Research

16 pages, 40738 KiB

Open AccessArticle

Numerical Investigation of Wind Flow and Speedup Effect at a Towering Peak Extending out of a Steep Mountainside: Implications for Landscape Platforms

by Mohammed Nabil, Fengqi Guo, Lizhong Jiang, Zhiwu Yu and Qiuliang Long

Mathematics 2024, 12(3), 467; https://doi.org/10.3390/math12030467 - 01 Feb 2024

Viewed by 1137

Abstract

Wind flow over complex terrain is strongly influenced by the topographical features of the region, resulting in unpredictable local wind characteristics. This paper employs numerical simulation to study the wind flow at a towering peak extending out of a steep mountainside and the [...] Read more.

Wind flow over complex terrain is strongly influenced by the topographical features of the region, resulting in unpredictable local wind characteristics. This paper employs numerical simulation to study the wind flow at a towering peak extending out of a steep mountainside and the wind-induced effect on onsite landscape platforms. First, the wind flow from seven different directions is explored via 3D numerical simulations, and the wind load distribution on the platforms is highlighted. Second, a 2D numerical simulation is conducted to evaluate the wind speedup effect at the side peak, examining the influence of the side peak height and the mountainside steepness on the wind speedup factor. The numerical simulations presented in this research were validated by replicating a published numerical and experimental study. The results illustrate the amplifying and blocking effects of the surrounding topography, yielding unpredictable and nonuniform wind pressure distribution on the platforms. The presence of the side peak leads to a significant increase in the speedup factor, and the side peak height and the mountainside steepness have a moderate influence on the value of the speedup factor. Additionally, the speedup factor obtained from this study varies significantly, especially near the surface, from the recommendations of several wind load standards. Consequently, the impact of the local terrain and the wind speedup effect must be thoroughly assessed to ensure the structural integrity of structures installed at a similar topography. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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33 pages, 5934 KiB

Open AccessArticle

Evolutionary Approach for DISCO Profit Maximization by Optimal Planning of Distributed Generators and Energy Storage Systems in Active Distribution Networks

by Rabea Jamil Mahfoud, Nizar Faisal Alkayem, Emmanuel Fernandez-Rodriguez, Yuan Zheng, Yonghui Sun, Shida Zhang and Yuquan Zhang

Mathematics 2024, 12(2), 300; https://doi.org/10.3390/math12020300 - 17 Jan 2024

Viewed by 582

Abstract

Distribution companies (DISCOs) aim to maximize their annual profits by performing the optimal planning of distributed generators (DGs) or energy storage systems (ESSs) in the deregulated electricity markets. Some previous studies have focused on the simultaneous planning of DGs and ESSs for DISCO [...] Read more.

Distribution companies (DISCOs) aim to maximize their annual profits by performing the optimal planning of distributed generators (DGs) or energy storage systems (ESSs) in the deregulated electricity markets. Some previous studies have focused on the simultaneous planning of DGs and ESSs for DISCO profit maximization but have rarely considered the reactive powers of DGs and ESSs. In addition, the optimization methods used for solving this problem are either traditional or outdated, which may not yield superior results. To address these issues, this paper simultaneously performs the optimal planning of DGs and ESSs in distribution networks for DISCO profit maximization. The utilized model not only takes into account the revenues of trading active and reactive powers but also addresses the active and reactive powers of DGs and ESSs. To solve the optimization problem, a new hybrid evolutionary algorithm (EA) called the oppositional social engineering differential evolution with Lévy flights (OSEDE/LFs) is proposed. The OSEDE/LFs is applied to optimize the planning model using the 30-Bus and IEEE 69-Bus networks as test systems. The results of the two case studies are compared with several other EAs. The results confirm the significance of the planning model in achieving higher profits and demonstrate the effectiveness of the proposed approach when compared with other EAs. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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16 pages, 617 KiB

Open AccessArticle

Calculation of Stationary Magnetic Fields Based on the Improved Quadrature Formulas for a Simple Layer Potential

by Igor Reznichenko, Primož Podržaj and Aljoša Peperko

Mathematics 2024, 12(1), 21; https://doi.org/10.3390/math12010021 - 21 Dec 2023

Viewed by 533

Abstract

This research deals with precision calculations of stationary magnetic fields of volumetric bodies. The electrostatics analogy allows for the use of a scalar magnetic potential, which reformulates the original task as a boundary value problem for the Laplace equation. We approach this with [...] Read more.

