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.

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.

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. .

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.

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.

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.

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.

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.

Grain boundary effects on spall behavior of high purity copper cylinder under sweeping detonation

A series of sweeping detonation experiments were conducted to study the grain boundary effects during the primary spallation of high-purity copper cylinder.The free surface velocity profile of the shocked samples was measured by Doppler pins systems.The soft-recovered samples were characterized by optical and electron backscatter diffraction microscopy,and the effects of microstructures like grain boundaries,and crystal orientation on spall behavior were investigated.The results indicated that the critical stress of deformation twinning in cylindrical copper increased.The nucleation sites of spallation damage were determined by the joint influence of the grain orientation(Taylor factor)and the angle between grain boundaries and radial impact-stress direction.Voids were prone to nucleating at the grain boundaries perpendicular to the radial impact-stress direction.Nevertheless,the number of voids nucleated at boundaries was relatively different from the results obtained from the plate impact experiment and plate sweeping detonation experiment,which is a result of the curvature that existed in the cylindrical copper and the obliquity of the impact-stress direction during sweeping detonation loading.

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.

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.

Study on divertor plasma behavior through sweeping strike point in new lower divertor on EAST

A series of L-mode discharges have been conducted in the new‘corner slot’divertor on the Experimental Advanced Superconducting Tokamak(EAST)to study the divertor plasma behavior through sweeping strike point.The plasma control system controls the strike point sweeping from the horizontal target to the vertical target through poloidal field coils,with keeping the main plasma stability.The surface temperature of the divertor target cools down as the strike point moves away,indicating that sweeping strike point mitigates the heat load.To avoid the negative effect of probe tip damage,a method based on sweeping strike point is used to get the normalized profile and study the decay length of particle and heat flux on the divertor target λ_(js),_λ(q).In the discharges with high radio-frequency(RF)heating power,electron temperature T_(e) is lower and λ_(js)is larger when the strike point locates on the horizontal target compared to the vertical target,probably due to the corner effect.In the Ohmic discharges,λ_(js),λ_(q) are much larger compared to the discharges with high RF heating power,which may be attributed to lower edge T_(e).

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.

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.

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 Sweeping Reshuffle at CAS Institutes

Reorganization of CAS institutes was conducted over the past four years. For example, with the merger of the former Institute of Mathematics,Institute of Applied Mathematics, Institute of Systems Science and Institute of Computational Mathematics & Scientific/Engineering Computing, an Academy of Mathematics & System Sciences was formed. In the Shanghai area, the eight former biological institutes was regrouped into four institutes and one center,which formed the newly established Shanghai Institutes for Biological Sciences.……