Particle Method Research Articles

Embedment of WENO-Z reconstruction in Lagrangian WLS scheme implemented on GPU for strongly-compressible multi-phase flows

It is a notoriously challenge problem for Lagrangian particle methods to solve compressible flows with strong discontinuities and large volume variations. To overcome the problems of numerical oscillations, an accurate and stable Lagrangian Weighted-Least-Square (LWLS) method embedded with WENO-Z scheme (LWLS-WENO-Z) is proposed. To further enhance the numerical accuracy and stability, the particle shifting technique, the multi-level local-refinement technique, and the interface repulsive force are appropriately employed in the numerical scheme. Moreover, the smooth and stable coupled particle method between the LWLS and Roe's Riemann solver (LWLS-RR) is considered for the comparisons, further demonstrating the merit of the proposed LWLS-WENO-Z scheme. To reduce the simulation time, parallel computing with a CUDA-based program for the proposed scheme is implemented on a single GPU. In the numerical experiments, several 1D/2D benchmarks are solved to test the accuracy of the proposed method. Particularly, the challenge 2D underwater explosion and the cavitation bubble collapse and jetting are numerically investigated. Compared to other reference solutions, the present coupled particle method demonstrates robustness and superior accuracy in simulating these strongly-compressible multi-phase flows.

Research on multi-velocity measurement method of solid particles based on interdigital electrostatic sensor

Abstract In gas-solid two-phase flow, the velocities of solid particles will show different distributions as the flow pattern changes, and it is a challenging task to achieve the measurement of different velocity parameters in the flow field. To obtain the velocity information of solid particles in the flow field, a novel method to achieve multi-velocity measurement of solid particles is proposed by using the spatial filtering characteristics of interdigital electrostatic sensor with variational mode decomposition (VMD). Firstly, a three-dimensional model of the interdigital electrostatic sensor is established using COMSOL simulation software. Based on its spatial dynamic sensitivity, a theoretical analysis of its spatial filtering characteristics is conducted to obtain a mathematical relationship for velocity measurement. Subsequently, the VMD decomposition method is applied to an experiment involving charged wires, with the experimental results verifying the effectiveness of VMD in achieving multi-scale decomposition of electrostatic signals. Finally, the proposed measurement method is validated on a gravity feeding device and a pneumatic conveying system. The experimental results demonstrate that the method exhibits good feasibility.

Regularized Stein Variational Gradient Flow

AbstractThe stein variational gradient descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the Wasserstein gradient flow corresponding to the KL-divergence minimization. In this work, we propose the Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein gradient flow. We establish various theoretical properties of the Regularized Stein Variational Gradient Flow (and its time-discretization) including convergence to equilibrium, existence and uniqueness of weak solutions, and stability of the solutions. We provide preliminary numerical evidence of the improved performance offered by the regularization.

Noise radiation from a partially opened and elevated tunnel-tube

Road or railway tunnels are considered in noise prediction programs generally by neglecting any emission from the tunnel structure between the openings and replacing each tunnel mouth by additional sources simulating the sound radiated from inside to outside through these openings. The sound pressure level inside the tunnel can be derived from the analog model of a room formed by a slice cut out of the extended tunnel with two perfect reflecting planes perpendicular to the tunnel axis. The paper presents a methodology for the case of an elevated tunnel tube with an upper ventilation gap running over the entire length of the tunnel to calculate the sound pressure levels in the surrounding area more approximately using engineering models like ISO 9613-2 or others and more detailed using a particle method developed to account for complete 3-dimensional propagation problems.

