Search Results (564)

Aiming at the problems of low thermal analysis efficiency and high computational cost of traditional computational fluid dynamics (CFD) methods for modular fault-tolerant permanent magnet synchronous motors (MFT-PMSMs) under complex working conditions, this paper proposes a fast modeling and calculation method of motor temperature field based on a high-efficiency and high-precision network algorithm. In this method, the physical structure of the motor is equivalent to a parameterized network model, and the computational efficiency is significantly improved by model partitioning and Fourth-order Runge Kutta method. The temperature change of the cooling medium is further considered, and the temperature rise change of the motor at different spatial positions is effectively considered. Based on the finite element method (FEM), the space loss distribution under rated, single-phase open circuit and overload conditions is obtained and mapped to the thermal network nodes. Through the transient thermal network solution, the rapid calculation of the temperature rise law of key components such as windings and permanent magnets is realized. The accuracy of the thermal network model was verified by using fluid-structure coupling simulation and prototype test for temperature analysis. This method provides an efficient tool for thermal safety assessment and optimization in the motor fault-tolerant design stage, especially for heat capacity check under extreme conditions and fault modes. Full article

An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation approximation. The quartic spline function and $(2,2)$ Padé approximation were utilized in space and time discretization, respectively. The stability and convergence were proven. Moreover, the dimensionality reduction formulas were derived using the proper orthogonal decomposition (POD) method, which is based on the matrix representation of the compact finite-difference scheme. The bases of the POD method were established by cumulative contribution rate of the eigenvalues of snapshot matrix that is different from the traditional ways in which the bases were established by the first eigenvalues. The method of cumulative contribution rate can optimize the degree of freedom. The error analysis of the reduced bases high-order POD finite-difference scheme was provided. Numerical experiments are conducted to validate the soundness and dependability of the reduced-order algorithm. The comparisons between the $(2,2)$ finite-difference method, the traditional POD method, and reduced dimensional method with cumulative contribution rate were discussed. Full article

In this paper, we propose a high-order compact difference scheme for a class of time-fractional convection–diffusion–reaction equations (CDREs) with variable coefficients. Using the Lagrange polynomial interpolation formula for the time-fractional derivative and a compact finite difference approximation for the spatial derivative, we establish an unconditionally stable compact difference method. The stability and convergence properties of the method are rigorously analyzed using the Fourier method. The convergence order of our discrete scheme is $\mathcal{O}({\tau }^{4-\alpha }+h^8)$, where $\tau$ and h represent the time step size and space step size, respectively. This work contributes to providing a better understanding of the dependability of the method by thoroughly examining convergence and conducting an error analysis. Numerical examples demonstrate the applicability, accuracy, and efficiency of the suggested technique, supplemented by comparisons with previous research. Full article

The prediction of microstructure evolution during thermal processing plays a crucial role in tailoring the mechanical properties of metallic components. Therefore, this work presents a comprehensive, multiscale modelling approach to simulating phase transformations in large-diameter steel rings during cooling. A finite-element-based thermal model was first used to simulate transient temperature distributions in a large-diameter ring under different cooling conditions, including air and water quenching. These thermal histories were subsequently employed in two complementary phase transformation models of different levels of complexity. The Avrami model provides a first-order approximation of the evolution of phase volume fractions, while a complex full-field cellular automata approach explicitly simulates the nucleation and growth of ferrite grains at the microstructural level, incorporating local kinetics and microstructural heterogeneities. The results highlight the sensitivity of final grain morphology to local cooling rates within the ring and initial austenite grain sizes. Simulations demonstrated the formation of heterogeneous microstructures, particularly pronounced in the ring’s surface region, due to sharp thermal gradients. This approach offers valuable insights for optimising heat treatment conditions to obtain high-quality large-diameter ring products. Full article

