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In this work, the influence of the geometry of lightweight perforated breakwaters on their performance against green water impact loads is investigated systematically through a series of numerical simulations. For this purpose, a fully Lagrangian meshfree particle-based method is adopted to model transient and impulsive hydrodynamic phenomenon with free surface and complex geometry. The green water flow is represented by a dam-break problem; the breakwater is modeled as a perforated plate and the protected installation as a vertical wall. Computed impact force, moment, and impulse on the breakwater and protected wall show nonlinear effects, and the main geometric parameter is the open-area ratio. In addition, the increase in the breakwater height is effective only for low open-area ratios. The influence of the arrangement of the holes are also investigated. Different flow patterns are obtained for small and large gaps between the breakwater and the wall. The relation between the loads on the breakwater and the wall also provides the basis for the optimal design of the breakwater, considering the tolerant hydrodynamic loads of protected structures., Comment: 37 pages, 27 figures

The radial basis reproducing kernel particle method (RRKPM) has been constructed by introducing the radial basis function (RBF) into the reproducing kernel particle method (RKPM). In this article, the RRKPM is extended to the elastic dynamic analysis of the functionally graded material (FGM), and the elastic dynamics governing equation of the FGM based on the RRKPM is obtained. Then, the influence of the penalty factor, the scaling parameter and the shaped parameter are discussed. Finally, numerical examples of the FGM verify that the RRKPM has a smaller calculation error than the RKPM, and prove the correctness of the RRKPM for solving the elastic dynamics problems of the FGM.

International audience; This paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this regime, the time step can be subject to stability constraints related to the interaction kernel. To avoid this limitation, our approach is based on higher-order implicit-explicit numerical schemes. Thus, when the magnitude of the interactions becomes large, this method provides a consistent discretization of the macroscopic reaction-diffusion FitzHugh-Nagumo system. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.

A new particle method code called PHALSER (PHysics-based particle AnaLyzer for SEveRe accident) was developed to simulate various phenomena involving phase changes, such as the melting and solidifi...

Friction stir welding (FSW) is one of the solid-state welding and it has been widely employed for joining aluminum alloys. In addition, as a result of R&D efforts about FSW tool, this method is expected to join the steels and/or various dissimilar materials. In order to examine the thermal and mechanical behavior in FSW, many numerical studies have been conducted and the heat generation behavior near FSW tool is precisely demonstrated by using the moving particle semi-implicit (MPS) method which is one of the particle method. In this research, in order to reduce the computational time, a new parcel method based on MPS is developed and its applicability is examined for simulating the friction stir welded dissimilar joint between V-ally and austenite stainless steel SUS316L. From the serial computational results, it is revealed that the influence of rotational speed on the heat generation during FSW seems to be larger than that of traveling speed. Moreover, the numerical result indicates that the sound dissimilar joint might be fabricated when V-alloy is set to be the retreating side (RS), the FSW tool is inserted in RS and the rotational speed increased appropriately although the two materials have not been joined in this welding condition of FSW experimentally.

In this paper, to improve the computational speed of the reproducing kernel particle method (RKPM), the dimension splitting reproducing kernel particle method (DSRKPM) is presented for solving three-dimensional (3D) transient heat conduction problems. The idea of the proposed method is transforming the 3D problem into a series of two-dimensional (2D) ones by using the finite difference method in the splitting direction. Since the shape function of the RKPM for 2D problem is much simpler than the one of 3D problem, the DSRKPM has higher computational speed than the RKPM. To demonstrate the applicability of the proposed method, four example problems are presented, and each of them is solved by the DSRKPM and the RKPM, respectively. And the numerical solutions show that the DSRKPM not only greatly improves the computational efficiency, but also has a higher computational accuracy.

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian, particle method, which combines the advantages of Euler and Lagrangian method and has special advantages in simulating violent non-linear fluid–structure interaction problems. In this study, an improved SPH method is used to simulate four fluid–structure interaction cases. Firstly, the violent flow in the mould filling process is simulated to validate that the SPH model can obtain accurate flow patterns with any complex solid boundaries. Secondly, the dam-break flow against a vertical wall is simulated, and the pressure curves are compared with the experiment. Then liquid sloshing problems under different external excitations are simulated, and the complex coupling characteristics can be captured. Finally, the interactions between fluid and floating bodies are researched. The obtained numerical results show good agreement with the results from other sources, and clearly demonstrate the effectiveness of the presented SPH method in modelling fluid–structure interaction problems.

