Search Results (153)

The combined finite–discrete element method (FDEM) is an advanced numerical calculation method that is highly suitable for simulating the entire rock blasting process. Considering that rock mass contains many joints, the present study introduces a rock joint constitutive model to capture the transmission and reflection phenomena of blasting stress waves when they reach the joint. At the same time, based on the original FDEM code, an optimized blasting calculation model is proposed. This model considers the effect of explosive gas and accurately describes the physical relationship between the explosive gas pressure and the change in the blasting chamber area caused by crack propagation. To overcome the limitation of previous blasting models that only apply the pressure of the explosive gas to the borehole wall, the present study optimizes the determination conditions for crack penetration and the calculation method for the blasting chamber area as well as further considered the influence of the embedding effect of explosive gas on crack propagation. Finally, through three examples, the transmission and reflection laws of stress waves at the joints and the entire process of rock mass throw blasting are simulated. The results illustrate that this model can capture the propagation of stress waves, the gas wedge effect of explosive gas, and the entire process of crack initiation, propagation, and penetration in the rock mass during the explosion, demonstrating the potential of FDEM in blasting simulation. Full article

Clarifying the mechanical properties and failure patterns of layered coal–rock combinations in coal-measure strata is critical to guiding hydraulic fracturing design in petroleum and mining engineering. This paper investigates the mechanical properties, failure patterns, and stress distributions of sandstone–coal–sandstone (SCS) and mudstone–coal–mudstone (MCM) combinations under different confining pressures and thickness ratios based on the 3D combined finite–discrete element method (3D FDEM). The results show that the mechanical strength of the SCS combination is higher than that of the MCM combination under the same conditions. As the thickness ratio increases, the overall peak stress and elastic modulus of the combination decrease gradually and eventually approach those of the pure coal. As confining pressure increases, the peak stress of layered coal–rock combinations rises gradually, plastic behaviors become increasingly prominent, and the failure mode of the mudstone layer transitions from tensile-dominated to shear-dominated. Under different thickness ratios and confining pressures, the coal layer in the combinations primarily develops shear-dominated cracks, whereas the sandstone layer mainly generates tensile-dominated cracks. An increase in confining pressure elevates the critical thickness ratio for sandstone layer failure in the SCS combination. Essentially, the changes in stress state caused by rock types, thickness ratios, and confining pressures are important reasons for the variations in the failure patterns of each layer in layered coal–rock combinations. The key findings of this paper are expected to provide theoretical guidance for the field design of petroleum and coal mine engineering. Full article

The construction of underground reservoirs in coal goafs is an innovative technology to alleviate the coal–water conflict in arid mining areas of northwest China. However, its widespread application is constrained by the challenge of accurately predicting water inflow, which fluctuates significantly due to the dynamic “expansion–closure” behavior of mining-induced fractures. This study focuses on the Shendong mining area, where repeated multi-seam mining occurs, and employs a coupled Finite Discrete Element Method (FDEM) and Computational Fluid Dynamics (CFD) numerical model, combined with in situ tests such as drilling fluid loss and groundwater level monitoring, to quantify the evolution of overburden fractures and their impact on reservoir water inflow during mining, 8 months post-mining, and after 7 years. The results demonstrate that the height of the water-conducting fracture zone decreased from 152 m during mining to 130 m after 7 years, while fracture openings in the key aquifer and aquitard were reduced by over 50%. This closure process caused a dramatic decline in water inflow from 78.3 m³/h to 2.6 m³/h—a reduction of 96.7%. The CFD-FDEM simulations showed a deviation of only 10.6% from field measurements, confirming fracture closure as the dominant mechanism driving inflow attenuation. This study reveals how fracture closure shifts water flow patterns from vertical to lateral recharge, providing a theoretical basis for optimizing the design and sustainable operation of underground reservoirs. Full article