This paper presents a new methodology for the design process of DC ripple filters for voltage source converters. It focuses on fast-switching, wide-bandgap-material-based converters. Therefore, a wide frequency range of up to 100 MHz is taken into consideration during the whole process. Different tools like analytic calculations, time-domain modelling, and the finite element method are used for different tasks in order to generate a realistic model in terms of filter effect and reliability. The models are validated by small-signal measurements using a vector network analyser as well as realistic high-power tests. The contribution of this paper is to provide a tool for DC link filter design to estimate the filter efficiency and the current stress on the filter elements with a special focus on WBG hardware. Full article

During the machining of unidirectional carbon fiber-reinforced polymers (UD-CFRPs), their anisotropic characteristics and the complex cutting conditions often lead to defects such as delamination, burrs, and surface/subsurface damage. This study systematically investigates the effects of different fiber orientation angles (0°, 45°, 90°, and 135°) on cutting force, chip formation, stress distribution, and damage characteristics using a coupled macro–micro finite element model. The model successfully captures key microscopic failure mechanisms, such as fiber breakage, resin cracking, and fiber–matrix interface debonding, by integrating the anisotropic mechanical properties and heterogeneous microstructure of UD-CFRPs, thereby more realistically replicating the actual machining process. The cutting speed is kept constant at 480 mm/s. Experimental validation using T700S/J-133 laminates (with a 70% fiber volume fraction) shows that, on a macro scale, the cutting force varies non-monotonically with the fiber orientation angle, following the order of 0° < 45° < 135° < 90°. The experimental values are 24.8 N/mm < 35.8 N/mm < 36.4 N/mm < 44.1 N/mm, and the simulation values are 22.9 N/mm < 33.2 N/mm < 32.7 N/mm < 42.6 N/mm. The maximum values occur at 90° (44.1 N/mm, 42.6 N/mm), while the minimum values occur at 0° (24.8 N/mm, 22.9 N/mm). The chip morphology significantly changes with fiber orientation: 0° produces strip-shaped chips, 45° forms block-shaped chips, 90° results in particle-shaped chips, and 135° produces fragmented chips. On a micro scale, the microscopic morphology of the chips and the surface damage characteristics also exhibit gradient variations consistent with the experimental results. The developed model demonstrates high accuracy in predicting damage mechanisms and material removal behavior, providing a theoretical basis for optimizing CFRP machining parameters. Full article

Laser-induced periodic surface structures (LIPSSs) produced via ultrafast laser-induced oxidation offer a promising route for high-quality nanostructuring, with reduced thermal damage compared to conventional ablation-based methods. However, the influence of laser repetition frequency on the formation and morphology of oxidized LIPSSs remains insufficiently explored. In this study, we systematically investigate the effects of varying the femtosecond laser repetition frequency from 1 kHz to 100 kHz while keeping the total pulse number constant on the oxidation-induced LIPSSs formed on amorphous silicon films. Scanning electron microscopy and Fourier analysis reveal a transition between two morphological regimes with increasing repetition frequency: at low frequencies, the long inter-pulse intervals result in irregular, disordered oxidation patterns; at high frequencies, closely spaced pulses promote the formation of highly ordered, periodic surface structures. Statistical measurements show that the laser-modified area decreases with frequency, while the LIPSS period remains relatively stable and the ridge width exhibits a peak at 10 kHz. Finite-difference time-domain (FDTD) and finite-element simulations suggest that the observed patterns result from a dynamic balance between light-field modulation and oxidation kinetics, rather than thermal accumulation. These findings advance the understanding of oxidation-driven LIPSS formation dynamics and provide guidance for optimizing femtosecond laser parameters for precise surface nanopatterning. Full article

