Bo Tang, Xuemin Wang, Leilei Wei and Xindong Zhang
This paper aims to apply fractional variational iteration method using He's polynomials (FVIMHP) to obtain exact solutions for variable-coefficient fractional heat-like and…
Abstract
Purpose
This paper aims to apply fractional variational iteration method using He's polynomials (FVIMHP) to obtain exact solutions for variable-coefficient fractional heat-like and wave-like equations with fractional order initial and boundary conditions.
Design/methodology/approach
The approach is based on FVIMHP. The authors choose as some examples to illustrate the validity and the advantages of the method.
Findings
The results reveal that the FVIMHP method provides a very effective, convenient and powerful mathematical tool for solving fractional differential equations.
Originality/value
The variable-coefficient fractional heat-like and wave-like equations with fractional order initial and boundary conditions are solved first. Illustrative examples are included to demonstrate the validity and applicability of the method.
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Leilei Wei, Xindong Zhang and Yinnian He
The purpose of this paper is to develop a fully discrete local discontinuous Galerkin (LDG) finite element method for solving a time‐fractional advection‐diffusion equation.
Abstract
Purpose
The purpose of this paper is to develop a fully discrete local discontinuous Galerkin (LDG) finite element method for solving a time‐fractional advection‐diffusion equation.
Design/methodology/approach
The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space.
Findings
By choosing the numerical fluxes carefully the authors' scheme is proved to be unconditionally stable and gets L2 error estimates of O(hk+1+(Δt)2+(Δt)α/2hk+(1/2)). Finally Numerical examples are performed to illustrate the effectiveness and the accuracy of the method.
Originality/value
The proposed method is different from the traditional LDG method, which discretes an equation in spatial direction and couples an ordinary differential equation (ODE) solver, such as Runger‐Kutta method. This fully discrete scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. Numerical examples prove that the authors' method is very effective. The present paper is the authors' first step towards an effective approach based on the discontinuous Galerkin method for the solution of fractional‐order problems.
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Xindong Zhang, Leilei Wei, Bo Tang and Yinnian He
In this article, the authors aim to present the homotopy analysis method (HAM) for obtaining the approximate solutions of space‐time fractional differential equations with initial…
Abstract
Purpose
In this article, the authors aim to present the homotopy analysis method (HAM) for obtaining the approximate solutions of space‐time fractional differential equations with initial conditions.
Design/methodology/approach
The series solution is developed and the recurrence relations are given explicitly. The initial approximation can be determined by imposing the initial conditions.
Findings
The comparison of the HAM results with the exact solutions is made; the results reveal that the HAM is very effective and simple. The HAM contains the auxiliary parameter h, which provides a simple way to adjust and control the convergence region of series solution. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter h on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders a and b on the solution behavior.
Originality/value
The idea can be used to find the numerical solutions of other fractional differential equations.
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Wei Li, Leilei Ji, Weidong Shi, Ling Zhou, Xiaoping Jiang and Yang Zhang
The purpose of this paper is to experimentally and numerically study the transient hydraulic impact and overall performance during startup accelerating process of mixed-flow pump.
Abstract
Purpose
The purpose of this paper is to experimentally and numerically study the transient hydraulic impact and overall performance during startup accelerating process of mixed-flow pump.
Design/methodology/approach
In this study, the impeller rotor vibration characteristics during the starting period under the action of fluid–structure interaction was investigated, which is based on the bidirectional synchronization cooperative solving method for the flow field and impeller structural response of the mixed-flow pump. Experimental transient external characteristic and the transient dimensionless head results were compared with the numerical calculation results, to validate the accuracy of numerical calculation method. Besides, the deformation and dynamic stress distribution of the blade under the stable rotating speed and accelerating condition were studied based on the bidirectional fluid–structure interaction.
Findings
The results show that the combined action of complex hydrodynamic environment and impeller centrifugal force in the startup accelerating process makes the deformation and dynamic stress of blade have the rising trend of reciprocating oscillation. At the end of acceleration, the stress and strain appear as transient peak values and the transient effect is nonignorable. The starting acceleration has a great impact on the deformation and dynamic stress of blade, and the maximum deformation near the rim of impeller outlet edge increases 5 per cent above the stable condition. The maximum stress value increases by about 68.7 per cent more than the steady-state condition at the impeller outlet edge near the hub. The quick change of rotating speed makes the vibration problem around the blade tip area more serious, and then it takes the excessive stress concentration and destruction at the blade root.