This research deals with precision calculations of stationary magnetic fields of volumetric bodies. The electrostatics analogy allows for the use of a scalar magnetic potential, which reformulates the original task as a boundary value problem for the Laplace equation. We approach this with the boundary element method, specifically in distance ranges close to the magnetized surface, where existing standard numerical methods are known to struggle. This work presents an approach based on the improved quadrature formulas for the simple layer potential and its normal derivative. Numerical tests confirm significant improvements in calculating the field at any distance from the surface of the magnet. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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19 pages, 3109 KiB

Open AccessArticle

Modeling the Five-Element Windkessel Model with Simultaneous Utilization of Blood Viscoelastic Properties for FFR Achievement: A Proof-of-Concept Study

by Maria Fernandes, Luisa C. Sousa, Carlos A. Conceição António and Sónia I. S. Pinto

Mathematics 2023, 11(24), 4877; https://doi.org/10.3390/math11244877 - 05 Dec 2023

Viewed by 933

Abstract

Coronary artery diseases (CADs) are a leading cause of death worldwide. Accurate numerical simulations of coronary blood flow, especially in high-risk atherosclerotic patients, have been a major challenge for clinical applications. This study pioneers a novel approach combining the physiologically accurate five-element Windkessel [...] Read more.

Coronary artery diseases (CADs) are a leading cause of death worldwide. Accurate numerical simulations of coronary blood flow, especially in high-risk atherosclerotic patients, have been a major challenge for clinical applications. This study pioneers a novel approach combining the physiologically accurate five-element Windkessel and sPTT models to enhance the accuracy of the hemodynamics and the fractional flow reserve (FFR) parameter. User-defined functions (UDFs) of the outlet pressure boundary condition (Windkessel model) and the viscoelastic characteristics of blood (sPTT model) were developed and dynamically loaded with ANSYS^® 2023 software. In a proof-of-concept study, a patient’s left coronary artery with 40% stenosis was provided by the hospital for further analysis. The numerical FFR value obtained in the present work skews only 0.37% from the invasive measurement in the hospital. This highlights the important roles of both blood viscoelasticity and the five-element Windkessel model in hemodynamic simulations. This proof-of-concept of the FFR numerical calculation tool provides a promising comprehensive assessment of atherosclerosis in a fast, accurate, more affordable, and fully non-invasive manner. After validation with more patient cases in the future, this tool could be employed in hospitals and offer a more accurate and individualized approach for the diagnosis and treatment of CAD. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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11 pages, 387 KiB

Open AccessArticle

Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method

by Seitkerim Bimurzaev, Seil Sautbekov and Zerde Sautbekova

Mathematics 2023, 11(13), 2933; https://doi.org/10.3390/math11132933 - 30 Jun 2023

Cited by 1 | Viewed by 588

Abstract

The paper presents an exact solution to the internal boundary value problem of the field distribution in an electrostatic lens formed by two identical semi-infinite coaxially located round cylinders separated by a slit of finite width and located inside an infinite outer cylinder. [...] Read more.

The paper presents an exact solution to the internal boundary value problem of the field distribution in an electrostatic lens formed by two identical semi-infinite coaxially located round cylinders separated by a slit of finite width and located inside an infinite outer cylinder. The problem is reduced to a system of singular Wiener–Hopf integral equations, which is further solved by the Wiener–Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues. Using the obtained formulas, a numerical calculation of the axial distribution of the potential of a two-electrode lens was made for various values of the radii of the outer and inner cylinders. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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26 pages, 5666 KiB

Open AccessArticle

Multi-Step-Ahead Wind Speed Forecast Method Based on Outlier Correction, Optimized Decomposition, and DLinear Model

by Jialin Liu, Chen Gong, Suhua Chen and Nanrun Zhou

Mathematics 2023, 11(12), 2746; https://doi.org/10.3390/math11122746 - 17 Jun 2023

Cited by 1 | Viewed by 1095

Abstract

Precise and dependable wind speed forecasting (WSF) enables operators of wind turbines to make informed decisions and maximize the use of available wind energy. This study proposes a hybrid WSF model based on outlier correction, heuristic algorithms, signal decomposition methods, and DLinear. Specifically, [...] Read more.

Precise and dependable wind speed forecasting (WSF) enables operators of wind turbines to make informed decisions and maximize the use of available wind energy. This study proposes a hybrid WSF model based on outlier correction, heuristic algorithms, signal decomposition methods, and DLinear. Specifically, the hybrid model (HI-IVMD-DLinear) comprises the Hampel identifier (HI), the improved variational mode decomposition (IVMD) optimized by grey wolf optimization (GWO), and DLinear. Firstly, outliers in the wind speed sequence are detected and replaced with the HI to mitigate their impact on prediction accuracy. Next, the HI-processed sequence is decomposed into multiple sub-sequences with the IVMD to mitigate the non-stationarity and fluctuations. Finally, each sub-sequence is predicted by the novel DLinear algorithm individually. The predictions are reconstructed to obtain the final wind speed forecast. The HI-IVMD-DLinear is utilized to predict the real historical wind speed sequences from three regions so as to assess its performance. The experimental results reveal the following findings: (a) HI could enhance prediction accuracy and mitigate the adverse effects of outliers; (b) IVMD demonstrates superior decomposition performance; (c) DLinear has great prediction performance and is suited to WSF; and (d) overall, the HI-IVMD-DLinear exhibits superior precision and stability in one-to-four-step-ahead forecasting, highlighting its vast potential for application. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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18 pages, 485 KiB

