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The boundary condition represented by polygons in the moving particle semi-implicit method can accurately represent geometries and treat complex geometry with high efficiency. However, inaccurate wall contribution to the Poisson's equation leads to drastic numerical oscillation. To address this issue, in this research, we analyzed the problems of the Poisson's equation used in the boundary condition represented by polygons. The new Poisson's equation is proposed based on the improved source term (Tanaka and Masunaga, Trans Jpn Soc Comput Eng Sci, 2008). The asymmetric gradient model (Khayyer and Gotoh, Coastal Engineering Journal, 2008) is also adopted to further suppress the numerical oscillation of fluid particles. The proposed method can dramatically improve the pressure distribution to arbitrary geometry in three dimensions and keep the efficiency. Four examples including the hydrostatic simulation, dam break simulation, and two complex geometries are verified to show the general applicability of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper investigates the energy conservation properties of two well-known projection-based particle methods, namely, MPS and ISPH methods. The enhancing effects of a set of refined schemes including Higher order Source term (HS), Higher order Laplacian (HL), Error Compensating Source (ECS), Dynamic Stabilizer (DS) and pressure Gradient Correction (GC) are shown through the simulations of a standing wave, oscillating drop and impacts of two fluid patches. The results highlight the superiority of corrected Taylor series consistent pressure gradient models for projection-based particle methods in providing accurate results with the best energy conservation as well as accurate reproductions of physical dissipations in fluid impact problems. [ABSTRACT FROM AUTHOR]

Unstable behavior of smoothed particle hydrodynamics (SPH) dust particles, such as clumping or fingering under certain conditions, has been reported by several researchers who have conducted studies on dusty fluid SPH. The simulation results in this study show that this instability is numerical, and the instability is mainly attributable to the ill-interpolated pressure gradient in the interaction term between 2 phases. In this paper, we introduce a new method to calculate the pressure force interaction term between dust and fluid particles. The key idea is to first interpolate the pressure gradient at SPH fluid particles and then use the values to calculate the pressure gradient at SPH dust particles, in a consecutive manner. To compare the new method with the existing method, we first conducted an interpolation of pressure gradient at hydrostatic equilibrium under gravity to estimate any error. The results show that the new method is more accurate. We then conducted additional numerical tests, namely, dust-liquid counterflow, sedimentation in a confined tank, and sedimentation in the presence of turbulence. The unphysical unstable behavior of SPH dust particles such as clumping or fingering was significantly reduced in the new method. The results also show that the instability becomes more significant when using the existing method especially for the case when simulating a flow with relatively high concentration of dust or for the case in which inertia dominates the dynamics of dust particles. Especially, in those cases, the existing method should be avoided, and the newly proposed method is highly recommended. [ABSTRACT FROM AUTHOR]

We present a new class of C∞-smooth finite element spaces on Cartesian grids, based on a partition of unity approach. We use these spaces to construct smooth approximations of particle fields, i.e., finite sums of weighted Dirac deltas. In order to use the spaces on general domains, we propose a fictitious domain formulation, together with a new high-order accurate stabilization. Stability, convergence, and conservation properties of the scheme are established. Numerical experiments confirm the analysis and show that the Cartesian grid-size σ should be taken proportional to the square-root of the particle spacing h, resulting in significant speed-ups in vortex methods. [ABSTRACT FROM AUTHOR]

We present a multiscale mathematical model for the regulation of the cell cycle by the circadian clock. Biologically, the model describes the proliferation of a population of heterogeneous cells connected to each other. The model consists of a high dimensional transport equation structured by molecular contents of the cell cycle-circadian clock coupled oscillator. We propose a computational method for resolution adapted from the concept of particle methods. We study the impact of molecular dynamics on cell proliferation and show an example where discordance of division rhythms between population and single cell levels is observed. This highlights the importance of multiscale modeling where such results cannot be inferred from considering solely one biological level. [ABSTRACT FROM AUTHOR]