In this paper, we derive an analytical expression for reproducing kernel particle method (RKPM) shape functions. Based on this, we propose a necessary and sufficient stability condition for general RKPM in arbitrary function space, and illustrate with degenerate cases. By selecting proper basis vectors and the support of the kernel functions, we demonstrate that the RKPM framework allows generating many kinds of shape functions, including the Lagrangian, B-spline and NURBS shape functions.

In this work, two modifications of an adaptive particle method based on the moments of the internal concentration of numerical particles are presented to introduce the effect of local shears on the mass transport in natural flows. This moment method uses a Taylor expansion of the flow velocity field to derive the transport equation of moments. The first modification is based on the introduction of a method of the local frame transport in order to perform an extension of the Taylor expansion of the flow velocity to a higher order. The second modification consists in applying a splitting or a merging to non-spherical numerical particles. When a non-spherical numerical particle becomes large compared to the scale of spatial variations of the velocity gradient, it is divided into two non-spherical numerical particles. On the contrary, when particles reach some other parts of the flow where they become small compared to spatial variations of the velocity gradient, then these particles should merge. The accuracy of both modifications is evaluated by simulating the mass transport in natural flows.

We propose a new segmentation method based on multiple walking particles (WP) bouncing from the image edges. The particles are able to segment objects characterized by deep concavities as narrow as one pixel and handle single or multiple objects characterized by a noisy background and broken boundaries (“weak edge”, “boundary leakage”). The particles are designed to segment the image by permanently staying inside the object and repairing the boundaries where necessary. The proposed WP combine the advantages of the continuous diffusion models with the principles of multi-agent systems. WP have been tested against recent active contours and the distance regularized level set method on a set of complex-shaped synthetic images and ultrasound (US) images of breast cancer ( http://onlinemedicalimages.com ). The method has also been compared with localizing region-based active contours, the fuzzy C-mean level set method, and morphological active contours. The WP are faster and more accurate for images characterized by low contrast, noise, broken boundaries, or boundary leakage. However, for good quality, simple shaped objects the WP work similarly to the conventional methods. There is still an important difference even in this case: the WP do not require initialization. A video demo of the algorithm is at https://drive.google.com/drive/folders/1SlTphINKtdUwvdjjxiakFrwI2dDlIUAU

A subgrid-scale capillary breakup model has been developed by coupling a Eulerian interface-capturing approach to a Lagrangian point particle method. At the fully resolved scale, the evolution of p...

The presence downstream of a dam of either rigid or erodible obstacles may strongly affect the flood wave propagation, and this complex interaction may lead to further dramatic consequences on people and structures. The open-source Lagrangian-based DualSPHysics solver was used to simulate a three-dimensional dam-break in a closed domain including an oriented obstacle that deflects the flow, thus increasing the complexity of fluid dynamics. By comparing numerical results with experimental data, the effectiveness of the model was evaluated and demonstrated with an extensive sensitivity analysis based on several parameters crucial to the smoothed particle hydrodynamics method, such as the resolution, the boundary conditions, and the properties of the interaction weight function. Charts and summary tables highlight the most suitable conditions for simulating such occurrences in the DualSPHysics framework. The presence of the obstacle, being also an opportunity for observation and study of complex fluid dynamics, opens the way to investigate the fluid interaction with solid objects involved in dam-break events and, possibly, to predict their effect with respect to the relative position between them and the flood and other relevant parameters. Finally, the numerical model presents a good overall agreement.

The paper is devoted to studying the features of the discontinuous particle method. The algorithmic fundamentals of the particle method are described in detail. The possibility of using limiters is investigated. The results of the calculations for the Hopf, Burgers, shallow water, and gas dynamics’ equations, including nonlinear acoustics, are presented. The numerical solutions are compared with some exact ones. The tests show that the method is suited for problems with discontinuities. It is shown that in order to obtain a more accurate numerical solution, it is necessary to refine the initial mathematical models. In other words, for the problem of the structure of the front of the shock wave if we take the equations of stochastic gas dynamics instead of the Navier-Stokes equations, then the need for limiters disappears.