Open AccessArticle

Magnetohydrodynamics Williamson Nanofluid Flow over an Exponentially Stretching Surface with a Chemical Reaction and Thermal Radiation

by Hillary Muzara and Stanford Shateyi

Mathematics 2023, 11(12), 2740; https://doi.org/10.3390/math11122740 - 16 Jun 2023

Cited by 2 | Viewed by 1163

Abstract

Presented in this current study is the numerical analysis of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface. The most important aspect of the investigation is that the effects of the magnetic field, chemical reaction and thermal radiation in the fluid flow [...] Read more.

Presented in this current study is the numerical analysis of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface. The most important aspect of the investigation is that the effects of the magnetic field, chemical reaction and thermal radiation in the fluid flow are taken into account. The partial differential equations governing the present Williamson nanofluid flow problem were observed to be highly nonlinear and coupled. Suitable similarity transformations were used to transmute the coupled system of nonlinear partial differential equations governing the fluid flow into a linear system. The linear system was solved numerically using the spectral quasi-linearization method. The MATLAB bvp4c numerical technique and a comparison with existing results for the skin friction coefficient were used to confirm the appropriateness of the method in solving the current problem. The influence of some pertinent physical parameters on the fluid’s velocity, temperature and concentration profiles were displayed graphically. The effects of all the physical parameters on the skin friction coefficient, Nusselt number and Sherwood number were portrayed in a tabular form. It was noted that enhancing the thermal radiation parameter reduces the fluid’s temperature, Nusselt number and the skin friction coefficient, while the Sherwood number is improved. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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15 pages, 7690 KiB

Open AccessArticle

Studies on Finite Element Analysis in Hydroforming of Nimonic 90 Sheet

by Fakrudeen Ali Ahamed J and Pandivelan Chinnaiyan

Mathematics 2023, 11(11), 2437; https://doi.org/10.3390/math11112437 - 24 May 2023

Viewed by 1125

Abstract

The primary goal of this study was to investigate the formability of Nimonic 90 sheet which performs well at high temperatures and pressures, making it ideal for applications in the aerospace, processing, and manufacturing industries. In this present study, finite element analysis (FEA) [...] Read more.

The primary goal of this study was to investigate the formability of Nimonic 90 sheet which performs well at high temperatures and pressures, making it ideal for applications in the aerospace, processing, and manufacturing industries. In this present study, finite element analysis (FEA) and optimization of process parameters for formability of Nimonic 90 in sheet hydroforming were investigated. The material’s mechanical properties were obtained by uniaxial tensile tests as per the standard ASTM E8/E8M. The sheet hydroforming process was first simulated to obtain maximum pressure (53.46 MPa) using the FEA and was then validated using an experiment. The maximum pressure obtained was 50.5 MPa in experimentation. Since fully experimental or simulation designs are impractical, the Box–Behnken design (BBD) was used to investigate various process parameters. Formability was measured by the forming limit diagram (FLD) and maximum deformation achieved without failure. Analysis of variance (ANOVA) results also revealed that pressure and thickness were the most effective parameters for achieving maximum deformation without failure. Response surface methodology (RSM) optimizer was used to predict optimized process parameter to achieve maximized response (deformation) without failure. Experimental validation was carried out for the optimized parameters. The percentage of error between experimental and simulation results for maximum deformation was less than 5%. The findings revealed that all the aspects in the presented regression model and FEM simulation were effective on response values. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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19 pages, 1828 KiB

Open AccessArticle

DNN-MLVEM: A Data-Driven Macromodel for RC Shear Walls Based on Deep Neural Networks

by German Solorzano and Vagelis Plevris

Mathematics 2023, 11(10), 2347; https://doi.org/10.3390/math11102347 - 18 May 2023

Cited by 4 | Viewed by 1192

Abstract

This study proposes the DNN-MVLEM, a novel macromodel for the non-linear analysis of RC shear walls based on deep neural networks (DNN); while most RC shear wall macromodeling techniques follow a deterministic approach to find the right configuration and properties of the system, [...] Read more.

