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.

Effects of Numerical Methods on the Calculation of Developing Plane Channel Flow

In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.

SOME DEVELOPMENTS IN VISCOUS FLUID DYNAMICS AND ITS NUMERICAL METHODS

Viscous fluid flows contain abundant "physical phenomena and the viscous fluid dynamics is of wide applications in the fields of natural and engineering sciences. After the basic equations of viscousfluiddynamics (i.e., the Navier-Stokes equations) came out, one of the most important contributions to the discipline was the boundary layer (BL) theory and the BL equations presented by Prandtl

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.

Stability analysis of slopes with planar failure using variational calculus and numerical methods

This study investigates the technique of variational calculus applied to estimate the slope stability considering the mechanism of planar failure.The critical plane failure surface should be determined because it theoretically indicates the most unfavorable plane to be considered when stabilizing a slope to rectify the instability generated by several statistically possible planes.This generates integrals that can be solved by numerical methods,such as the Newton Cotes and the finite differences methods.Additionally,a system of nonlinear equations is obtained and solved.The surface of the critical planar failure is determined by applying the condition of transversality in mobile boundaries,for which various examples are provided.The number of slices is varied in one of the examples,while the surface of the critical planar failure is determined in the others.Results are compared using analytical methods through axis rotations.All the results obtained by considering normal stress,safety factors,and critical planar failure are nearly the same;however,in this research,a study is carried out for“n”number of slices using programming methods.Sub-routines are important because they can be applied in slopes with different geometry,surcharge,interstitial pressure,and pseudo-static load.

Recent Progress in Numerical Methods for the Poisson-Boltzmann Equation in Biophysical Applications

Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics.Recent developments in boundary element methods,interface methods,adaptive methods,finite element methods,and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed.We also discussed the challenging problems and possible future work,in particular,for the aim of biophysical applications.

Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

The human immunodeficiency viruses are two species of Lentivirus that infect humans.Over time,they cause acquired immunodeficiency syndrome,a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive.Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa.Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s.Over decades,human immunodeficiency viruses slowly spread across Africa and later into other parts of the world.The Susceptible-Infected-Recovered(SIR)models are significant in studying disease dynamics.In this paper,we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods.Euler,Runge Kutta,and a Non-standardfinite difference(NSFD)method are developed for the same problem.Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes‘ℎ’.The results reveal that,unlike Euler and Runge Kutta,which fail for large time step sizes,the proposed Non-standardfinite difference(NSFD)method gives a convergence solution for any time step size.Our proposed numerical method is bounded,dynamically con-sistent,and preserves the positivity of the continuous solution,which are essential requirements when modeling a prevalent disease.

Numerical Simulation of Saint-Venant Equations with Thermal Energy Dependency: Applications on Global Warming

Since the Industrial Revolution, humanity has been intensifying the burning of fossil fuels and as a consequence, the average temperature on Earth has been increasing. The 20th century was the warmest and future prospects are not favorable, that is, even higher temperatures are expected. This demonstrates the importance of studies on the subject, mainly to predict possible environmental, social and economic consequences. The objective of this work was to identify the interference of the increase in ambient temperature in the dynamics of fluids, such as ocean waves advancing over the continent. For this, thermal energy was considered in the Saint-Venant equations and computational implementations were performed via Lax-Friedrichs and Adams-Moulton methods. The results indicated that, in fact, depending on the amount of thermal energy transferred to the fluid, the advance of water towards the continent can occur, even in places where such a phenomenon has never been observed.

Theoretical and numerical studies of rock breaking mechanism by double disc cutters

A plane mechanical model of rock breaking process by double disc cutter at the center of the cutterhead is established based on contact mechanics to analyze the stress evolution in the rock broken by cutters with different spacings. A continuous-discontinuous coupling numerical method based on zero-thickness cohesive elements is developed to simulate rock breaking using double cutters. The process, mechanism,and characteristics of rock breaking are comprehensively analyzed from five aspects: peak force, breaking form, breaking efficiency, crack mode, and breaking degree. The results show that under the penetrating action of cutters, dense cores are formed due to shear failure under respective cutters. The tensile cracks propagate in the rock, and then rock chips form with increasing penetration depth. When the cutter spacing is increased from 10 to 80 mm, the peak force gradually increases, the rock breaking range increases first and then decreases, the specific energy decreases first and then rises, and the breaking coefficient of intermediate rock decreases from 0.955 to 0.788. The area of rock breaking is positively correlated with the length of the tensile crack. Furthermore, the length of the tensile crack accounts for 14.4%–33.6% of the total crack length.

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific problems.Important research and expository papers devoted to the numerical solution of mathematical problems arising in all areas of science and technology are expected.The journal originates from the journal Numerical Mathematics:A Journal of Chinese Universities (English Edition).

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications(NM-TMA) publishes high-quality original

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.

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.

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.

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.

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.

A two scaled numerical method for global analysis of high dimensional nonlinear systems

This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.

An Effective Numerical Method for the Solution of a Stochastic Coronavirus(2019-nCovid)Pandemic Model

Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are fundamental properties of stochastic modeling.A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation.Well-known explicit methods such as Euler Maruyama,stochastic Euler,and stochastic Runge–Kutta are investigated for the stochastic model.Regrettably,the above essential properties are not restored by existing methods.Hence,there is a need to construct essential properties preserving the computational method.The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model.The comparison of the results of deterministic and stochastic models is also presented.Our proposed efficient computational method well preserves the essential properties of the model.Comparison and convergence analyses of the method are presented.

2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation.The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conventional NMM.The stiffness matrix of the new element is well-conditioned.The proposed method is applied for the numerical example of thin plate bending.Based on the principle of minimum potential energy, the manifold matrices and equilibrium equation are deduced.Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.