International audience; This paper is devoted to the development and application of hybrid methods combining, on the one hand, semi-lagrangian methods for the advection-diffusion of scalars, and, on the other hand, either finite volume or spectral methods, depending on the flow geometry, for the Navier-Stokes equations. A particular focus is made on the accuracy and scalability of the methods. These methods are then used to study differential diffusion of scalars on two canonical cases: Homogeneous Isotropic Turbulence and a jet flow. We first characterize differential diffusion in terms of spectral distribution. We then use the Reynolds decomposition to bring out the different mechanisms involved in the energy budget of the scalar and we analyze their spatial distribution.

The spreading-solidification behaviour of the stratified molten metals was investigated. This is important in understanding the practical fuel debris distribution spread and solidified in the primary containment vessel (PCV) of Fukushima Daiichi Nuclear Power Plants (1F NPPs). In this study, the effect of outflow diameter on the material distribution before discharging was studied both experimentally and numerically. The two simulant metals were chosen so that the density ratio could be similar to the practical fuel and structure elements of the plant. They were arranged in a vessel and discharged on a receiving plate. The spreading experiments were performed using various outlet diameters with a density and reverse density stratification arrangement. After the experiment, X-ray analysis was performed to evaluate the material distribution in the solidified material. Moreover, a numerical analysis was performed to reveal the mechanisms that affect the material distribution after solidification. As a result, the low-density metal accumulated at the centre region regardless of the outlet diameters in the density stratification. In contrast, the outlet diameters affected the material distribution in the reverse density stratification because they affected the material outflow order. These findings may help increase our understanding of the fuel debris distribution in 1F NPPs.

In the early morning of 24 June 2017, a slow-moving landslide suddenly accelerated and impacted Xinmo village after a sustained period of low-intensity rainfall. The landslide caused more than 80 casualties and damaged approximately 100 houses. Although many studies have been performed to understand the failure mechanism, the entire failure process of the Xinmo landslide is still not clear. In this study, a depth-integrated particle method coupled with a soil–water mixing model is used to back-analyse both slowly progressive movement and sudden failure processes of the Xinmo event. A representative volume element of the sliding zone is modeled, with consideration of erosion that progressively changes the solid concentration of the sliding mud. Numerical results show that the continuous erosion of sliding mud by rainwater accelerates the displacement rate of the landslide body. During the slow-moving stage, the simulated displacement rate is approximately 0.6 mm/year. On the other hand, the rapid failure process lasts 105 s from sudden failure to final deposition, with a maximum velocity of 58.6 m/s. As evidenced by the analysis of the seismic signals, the depth-integrated particle method has a good performance in simulating the rapid failure process of a landslide. The results demonstrate that the erosion of sliding mud resulted from the rainwater may play a critical role in the Xinmo landslide. This study contributes to understanding failure processes of rainfall-induced slow-moving landslides and provides guidelines on hazard prevention and mitigation.

The non-symmetrical collapse of an empty cylindrical cavity is modeled using Smoothed Particle Hydrodynamics. The presence of a nearby surface produces an anisotropic pressure field generating a high-velocity jet that hits the surface. The collapse follows a different dynamic based on the initial distance between the center of the cavity and the surface. When the distance is greater than the cavity radius (detached cavity) the surface is hit by traveling shock waves. When the distance is less than the cavity radius (attached cavity) the surface is directly hit by the jet and later by other shock waves generated in the last stages of the of the collapse. The results show that the surface is hit by a stronger shock when distance between the center of the cavity and the surface is zero while showing more complex double peaks behavior for other distances.

Viscoelastic bonds intended for Discrete Multiphysics (DMP) models are developed to allow the study of viscoelastic particles with arbitrary shape and mechanical inhomogeneity that are relevant to the pharmaceutical sector and that have not been addressed by the Discrete Element Method (DEM). The model is applied to encapsulate particles with a soft outer shell due, for example, to the partial ingress of moisture. This was validated by the simulation of spherical homogeneous linear elastic and viscoelastic particles. The method is based on forming a particle from an assembly of beads connected by springs or springs and dashpots that allow the sub-surface stress fields to be computed, and hence an accurate description of the gross deformation. It is computationally more expensive than DEM, but could be used to define more effective interaction laws.