This study proposes the DNN-MVLEM, a novel macromodel for the non-linear analysis of RC shear walls based on deep neural networks (DNN); while most RC shear wall macromodeling techniques follow a deterministic approach to find the right configuration and properties of the system, in this study, an alternative data-driven strategy is proposed instead. The proposed DNN-MVLEM is composed of four vertical beam-column elements and one horizontal shear spring. The beam-column elements implement the fiber section formulation with standard non-linear uniaxial material models for concrete and steel, while the horizontal shear spring uses a multi-linear force–displacement relationship. Additionally, three calibration factors are introduced to improve the performance of the macromodel. The data-driven component of the proposed strategy consists of a large DNN that is trained to predict the force–displacement curve of the shear spring and the three calibration factors. The training data is created using a parametric microscopic FEM model based on the multi-layer shell element formulation and a genetic algorithm (GA) that optimizes the response of the macromodel to match the behavior of the microscopic FEM model. The DNN-MVLEM is tested in two types of examples, first as a stand-alone model and then as part of a two-bay multi-story frame structure. The results show that the DNN-MVLEM is capable of reproducing the results obtained with the microscopic FEM model up to 100 times faster and with an estimated error lower than 5%. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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19 pages, 3873 KiB

Open AccessArticle

Mechanical Stability of the Heterogenous Bilayer Solid Electrolyte Interphase in the Electrodes of Lithium–Ion Batteries

by Yasir Ali, Noman Iqbal, Imran Shah and Seungjun Lee

Mathematics 2023, 11(3), 543; https://doi.org/10.3390/math11030543 - 19 Jan 2023

Viewed by 1569

Abstract

Mechanical stability of the solid electrolyte interphase (SEI) is crucial to mitigate the capacity fade of lithium–ion batteries because the rupture of the SEI layer results in further consumption of lithium ions in newly generated SEI layers. The SEI is known as a [...] Read more.

Mechanical stability of the solid electrolyte interphase (SEI) is crucial to mitigate the capacity fade of lithium–ion batteries because the rupture of the SEI layer results in further consumption of lithium ions in newly generated SEI layers. The SEI is known as a heterogeneous bilayer and consists of an inner inorganic layer connecting the particle and an outer organic layer facing the electrolyte. The growth of the bilayer SEI over cycles alters the stress generation and failure possibility of both the organic and inorganic layers. To investigate the probability of mechanical failure of the bilayer SEI, we developed the electrochemical-mechanical coupled model with the core–double-shell particle/SEI layer model. The growth of the bilayer SEI is considered over cycles. Our results show that during charging, the stress of the particle changes from tensile to compressive as the thickness of bilayer SEI increases. On the other hand, in the SEI layers, large compressive radial and tensile tangential stress are generated. During discharging, the compressive radial stress of the bilayer SEI transforms into tensile radial stress. The tensile tangential and radial stresses are responsible for the fracture and debonding of the bilayer SEI, respectively. As the thickness ratio of the inorganic to organic layers increases, the fracture probability of the inorganic layer increases, while that of the organic layer decreases. However, the debonding probability of both layers is decreased. In addition, the SEI covering large particles is more vulnerable to fracture, while that covering small particles is more susceptible to debonding. Therefore, tailoring the thickness ratio of the inorganic to organic layers and particle size is important to reduce the fracture and debonding of the heterogeneous bilayer SEI. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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27 pages, 9122 KiB

Open AccessArticle

The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media

by Cong Liu, Shaosong Min, Yandong Pang and Yingbin Chai

Mathematics 2023, 11(3), 523; https://doi.org/10.3390/math11030523 - 18 Jan 2023

Cited by 13 | Viewed by 1488

Abstract

This work presents a novel simulation approach to couple the meshfree radial point interpolation method (RPIM) with the implicit direct time integration method for the transient analysis of wave propagation dynamics in non-homogeneous media. In this approach, the RPIM is adopted for the [...] Read more.

This work presents a novel simulation approach to couple the meshfree radial point interpolation method (RPIM) with the implicit direct time integration method for the transient analysis of wave propagation dynamics in non-homogeneous media. In this approach, the RPIM is adopted for the discretization of the overall space domain, while the discretization of the time domain is completed by employing the efficient Bathe time stepping scheme. The dispersion analysis demonstrates that, in wave analysis, the amount of numerical dispersion error resulting from the discretization in the space domain can be suppressed at a very low level when the employed nodal support domain of the interpolation function is adequately large. Meanwhile, it is also mathematically shown that the amount of numerical error resulting from the time domain discretization is actually a monotonically decreasing function of the non-dimensional time domain discretization interval. Consequently, the present simulation approach is capable of effectively handling the transient analysis of wave propagation dynamics in non-homogeneous media, and the disparate waves with different speeds can be solved concurrently with very high computation accuracy. This numerical feature makes the present simulation approach more suitable for complicated wave analysis than the traditional finite element approach because the waves with disparate speeds always cannot be concurrently solved accurately. Several numerical tests are given to check the performance of the present simulation approach for the analysis of wave propagation dynamics in non-homogeneous media. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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17 pages, 3585 KiB

Open AccessArticle

A Novel and Robust Wind Speed Prediction Method Based on Spatial Features of Wind Farm Cluster

by Mumin Zhang, Yuzhi Wang, Haochen Zhang, Zhiyun Peng and Junjie Tang

Mathematics 2023, 11(3), 499; https://doi.org/10.3390/math11030499 - 17 Jan 2023

Cited by 3 | Viewed by 1115

Abstract

Wind energy has been widely used in recent decades to achieve green and sustainable development. However, wind speed prediction in wind farm clusters remains one of the less studied areas. Spatial features of cluster data of wind speed are not fully exploited in [...] Read more.