Enhanced schemes for resolution of the continuity equation in projection-based SPH

To the best knowledge of the authors, the numerical resolution of the continuity equation, i.e., the simultaneous achievement of accurate and physically consistent velocity divergence and density fields, has not been investigated in the context of projection-based particle methods. In this study, based on the Velocity-divergence Error Mitigating (VEM)/Volume Conservation Shifting (VCS) schemes developed for the WCSPH method, which improve the numerical resolution of the continuity equation, VEM/VCS schemes are proposed for projection-based particle methods. Furthermore, two other novel schemes are introduced. First, a Dynamic VEM (DVEM) scheme is proposed, where VEM is dynamically activated only when the velocity divergence instantaneously diverge from the reference solution at individual particles. The second scheme is referred to as Enhanced VCS by reference density (EVCS), where precise imposition of dynamic free surface boundary condition is considered. Several benchmark tests with different features have been conducted, and it is shown that the proposed schemes enhance the numerical resolution of the continuity equation for incompressible flows, i.e., the divergence free velocity and the constant density conditions. Application of DVEM and EVCS has provided enhanced resolution of the continuity equation along with clear reductions in the numerical energy dissipation associated with the approximated additional numerical terms.

Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier–Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the ’90s and have several interesting features, such as being grid-free, automatically adapting to the solution by concentrating elements where the gradient is large, and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws. To achieve this goal, we first extend the classical Monte Carlo method to relaxation approximation of systems of conservation laws, and subsequently consider a novel particle dynamics based on the spatial derivatives of the solution. The methodology, combined with asymptotic-preserving splitting discretization, yields a way to construct a new class of gradient-based Monte Carlo methods for hyperbolic systems of conservation laws. Several results in one spatial dimension for scalar equations and systems of conservation laws show that the new methods are very promising and yield remarkable improvements compared to standard Monte Carlo approaches, either in terms of variance reduction as well as in describing the shock structure.

Fluid–Structure Interaction Analysis of Manta-Bots with Self-Induced Vertical Undulations during Fin-Based Locomotion

Driven by the demands of ocean exploration, an increasing number of manta ray-inspired robots have been designed and manufactured, primarily utilizing flexible skeletons combined with motor-driven mechanisms. However, the mechanical analysis of these designs remains underdeveloped, often relying on simplistic imitation of biological prototypes and typically neglecting the vertical motion induced by pectoral fin flapping. This paper presents a fluid–structure interaction analysis framework that couples rigid body motion with elastic deformation using flexible multibody dynamics and the vortex particle method. An implicit iterative algorithm with Aitken relaxation is employed to address added-mass instability, and the framework has been validated against experimental data. An analysis of a representative manta-bot model shows that self-induced vertical undulations reduce the thrust coefficient by approximately 40% compared to fixed vertical degrees of freedom, while slightly improving overall propulsive efficiency. The study also highlights the critical role of mass distribution in manta-bots, noting that excessive focus on complex pectoral fin movements and large fin mass can significantly reduce thrust by increasing vertical displacement, ultimately proving counterproductive.

Deterministic particle method for Fokker–Planck equation with strong oscillations

Deterministic particle method for Fokker–Planck equation with strong oscillations

Ghost Red Blood Cells For Enhanced Particle Detection With Defocusing PTV In Microcirculation Experiments

Particle tracking of rigid fluorescent particles in microcirculation environments is often found to be difficult, since the presence of red blood cells (RBCs) at physiologically relevant conditions (i.e., hematocrit) masks the particle images. In turn, making particle detection challenging. To overcome this difficulty, we propose to use ghost RBCs for enhanced particle detection. These are quasi-transparent RBCs obtained by removing the hemoglobin from normal RBCs. To understand whether the ghost RBCs can improve the particle detection, we performed defocusing particle tracking measurements with the general defocusing particle tracking (GDPT) method of the rigid fluorescent particles in normal and ghost RBC flows. The measurements were performed at physiological relevant hematocrit and for three different flow rates. From the three-dimensional particle trajectories, we evaluated the correlation coefficient from the GDPT evaluations and compared the fluid dynamic behavior of the two types of cells. Overall, the results show that ghost RBCs are an attractive solution for this type of experiments, since they improve the correlation coefficients up to values similar to cell-free experiments, while exhibiting a fluid dynamic behavior similar to normal RBCs i.e., in terms of velocity and relative viscosity data.

