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1 – 10 of 121Yahya Alnashri and Hasan Alzubaidi
The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary…
Abstract
Purpose
The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.
Design/methodology/approach
In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.
Findings
The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.
Originality/value
This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.
Details
Keywords
- A gradient discretisation method (GDM)
- Gradient schemes
- Convergence analysis
- Existence of weak solutions
- Two-dimensional reaction–diffusion Brusselator system
- Dirichlet boundary conditions
- Non-conforming finite element methods
- Finite volume schemes
- Hybrid mixed mimetic (HMM) method
- 35K57
- 65N12
- 65M08
J.I. Ramos and Carmen María García López
The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the…
Abstract
Purpose
The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.
Design/methodology/approach
An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.
Findings
The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.
Originality/value
The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.
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Keywords
Xingwen Wu, Zhenxian Zhang, Wubin Cai, Ningrui Yang, Xuesong Jin, Ping Wang, Zefeng Wen, Maoru Chi, Shuling Liang and Yunhua Huang
This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.
Abstract
Purpose
This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.
Design/methodology/approach
Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators. Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration. This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration, including a brief introduction of short-pitch irregularities, associated high frequency vibration in railway bogie, typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.
Findings
The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms. The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components. The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure, and the fatigue crack usually initiates from the defect of the weld seam. Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities. The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment, and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.
Originality/value
The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.
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Keywords
Andreas Gschwentner, Manfred Kaltenbacher, Barbara Kaltenbacher and Klaus Roppert
Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various…
Abstract
Purpose
Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.
Design/methodology/approach
The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.
Findings
The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.
Originality/value
The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.
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Keywords
M.S. Daoussa Haggar and M. Mbehou
This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is…
Abstract
Purpose
This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.
Design/methodology/approach
A rigorous error analysis is done, and optimal L2 error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.
Findings
Optimal L2 error estimates and energy norm.
Originality/value
The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.
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Keywords
Tiprawee Tongtummachat, Attasak Jaree and Nattee Akkarawatkhoosith
This article presents our experience in implementing the assessment for learning process (AfL) to enhance the teaching–learning quality, which has faced numerous challenges…
Abstract
Purpose
This article presents our experience in implementing the assessment for learning process (AfL) to enhance the teaching–learning quality, which has faced numerous challenges impacting educational quality. The effectiveness of this technique is demonstrated through a case study conducted in a core course of chemical engineering.
Design/methodology/approach
The article shares insights into the systematic course design and planning processes that were discussed and developed through AfL practices. Significant emphasis is placed on implementing formative and summative student self-assessment surveys as simple yet effective methods to meet this purpose. Quantitative data were collected and analyzed over three consecutive academic years (2020–2022) using various statistical parameters such as percentage, interquartile range and the program’s numerical goal (%G).
Findings
The AfL process via formative and summative surveys could significantly and effectively improve teaching–learning quality. These findings assist educators in identifying appropriate teaching methods and recognizing areas of weakness and strength, thereby facilitating continuous improvement in the teaching–learning quality. Validation methods, including quizzes and numerical grades, were employed to practically verify the outcome obtained from the questionnaires.
Practical implications
The AfL techniques demonstrated in this study can be directly implemented or adapted for various educational fields to enhance the teaching–learning quality.
Originality/value
The practical implementation of AfL in an engineering context has hardly been reported, particularly in chemical engineering. This work represents the practical implementation of AfL to enhance engineering field education.
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Keywords
Rene Prieler, Simon Pletzer, Stefan Thusmer, Günther Schwabegger and Christoph Hochenauer
In fire resistance tests (FRTs) of building materials, a crucial criterion to pass the test procedure is to avoid the leakage of the hot flue gases caused by gaps and cracks…
Abstract
Purpose
In fire resistance tests (FRTs) of building materials, a crucial criterion to pass the test procedure is to avoid the leakage of the hot flue gases caused by gaps and cracks occurring due to the thermal exposure. The present study's aim is to calculate the deformation of a steel door, which is embedded within a wall made of bricks, and qualitatively determine the flue gas leakage.
Design/methodology/approach
A computational fluid dynamics/finite element method (CFD/FEM) coupling was introduced representing an intermediate approach between a one-way and a full two-way coupling methodology, leading to a simplified two-way coupling (STWC). In contrast to a full two way-coupling, the heat transfer through the steel door was simulated based on a one-way approach. Subsequently, the predicted temperatures at the door from the one-way simulation were used in the following CFD/FEM simulation, where the fluid flow inside and outside the furnace as well as the deformation of the door were calculated simultaneously.
Findings
The simulation showed large gaps and flue gas leakage above the door lock and at the upper edge of the door, which was in close accordance to the experiment. Furthermore, it was found that STWC predicted similar deformations compared to the one-way coupling.
Originality/value
Since two-way coupling approaches for fluid/structure interaction in fire research are computationally demanding, the number of studies is low. Only a few are dealing with the flue gas exit from rooms due to destruction of solid components. Thus, the present study is the first two-way approach dealing with flue gas leakage due to gap formation.
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Keywords
Weihua Zhang, Yuanchen Zeng, Dongli Song and Zhiwei Wang
The safety and reliability of high-speed trains rely on the structural integrity of their components and the dynamic performance of the entire vehicle system. This paper aims to…
Abstract
Purpose
The safety and reliability of high-speed trains rely on the structural integrity of their components and the dynamic performance of the entire vehicle system. This paper aims to define and substantiate the assessment of the structural integrity and dynamical integrity of high-speed trains in both theory and practice. The key principles and approaches will be proposed, and their applications to high-speed trains in China will be presented.
Design/methodology/approach
First, the structural integrity and dynamical integrity of high-speed trains are defined, and their relationship is introduced. Then, the principles for assessing the structural integrity of structural and dynamical components are presented and practical examples of gearboxes and dampers are provided. Finally, the principles and approaches for assessing the dynamical integrity of high-speed trains are presented and a novel operational assessment method is further presented.
Findings
Vehicle system dynamics is the core of the proposed framework that provides the loads and vibrations on train components and the dynamic performance of the entire vehicle system. For assessing the structural integrity of structural components, an open-loop analysis considering both normal and abnormal vehicle conditions is needed. For assessing the structural integrity of dynamical components, a closed-loop analysis involving the influence of wear and degradation on vehicle system dynamics is needed. The analysis of vehicle system dynamics should follow the principles of complete objects, conditions and indices. Numerical, experimental and operational approaches should be combined to achieve effective assessments.
Originality/value
The practical applications demonstrate that assessing the structural integrity and dynamical integrity of high-speed trains can support better control of critical defects, better lifespan management of train components and better maintenance decision-making for high-speed trains.
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Keywords
Marcin Nowak, Marta Pawłowska-Nowak, Małgorzata Kokocińska and Piotr Kułyk
With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (εij), relative degree of grey incidence (rij) or synthetic degree of…
Abstract
Purpose
With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (εij), relative degree of grey incidence (rij) or synthetic degree of grey incidence (ρij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.
Design/methodology/approach
To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).
Findings
It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.
Research limitations/implications
Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.
Originality/value
In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.
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Armando Di Meglio, Nicola Massarotti and Perumal Nithiarasu
In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the…
Abstract
Purpose
In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.
Design/methodology/approach
To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.
Findings
The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.
Originality/value
The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.
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