A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

Multiply accumulate operations in memristor crossbar arrays for analog computing

Memristors are now becoming a prominent candidate to serve as the building blocks of non-von Neumann inmemory computing architectures.By mapping analog numerical matrices into memristor crossbar arrays,efficient multiply accumulate operations can be performed in a massively parallel fashion using the physics mechanisms of Ohm’s law and Kirchhoff’s law.In this brief review,we present the recent progress in two niche applications:neural network accelerators and numerical computing units,mainly focusing on the advances in hardware demonstrations.The former one is regarded as soft computing since it can tolerant some degree of the device and array imperfections.The acceleration of multiple layer perceptrons,convolutional neural networks,generative adversarial networks,and long short-term memory neural networks are described.The latter one is hard computing because the solving of numerical problems requires high-precision devices.Several breakthroughs in memristive equation solvers with improved computation accuracies are highlighted.Besides,other nonvolatile devices with the capability of analog computing are also briefly introduced.Finally,we conclude the review with discussions on the challenges and opportunities for future research toward realizing memristive analog computing machines.

Sheltering effect of punched steel plate sand fences for controlling blown sand hazards along the Golmud-Korla Railway:Field observation and numerical simulation studies

Sand fences made of punched steel plate(PSP)have recently been applied to control wind-blown sand in desertified and Gobi areas due to their strong wind resistance and convenient in situ construction.However,few studies have assessed the protective effect of PSP sand fences,especially through field observations.This study analyzes the effects of double-row PSP sand fences on wind and sand resistance using field observations and a computational fluid dynamics(CFD)numerical simulation.The results of field observations showed that the average windproof efficiencies of the first-row and second-row sand fences were 79.8%and 70.8%,respectively.Moreover,the average windproof efficiencies of the numerical simulation behind the first-row and second-row sand fences were 89.8%and 81.1%,respectively.The sand-resistance efficiency of the double-row PSP sand fences was 65.4%.Sand deposition occurred close to the first-row sand fence;however,there was relatively little sand on the leeward side of the second-row sand fence.The length of sand accumulation near PSP sand fences obtained by numerical simulation was basically consistent with that through field observations,indicating that field observations combined with numerical simulation can provide insight into the complex wind-blown sand field over PSP sand fences.This study indicates that the protection efficiency of the double-row PSP sand fences is sufficient for effective control of sand hazards associated with extremely strong wind in the Gobi areas.The output of this work is expected to improve the future application of PSP sand fences.

Numerical Computation in Airflow Field of Compact Spinning with Pneumatic Groove

In compact spinning with pneumatic groove,the computational fluid dynamic model,computed with parallel technologies & Fluent 6.3,is developed to simulate the flow field in condensing zone with 3D computational fluid dynamic (CFD) technology.Flowing state,distribution rules of static pressure,and velocity in condensing zone are characterized and analyzed.The results show that the fiber bundle in compact spinning with pneumatic groove is compacted by airflow and the shape of the pneumatic groove,and the static pressure in condensing zone is negative,as well as the velocity of airflow in condensing zone is not zero.The fluctuation frequencies of the static pressure and velocity near the bottom of the pneumatic groove are relatively higher,and the number of the fluctuation is equal to that of the round holes in condensing zone.

Ultrasonic prediction of crack density using machine learning:A numerical investigation

Cracks are accounted as the most destructive discontinuity in rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems. The most well-known mechanical parameter for such an evaluation is wave velocity through which one can qualitatively or quantitatively characterize the porous media. In small scales, such information is obtained using the ultrasonic pulse velocity(UPV) technique as a non-destructive test. In large-scale geo-systems, however, it is inverted from seismic data. In this paper, we take advantage of the recent advancements in machine learning(ML) for analyzing wave signals and predict rock properties such as crack density(CD) – the number of cracks per unit volume. To this end, we designed numerical models with different CDs and, using the rotated staggered finite-difference grid(RSG) technique, simulated wave propagation. Two ML networks, namely Convolutional Neural Networks(CNN) and Long Short-Term Memory(LSTM), are then used to predict CD values. Results show that, by selecting an optimum value for wavelength to crack length ratio, the accuracy of predictions of test data can reach R2> 96% with mean square error(MSE) < 25e-4(normalized values). Overall, we found that:(i) performance of both CNN and LSTM is highly promising,(ii) accuracy of the transmitted signals is slightly higher than the reflected signals,(iii) accuracy of 2D signals is marginally higher than 1D signals,(iv)accuracy of horizontal and vertical component signals are comparable,(v) accuracy of coda signals is less when the whole signals are used. Our results, thus, reveal that the ML methods can provide rapid solutions and estimations for crack density, without the necessity of further modeling.