Numerical analysis of fast ions transport induced by magnetic islands in HL-2A

The transport of beam ions in the presence of single/multiple tearing modes (TMs) under HL-2A geometry has been investigated by test particle method. Simulation results show that there exists a threshold behavior in the number of lost beam ions in the plasma under perturbation of a (2,1) TM with amplitude α0 : when the amplitude α0 is over a critical value, the number of lost beam ions increases linearly with α0 at a much faster pace. Further analysis finds that the lost beam ions have relatively higher percentage of high energy at α0 around the critical value. It also finds that the distribution of lost beam ions which is initially concentrated on the high field side expands gradually toward the low field side as the perturbation amplitude α0 increases. From the phase space analysis, it shows that the enhanced outward transport of fast ions in the presence of magnetic islands results from orbit stochasticity, which is due to the overlap of the drift islands in the interaction of fast ions with TMs. When two TMs are simultaneously present, the stochastic threshold of fast ion orbit is found to be lower than that in their individual TM case. The phase space analysis shows that in the presence of two modes with the same toroidal mode number, the modes increase the loss of fast ions when they are out of phase; however, such the effect of strengthening transport of fast ions turns to weaken when they are in phase. In contrast, when two modes each with a different toroidal mode number, their phase difference phase hardly has any effect on the transport of fast ions.

The Impact of Velocity Update Frequency on Time Accuracy for Mantle Convection Particle Methods

AbstractComputing the velocity field is an expensive process for mantle convection codes. This has implications for particle methods used to model the advection of quantities such as temperature or composition. A common choice for the numerical treatment of particle trajectories is classical fourth‐order explicit Runge–Kutta (ERK4) integration, which involves a velocity computation at each of its four stages. To reduce the cost per time step, it is possible to evaluate the velocity for a subset of the four time integration stages. We explore two such alternative schemes, in which velocities are only computed for: (a) stage 1 on odd‐numbered time steps and stages 2–4 for even‐numbered time steps, and (b) stage 1 for all time steps. A theoretical analysis of stability and accuracy is presented for all schemes. It was found that the alternative schemes are first‐order accurate with stability regions different from that of ERK4. The efficiency and accuracy of the alternate schemes were compared against ERK4 in four test problems covering isothermal, thermal, and thermochemical flows. Exact solutions were used as reference solutions when available. In agreement with theory, the alternate schemes were observed to be first‐order accurate for all test problems. Accordingly, they may be used to efficiently compute solutions to within modest error tolerances. For small error tolerances, however, ERK4 was the most efficient.

Simulation of the key phenomena in nuclear reactor two-phase flow and severe accident with particle method

Simulation of the key phenomena in nuclear reactor two-phase flow and severe accident with particle method

Simulation of flip-flow screening adhesive organic fertilizer particles based on DEM-MBD coupling method

For screening adhesive organic fertilizer particles, a Discrete Element Method (DEM) and Multi-Body Dynamics (MBD) coupling model of screening adhesive organic fertilizer particles using a flip-flow screen is established. Then, the velocity, the distribution and the trajectory of the particles during the screening process are observed. Finally, the effects of the surface energy γ, the rotational speed n, the tensional amount ∆l and the feed rate M are investigated. The results show that the flip-flow screen could provide a high velocity for depolymerization of agglomerated particles and separation of adhesive particles from the screen panels, so adhesive organic fertilizer particles can be successfully screened by using the flip-flow screen and organic fertilizer particles in an easily absorbed range are obtained. With the increase of γ, both the flow rate and the screening efficiency decrease. With the increase of n, both first increase and then slightly decrease. With the increase of ∆l, both increase at a low n, or slightly decrease at a high n. With the increase of M, the screening efficiency decreases, while the total flow rate first increases and then decreases. Through adjusting n, ∆l, M, flip-flow screen can also be used to screen other adhesive particles.

Biocompatible Janus microparticle synthesis in a microfluidic device.