Wind energy has been widely used in recent decades to achieve green and sustainable development. However, wind speed prediction in wind farm clusters remains one of the less studied areas. Spatial features of cluster data of wind speed are not fully exploited in existing work. In addition, missing data, which dramatically deteriorate the forecasting performance, have not been addressed thoroughly. To tackle these tough issues, a new method, termed input set based on wind farm cluster data–deep extreme learning machine (IWC-DELM), is developed herein. This model builds an input set based on IWC, which takes advantage of the historical data of relevant wind farms to utilize the spatial characteristics of wind speed sequences within such wind farm clusters. Finally, wind speed prediction is obtained after the training of DELM, which results in a better performance in forecasting accuracy and training speed. The structure IWC, complete with the multidimensional average method (MDAM), is also beneficial to make up the missing data, thus enhancing data robustness in comparison to the traditional method of the moving average approach (MAA). Experiments are conducted with some real-world data, and the results of gate recurrent unit (GRU), long- and short-term memory (LSTM) and sliced recurrent neural networks (SRNNs) are also taken for comparison. These comparative tests clearly verify the superiority of IWC-DELM, whose accuracy and efficiency both rank at the top among the four candidates. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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18 pages, 19807 KiB

Open AccessArticle

Numerical Investigation on a Diffuser-Augmented Horizontal Axis Tidal Stream Turbine with the Entropy Production Theory

by Wei Zang, Yuan Zheng, Yuquan Zhang, Xiangfeng Lin, Yanwei Li and Emmanuel Fernandez-Rodriguez

Mathematics 2023, 11(1), 116; https://doi.org/10.3390/math11010116 - 27 Dec 2022

Cited by 18 | Viewed by 1364

Abstract

An implication of a turbine current is the development of a wake, a reduced speed flow, thus affecting the performance of an adjoined turbine. The aim of this study is to examine the turbine wake properties to offer a basic framework for the [...] Read more.

An implication of a turbine current is the development of a wake, a reduced speed flow, thus affecting the performance of an adjoined turbine. The aim of this study is to examine the turbine wake properties to offer a basic framework for the exploration of efficient turbine arrangements through the OpenFOAM source package and the entropy production theory. The results indicate that the diffuser inlet produces the largest entropy rate; however, this dissipates quickly after the rotor plane. In terms of vorticity, the Q and λ₂-criterion results are sensitive to the isosurface thresholds. In general, the Ω-Rortex method proves a convenient and accurate solution for vortex visualization and identification. For the overall mean wake structure, the velocity profile follows a tadpole-shape, whilst the velocity deficits above 100% are observed around the nacelle and throat (diffuser) and behind the tower. The concentration of maximum turbulent intensities appears behind the throat of the diffuser and at the top and bottom of the tower. Owing to the swirling effect after rotor, we proposed recommended values of b₀ = 10⁻⁵ for the hydrodynamic investigation of tidal stream turbines. The present findings extend our knowledge on the flow disruption due to shrouded turbines and are particularly relevant for farm project advisors. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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17 pages, 6222 KiB

Open AccessArticle

Effects of Diffusion-Induced Nonlinear Local Volume Change on the Structural Stability of NMC Cathode Materials of Lithium-Ion Batteries

by Noman Iqbal, Jinwoong Choi, Changkyu Lee, Hafiz Muhammad Uzair Ayub, Jinho Kim, Minseo Kim, Younggee Kim, Dongjae Moon and Seungjun Lee

Mathematics 2022, 10(24), 4697; https://doi.org/10.3390/math10244697 - 11 Dec 2022

Cited by 5 | Viewed by 1987

Abstract

Electrochemical stress induced by the charging/discharging of electrode materials strongly affects the lifetime of lithium-ion batteries (LIBs) by regulating mechanical failures. Electrochemical stress is caused by a change in the local volume of the active materials associated with the lithium-ion concentration. The local [...] Read more.

Electrochemical stress induced by the charging/discharging of electrode materials strongly affects the lifetime of lithium-ion batteries (LIBs) by regulating mechanical failures. Electrochemical stress is caused by a change in the local volume of the active materials associated with the lithium-ion concentration. The local volume change of certain active materials, such as nickel-rich LiNi_xMn_yCo_zO₂ (NMC), varies nonlinearly with the lithium content, which has not been considered in the stress calculations in previous studies. In this paper, the influence of nonlinear local volume change on the mechanical response of NMC-active materials is investigated numerically. The goal is achieved by using a concentration-dependent partial molar volume calculated from the previously obtained local volume change experimental results. A two-dimensional axisymmetric model was developed to perform finite element simulations by fully coupling lithium diffusion and stress generation at a single particle level. The numerical results demonstrate that (1) the global volume change of the particle evolves nonlinearly, (2) the stress response correlates with the rate of change of the active particle’s volume, and (3) stress–concentration coupling strongly affects the concentration levels inside the particle. We believe this is the first simulation study that highlights the effect of a concentration-dependent partial molar volume on diffusion-induced stresses in NMC materials. The proposed model provides insight into the design of next-generation NMC electrode materials to achieve better structural stability by reducing mechanical cracking issues. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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19 pages, 12436 KiB

