Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Efficient method to calculate the eigenvalues of the Zakharov–Shabat system

A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.

A Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

The Adjustment Analysis Method of the Active Surface Antenna Based on Convolutional Neural Network

Active surface technique is one of the key technologies to ensure the reflector accuracy of the millimeter/submillimeter wave large reflector antenna.The antenna is complex,large-scale,and high-precision equipment,and its active surfaces are affected by various factors that are difficult to comprehensively deal with.In this paper,based on the advantage of the deep learning method that can be improved through data learning,we propose the active adjustment value analysis method of large reflector antenna based on deep learning.This method constructs a neural network model for antenna active adjustment analysis in view of the fact that a large reflector antenna consists of multiple panels spliced together.Based on the constraint that a single actuator has to support multiple panels(usually 4),an autonomously learned neural network emphasis layer module is designed to enhance the adaptability of the active adjustment neural network model.The classical 8-meter antenna is used as a case study,the actuators have a mean adjustment error of 0.00252 mm,and the corresponding antenna surface error is0.00523 mm.This active adjustment result shows the effectiveness of the method in this paper.

FFT-Based Numerical Method for Nonlinear Elastic

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

An Integrated Structure Analysis Method of Active Surface Antenna by Using the Simplified Actuator

The main surface of a large reflector antenna is composed of thousands of panels,which are inevitably deformed under natural load,leading to a great deterioration of electrical performance of the antenna.The active surface technique is an effective method to compensate antenna deformation error and has been widely used.The actuator is a complex component,it has not been established in the antenna structure analysis model,which limits the theoretical analysis ability of the active surface technology.To solve this problem,an integrated structure analysis method of active surface antenna by using the simplified actuator is proposed.First,according to the supporting characteristics and adjusting function of the actuator,the complex actuator is simplified a simple structure of support beams,support truss and adjustment beam.Second,the finite element model of the active surface antenna including the simplified actuator is established.Then,the relationship between the adjustment value(load)of adjustment beam and the deformation of the antenna structure is deduced,and the integrated analysis method for realizing the active adjustment of panels is established.Finally,the model and adjustment analysis method of the active surface antenna in this paper is applied to an 8 m antenna,and satisfactory structural analysis results are obtained,which shows the effectiveness and universality of the method,and provides a reference for the modeling and adjustment analysis of the active surface antenna.

Comparative Analysis for Evaluating Wind Energy Resources Using Intelligent Optimization Algorithms and Numerical Methods

Statistical distributions are used to model wind speed,and the twoparameters Weibull distribution has proven its effectiveness at characterizing wind speed.Accurate estimation of Weibull parameters,the scale(c)and shape(k),is crucial in describing the actual wind speed data and evaluating the wind energy potential.Therefore,this study compares the most common conventional numerical(CN)estimation methods and the recent intelligent optimization algorithms(IOA)to show how precise estimation of c and k affects the wind energy resource assessments.In addition,this study conducts technical and economic feasibility studies for five sites in the northern part of Saudi Arabia,namely Aljouf,Rafha,Tabuk,Turaif,and Yanbo.Results exhibit that IOAs have better performance in attaining optimal Weibull parameters and provided an adequate description of the observed wind speed data.Also,with six wind turbine technologies rating between 1 and 3MW,the technical and economic assessment results reveal that the CN methods tend to overestimate the energy output and underestimate the cost of energy($/kWh)compared to the assessments by IOAs.The energy cost analyses show that Turaif is the windiest site,with an electricity cost of$0.016906/kWh.The highest wind energy output is obtained with the wind turbine having a rated power of 2.5 MW at all considered sites with electricity costs not exceeding$0.02739/kWh.Finally,the outcomes of this study exhibit the potential of wind energy in Saudi Arabia,and its environmental goals can be acquired by harvesting wind energy.

A Filtered Milne-Simpson ODE Method with Enhanced Stability Properties

The Milne-Simpson method is a two-step implicit linear multistep method for the numerical solution of ODEs that obtains the theoretically highest order of convergence for such a method. The stability region of the method is only an interval on the imaginary axis and the method is classified as weakly stable which causes non-physical oscillations to appear in numerical solutions. For this reason, the method is seldom used in applications. This work examines filtering techniques that improve the stability properties of the Milne-Simpson method while retaining its fourth-order convergence rate. The resulting filtered Milne-Simpson method is attractive as a method of lines integrator of linear time-dependent partial differential equations.