This study presents the implementation of a scalar transport algorithm in the recently developed General Ocean Model (GOM), a three-dimensional, unstructured grid, finite volume/finite difference model. Solving the advection–diffusion transport equation is an essential part of any ocean circulation model since the baroclinic density gradient distinguishes saline water from freshwater. To achieve both high accuracy and computational efficiency, we adopted a second-order semi-implicit Total Variation Diminishing (TVD) scheme. The TVD approach, known for its ability to suppress non-physical oscillations near steep gradients, provides a higher-fidelity representation of salinity fronts without introducing significant numerical artifacts. The TVD algorithm is constructed with the first-order Upwind scheme, which is known for suffering from excessive numerical diffusion, and the higher-order anti-diffusive flux term. The implemented transport algorithm is evaluated using two standard test cases, an ideal lock exchange problem and a U-shaped channel problem, and it is further applied to simulate salinity dynamics in Mobile Bay, Alabama. The model results from both the first-order Upwind and second-order TVD schemes are compared. The results indicate that the TVD scheme marginally improves the resolution of salinity fronts while maintaining computational stability and efficiency. The implementation enables a flexible and straightforward transition between the first-order scheme, which is faster than the second-order scheme, and the second-order scheme, which is less diffusive than the first-order scheme, enhancing the GOM’s capability for realistic and efficient salinity simulations in a tidally driven estuarine system. Full article

This paper introduces an enhanced Iterative Finite Difference (IFD) method for efficiently solving strongly nonlinear, time-dependent problems. Extending the original IFD framework for nonlinear ordinary differential equations, we generalize the approach to address nonlinear partial differential equations with time dependence. An improved strategy is developed to achieve high-order accuracy in space and time. A finite difference discretization is applied at each iteration, yielding a flexible and robust iterative scheme suitable for complex nonlinear equations, including the Sine-Gordon, Klein–Gordon, and generalized Sinh-Gordon equations. Numerical experiments confirm the method’s rapid convergence, high accuracy, and low computational cost. Full article

In order to conduct an in-depth and exhaustive investigation into the mechanical properties of steel tubes filled with wood, a thin-walled steel–wood composite column was elaborately designed. The damage progression, failure mode, and mechanical performance of this column under eccentric compression were systematically investigated through both experimental research and finite element simulations. The impacts of different numbers of bolts on the mechanical properties of the composite column were minutely analyzed, and the test results of composite columns were compared with the pure steel pipe column under the same experimental conditions. It was clearly observed that the pure thin-walled steel pipe specimen was highly susceptible to elastic instability under eccentric compression, and the high-strength and high-ductility potential of structural steel was not fully developed. However, after filling with wood and applying bolt restraints, the greater the number of bolts in the specimen of thin-walled steel–wood composite column under the identical eccentricity condition, the higher the ultimate load-bearing capacity. Specifically, the ultimate load-bearing capacity of the columns filled with wood increased by 77.78–114% in comparison with that of the pure steel pipe column. Through a meticulous comparison between the test and finite element analysis results, the error was ascertained to be in the range of 4.9–11.1%. In addition, filling the thin-walled steel tube with wood and restraining it with bolts can effectively enhance the lateral deformation resistance of the specimens, and the reduction rate of lateral deflection exceeded 50%. Moreover, the greater the number of filling bolts, the smaller the strain of components subjected to the eccentric compression occurred, and the better the mechanical properties. Full article

With growing demands for improved blast resistance in concrete protective structures, developing new concrete materials that combine high toughness, impact resistance, and efficient energy dissipation is essential. This study replaces conventional aggregates with titanium slag and prepares three specimen groups: pure cement mortar (control), cement mortar with large titanium slag particles, and an optimized mix with titanium slag aggregates. Using Split Hopkinson Pressure Bar (SHPB) tests and AUTODYN finite difference simulations, stress-wave absorption and attenuation performance were systematically investigated. Results show that, under identical impact loading rates, the large-particle titanium slag group increased energy absorption by 23.5% compared with the control, while the optimized mix improved by 19.2%. Both groups maintained stable absorption efficiencies across different loading rates. Numerical simulations reveal that the porous titanium slag model attenuated stress waves by approximately 67.9% after passing through three slag layers, significantly higher than the 51.4% attenuation in the non-porous model. This improvement is attributed to multiple wave reflections and interferences caused by a two-order-magnitude difference in the elastic modulus between the slag and air interfaces, creating ring-shaped stress concentrations that disrupt wave propagation and dissipate impact energy. This research provides experimental support and mechanistic insights for titanium slag application in novel blast-resistant concrete. Full article

