A new model of flow over stretching(shrinking)and porous sheet with its numerical solutions

The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.

Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems

To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.

Analysis of debris flow control effect and hazard assessment in Xinqiao Gully,Wenchuan M_(s)8.0 earthquake area based on numerical simulation

Xinqiao Gully is located in the area of the 2008 Wenchuan M_(s)8.0 earthquake in Sichuan province,China.Based on the investigation of the 2023"6-26"Xinqiao Gully debris flow event,this study assessed the effectiveness of the debris flow control project and evaluated the debris flow hazards.Through field investigation and numerical simulation methods,the indicators of flow intensity reduction rate and storage capacity fullness were proposed to quantify the effectiveness of the engineering measures in the debris flow event.The simulation results show that the debris flow control project reduced the flow intensity by41.05%to 64.61%.The storage capacity of the dam decreases gradually from upstream to the mouth of the gully,thus effectively intercepting and controlling the debris flow.By evaluating the debris flow of different recurrence intervals,further measures are recommended for managing debris flow events.

改变导叶翼型对水泵水轮机“S”特性的影响

针对水泵水轮机“S”特性区域的不稳定性问题,提出使用改型活动导叶翼型进行性能提升.以某水泵水轮机模型为研究对象,采用SST k-ω湍流模型对水泵水轮机全流道进行三维数值计算,通过对活动导叶翼型的改型设计,得出流量-转速模拟曲线,分析水泵水轮机组“S”特性改善情况.将计算与试验结果进行对比,并对改型活动导叶翼型前后机组的无叶区进行压力脉动分析.结果表明:在保证整体效率依然保持在92%附近的前提下,新的活动导叶翼型对机组的“S”特性依旧具有改善效果;无叶区压力脉动主要是受到活动导叶叶栅区域的分流在此重新聚集影响,并且与转轮叶片的动静相互扰动引起的;改型后的活动导叶降低了无叶区的压力脉动幅值,提升了水泵水轮机运行中的并网稳定性.

宽负荷下切圆燃煤锅炉H_(2)S分布特性的数值模拟

锅炉采用空气分级燃烧降低NO_(x)排放的同时也提高了主燃区H_(2)S体积分数。炉墙壁面过高的H_(2)S体积分数是加剧水冷壁高温腐蚀的重要因素。为保障新能源并网发电,大型燃煤机组灵活调峰的需求增加,不同负荷下的水冷壁近壁面H_(2)S分布特性值得关注。通过正交试验分析了切圆燃煤锅炉运行参数对水冷壁近壁面H_(2)S体积分数分布的影响。选取一台超临界600 MW切圆燃煤锅炉建立数值模型,设计L_(16)(4^(5))正交工况,覆盖100%BMCR、75%THA,50%THA以及35%BMCR四种负荷。建立了自定义SO_(x)生成模型以确定燃料硫的析出和转化路径,模型包含多表面反应子模型以描述焦炭与O_(2)/CO_(2)/H_(2)O等3种气体的异相反应,并确定焦炭气化反应消耗量占总消耗量的比例,进而对炉膛H_(2)S空间分布进行了模拟计算。研究表明,近壁面高体积分数H_(2)S区域主要位于投运燃烧器层中最下层燃烧器以下以及最上层燃烧器以上至SOFA层之间,烟气切圆沿炉膛高度增加逐渐增大是造成后一区域H_(2)S体积分数较高的重要原因。35%BMCR负荷下水冷壁重点区域的H_(2)S平均体积分数为364μL/L,明显低于其他负荷。锅炉运行参数对重点区域H_(2)S体积分数影响程度的排序为:锅炉负荷>一次风率>主燃区空气过量系数>假想切圆直径>燃烧器竖直摆角。

2022年四川芦山M_(S)6.1地震前应力状态研究

为研究2022年6月1日四川芦山M_(S)6.1地震的孕育和发生过程,采用CAP方法反演了2013年芦山M_(S)7.0主震及M_(S)≥5.0余震的震源机制解,并基于应力张量方差与b值时空分布特征,探讨了芦山M_(S)6.1地震的力学机制和震源区的应力状态。结果表明:2022年芦山M_(S)6.1地震震源机制表现出与2013年芦山M_(S)7.0主震和5级余震相似的逆冲型破裂特征,压应力轴方位与龙门山断裂带南段区域应力场一致。2013年芦山M_(S)7.0地震后震中及附近的应力张量方差和b值长期处于低值状态,2022年芦山M_(S)6.1地震前震中及附近出现了应力张量方差和b值的低值异常,表明芦山余震区处于较高的应力水平。分析认为:巴颜喀拉块体持续东向运动受到华南块体的阻挡,震中所在区域长期受挤压逆冲作用,从而使芦山余震区长期处于应力积累的状态,芦山M_(S)6.1地震也是在这种动力学背景下发生的。

A Study of Traveling Wave Structures and Numerical Investigation of Two-Dimensional Riemann Problems with Their Stability and Accuracy

The Riemann wave system has a fundamental role in describing waves in various nonlinear natural phenomena,for instance,tsunamis in the oceans.This paper focuses on executing the generalized exponential rational function approach and some numerical methods to obtain a distinct range of traveling wave structures and numerical results of the two-dimensional Riemann problems.The stability of obtained traveling wave solutions is analyzed by satisfying the constraint conditions of the Hamiltonian system.Numerical simulations are investigated via the finite difference method to verify the accuracy of the obtained results.To extract the approximation solutions to the underlying problem,some ODE solvers in FORTRAN software are applied,and outcomes are shown graphically.The stability and accuracy of the numerical schemes using Fourier’s stabilitymethod and error analysis,respectively,to increase the reassurance are investigated.A comparison between the analytical and numerical results is obtained and graphically provided.The proposed methods are effective and practical to be applied for solving more partial differential equations(PDEs).