This study analyzes a hybrid computational framework that combines peridynamics (PD) and the finite element (FE) method to model wave propagation in a one-dimensional bar, focusing on their integration for enhanced accuracy and efficiency. The analysis investigates PD’s ability to capture non-local interactions in regions near loading points, with computationally efficient coarse discretization in other areas through finite element methods. The dynamic response to symmetric and asymmetric axial loading, including loading and unloading phases, is analyzed through time-dependent external forces, solving displacement, velocity, and acceleration fields at each time step. The effects of PD-specific parameters, such as the horizon size, and the FE–PD node spacing size ratios on the performance of the hybrid model in wave propagation are investigated. Additionally, the study examines the von Neumann stability for PD to ensure stability and reliability, offering a robust framework for integrating PD and FE in dynamic analyses. Full article

The numerical solution of space-fractional diffusion problems is investigated focusing on stability and non-negativity issues. The extension of classical schemes is analyzed for the case of the spectral fractional Dirichlet Laplacian operator. For the spatial discretization, both finite differences and finite elements are used. The finite element case needs special care and is discussed in detail. Both spatial discretizations are combined with the matrix transformation method, leading to fractional powers of matrices in the discretized problems. In the time stepping, $\theta$-methods are utilized with $\theta =0,{\displaystyle \frac{1}{2}}$ and 1. In the analysis, it is pointed out that the stability condition in the case of $\theta =0$ depends on the fractional power $\alpha \in (0,1]$, which results in a weaker condition on the time discretization compared to the conventional diffusion. In this case, we also obtain non-negativity preservation. Also, unconditional stability is established for $\theta ={\displaystyle \frac{1}{2}}$ and $\theta =1$, where for the spatial discretization rather general conditions are posed. The results containing stability conditions are also confirmed in a series of numerical experiments. In the course of the corresponding algorithms, an efficient matrix power–vector product procedure is employed to keep simulation time at an affordable level. The associated computational algorithm is also described in detail. Full article

Propagation phase metasurfaces have excellent electromagnetic regulation and polarization-insensitive properties, while roll-to-plate nanoimprint lithography (R2P-NIL) is ideal for their large-scale low-cost fabrication. Existing demolding simulations for R2P-NIL are limited to 2D analysis, ignore elastomeric roller impacts, and cannot handle the discrete pillar/hole structures of such metasurfaces. This study establishes a 3D multiscale simulation model using a finite element method combining a macroscopic elastomeric roller deformation model and a microscopic demolding stress model with motion equation-based parameter transfer. Simulation results show macroscopically that zero elastomeric layer thickness minimizes stress, while stress rises and then stabilizes with increasing thickness; a moderately larger roller radius disperses stress; excessive pressure amplifies stress; a microscopically higher resist elastic modulus lowers stress; cylindrical structures have less stress than cuboids; and the limit aspect ratio peaks at a 100 nm line width. This work provides theoretical support for R2P-NIL parameter optimization and promotes the stable large-scale production of propagation phase metasurfaces. Full article

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (${\mathrm{H}}_2^{+}$) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields. Full article

Efficient and accurate forward modeling of electromagnetic fields is essential for advancing geophysical exploration in complex marine environments. However, realistic survey conditions characterized by low-frequency spectra, fine sedimentary strata, irregular bathymetry, and anisotropic materials pose significant challenges for conventional numerical methods. To address these issues, this work presents a parallel modeling framework that combines coordinate transformations with an adaptive high-order finite-element approach for 3D marine controlled-source electromagnetic (MCSEM) simulations. The algorithm exploits the form invariance of Maxwell’s equations to map the original boundary value problem over the physical domain to one defined over a computationally favorable domain filled with anisotropic media. The transformed model is then discretized and solved using a parallel high-order finite-element scheme enhanced with a goal-oriented adaptive mesh refinement strategy. We examine the performance of the proposed framework using both synthetic models and the realistic Marlim R3D benchmark dataset. The results demonstrate that the proposed approach can effectively reduce computational costs while maintaining high accuracy across a wide frequency range and varying water depths. These findings highlight the framework’s potential for large-scale, high-resolution CSEM exploration of offshore resources. Full article