Projectile impact point prediction method based on GRNN

In order to forecast projectile impact points quickly and accurately,aprojectile impact point prediction method based on generalized regression neural network（GRNN）is presented.Firstly,the model of GRNN forecasting impact point is established;secondly,the particle swarm algorithm（PSD）is used to optimize the smooth factor in the prediction model and then the optimal GRNN impact point prediction model is obtained.Finally,the numerical simulation of this prediction model is carried out.Simulation results show that the maximum range error is no more than 40 m,and the lateral deviation error is less than0.2m.The average time of impact point prediction is 6.645 ms,which is 1 300.623 ms less than that of numerical integration method.Therefore,it is feasible and effective for the proposed method to forecast projectile impact points,and thus it can provide a theoretical reference for practical engineering applications.

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control.We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians.Additionally,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of dimensionality.Using existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial costs.We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can achieve.Our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

水下航行体湍流数值模拟方法研究进展综述

In this paper,we present an overview of numerical simulation methods for the flow around typical underwater vehicles at high Reynolds numbers,which highlights the dominant flow structures in different regions of interest.This overview covers the forebody,midbody,stern,wake region,and appendages and summarizes flow phenomena,including laminar-to-turbulent transition,turbulent boundary layers,flow under the influence of curvatures,wake interactions,and all associated complex vortex structures.Furthermore,the current issues and challenges of capturing these flow structures are addressed.This overview provides a deep insight into the use of numerical simulation methods,including the Reynolds-averaged Navier–Stokes(RANS)method,large eddy simulation(LES)method,and the hybrid RANS/LES method,and evaluates their applicability in capturing detailed flow features.

Multiparameter Numerical Investigation of Two Types of Moving Interactions Between the Deep-Sea Mining Vehicle Track Plate and Seabed Soil:Digging and Rotating Motions

To ensure the safe performance of deep-sea mining vehicles(DSMVs),it is necessary to study the mechanical characteristics of the interaction between the seabed soil and the track plate.The rotation and digging motions of the track plate are important links in the contact between the driving mechanism of the DSMV and seabed soil.In this study,a numerical simulation is conducted using the coupled Eulerian–Lagrangian(CEL)large deformation numerical method to investigate the interaction between the track plate of the DSMV and the seabed soil under two working conditions:rotating condition and digging condition.First,a soil numerical model is established based on the elastoplastic mechanical characterization using the basic physical and mechanical properties of the seabed soil obtained by in situ sampling.Subsequently,the soil disturbance mechanism and the dynamic mechanical response of the track plate under rotating and digging conditions are obtained through the analysis of the sensitivity of the motion parameters,the grouser structure,the layered soil features and the soil heterogeneity.The results indicate that the above parameters remarkably influence the interaction between the DSMV and the seabed soil.Therefore,it is important to consider the rotating and digging motion of the DSMV in practical engineering to develop a detailed optimization design of the track plate.

Numerical investigation of geostress influence on the grouting reinforcement effectiveness of tunnel surrounding rock mass in fault fracture zones

Grouting is a widely used approach to reinforce broken surrounding rock mass during the construction of underground tunnels in fault fracture zones,and its reinforcement effectiveness is highly affected by geostress.In this study,a numerical manifold method(NMM)based simulator has been developed to examine the impact of geostress conditions on grouting reinforcement during tunnel excavation.To develop this simulator,a detection technique for identifying slurry migration channels and an improved fluid-solid coupling(FeS)framework,which considers the influence of fracture properties and geostress states,is developed and incorporated into a zero-thickness cohesive element(ZE)based NMM(Co-NMM)for simulating tunnel excavation.Additionally,to simulate coagulation of injected slurry,a bonding repair algorithm is further proposed based on the ZE model.To verify the accuracy of the proposed simulator,a series of simulations about slurry migration in single fractures and fracture networks are numerically reproduced,and the results align well with analytical and laboratory test results.Furthermore,these numerical results show that neglecting the influence of geostress condition can lead to a serious over-estimation of slurry migration range and reinforcement effectiveness.After validations,a series of simulations about tunnel grouting reinforcement and tunnel excavation in fault fracture zones with varying fracture densities under different geostress conditions are conducted.Based on these simula-tions,the influence of geostress conditions and the optimization of grouting schemes are discussed.

