N = 3：1） of CBZ was 0.10 μg·mL^-1. The sweeping-MEKC method has been successfully applied to the analysis of CBZ in human serum.

Improvement of porous polyvinylidene fluoride-co-hexafluropropylene hollow fiber membranes for sweeping gas membrane distillation of ethylene glycol solution

Porous polyvinylidene fluoride-co-hexafluropropylene(PVDF-HFP)hollow fiber membranes were fabricated through a wet spinning process.In order to improve the membrane structure,composition of the polymer solution was adjusted by studying ternary phase diagrams of polymer/solvent/non-solvent.The prepared membranes were used for sweeping gas membrane distillation(SGMD)of 20 wt% ethylene glycol(EG)aqueous solution.The membranes were characterized by different tests such as N2 permeation,overall porosity,critical water entry pressure(CEPw),water contact angle and collapsing pressure.From FESEM examination,addition of 3 wt% glycerol in the PVDF-HFP solution,produced membranes with smaller finger-likes cavities,higher surface porosity and smaller pore sizes.Increasing the polymer concentration up to 21 wt% resulted in a dense spongy structure which could significantly reduce the N2 permeance.The membrane prepared by 3 wt% glycerol and 17 wt% polymer demonstrated an improved structure with mean pore size of 18 nm and a high surface porosity of 872 m^−1.CEPw of 350 kPa and overall porosity of 84% were also obtained for the improved membrane.Collapsing pressure of the membranes relatively improved by increasing the polymer concentration.From the SGMDtest,the developed membrane represented a maximumpermeate flux of 28 kg·m^−2·h^−1 which is almost 19% higher than the flux of plain membrane.During 120 h of a long-termSGMD operation,a gradual flux reduction of 30% was noticed.In addition,EG rejection reduced from 100% to around 99.5% during 120 h of the operation.

Accelerating an adiabatic process by nonlinear sweeping

We investigate the acceleration of an adiabatic process with the same survival probability of the ground state by sweeping a parameter nonlinearly, fast in the wide gap region and slowly in the narrow gap region, in contrast to the usual linear sweeping. We find the expected acceleration both in the Landau-Zener tunneling model and in the adiabatic quantum computing model for factorizing the number N - 21.

Combination of hollow fiber-based liquid-phase microextraction with sweeping techniques in micellar electrokinetic chromatography for the determination of Strychnos alkaloids in human urine

A new method for the enrichment of Strychnos alkaloids in biological samples via liquid-phase microextxaodon （LPME） based on porous polypropylene hollow fibers in combination with on-line sweeping in micellar electrokinodc chromatography was developed. The calibration curve was linear over the range of 20-200 ng mL^-1 for both strychnine and brucine in human urine sample. The detection limits （S/N = 3：1） for strychnine and brucine were 1 ng mL^-1 and 2 ng mL^-1, respectively. The LPME-sweeping method has been successfully applied to the analysis of strychnine and brucine in real urine samples.

Determination of Isocarbophos by Cathodically Sweeping Oscilliopolarography

Determination of isocarbophos by cathodically sweeping oscilliopolarography is described. In a 1.0×10?5 mol/L sodium dodecylbenzene sulfonate (SDS)+0.1 mol/L HAC-NaAC (pH=4.0) buffer medium, isocarbophos and its alkaline hydrolysate exhibited sensitive second derivative wave at ?0.50 V and ?0.48 V respectively. The peak current was linearly proportional to the concentration of isocarbophos in the range of 5.40×10?6?1.05×10?4 mol/L by detecting isocarbophos directly. The detection limit was 3.60×10?6 mol/L with the relative standard derivation (RSD) of 7.3%. By employing an alkaline hydrolysis, the peak current was linearly proportional to the concentration of isocarbophos in the range from 7.70×10?7 mol/L to 1.24×10?4 mol/L, and the detection limit was 5.80×10?7 mol/L with RSD of 3.1%. The hydrolysis procedure and the electrode reaction were studied by voltammetry.

Determination of ephedrine and codeine in human urine by cation-selective exhaustive injection and sweeping micellar electrokinetic chromatography

A sensitive method for the determination of ephedrine and codeine in human urine by capillary electrophoresis （CE） was described. In order to improve the sensitivity, two online concentration techniques including cation-selective exhaustive injection （CSEI） and sweeping micellar electrokinetic chromatography （sweeping-MEKC） were used. Under the optimum conditions, the detection limits （S/N = 3） were 0.10 μg/L for ephedrine and 0.80 μg/L for codeine. This method was successfully applied to real urine sample analysis.

Effect of Landau Zener tunneling by the varying sweeping rate of external field

We study the effect of Landau-Zener （LZ） tunneling caused by the varying sweeping rate of the external field, and solve the problem about the LZ tunneling rate among many levels. The LZ tunneling rate is essentially changed by the unsteady variation of the time-dependent sweeping field and is different from the steadily varying sweeping field, which makes the particles in lower states transit periodically to upper states within a finite time.

Time frequency spectrum of atmospheric turbulence and sweeping hypothesis

The present study is focused on the structure of time frequency spectrum.A scaling law for Eulerian time frequency spectrum and the corresponding temporal structure function are calculated from the sweeping hypothesis and Kolmogorov’s similarity law regarding spatial structure function.An experiment is designed to study this scaling law in the atmospheric turbulent boundary layer.The results well support the conclusion derived from relevant theoretical analysis.

A computational method for wide-azimuth 3D dip-angle gathers using Gaussian beam migration

The dip-angle-domain common-image gather(DDCIG)is a key tool to separate the diffraction and reflection imaging results.Reflectors with different spatial geometries produce different responses in DDCIGs.Compared with Kirchhoff migration,Gaussian beam migration(GBM)is more effective and robust to overcome the multipathing problem.As a ray-based method,it has explicit angle information naturally during the propagation.We have developed a 3D DDCIG computational method using GBM,which obtain both the imaging result and angle-domain gathers with only one pass of calculation.The angle-gather computation is based on geometrical optics,and multiple angle conversions are implemented under the rules of space geometry,which helps to avoid rounding errors and improve accuracy.Additionally,the multi-azimuth joint presentation strategy is proposed to describe the characteristic of omnidirectional dip angles using a finite number of gathers.After using a 2D model to illustrate application advantages of DDCIG,we apply the proposed method to two 3D models to test its feasibility and accuracy.A field data example further demonstrates the adaptability of our method to seismic imaging for a land survey.