This study investigates the influence of particle morphology on two-dimensional (2D) single rock particle breakage using the combined finite-discrete element method (FDEM) coupled with fractal dimension analysis. Three key shape descriptors (elongation index EI, roundness index Rd, and roughness index Rg) were systematically varied to generate realistic particle geometries using the Fourier transform and inverse Monte Carlo. Numerical uniaxial compression tests revealed distinct morphological influences: EI showed negligible impact on crushing strength or fragmentation, and Rd significantly increased crushing strength and fragmentation due to improved energy absorption and stress distribution. While Rg reduced strength through stress concentration at asperities, suppressing fragmentation and elastic energy storage. Fractal dimension analysis demonstrated an inverse linear correlation with crushing strength, confirming its predictive value for mechanical performance. The validated FDEM framework provides critical insights for optimizing granular materials in engineering applications requiring morphology-controlled fracture behavior. Full article

This paper considers the multi-term subdiffusion equation with weakly singular solutions. In order to use sparser meshes near the initial time, a novel scheme (which we call the corrected L1 scheme) on graded meshes is constructed to estimate the multi-term Caputo fractional derivative by investigating a corrected term for the nonuniform L1 scheme. Combining this nonuniform corrected L1 scheme in the temporal direction and the finite element method (FEM) in the spatial direction, a fully discrete scheme for solving the multi-term subdiffusion equation is developed. The stability result of the developed scheme is given. Furthermore, the optimal pointwise-in-time error estimate of the developed scheme is derived. Finally, several numerical experiments are conducted to verify our theoretical findings. Full article

The dynamic fracture of rocks under impact loads has many engineering applications such as rock blasting. This study reviews the recent achievements of investigating rock dynamic fracturing and its application in rock blasting using computational mechanics methods and highlights the prospects of modelling them with a hybrid finite-discrete element method (HFDEM) originally developed by the authors. The review first summarizes the peculiarities of rock dynamic fracturing compared with static fracturing, which are that the physical-mechanical properties of rocks, including stress wave propagation, strength, fracture toughness, energy partition and cracking mechanism, depend on loading rate. Then the modelling of these peculiarities and their applications in rock blasting using fast developing computational mechanics methods are reviewed with a focus on the advantages and disadvantages of prevalent finite element method (FEM) as representative continuum method, discrete element method (DEM) as representative discontinuum method and combined finite-discrete element (FDEM) as representative hybrid method, which highlights FDEM is the most promising method for modelling rock dynamic fracture and blasting application as well as points out the research gaps in the field of modelling the dynamic fracture of rocks under impact loads. After that, the progress of shortening some of these gaps by developing and applying HFDEM, i.e., the authors’ version of FDEM, for modelling rock dynamic fracture and applications in rock blasting are reviewed, which include the features of modelling the effects of loading rate; stress wave propagation, reflection and absorbing as well as stress wave-induced fracture; explosive-rock interaction including detonation-induced gas expansion and flow through fracturing rock; coupled multiaxial static and dynamic loads; heterogeneous rock and rock mass with pre-existing discrete fracture network; and dynamic fracturing-induced fragment size distribution. Finally, the future directions of modelling the dynamic fracture of rocks under impact loads are highlighted and a systematic numerical approach is proposed for modelling rock blasting. Full article

To prevent the occurrence of excavation face instability incidents during shield tunneling, this study takes the Bailuyuan tunnel of the ‘Hanjiang-to-Weihe River Water Diversion Project’ as the engineering background. A three-dimensional discrete element method simulation was employed to analyze the tunneling process, revealing the displacement response of the excavation face to various tunneling parameters. This led to the development of a risk assessment method that considers both tunneling parameters and geological conditions for deep-buried shield tunnels. The above method effectively overcomes the limitations of finite element method (FEM) studies on shield tunneling parameters and, combined with the Analytic Hierarchy Process (AHP), enables rapid tunnel analysis and assessment. The results demonstrate that the displacement of the excavation face in shield tunnel engineering is significantly influenced by factors such as the chamber earth pressure ratio, cutterhead opening rate, cutterhead rotation speed, and tunneling speed. Specifically, variations in the chamber earth pressure ratio have the greatest impact on horizontal displacement, occurring predominantly near the upper center of the tunnel. As the chamber earth pressure ratio decreases, horizontal displacement increases sharply from 12.9 mm to 267.3 mm. Conversely, an increase in the cutterhead opening rate leads to displacement that first rises gradually and then rapidly, from 32.1 mm to 121.1 mm. A weighted index assessment model based on AHP yields a risk level of Grade II, whereas methods from other scholars result in Grade III. By implementing measures such as adjusting the grouting range, cutterhead rotation speed, and tunneling speed, field applications confirm that the risk level remains within acceptable limits, thereby verifying the feasibility of the constructed assessment method. Construction site strategies are proposed, including maintaining a chamber earth pressure ratio greater than 1, tunneling speed not exceeding 30 mm/min, cutterhead rotation speed not exceeding 1.5 rpm, and a synchronous grouting range of 0.15 m. Following implementation, the tunnel construction successfully passed the high-risk section without any incidents. This research offers a decision-making framework for shield TBM operation safety in complex geological environments. Full article