Feedback of Efficient Shock Acceleration on Magnetic-field Structure Inside Young Type Ia Supernova Remnants

Using an effective adiabatic index γ_(eff) to mimic the feedback of efficient shock acceleration,we simulate the temporal evolution of a young type Ia supernova remnant (SNR) with two different background magnetic field(BMF) topologies:a uniform and a turbulent BMF.The density distribution and magnetic-field characteristics of our benchmark SNR are studied with two-dimensional cylindrical magnetohydrodynamic simulations.When γ_(eff)is considered,we find that:(1) the two-shock structure shrinks and the downstream magnetic-field orientation is dominated by the Rayleigh–Taylor instability structures;(2) there exists more quasi-radial magnetic fields inside the shocked region;and (3) inside the intershock region,both the quasi-radial magnetic energy density and the total magnetic energy density are enhanced:in the radial direction,with γ_(eff)=1.1,they are amplified about 10–26 times more than those with γ_(eff)=5/3.While in the angular direction,the total magnetic energy densities could be amplified about 350 times more than those with γ_(eff)=5/3,and there are more grid cells within the intershock region where the magnetic energy density is amplified by a factor greater than 100.

Disturbance Observer-based Pointing Control of Leighton Chajnantor Telescope

Leighton Chajnantor Telescope(LCT), i.e., the former Caltech Submillimeter Observatory telescope, will be refurbished at the new site in Chajnantor Plateau, Chile in 2023. The environment of LCT will change significantly after its relocation, and the telescope will be exposed to large wind disturbances directly because its enclosure will be completely open during observation. The wind disturbance is expected to be a challenge for LCT's pointing control since the existing control method cannot reject this disturbance very well. Therefore, it is very necessary to develop a new pointing control method with good capability of disturbance rejection. In this research, a disturbance observer—based composite position controller(DOB-CPC) is designed, in which an H∞feedback controller is employed to compress the disturbance, and a feedforward linear quadratic regulator is employed to compensate the disturbance precisely based on the estimated disturbance signal. Moreover, a controller switching policy is adopted, which applies the proportional controller to the transient process to achieve a quick response and applies the DOB-CPC to the steady state to achieve a small position error. Numerical experiments are conducted to verify the good performance of the proposed pointing controller(i.e., DOB-CPC) for rejecting the disturbance acting on LCT.

Accelerating Asteroidal Period and Pole Inversion from Multiple Lightcurves Using Parallel Differential Evolution and Cellinoid Shape Model

Determining asteroid properties provides valuable physical insights but inverting them from photometric lightcurves remains computationally intensive.This paper presents a new approach that combines a simplified Cellinoid shape model with the Parallel Differential Evolution(PDE)algorithm to accelerate inversion.The PDE algorithm is more efficient than the Differential Evolution algorithm,achieving an extraordinary speedup of 37.983 with 64 workers on multicore CPUs.The PDE algorithm accurately derives period and pole values from simulated data.The analysis of real asteroid lightcurves validates the method’s reliability:in comparison with results published elsewhere,the PDE algorithm accurately recovers the rotational periods and,given adequate viewing geometries,closely matches the pole orientations.The PDE approach converges to solutions within 20,000 iterations and under one hour,demonstrating its potential for large-scale data analysis.This work provides a promising new tool for unveiling asteroid physical properties by overcoming key computational bottlenecks.