Wind Tunnel Test and Numerical Computation on Ice Accretion on Blade Airfoil for Straight-bladed VAWT

To invest the condition of ice accretion on the blade used for straight-bladed vertical axis wind turbine (SB-VAWT), wind tunnel tests were carried out on a blade with NACA0015 airfoil by using a small simple icing wind tunnel. Tests were carried out at some typical attack angles under different wind speeds and flow discharges of a water spray with wind. The icing shape and area on blade surface were recorded and measured. Then the numerical computation was carried out to calculate the lift and drag coefficients of the blade before and after ice accretion according to the experiment result, the effect of icing on the aerodynamic characteristics of blade were discussed.

Design of a Computational Heuristic to Solve the Nonlinear Liénard Differential Model

In this study,the design of a computational heuristic based on the nonlinear Liénard model is presented using the efficiency of artificial neural networks(ANNs)along with the hybridization procedures of global and local search approaches.The global search genetic algorithm(GA)and local search sequential quadratic programming scheme(SQPS)are implemented to solve the nonlinear Liénard model.An objective function using the differential model and boundary conditions is designed and optimized by the hybrid computing strength of the GA-SQPS.The motivation of the ANN procedures along with GA-SQPS comes to present reliable,feasible and precise frameworks to tackle stiff and highly nonlinear differentialmodels.The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models.The achieved numerical outcomes on multiple trials using the designed procedures are compared to authenticate the correctness,viability and efficacy.Moreover,statistical performances based on different measures are also provided to check the reliability of the ANN along with GASQPS.

A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH

The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

Swarming Computational Approach for the Heartbeat Van Der Pol Nonlinear System

The present study is related to design a stochastic framework for the numerical treatment of the Van der Pol heartbeat model(VP-HBM)using the feedforward artificial neural networks(ANNs)under the optimization of particle swarm optimization(PSO)hybridized with the active-set algorithm(ASA),i.e.,ANNs-PSO-ASA.The global search PSO scheme and local refinement of ASA are used as an optimization procedure in this study.An error-based merit function is defined using the differential VP-HBM form as well as the initial conditions.The optimization of the merit function is accomplished using the hybrid computing performances of PSO-ASA.The designed performance of ANNs-PSO-ASA is implemented for the numerical treatment of the VP-HBM dynamics by fluctuating the pulse shape adjustment terms,external forcing factor and damping coefficient with fixed ventricular contraction period.To perform the correctness of the present scheme,the obtained numerical results through the designed ANN-PSO-ASA will be compared with the Adams numerical method.The statistical investigations with larger dataset are provided using the“mean absolute deviation”,“Theil’s inequality coefficient”and“variance account for”operators to perform the applicability,reliability,and effectiveness of the designed ANNs-PSO-ASA scheme for solving the VP-HBM.

Numerical study on morphological characteristics of rotational natural supercavitation by rotational supercavitating evaporator with optimized blade shape

In view of the supercavitation effect, a novel device named the rotational supercavitating evaporator (RSCE) has been designed for the desalination. In order to improve the blade shape of the rotational cavitator in the RSCE for the performance optimization, the blade shapes of different sizes are designed by utilizing the improved calculation method for the blade shape and the validated empirical formulae based on previous two-dimensional numerical simulations, from which the optimized blade shape with the wedge angle of 45° and the design speed of 5 000 r/min is selected. The estimation method for the desalination performance parameters is developed to validate the feasibility of the utilization of the results obtained by the two-dimensional numerical simulations in the design of the three-dimensional blade shape. Three-dimensional numerical simulations are then conducted for the supercavitating flows around the rotational cavitator with the optimized blade shape at different rotational speeds to obtain the morphological characteristics of the rotational natural supercavitation. The results show that the profile of the supercavity tail is concaved toward the inside of the supercavity due to the re-entrant jet. The empirical formulae for estimating the supercavity size with consideration of the rotation are obtained by fitting the data, with the exponents different from those obtained by the previous two-dimensional numerical simulations. The influences of the rotation on the morphological characteristics are analyzed from the perspectives of the tip and hub vortices and the interaction between the supercavity tail and the blade. Further numerical simulation of the supercavitating flow around the rotational cavitator made up by the blades with exit edge of uniform thickness illustrate that the morphological characteristics are also affected by the blade shape.