Open AccessArticle

Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method

by Dongdong Liu, Xing Wei, Chengbin Li, Chunguang Han, Xiaxi Cheng and Linlin Sun

Mathematics 2022, 10(22), 4323; https://doi.org/10.3390/math10224323 - 17 Nov 2022

Cited by 1 | Viewed by 912

Abstract

In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM [...] Read more.

In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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13 pages, 3769 KiB

Open AccessArticle

A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures

by Liyuan Lan, Suifu Cheng, Xiatao Sun, Weiwei Li, Chao Yang and Fajie Wang

Mathematics 2022, 10(20), 3817; https://doi.org/10.3390/math10203817 - 16 Oct 2022

Cited by 5 | Viewed by 1049

Abstract

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the [...] Read more.

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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15 pages, 5640 KiB

Open AccessArticle

Fluid–Structure Interaction Modeling of Structural Loads and Fatigue Life Analysis of Tidal Stream Turbine

by Yuquan Zhang, Zhiqiang Liu, Chengyi Li, Xuemei Wang, Yuan Zheng, Zhi Zhang, Emmanuel Fernandez-Rodriguez and Rabea Jamil Mahfoud

Mathematics 2022, 10(19), 3674; https://doi.org/10.3390/math10193674 - 07 Oct 2022

Cited by 2 | Viewed by 1325

Abstract

Developing reliable tidal-energy turbines of a large size and capacity links to preservation of the structural safety and stability of the blades. In this study, a bidirectional fluid–structure coupling method was applied to analyze the hydrodynamic performance and structural characteristics of the blade [...] Read more.

Developing reliable tidal-energy turbines of a large size and capacity links to preservation of the structural safety and stability of the blades. In this study, a bidirectional fluid–structure coupling method was applied to analyze the hydrodynamic performance and structural characteristics of the blade of a tidal-stream turbine. Analyses were conducted on the transient and stable structural stresses, fatigue, and deformations under the influence of water depth and turbine rotational speed. The performance predictions with and without fluid–structure coupling are similar to measurements. The water-depth change has little effect on the stress and deformation change of the blade, while the turbine-speed change has the most significant effect on it. When the turbine just starts, the blade will be subject to a sudden change load. This is due to the increase in turbine speed, resulting in the sudden load. Similar to the trend of blade stress, the blade safety factor is lower near the root of the blade, and the turbine-speed change has a more significant impact on the blade structure’s safety. However, the number of stress cycles in the blade at different rotational speeds is within the safety range. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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20 pages, 6187 KiB

Open AccessArticle

A Stacking Learning Model Based on Multiple Similar Days for Short-Term Load Forecasting

by Qi Jiang, Yuxin Cheng, Haozhe Le, Chunquan Li and Peter X. Liu

Mathematics 2022, 10(14), 2446; https://doi.org/10.3390/math10142446 - 13 Jul 2022

Cited by 7 | Viewed by 1481

Abstract

It is challenging to obtain accurate and efficient predictions in short-term load forecasting (STLF) systems due to the complexity and nonlinearity of the electric load signals. To address these problems, we propose a hybrid predictive model that includes a sliding-window algorithm, a stacking [...] Read more.

It is challenging to obtain accurate and efficient predictions in short-term load forecasting (STLF) systems due to the complexity and nonlinearity of the electric load signals. To address these problems, we propose a hybrid predictive model that includes a sliding-window algorithm, a stacking ensemble neural network, and a similar-days predictive method. First, we leverage a sliding-window algorithm to process the time-series electric load data with high nonlinearity and non-stationarity. Second, we propose an ensemble learning scheme of stacking neural networks to improve forecasting performance. Specifically, the stacking neural networks contain two types of networks: the base-layer and the meta-layer networks. During the pre-training process, the base-layer network integrates a radial basis function (RBF), random vector functional link (RVFL), and backpropagation neural network (BPNN) to provide a robust predictive model. The meta-layer network utilizes a deep belief network (DBN) and the improved broad learning system (BLS) to enhance predictive accuracy. Finally, the similar-days prediction method is developed to extract the relationship of electric load data in different time dimensions, further enhancing the robustness and accuracy of the model. To demonstrate the effectiveness of our model, it is evaluated using real data from five regions of the United States in three consecutive years. We compare our method with several state-of-the-art and conventional neural-network-based models. Our proposed algorithm improves the prediction accuracy by 16.08%, 16.83%, and 22.64% compared to DWT-EMD-RVFL, SWT-LSTM, and EMD-BLS, respectively. Empirical results demonstrate that our model achieves better accuracy and robustness compared with the baselines. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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18 pages, 12801 KiB