Janus particles are popular in recent years due to their anisotropic physical and chemical properties. Even though there are several established synthesis methods for Janus particles, microfluidics-based methods are convenient and reliable due to low reagent consumption, monodispersity of the resultant particles and efficient control over reaction conditions. In this work a simple droplet-based microfluidic technique is utilized to synthesize magnetically anisotropic TiO2-Fe2O3 Janus microparticles. Two droplets containing reagents for Janus particle were merged by using an asymmetric device such that the resulting droplet contained the constituents within its two hemispheres distinct from each other. The synthesized Janus particles were observed under the optical microscope and the scanning electron microscope. Moreover, a detailed in vitro characterization of these particles was completed, and it was shown that these particles have a potential use for biomedical applications.

Influence of WC particle size and morphology on the performance of NiCu-based composite coatings deposited by laser direct energy deposition

NiCu alloys are commonly utilized due to their outstanding plasticity, toughness, corrosion resistance, and thermal conductivity. Nevertheless, their limited hardness and wear resistance have hindered their further development. In this study, 24CrNiMo alloy brake disc was coated with NiCu-based composite coatings containing different sizes and shapes of tungsten carbide, in order to investigate the effects of tungsten carbide particle characteristics on the microstructure, microhardness and wear resistance of Nickel‑copper composite coating. The results show that the microstructure of the coatings was minimally affected by the size and morphology of the WC particles, while non-spherical WC particles exhibited superior uniformity within the coatings. In terms of microhardness, smaller WC particles demonstrated a more consistent distribution. The ball-disk wear tests revealed that coatings with larger WC particles displayed better wear resistance in sizes, while those with non-spherical WC particles exhibited excellent resistance to wear in morphologies. Additionally, in abrasive wear tests, composite coatings containing spherical WC particles demonstrated superior wear resistance compared to those containing non-spherical WC particles. The diverse wear resistance observed in different wear experiments among the various WC coatings can be attributed primarily to differences in the distribution and preparation methods of the WC particles. Consequently, these findings hold significant promise for the practical application of NiCu-based composite coatings in industry.

Segment-based wall treatment model for heat transfer rate in smoothed particle hydrodynamics

We propose a new smoothed particle hydrodynamics (SPH) model that applies a segment-based wall boundary treatment method (SBWM) for heat transfer applications. We begin by focusing on natural convection simulations, where accurately modeling heat-transferring wall boundaries is crucial as they are the energy source driving the flow. A conventional SPH approach that handles such tasks is the boundary particle (BP) method, which constructs wall boundaries by placing multiple layers of particles on and behind the walls. Despite its capability of imposing accurate boundary conditions, the BP approach becomes a non-trivial task when the fluid domain involves complex boundaries. Moreover, computational costs may significantly increase because of the increased number of SPH particles necessary for modeling walls. Therefore, we utilize the recent development of SBWM to efficiently model energy-transferring wall boundaries. Specifically, SBWM is applied to the energy conservation equation for the wall heat transfer model, using the boundary truncation terms derived in this work. The SBWM-SPH method is verified in various numerical examples, comparing the results with BP-SPH and finite volume method as well as experimental data in the literature. Our study finally extends to investigating a heat exchanger with an optimized shape, demonstrating how SBWM-SPH effectively handles practical issues associated with the BP method while providing accurate heat transfer calculations for the wall.

Implementation and Linearization of a Coupled Panel and Vortex Particle Method in State-Space Form

This paper describes the implementation and linearization of a coupled panel and vortex particle method in a state-variable form. More specifically, the coupled panel and vortex particle dynamics are formulated as a nonlinear system of ordinary differential equations in first-order form to be self-contained and inherently linearizable. Linearization of this coupled panel and vortex particle method is demonstrated via finite differencing and a novel analytical linearization technique to yield a linear time-invariant representation. The code is implemented in MATLAB® and validated against an open-source aerodynamic solver for a fixed wing in both stationary and unsteady conditions. The linearized models are verified against the nonlinear dynamics both in the time and frequency domains. Linearized models accurately represent the wake dynamics about the equilibrium condition for moderate amplitude inputs and for input frequencies covering the typical frequency range of flight dynamics and flight controls, i.e., 0.3–30 rad/s. Analytical linearization is shown to abate the cost of linearization over perturbation methods by O(n2), where n is the total number of states of the system. Linearized models of the coupled panel and vortex particle dynamics have applications in the flight dynamics of both fixed- and rotary-wing vehicles, where these dynamics can be used to augment the rigid-body dynamics. The coupled rigid-body and wake dynamics can be leveraged to assess the stability, response characteristics, and handling qualities of vehicles experiencing aerodynamic interactions between rotors, wings, and/or obstacles.