We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative ($0<\alpha <1$) with mixed finite element methods (P1b–P1 and $P_2$–$P_1$) for spatial discretization of velocity and pressure. This approach addresses the key challenges of fractional models, including nonlocality and memory effects, while maintaining stability in the presence of the nonlinear damping term ${\gamma \left|\mathbf{u}\right|}^{r-2}\mathbf{u}$, for $r\ge 2$. We prove unconditional stability for both semi-discrete and fully discrete schemes and derive optimal error estimates for the velocity and pressure components. Numerical experiments validate the theoretical results. Convergence tests using exact solutions, along with benchmark problems such as backward-facing channel flow and lid-driven cavity flow, confirm the accuracy and reliability of the method. The computed velocity contours and streamlines show close agreement with analytical expectations. This scheme is particularly effective for capturing anomalous diffusion in Newtonian and turbulent flows, and it offers a strong foundation for future extensions to viscoelastic and biological fluid models. Full article

Gas turbines in land-based microgrids and shipboard-isolated power grids frequently face operational challenges, such as the startup and shutdown of high-power equipment and sudden load fluctuations, which significantly impact their performance. To examine the dynamic behavior of gas turbines under transitional operating conditions, a three-dimensional computational fluid dynamic simulation is employed to create a model of the gas turbine rotor, incorporating thermal inertia, which is then analyzed in conjunction with three-dimensional finite element methods. The governing equations of the flow field are discretized, providing results for the flow and temperature fields throughout the entire flow path. A hybrid approach, combining temperature differences and heat flux density, is applied to set the thermal boundary conditions for the walls, with the turbine’s operational state determined based on the direction of heat transfer. Additionally, mesh division techniques and turbulence models are selected based on the geometric dimensions and operating conditions of the compressor and turbine. The simulation results reveal that thermal inertia induces a shift in the dynamic characteristics of the rotor components. Under the same heat transfer conditions, variations in rotational speed have a minimal impact on the shift in the characteristic curve. The working fluid temperature inside the compressor components is lower, with a smaller temperature difference from the wall, resulting in less intense heat transfer compared to the turbine components. Overall, heat transfer accounts for only about 0.1% of the total enthalpy at the inlet. When heat exchange occurs between the working fluid and the walls, around 6–15% of the exchanged heat is converted into changes in technical work, with this percentage increasing as the temperature difference rises. Full article

Multi-tethered spacecraft formation refers to a group of spacecraft that are connected by tethers. These spacecraft work together to perform tasks, such as encircling and capturing small celestial bodies. When the multi-tethered spacecraft formation is in the process of encircling and capturing small celestial bodies, there is a significant risk of the tethers colliding with the soil (or surface material) of the small celestial body. Such a collision can affect the trajectory of the small celestial body detector. To address this issue, a coupled dynamic model has been proposed. This model takes the interaction between the tethers and the soil of the small celestial body into account. The discrete element method is used to establish the asteroid soil model, and the multi-body-tethered spacecraft system is simplified into a two-spacecraft system. The detector model is established by using the dual quaternion, and the tether model is established by using the chain rod model combined with the finite element method. Finally, a multi-condition simulation test is carried out. The results show that the influence of tether–soil coupling on the trajectory of the detector is mainly as follows: the influence of tether–soil interaction on the trajectory of the detector is mainly reflected in the displacement of the detector along the axial direction of the tether. Full article