Abstract The lattice Boltzmann method (LBM) has been successfully applied to the simulation of fluid flows for over three decades. In recent years, it has also been extended to solid mechanics, particularly for elastodynamics. This work presents a comprehensive introduction to the moment chain LBM for solids, focusing on the two-relaxation-time (TRT) scheme. The method is based on a chain of balance equations, which allows for the simulation of wave propagation in elastic solids. The TRT scheme improves stability and accuracy, making it suitable for a wide range of material parameters. The method is applied to wave propagation in solids with an analysis of the energy dissipation. The results demonstrate the effectiveness of the moment chain LBM for simulating elastodynamics and highlight its potential for future applications in solid mechanics.

Abstract This study investigates the size-dependent breakage force of brittle, near-spherical particles under quasi-static compressive loading. A physically motivated analytical model is derived, predicting a power-law relationship between particle size and breakage force—specifically, a quadratic scaling with diameter and a 2/3-power scaling with mass. To validate this model, a multi-material experimental campaign using synthetically produced spherical specimens was conducted, followed by a numerical simulation campaign using the Discrete Element Method (DEM) with a bonded particle modelling (BPM) approach. The experimental results confirmed the proposed scaling law, with coefficients of determination (R 2 ) exceeding 0.94 for a combined material consideration. The DEM simulations, calibrated using experimental data, reproduced breakage forces, and scaling patterns with high fidelity and enabled extension of the size range by a factor of more than two in diameter and four in mass, whilst also increasing statistical resolution through a higher number of replicates per size class. This numerical extension not only enabled broader parameter exploration but also mitigated experimental limitations, such as specimen variability, preparation inconsistency, and practical size constraints.Across analytical, experimental, and numerical approaches, consistent agreement was found, supporting the general applicability of the model. The findings provide a robust basis for defining breakage thresholds in DEM-based simulations—e.g. for replacement-based approaches—and offer a scalable alternative to physical testing. The validated framework facilitates improved prediction of breakage behaviour in slow compression systems such as jaw crushers and contributes to the broader understanding of particle-scale mechanics in brittle materials.

Abstract Reliable pore-scale particle tracking is pivotal for understanding non-Fickian transport in dual-porosity media, yet the computational burden of deep-learning pipelines can limit their practical use. This study systematically quantifies how two fundamental hyper-parameters—image resolution and training batch size—jointly shape accuracy and efficiency in a state-of-the-art tracker that couples SimVP video prediction with Trackpy-derived ground truth. Fluorescence microscopy movies (1328 frames, 3672 × 4100 px) of colloid migration through a PDMS micromodel were down-scaled to 64–400 px and trained with batch sizes of 4 or 8. Point-wise errors (MSE, MAE, RMSE), structural fidelity (SSIM, PSNR), and perceptual quality (LPIPS) were evaluated on validated trajectories, 1000 unseen pairs, and a blind hold-out set. Increasing resolution from 64 to 300 px raises pixel-based errors (MSE × ≈700) and inference time (0.26 s → 5 s batch⁻ 1 ) but unlocks a 20-fold rise in detected particles, while perceptual metrics remain above high-quality thresholds (SSIM > 0.999). Reducing the batch from 8 to 4 consistently halves to tenfold improves all error metrics, boosts PSNR by ~ 8 dB, and lowers LPIPS by up to 85%, with minimal variance penalties. Recommended operating points are: batch 4 @ 300 px for maximum fidelity, batch 4 @ 400 px for the densest particle fields, and batch 8 @ 128–256 px where real-time throughput dominates. These results provide concrete guidelines for balancing accuracy, particle yield, and computational cost in next-generation pore-scale imaging studies.

Abstract Particle-laden flows are fundamental in numerous engineering fields, including environmental hydraulics, sediment transport, and process engineering, where understanding the interaction between fluid and particulate phases is critical for design and prediction. This work presents a novel mixture model for sediment transport within the Particle Finite Element Method (PFEM) framework. The model couples the Navier–Stokes equations for fluid flow with a transport-diffusion equation for sediment concentration, treating sediment as a scalar field rather than discrete particles. This approach enables efficient simulation of fluid–sediment interactions without the computational cost of tracking individual sediment particles and their contacts. PFEM’s Lagrangian nature allows the mesh to follow the flow motion, with remeshing strategies implemented to maintain mesh quality during large deformations. The model incorporates both Neumann and Robin boundary conditions for sediment concentration, enabling a realistic representation of sediment deposition and exchange at fluid–bed interfaces. Validation is conducted through two- and three-dimensional test cases, including channel flows, gravity current intrusion with multiple fluids, and sediment deposition in tanks with orifices. Comparisons with experimental data and particle-based simulations demonstrate that the model captures key sediment transport phenomena accurately under low-concentration conditions. The proposed mixture model offers a robust and computationally efficient tool for simulating sediment-laden flows in engineering applications.