Wall-bounded flow simulation on vortex dynamics

Vortical flow animation has attracted considerable attention within the realm of computer graphics. Given that boundaries are the source of vorticity, we introduce a novel approach for the wall-bounded flow simulation in the vortex dynamics framework. We enhance the traditional Lagrangian vortex particle method in terms of boundary treatment and viscosity computation for boundary layer to furnish support for the simulation of the vortex shedding phenomenon behind the moving solids. We extend the boundary treatment strategy based on the idea of vortex generation with a reasonable placement algorithm for the generated vortex element to better satisfy the impermeability of solids. Furthermore, we modify the particle strength exchange method at solid boundaries to capture momentum transfer of moving solids. We demonstrate the efficacy of our approach by simulating a series of wall-bounded flows, such as the wake behind a delta wing and the vortex shedding behind the rotating sphere.

Eulerian–Lagrangian hybrid solvers in external aerodynamics: Modeling and analysis of airfoil stall

Hybrid computational solvers that integrate Eulerian and Lagrangian methods are emerging as powerful tools in computational fluid dynamics, particularly for external aerodynamics. These solvers rely on the strengths of both approaches: Eulerian methods efficiently handle boundary layers, while Lagrangian methods excel in reducing numerical diffusion in flow convection. Building on our prior development of a two-dimensional hybrid solver that combines OpenFOAM with vortex particle method, this paper extends its application to the complex phenomena of airfoil stall at low Reynolds numbers. Specifically, we examine both static and dynamic stall conditions of a National Advisory Committee for Aeronautics (NACA) airfoil series 0012 (NACA0012) across a wide range of attack angles and oscillation frequencies, comparing our results with established data. The findings demonstrate the accuracy of hybrid Eulerian–Lagrangian solvers in replicating known stall behaviors, underscoring their potential for advanced aerodynamic studies. This work not only confirms the capability of hybrid solvers in accurately modeling challenging flows but also paves the way for their increased involvement in the field of external aerodynamics.

Analysis of particles containing alpha emitters in stagnant water in Fukushima Daiichi Nuclear Power Station’s Unit 3 reactor building

Particles containing alpha (α) nuclides were identified from sediment in stagnant water in the Unit 3 reactor building of the Fukushima Daiichi Nuclear Power Station (FDiNPS). We analyzed different concentrations of α-nuclide samples collected at two sampling sites, the torus room and the main steam isolation valve (MSIV) room. The solids in the stagnant water samples were classified, and the uranium (U) and total alpha concentrations of each fraction were measured by dissolution followed by inductively coupled plasma mass spectrometry and α-spectrometry. Most of the α-nuclides in the stagnant water samples from the torus and MSIV rooms were in particle fractions larger than 10 μm. We detected uranium-bearing particles ranging from sub-µm to 10 µm in size by scanning electron microscopy–energy-dispersive X-ray (SEM–EDX) observations. The chemical forms of U particles were determined in U–Zr oxides, oxidized UO2, and U3O8 with micro-Raman spectroscopy. Other short-lived α-nuclides (plutonium [Pu], americium [Am], and curium [Cm]) were detected by alpha track detection, and the particles with α-nuclides was characterized by SEM–EDX analysis. α-nuclide-containing particles with several tens to several 100 µm in size mainly comprised iron (Fe) oxyhydroxides. In addition, we detected adsorbed U onto Fe oxyhydroxide particles in the MSIV room sample, which indicated nuclear fuel dissolution and secondary U accumulation. This study clarifies the major characteristics of U and other α-nuclides in sediment in stagnant water in the FDiNPS Unit 3 reactor building, which significantly contribute to the consideration of removal methods for particles containing α-nuclides in the stagnant water.