A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem:Application to the 1D Euler Equations

We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.

Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X－Ray Scattering

The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.

Numerical method for wave height distribution within the artificial harbor with water depth of steep variation

ＮｕｍｅｒｉｃａｌｍｅｔｈｏｄｆｏｒｗａｖｅｈｅｉｇｈｔｄｉｓｔｒｉｂｕｔｉｏｎｗｉｔｈｉｎｔｈｅａｒｔｉｆｉｃｉａｌｈａｒｂｏｒｗｉｔｈｗａｔｅｒｄｅｐｔｈｏｆｓｔｅｅｐｖａｒｉａｔｉｏｎＩＮＴＲＯＤＵＣＴＩＯＮＡｎａｒｔｉｆｉｃｉａｌｈａｒｂｏｒ...

THE CHARACTERISTICS OF THUNDERSTORM FREQUENCY VARIATION AND THEIR POSSIBLE RELATION WITH THE ADJUSTMENT OF CROP DISTRIBUTION IN THE LEIZHOU PENINSULA

In order to research possible influences of the adjustment of plant distribution on the development frequency of thunderstorms over the Leizhou Peninsula, mathematic statistic methods, including correlation analyses, 11 kinds of fitting models and all-variable regression methods, were used for analyses and research. The results show that the average trend of the number of annual thunderstorm days is descending obviously, and there are thunderstorms in all seasons, in which warm post-midday thunderstorms have taken up the most part, and high frequency is found from May to September, and the starting and ending dates of thunderstorms have a great annual discrepancy. The vegetation structure has been improved along with the reduction of rice fields and the area increment of sugarcane and fruits planting, which results in the decrease of the number of thunderstorm days; the change in the characteristics of winter spare fields, which is caused by the planting of vegetables, limits the formation of thunderstorms in early winter and late spring. Meanwhile, the area adjustment of peanut planting has little influence on the variation of thunderstorm days. The adjustment of principal crop distribution, such as rice, sugarcane, fruits and vegetables, may have obvious influence on the formation of thunderstorms, and sugarcane has the largest effect, followed in turn by rice, vegetables and fruits, and the adjustment of crop distribution has little influence on the starting and ending dates of thunderstorms.

Xiaomi India's New Distribution Method in the Post-Pandemic Era

In recent years,the Indian smartphone market has grown rapidly,and Xiaomi's expansion in this market has never stopped.However,Xiaomi India has and would face even more changes and challenges due to the impact of the COVID-19 pandemic.This paper focuses on how Xiaomi India can adhere to its ethical business practices in changes and developments that will improve its distribution layout.

Measurement of the g Factor of the 3.1232 MeV 19/2^(-) Level in ^(43)Sc by Perturbed Angular Distribution Method

The g-factor hence the magnetic moment,of the isomeric state 43Sc（|9/2-,3.1232 MeV）has been measured by the time differential perturbed angular distributionmethod.The measured values are g=0.3279（19）and μ=3.108（18）nm.

A Study on the Reasonable Distribution of Total Funds

How to distribute total sum of funds among different investment priorities？ It is not only a theoretical problem in Management Accounting, but also a realistic problem in the investment decision of an enterprise. In this paper, the author queries the method of ＂use linear programming to find out optimum combination＂, which put forward in management accounting, and gives a convenient and reasonable method---effective gradient method.

Fiber Bundle Topology Optimization for Surface Flows

This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equations,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dissipation and pressure drop is used as the design objective.