Originality/value
This study provides basis and reference for the safety operation of pumps during starting period
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Wei Li, Yuxin Huang, Leilei Ji, Lingling Ma and Ramesh Agarwal
The purpose of this study is to explore the transient characteristics of mixed-flow pumps during startup process.
Abstract
Purpose
The purpose of this study is to explore the transient characteristics of mixed-flow pumps during startup process.
Design/methodology/approach
This study uses a full-flow field transient calculation method of mixed-flow pump based on a closed-loop model.
Findings
The findings show the hydraulic losses and internal flow characteristics of the piping system during the start-up process.
Research limitations/implications
Large computational cost.
Practical implications
Improve the accuracy of current numerical simulation results in transient process of mixed-flow pump.
Originality/value
Simplify the setting of boundary conditions in the transient calculation.
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Wei Li, Yang Zhang, Weidong Shi, Leilei Ji, Yongfei Yang and Yuanfeng Ping
This paper aims to study the transient flow characteristics in a mixed-flow pump during the start-up period.
Abstract
Purpose
This paper aims to study the transient flow characteristics in a mixed-flow pump during the start-up period.
Design/methodology/approach
In this study, numerical calculation of the internal flow field in a mixed-flow pump using the sliding mesh method was carried out. The regulation of the pressure, streamline and the relative speed during the start-up period was analyzed.
Findings
The trend of the simulated head is consistent with the experimental results, and the calculated head is around 0.3 m higher than the experimental head when the rotation speed reached the stable stage, indicating that the numerical method for the start-up process simulation of the mixed-flow pump has a high accuracy. At the beginning, the velocity inside the impeller changes little along the radius direction and the flow rate increases slowly during the start-up process. As the rotation speed reached the stable stage, the flow inside the impeller became steady, the vortex reduced and transient effects disappeared gradually.
Originality/value
The study results have significant value for revealing the internal unsteady flow characteristics of the mixed-flow pump and providing the reference for the design optimization of the mixed-flow pump.
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Jianping Zhang, Leilei Wang and Guodong Wang
With the rapid advancement in the automotive industry, the friction coefficient (FC), wear rate (WR) and weight loss (WL) have emerged as crucial parameters to measure the…
Abstract
Purpose
With the rapid advancement in the automotive industry, the friction coefficient (FC), wear rate (WR) and weight loss (WL) have emerged as crucial parameters to measure the performance of automotive braking systems, so the FC, WR and WL of friction material are predicted and analyzed in this work, with an aim of achieving accurate prediction of friction material properties.
Design/methodology/approach
Genetic algorithm support vector machine (GA-SVM) model is obtained by applying GA to optimize the SVM in this work, thus establishing a prediction model for friction material properties and achieving the predictive and comparative analysis of friction material properties. The process parameters are analyzed by using response surface methodology (RSM) and GA-RSM to determine them for optimal friction performance.
Findings
The results indicate that the GA-SVM prediction model has the smallest error for FC, WR and WL, showing that it owns excellent prediction accuracy. The predicted values obtained by response surface analysis are closed to those of GA-SVM model, providing further evidence of the validity and the rationality of the established prediction model.
Originality/value
The relevant results can serve as a valuable theoretical foundation for the preparation of friction material in engineering practice.
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Wang Leilei, Sowmipriya Rajendiran and K. Gayathri
The main goal of the physical education (PE) environment is that each individual trained should achieve self-fulfillment with the large group of students involved with their own…
Abstract
Purpose
The main goal of the physical education (PE) environment is that each individual trained should achieve self-fulfillment with the large group of students involved with their own efforts. Deep learning is applying transferrable knowledge in new situations to help the students master in tough circumstances. In PE training, injuries occur when working together as a team. Safety measures are taken immediately as an emergency response to reduce the potential risk in students by providing first aid. To provide safety measures for the injured student immediately, the environment is monitored in real-time using a GPS.
Design/methodology/approach
Theory of Humanities Education (ToHE) infers that it has less collection of theories and a wide range of applications than the state-of-the-art systems. ToHE allows students to think creatively and play a vital role in one’s health which is a critical aspect in PE. The ToHE theory focuses on two main concepts, i.e. by using a methodological approach to analyse and deep learning to solve the problem. PE motivates college students to follow a healthy and active lifestyle.
Findings
The proposed system is deployed in real time for monitoring the student’s performance and provides an emergency response with an accuracy rate of 90%.
Originality/value
The deep learning offers solutions to the injuries by using the deep convolutional neural network to provide interpretability of the consequence by training it with various injuries that occur in the playground and inappropriate use of sports equipment. A case study provided in this paper outlines an emergency response scenario to an injured student in sports training.