A computing capability test for a switched system control design using the Haris-Rogers method

The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these systems.Many solutions have been proposed,most of which are based on finding the existence of a common Lyapunov function(CLF) or a multiple Lyapunov function(MLF) where the key is to formulate the problem into a set of linear matrix inequalities(LMIs).An alternative method for finding the existence of a CLF by solving two sets of linear inequalities(LIs) has previously been presented.This method is seen to be less computationally taxing compared to methods based on solving LMIs.To substantiate this,the computational ability of three numerical computational solvers,LMI solver,cvx,and Yalmip,as well as the symbolic computational program Maple were tested.A specific switched system comprising four second-order subsystems was used as a test case.From the obtained solutions,the validity of the controllers and the corresponding CLF was verified.It was found that all tested solvers were able to correctly solve the LIs.The issue of rounding-off error in numerical computation based software is discussed in detail.The test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal precision.The use of different external solvers led to the same conclusion in terms of the stability of switched systems.As a result,a shift from using a conventional numerical computation based program to using computer algebra is suggested.

Analysis of threshed rice mixture separation through vibration screen using discrete element method

The discrete element method was utilized to construct three-dimensional discrete element models for the rice mixture,and their motions were analyzed numerically on a planar vibration screening device.The results showed that,after falling onto the vibrating screen surface,the mixture undergoes a reciprocating motion within the same cycle.During the screening process,the mixture undergoes segregation,slides along the screen surface,passes through the screen and then falls.In comparing the movement of grains and shriveled grains,it can be seen that the velocity of shriveled grains experiences cyclical changes,which is consistent with the grains’motion cycle.The impact on grains is shown to be greater than that on shriveled grains,and the average speeds of shriveled grains and grains converge.The curve shows that the screening of repetitive movements has a significant effect on the average velocity of shriveled grains,but also the velocity of shriveled grains and the vibration parameters can be well represented by a fitting equation.It is beneficial for the separation of grains from shriveled grains to choose a greater vibration frequency and screen surface inclination in the range of commonly used.

The effects of caudal fin deformation on the hydrodynamics of thunniform swimming under self-propulsion

To investigate the effects of the caudal fin deformation on the hydrodynamic performance of the self-propelled thunniform swimming,we perform fluid-body interaction simulations for a tuna-like swimmer with thunniform kinematics.The 3-D vortices are visualized to reveal the role of the leading-edge vortex(LEV)in the thrust generation.By comparing the swimming velocity of the swimmer with different caudal fin flexure amplitudes fa,it is shown that the acceleration in the starting stage of the swimmer increases with the increase of fa,but its cruising velocity decreases.The results indicate that the caudal fin deformation is beneficial to the fast start but not to the fast cruising of the swimmer.During the entire swimming process,the undulation amplitudes of the lateral velocity and the yawing angular velocity decrease as fa increases.It is found that the formation of an attached LEV on the caudal fin is responsible for generating the low-pressure region on the surface of the caudal fin,which contributes to the thrust.Furthermore,the caudal fin deformation can delay the LEV shedding from the caudal fin,extending the duration of the low pressure on the caudal fin,which will cause the caudal fin to generate a drag-type force over a time period in one swimming cycle and reduce the cruising speed of the swimmer.

Foundations bearing capacity subjected to seepage by the kinematic approach of the limit analysis

An estimate of the ultimate load on foundations on soil layers subject to groundwater flow has been presented.The kinematic approach of the limit analysis was employed to find the upper-bound limit of the bearing capacity.Both smooth and rough base strip foundations were considered associated with different collapse patterns.Presence of the groundwater flow leads to a non-symmetric collapse pattern,i.e.,a weak side and a strong side in twosided collapse patterns,depending on the direction of the flow.It was found that the bearing capacity has a decreasing trend with increase in the groundwater flow gradient and hence,a reduction factor has been introduced to the third term in the bearing capacity equation as a function of the flow gradient.

A Note on the GMRES Method for Linear Discrete Ill-Posed Problems

In this paper,we are presenting a proposal for new modified algorithms for RRGMRES and AGMRES.It is known that RRGMRES and AGMRES are viable methods for solving linear discrete ill-posed problems.In this paper we have focused on the residual norm and have come-up with two improvements where successive updates and the stabilization of decreases for the residual norm improve performance respectively.Our numerical experiments confirm that our improved algorithms are effective for linear discrete ill-posed problems.