Open AccessArticle

Study on Failure Characteristics and Control Technology of Roadway Surrounding Rock under Repeated Mining in Close-Distance Coal Seam

by Yuqi Shang, Dezhong Kong, Shijiang Pu, Yu Xiong, Qiang Li and Zhanbo Cheng

Mathematics 2022, 10(13), 2166; https://doi.org/10.3390/math10132166 - 21 Jun 2022

Cited by 13 | Viewed by 1486

Abstract

In this study, taking the Sheng’an coal mine as an engineering background, the failure characteristics of the surrounding rock of a roadway under repeated mining in a close-distance coal seam is comprehensively illustrated through field measurements (e.g., drilling imaging), theory analysis and numerical [...] Read more.

In this study, taking the Sheng’an coal mine as an engineering background, the failure characteristics of the surrounding rock of a roadway under repeated mining in a close-distance coal seam is comprehensively illustrated through field measurements (e.g., drilling imaging), theory analysis and numerical simulation (finite difference method (FDM)). The results show that although the return airway 10905 remains intact, the apparent failure of the roadway’s roof and the coal pillar can be observed. In addition, the expression of floor failure depth caused by upper coal seam mining is obtained through elastic-plastic theory. Meanwhile, the deformation of the surrounding rock of the roadway increases with the increase of repeated mining times, especially for the horizontal displacement of the roadway on the coal pillar side. Moreover, the cracks’ evolution of surrounding rock in the roadway can be observed as asymmetric characteristics. Finally, the stability control technology of “asymmetric anchor net cable + I-steel” is proposed to prevent potential mining disasters, and the feasibility of this support scheme is verified by numerical simulation and field practices. It can meet the requirement of safe mining and provide guidelines to effectively solve the failure of a roadway in close-distance coal seam mining. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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20 pages, 3790 KiB

Open AccessArticle

A Multi-View Ensemble Width-Depth Neural Network for Short-Term Wind Power Forecasting

by Jing Wan, Jiehui Huang, Zhiyuan Liao, Chunquan Li and Peter X. Liu

Mathematics 2022, 10(11), 1824; https://doi.org/10.3390/math10111824 - 25 May 2022

Cited by 3 | Viewed by 1398

Abstract

Short-term wind power forecasting (SWPF) is essential for managing wind power systems management. However, most existing forecasting methods fail to fully consider how to rationally integrate multi-view learning technologies with attention mechanisms. In this case, some potential features cannot be fully extracted, degenerating [...] Read more.

Short-term wind power forecasting (SWPF) is essential for managing wind power systems management. However, most existing forecasting methods fail to fully consider how to rationally integrate multi-view learning technologies with attention mechanisms. In this case, some potential features cannot be fully extracted, degenerating the predictive accuracy and robustness in SWPF. To solve this problem, this paper proposes a multi-view ensemble width-depth neural network (MVEW-DNN) for SWPF. Specifically, MVEW-DNN consists of local and global view learning subnetworks, which can effectively achieve more potential global and local view features of the original wind power data. In MVEW-DNN, the local view learning subnetwork is developed by introducing the deep belief network (DBN) model, which can efficiently extract the local view features. On the other hand, by introducing the attention mechanism, a new deep encoder board learning system (deBLS) is developed as the global view learning subnetwork, which provides more comprehensive global information. Therefore, by rationally learning the effective local and global view features, MVEW-DNN can achieve competitive predictive performance in SWPF. MVEW-DNN is compared with the state-of-the-art models in SWPF. The experiment results indicate that MVEW-DNN can provide competitive predictive accuracy and robustness. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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24 pages, 15217 KiB

Open AccessArticle

“Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations

by Maoxiong Liao, Tao Zhang and Jinggu Cao

Mathematics 2022, 10(10), 1722; https://doi.org/10.3390/math10101722 - 18 May 2022

Viewed by 1057

Abstract

A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in [...] Read more.

A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in each step. The high-order series of expanded variables bring high accuracy in the time domain, especially for the elasto-dynamic equations, which are second-order PDE in the time domain. In the present mixed MLPG5 dynamic formulation, the strains are interpolated independently, as are displacements in the local weak form, which eliminates the expensive differential of the shape function. In the traditional MLPG5, both shape function and its derivative for each node need to be calculated. By taking the Heaviside function as the test function, the local domain integration of stiffness matrix is avoided. Several numerical examples, including the comparison of our method, the MLPG5–Newmark method and FEM (ANSYS) are given to demonstrate the advantages of the presented method: (1) a large time step can be used in solving a elasto-dynamics problem; (2) computational efficiency and accuracy are improved in both space and time; (3) smaller support sizes can be used in the mixed MLPG5. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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17 pages, 9693 KiB

Open AccessArticle

Localized Boundary Knot Method for Solving Two-Dimensional Inverse Cauchy Problems

by Yang Wu, Junli Zhang, Shuang Ding and Yan-Cheng Liu

Mathematics 2022, 10(8), 1324; https://doi.org/10.3390/math10081324 - 15 Apr 2022

Cited by 1 | Viewed by 1323

Abstract

In this paper, a localized boundary knot method is adopted to solve two-dimensional inverse Cauchy problems, which are controlled by a second-order linear differential equation. The localized boundary knot method is a numerical method based on the local concept of the localization method [...] Read more.