Optical Transient Source AT2021lfa:A Possible“Dirty Fireball”

AT2021lfa,also known as ZTF21aayokph,was detected by the Zwicky Transient Facility on 2021 May 4,a 05:34:48 UTC.Follow-up observations were conducted using a range of ground-based optical telescopes,as wel as Swift/XRT and VLA instruments.AT2021lfa is classified as an“orphan afterglow”candidate due to its rapid flux decline and its reddened color(g-r=0.17±0.14 mag).For an optical transient source without promp gamma-ray detection,one key point is to determine its burst time.Here we measure the burst time through fitting the initial bump feature of AT2021lfa and obtain its burst time as 2021 May 3,at 22:09:50 UTC.Using afterglowpy,we model the multi-band afterglow of AT2021lfa and find that the standard model canno reproduce the late radio observations well.Considering that the microphysical parameters ε_(e),ε_(B)(the energy fraction given to electrons and magnetic field),andξN(the fraction of accelerated electrons)may vary with time we then model the afterglow of AT2021lfa taking into account the temporal evolution of the physical parameters ε_(e),ε^(B),and ξ_(N) and find in this case the multi-wavelength observations can be reproduced well.The initial Lorentz factor of AT2021lfa can be estimated from the peak time of the early afterglow,which yields a value of about 18 suggesting that AT2021lfa should be classified as a“dirty fireball.”From the upper limit for the prompt emission energy of AT2021lfa,we obtain that the radiation efficiency is less than 0.02%,which is much smaller than that of ordinary gamma-ray bursts(GRBs).It is also interesting that the fitted values of jet angle and viewing angle are very large,θ_(c)~0.66 rad,θ_(v)~0.53 rad,which may lead to the low Lorentz factor and radiation efficiency.When compared with GRB afterglow samples,it is evident that the onset bump timescale of AT2021lfa satisfies the empirical relationships observed in GRB samples.Additionally,the luminosity of AT2021lfa falls within the range of observations for GRB samples;however,approximately 1 day after the burst,its luminosity exceeds that of the majority of GRB samples.

Influence of Temperature-Dependent Thermophysical Properties of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra-Hybrid Nanofluid along a Vertical Porous Surface with Suction

The significance of the thermophysical properties of Tetra hybrid nanofluid in enhancing heat transmission in various applications like heat exchangers, automobiles, and solar storage cannot be overstated. These features can be tampered with when nanoparticles are been introduced into the base fluid to produce an improved heat carrier fluid for the system. This study investigates the impact of temperature-dependent properties on the movement of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra hybrid nanofluid along a vertical porous surface with suction. The system of governing Partial Differential Equations (PDEs) was formulated and transformed into the system of coupled nonlinear third-order Ordinary Differential Equations (ODEs) by similarity techniques. The resulting ODEs were solved numerically using the shooting method and fourth order Runge-Kutta method with the aid of Maple 18.0 software. Using numerical and statistical methods, the study analyzes velocity, temperature profiles, skin friction coefficient, and Nusselt number. It was found that as the variable thermal conductivity parameter upsurges both the skin friction coefficient and Nusselt number intensify at the rate of 0.011697519 and 8.043581616 respectively. This study underscores the vital role of Tetra hybrid nanofluid’s thermophysical properties in improving heat transmission for diverse appli cations. By manipulating nanoparticles within the base fluid, the heat carrier fluid’s efficiency can be enhanced, critical for industries like automotive and enewable energy. These insights inform the design of more efficient heat exchange systems, advancing sustainability and performance in real-world scenarios.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

FORMULATIONS OF THE THREE-DIMENSIONAL DISCONTINUOUS DEFORMATION ANALYSIS METHOD

This paper extends the original 2D discontinuous deformation analysis(DDA)method proposed by Shi to 3D cases,and presents the formulations of the 3D DDA.The formulations maintain the characteristics of the original 2D DDA approach.Contacts between the blocks are detected by using Common-Plane (C-P) approach and the non-smooth contact,such as of vertex-to-vertex,vertex- to-edge and edge-to-edge types,can be handled easily based on the C-P method.The matrices of equilibrium equations have been given in detail for programming purposes.The C program codes for the 3D DDA are developed.The ability and accuracy of the formulations and the program are verified by the analytical solutions of several dynamic examples.The robustness and versatility of the algorithms presented in this paper are demonstrated with the aid of an example of scattering of densely packed cubes.Finally,implications and future extensions are discussed.