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

NUMERICAL SOLUTIONS OF DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR GENERAL ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER

In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.

Numerical solutions to heat transfer of nanofluid flow over stretching sheet subjected to variations of nanoparticle volume fraction and wall temperature

The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.

New Soliton Wave Solutions to a Nonlinear Equation Arising in Plasma Physics

The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics,physics,and engineering disciplines.This article intends to analyze several traveling wave solutions for themodified regularized long-wave(MRLW)equation using several approaches,namely,the generalized algebraic method,the Jacobian elliptic functions technique,and the improved Q-expansion strategy.We successfully obtain analytical solutions consisting of rational,trigonometric,and hyperbolic structures.The adaptive moving mesh technique is applied to approximate the numerical solution of the proposed equation.The adaptive moving mesh method evenly distributes the points on the high error areas.This method perfectly and strongly reduces the error.We compare the constructed exact and numerical results to ensure the reliability and validity of the methods used.To better understand the considered equation’s physical meaning,we present some 2D and 3D figures.The exact and numerical approaches are efficient,powerful,and versatile for establishing novel bright,dark,bell-kink-type,and periodic traveling wave solutions for nonlinear PDEs.

On numerical stationary distribution of overdamped Langevin equation in harmonic system

Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.

A Review and Update of Analytical and Numerical Solutions of the Terzaghi One-Dimensional Consolidation Equation

Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.

双S弯进气道锤激波动态特性研究

发动机喘振产生的瞬时高压引起的进气道内锤激波载荷是飞机进气道结构强度设计的关键因素之一。通过对飞行器进行内外流一体化非定常三维数值计算,分析双S弯进气道内锤激波三维流场非定常特性的演化过程,研究了不同马赫数,不同超压比对双S弯进气道锤激波载荷的影响。研究表明:锤激波经过进气道弯道时,弯道外侧流场压力远大于内侧;锤激波离开进气道入口后,进气道内流场经过数个周期逐渐恢复至初始状态;相同进气道反压时,来流马赫数越小,锤激波在进气道内部传播速度越快,且进气道内部压力系数峰值越大;相同来流马赫数下,随着超压比的增大,锤激波在进气道内部传播速度加快,进气道内部压力系数峰值增大。

Numerical simulation of the sensor output on Macao Science Satellite-1

Macao Science Satellite-1(MSS-1)will be launched at the early of 2023 into a near-circular orbit.The mission is designed to measure the Earth’s geomagnetic field with unpreceded accuracy through a new perspective.The most important component installed on the satellite,to ensure high accuracy,is the deployable boom(Optical Bench).A Vector Field Magnetometer(VFM),an Advanced Stellar Compass(ASC),and a Couple Dark State Magnetometers(CDSM)are deployed on the deployable boom.In order to maximize the mission’s scientific output,a numerical simulator on MSS-1’s deployable boom was required to evaluate the adaptability of all devices on the deployable boom and assist the satellite’s data pre-processing.This paper first briefly describes the synthesis of the Earth’s total magnetic field and then describes the method simulating the output of scalar and vector magnetometers.Finally,the calibration method is applied to the synthetic magnetometer data to analyze the possible noise/error of the relevant instruments.Our results show that the simulator can imitate the disturbance of different noise sources or errors in the measuring system,and is especially useful for the satellite’s data processing group.

The Numerical Solutions of Systems of Nonlinear Integral Equations with the Spline Functions

The main goal of this work is to develop an effective technique for solving nonlinear systems of Volterra integral equations. The main tools are the cardinal spline functions on small compact supports. We solve a system of algebra equations to approximate the solution of the system of integral equations. Since the matrix for the algebraic system is nearly triangular, It is relatively painless to solve for the unknowns and an approximation of the original solution with high precision is accomplished. In order to enhance the accuracy, several cardinal splines are employed in the paper. Our schemes were compared with other techniques proposed in recent papers and the advantage of our method was exhibited with several numerical examples.

多因素影响下的S型管道冲刷腐蚀速率分析

S型管道应用于输运过程中的复杂地形,在上下游弯头处,会形成不同程度的冲刷腐蚀,造成安全隐患。为分析其腐蚀影响因素,建立S型管道腐蚀模型,采用ANSYS的Workbench平台搭建Fluent模块对不同影响因素下的腐蚀模型进行研究,创建数据传输,进而研究流体在流入弯管后各因素与冲蚀速率的关系。结果表明,S型管道冲刷腐蚀受到多因素的影响,尤其是下游弯头处的冲刷腐蚀更为明显。适当减小颗粒物直径、颗粒物质量流量,增大管径和弯径比可以减缓腐蚀及减小腐蚀区域。研究可为管道安全稳定运行提供理论依据。

Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches

In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.