Achieving high-order accuracy in finite difference/spectral methods for space-time fractional differential equations often relies on very restrictive and usually unrealistic smoothness assumptions in the spatial and/or temporal domains. For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial–fractional derivatives pose challenges, as they often lack guaranteed spatial smoothness, requiring non-smooth basis functions. In the temporal domain, finite difference schemes on uniformly graded meshes are commonly employed; however, achieving accuracy remains challenging for non-smooth solutions. In this paper, an efficient algorithm is adopted to improve the accuracy of finite difference/Pertrov–Galerkin spectral schemes for a time-space fractional reaction–diffusion equation, with a hyper-singular integral fractional Laplacian and non-smooth solutions in both time and space domains. The Pertrov–Galerkin spectral method is adapted using non-smooth generalized basis functions to discretize the spatial variable, and the L1 scheme on a non-uniform graded mesh is used to approximate the Caputo fractional derivative. The unconditional stability and convergence are established. The rate of convergence is $O\left(N^{\mu -\gamma }+K^{-min\{\rho \beta ,2-\beta \}}\right),$ achieved without requiring additional regularity assumptions on the solution. Finally, numerical results are provided to validate our theoretical findings. Full article

Implementing a computationally efficient numerical model for a single streamer discharge is essential to understand the complex processes such as lightning initiation and electrical discharges in high voltage systems. In this paper, we present a streamer discharge simulation in air, by solving one-dimensional (1D) drift diffusion reaction (DDR) equations for charged species with the disc approximation for electric field. A recently developed fourth-order space and time-centered implicit finite difference method (FDM) with a flux-corrected transport (FCT) method is applied to solve the DDR equations, followed by a comparative simulation using the well-established explicit FDM with FCT. The results demonstrate good agreement between implicit and explicit FDMs, verifying their reliability for streamer modeling. The total electrons, total charge, streamer position, and hence the streamer bridging time obtained using the FDMs with FCT agree with the same streamer computed in the literature using different numerical methods and dimensions. The electric field is obtained with good accuracy due to the inclusion of image charges representing the electrodes in the disc method. This accuracy can be further improved by introducing more image charges. Both implicit and explicit FDMs effectively capture the key streamer behavior, including the variations in charged particle densities and electric field. However, the implicit FDM is computationally more efficient. Full article

Composite integral formulas offer greater accuracy by dividing the interval into smaller subintervals, which better capture the local behavior of function. In the finite volume method for solving differential equations, composite formulas are mostly used on control volumes to achieve high-accuracy solutions. In this work, error estimates of the composite Simpson’s formula for differentiable convex functions are established. These error estimates can be applied to general subdivisions of the integration interval, provided the integrand satisfies a first-order differentiability condition. To this end, a novel and general integral identity for differentiable functions is established by considering general subdivisions of the integration interval. The new integral identity is proved in a manner that allows it to be transformed into different identities for different subdivisions of the integration interval. Then, under the convexity assumption on the integrand, sharp error bounds for the composite Simpson’s formula are proved. Moreover, the well-known Hölder’s inequality is applied to obtain sharper error bounds for differentiable convex functions, which represents a significant finding of this study. Finally, to support the theoretical part of this work, some numerical examples are tested and demonstrate the efficiency of the new bounds for different partitions of the integration interval. Full article

This paper introduces a stable non-standard finite difference (NSFD) method to solve time-fractional singularly perturbed convection–diffusion problems. The fractional derivative in time is defined in the Caputo sense. The proposed method shows high efficiency when applied using a uniform mesh and can be easily extended to a Shishkin mesh in the spatial domain. We discuss error estimates to demonstrate the convergence of the numerical scheme. Additionally, various numerical examples are presented to illustrate the behavior of the solution for different values of the perturbation parameter $ϵ$ and the order of the fractional derivative. Full article