A numerical study on violent liquid sloshing phenomenon in a partially filled rectangular container is carried out by using moving particle semi-implicit (MPS) method. The present study deals with the implementation of five modifications all together over the original MPS method. The modifications include improved source terms for pressure Poisson equation, special approximation technique for the representation of gradient differential operator, collective action of mixed free surface particle identification boundary conditions, effecting Neumann boundary condition on solving the PPE and fixing judiciously the parting distance among particles to prevent collision. The suitability of the kernel function used in the original MPS method along with these five modifications is investigated for violent sloshing problems. The present model ensures a good agreement between numerical results with the existing experimental observations. The model is successfully applied to a partially filled tank undergoing horizontal sinusoidal excitation to compute the sloshing wave amplitudes and pressure on tank walls. The assessment of dynamic behaviour manifested in terms of base shear, overturning moment and impact pressure load exerted on tank ceiling induced by violent sloshing motion using MPS method is not reported in the open literature and has been efficiently carried out in the present study. [ABSTRACT FROM AUTHOR]

The Moving Particle Semi-implicit (MPS) method is a Lagrangian particle method based on the prediction-correction calculation of the velocity field and the Helmhotz-Hodge decomposition. Initially the predicted velocity is calculated with the viscous and external forces terms and then corrected by the gradient of the pressure which is obtained by the solution of the Poisson Pressure's equation. The MPS was developed for non-compressible bodies and it is adequate for free surface problems. However, when used to simulate fluid structure interaction problems, like ship resistance, the original formulation of the method can not accurately compute the pressure distribution over the bodies. This paper proposes a modified MPS method for modelling immerse bodies in an free surface flow. It was found that small variations in the source term of the Poisson Pressure's equation can destabilise simulations. Therefore, a reformulation of the Poisson pressure equation was developed. The results show that the proposed variation produced numerical stabilisation. The free surface particles behave in a good agreement with experimental observations. Also, although pressure fluctuations were still present, satisfactory results were obtained when comparing the drag coefficient with those reported values in the literature. [ABSTRACT FROM AUTHOR]

Computational approaches of mechanical systems based on the continuum hypothesis, are sometimes inaccurate and not reliable. As an example, problems involving severe mesh distortion, geometric discontinuities or characterized by an assembly of discrete parts, are not easily solvable within the Lagrangian continuum framework, such as by using the classical finite element method. Computational approaches based on the description of the domain without the need of a mesh connectivity, would be useful to overcome this drawbacks. On the other hand a discrete approach is a particularly suitable tool for modeling materials at the microscale where its particulate nature becomes evident. The Lagrangian-based meshless formulation-known as smoothed particle hydrodynamics (SPH)-has been widely applied to different engineering fields. In the present research a general force potential-based particle method falling within the SPH framework for the mechanical simulation of granular and continuum materials under dynamic condition, is developed. The particle-particle and particle-boundary interaction is modeled through force functionals, tuned according to the nature of the material being analyzed (solid, granular, ...). The proposed potential-based formulation allows the description of the forces existing between the discrete elements of generic materials. Thanks to the capability to deal with short and long distance actions (namely mechanical and/or electrostatic), general force-deformation laws, etc. it allows a straightforward mechanical simulation of fine particles assemblies such as powders. The theoretical basis of the computational approach are presented and some examples involving powder motion and a continuum mechanical problem are illustrated and discussed. [ABSTRACT FROM AUTHOR]

New computational approach for hydrogen leakage with wall crack propagation problem was conducted by using a hybrid of the coupled particle and Eulerian methods. This computational method provides useful safety information for predicting crack propagation and hydrogen leakage in pressure vessels as an important part of assessing hydrogen as an energy vector. The present computational analysis procedures consisted of two main parts. The first part was crack propagation analysis of a thin square plate, which simulated the wall of a high-pressure hydrogen vessel by using a particle method. The crack propagation was analyzed in high-pressure tank walls under two different types of initial conditions, and in both cases, the direction of crack propagation was freely determined by the direction of the stress field. This confirms the superiority of particle methods for modeling destructive phenomena. After the crack propagation analysis, the particle location and coordinate data of the barrier wall were converted to Euler mesh data. The geometric data of particle location were fitted to Euler numerical space, which was used for simulating high-pressure hydrogen leakage into air at atmospheric pressure. The differences and features of hydrogen diffusion during hydrogen leakage were analyzed for two types of wall data and two types of boundary conditions, as a result, the effect of wall boundaries on the hydrogen concentration distribution was computationally predicted. [ABSTRACT FROM AUTHOR]