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

基于WVD/ATDM的铝合金板孔损伤位置与区域识别

为识别铝合金板孔损伤位置及区域,以Lamb波为研究基础,提出基于魏格纳-威利分布(WVD,WignerVille distribution)和到达时间差值法(ATDM,arrival time difference method)的损伤识别技术。首先,采集实验铝合金板健康和有损模型的Lamb信号,对其差值信号进行WVD分析,准确提取损伤反射信号到达时间;其次,通过ATDM建立各传感器间的距离差值关系,确定孔损伤位置中心并预测最大损伤半径,从而实现对孔损伤关键指标的识别;最后,通过数值模拟进一步验证该方法,结果表明,基于WVD/ATDM的损伤识别技术不仅能准确识别出孔损伤位置,而且能够有效地识别损伤区域面积。

Distributed Collaborative Response Surface Method for Mechanical Dynamic Assembly Reliability Design

Because of the randomness of many impact factors influencing the dynamic assembly relationship of complex machinery, the reliability analysis of dynamic assembly relationship needs to be accomplished considering the randomness from a probabilistic perspective. To improve the accuracy and efficiency of dynamic assembly relationship reliability analysis, the mechanical dynamic assembly reliability（MDAR） theory and a distributed collaborative response surface method（DCRSM） are proposed. The mathematic model of DCRSM is established based on the quadratic response surface function, and verified by the assembly relationship reliability analysis of aeroengine high pressure turbine（HPT） blade-tip radial running clearance（BTRRC）. Through the comparison of the DCRSM, traditional response surface method（RSM） and Monte Carlo Method（MCM）, the results show that the DCRSM is not able to accomplish the computational task which is impossible for the other methods when the number of simulation is more than 100 000 times, but also the computational precision for the DCRSM is basically consistent with the MCM and improved by 0.40-4.63% to the RSM, furthermore, the computational efficiency of DCRSM is up to about 188 times of the MCM and 55 times of the RSM under 10000 times simulations. The DCRSM is demonstrated to be a feasible and effective approach for markedly improving the computational efficiency and accuracy of MDAR analysis. Thus, the proposed research provides the promising theory and method for the MDAR design and optimization, and opens a novel research direction of probabilistic analysis for developing the high-performance and high-reliability of aeroengine.

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.

NUMERICAL ANALYSIS OF FLUID FLOW AND ADDED MASS INDUCED BY VIBRATION OF STRUCTURE

The fluid flow induced by light-density, low-stiffness structures was treated as inviscid, incompressible irrotational and steady plane flow. On the basis of the dipole configuration method, a singularity distribution method of distributing sources/sinks and dipoles on interfaces of the structure and fluid was developed to solve the problem of fluid flow induced by the vibration of common structures, such as columns and columns with fins, deduce the expression of kinetic energy of the fluid flow, and obtain the added mass finally. The calculational instances with analytical solutions prove the reliability of this method.

Sedimentation of a single particle between two parallel walls

The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result.

A Lifting Line Theory for a Three-dimensional Hydrofoil

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

Distributed collaborative extremum response surface method for mechanical dynamic assembly reliability analysis

To make the dynamic assembly reliability analysis more effective for complex machinery of multi-object multi-discipline(MOMD),distributed collaborative extremum response surface method(DCERSM)was proposed based on extremum response surface method(ERSM).Firstly,the basic theories of the ERSM and DCERSM were investigated,and the strengths of DCERSM were proved theoretically.Secondly,the mathematical model of the DCERSM was established based upon extremum response surface function(ERSF).Finally,this model was applied to the reliability analysis of blade-tip radial running clearance(BTRRC)of an aeroengine high pressure turbine(HPT)to verify its advantages.The results show that the DCERSM can not only reshape the possibility of the reliability analysis for the complex turbo machinery,but also greatly improve the computational speed,save the computational time and improve the computational efficiency while keeping the accuracy.Thus,the DCERSM is verified to be feasible and effective in the dynamic assembly reliability(DAR)analysis of complex machinery.Moreover,this method offers an useful insight for designing and optimizing the dynamic reliability of complex machinery.

INTERACTIONS BETWEEN TWO SEDIMENTING PARTICLES WITH DIFFERENT SIZES

An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two_dimensional channel. The simulation results were verified by comparison with experiments. The results show that the interactions between two particles with different sizes can be described as drafting, kissing, tumbling and separating. Only for small diameter ratio, the two particles will interact undergoing repeated DKT (Drafting, Kissing and Tumbling) process. Otherwise, the two particles will separate after their tumbling. The results also show that, during the interaction process, the motion of the small particle is strongly affected while the large particle is affected slightly.