In this paper, a localized boundary knot method is adopted to solve two-dimensional inverse Cauchy problems, which are controlled by a second-order linear differential equation. The localized boundary knot method is a numerical method based on the local concept of the localization method of the fundamental solution. The approach is formed by combining the classical boundary knot method with the localization method. It has the potential to solve many complex engineering problems. Generally, in an inverse Cauchy problem, there are no boundary conditions in specific boundaries. Additionally, in order to be close to the actual engineering situation, a certain level of noise is added to the known boundary conditions to simulate the measurement error. The localized boundary knot method can be used to solve two-dimensional Cauchy problems more stably and is truly free from mesh and numerical quadrature. In this paper, the stability of the method is verified by using multi-connected domain and simply connected domain examples in Laplace equations. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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15 pages, 5339 KiB

Open AccessArticle

A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation

by Lin Chen, Wenzhi Xu and Zhuojia Fu

Mathematics 2022, 10(6), 897; https://doi.org/10.3390/math10060897 - 11 Mar 2022

Cited by 1 | Viewed by 1604

Abstract

In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz collocation method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations. Unlike the traditional time discretization strategies, the proposed numerical scheme introduces the spatial–temporal radial Trefftz [...] Read more.

In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz collocation method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations. Unlike the traditional time discretization strategies, the proposed numerical scheme introduces the spatial–temporal radial Trefftz functions (STRTFs) as the basis functions for the spatial and temporal discretization of the transient wave equations. The STRTFs are constructed in the spatial–temporal domain, which is a combination of 3D Euclidean space and time into a 4D manifold. Moreover, since the initial and boundary conditions are imposed on the spatial–temporal domain boundaries, the original transient wave propagation problem can be converted to an inverse boundary value problem. To deal with the specified time-dependent sound source excitations, the composite multiple reciprocity technique is extended from the spatial domain to the spatial–temporal domain, which transforms the original problem with a source term into a high-order problem without a source term. By deriving the related STRTFs for the considered high-order problem, the proposed scheme only requires the node discretization on the spatial–temporal domain boundaries. The efficiency of the proposed method is numerically verified by four benchmark examples under 3D transient wave equations with specified time-dependent sound source excitation. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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14 pages, 5498 KiB

Open AccessArticle

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

by Qiang Wang, Pyeoungkee Kim and Wenzhen Qu

Mathematics 2022, 10(3), 515; https://doi.org/10.3390/math10030515 - 05 Feb 2022

Cited by 2 | Viewed by 1360

Abstract

In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation [...] Read more.

In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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10 pages, 2220 KiB

Open AccessArticle

Vibrational Resonance and Electrical Activity Behavior of a Fractional-Order FitzHugh–Nagumo Neuron System

by Jia-Wei Mao and Dong-Liang Hu

Mathematics 2022, 10(1), 87; https://doi.org/10.3390/math10010087 - 27 Dec 2021

Cited by 1 | Viewed by 1730

Abstract

Making use of the numerical simulation method, the phenomenon of vibrational resonance and electrical activity behavior of a fractional-order FitzHugh–Nagumo neuron system excited by two-frequency periodic signals are investigated. Based on the definition and properties of the Caputo fractional derivative, the fractional L1 [...] Read more.

Making use of the numerical simulation method, the phenomenon of vibrational resonance and electrical activity behavior of a fractional-order FitzHugh–Nagumo neuron system excited by two-frequency periodic signals are investigated. Based on the definition and properties of the Caputo fractional derivative, the fractional L1 algorithm is applied to numerically simulate the phenomenon of vibrational resonance in the neuron system. Compared with the integer-order neuron model, the fractional-order neuron model can relax the requirement for the amplitude of the high-frequency signal and induce the phenomenon of vibrational resonance by selecting the appropriate fractional exponent. By introducing the time-delay feedback, it can be found that the vibrational resonance will occur with periods in the fractional-order neuron system, i.e., the amplitude of the low-frequency response periodically changes with the time-delay feedback. The weak low-frequency signal in the system can be significantly enhanced by selecting the appropriate time-delay parameter and the fractional exponent. In addition, the original integer-order model is extended to the fractional-order model, and the neuron system will exhibit rich dynamical behaviors, which provide a broader understanding of the neuron system. Full article

(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)

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