Numerical simulation of wave-structure interaction is an important but challenging topic due to the movement, deformation and even breakup of free surface, and strong fluid-structure interaction. T...

Hypervelocity impact (HVI) is associated with large deformations of structures, phase transitions of materials and scattered debris cloud. It is a great challenge to accurately model the HVI process and predict the damage produced by HVI for conventional numerical methods. In this paper, a recently developed corrective smoothed particle hydrodynamics (SPH) method, decoupled finite particle method (DFPM), is extended to model HVI problems. Validation examples show that DFPM is as flexible as SPH while having much better performance in improving accuracy and removing tensile instability. DFPM is also very attractive for modeling problems with extremely disordered particle distribution (e.g., HVI) as no matrix inversion is required. DFPM is then applied to model the penetration of a sphere on a target plate at various impact velocities and impact angles. It is found that as the impact velocity increases, the hole size increases accordingly and maintains basically constant in a steady state after the impact velocity reaches a critical value. Based on extensive DFPM simulation results, novel formulae are given for predicting the hole size produced by normal and oblique HVIs, which can reproduce experimental data and shows better performance than existing empirical formulae in a wider range of impact velocity.

A multiscale meshfree particle method for macroscopic mean field approximations of generalized interacting particle models is developed and investigated. The method is working in a uniform way for ...

In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.

In this paper, we study the regularity of the laws of stochastic differential equations with jumps using the recently well-developed lent particle method introduced by Bouleau and Denis under some kind of Hormander’s conditions.

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit (MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value. Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials. Keywords: Particle method, Moving particle semi-implicit (MPS) method, Large deformation analysis, Geomaterials, Bingham model

The moving particle semi-implicit method is a meshless particle method for incompressible fluid and has proven useful in a wide variety of engineering applications of free-surface flows. Despite its wide applicability, the moving particle semi-implicit method has the defects of spurious unphysical pressure oscillation. Three various divergence approximation formulas, including basic divergence approximation formula, difference divergence approximation formula, and symmetric divergence approximation formula are proposed in this paper. The proposed three divergence approximation formulas are then applied for discretization of source term in pressure Poisson equation. Two numerical tests, including hydrostatic pressure problem and dam-breaking problem, are carried out to assess the performance of different formulas in enhancing and stabilizing the pressure calculation. The results demonstrate that the pressure calculated by basic divergence approximation formula and difference divergence approximation formula fluctuates severely. However, application of symmetric divergence approximation formula can result in a more accurate and stabilized pressure.

To reduce the negative effect of different kernel functions on calculating accuracy, the radial basis function (RBF) is introduced into the reproducing kernel particle method (RKPM), and the radial basis reproducing kernel particle method (RRKPM) is proposed, the corresponding governing equations are derived. The RRKPM is more efficient to solve the local problem domain, and can improve the accuracy and stability of the RKPM. Then the RRKPM is applied to the numerical simulation of piezoelectric materials, the corresponding formulae for piezoelectric materials are derived. The numerical results illustrate the proposed method is more stable and accurate than the RKPM.

We establish some new derivative formulae of Bismut–Elworthy–Li's type for stochastic differential equations with respect to Poisson point processes using the lent particle method created by Bouleau and Denis.

The volume of debris flows occurred in mountainous areas is mainly affected by the volume of debris materials deposited at the valley bottom. Quantitative evaluation of debris materials prior to debris flow hazards is important to predict and prevent hazards. At midnight on 7th August 2010, two catastrophic debris flows were triggered by the torrential rain from two valleys in the northern part of Zhouqu City, NW China, resulting in 1765 fatalities and huge economic losses. In the present study, a depth-integrated particle method is adopted to simulate the debris materials, based on 2.5 m resolution satellite images. In the simulation scheme, the materials are modeled as dry granular solids, and they travel down from the slopes and are deposited at the valley bottom. The spatial distributions of the debris materials are investigated in terms of location, volume and thickness. Simulation results show good agreement with post-disaster satellite images and field observation data. Additionally, the effect of the spatial distributions of the debris materials on subsequent debris flows is also evaluated. It is found that the spatial distributions of the debris materials strongly influence affected area, runout distance and flow discharge. This study might be useful in hazard assessments prior to debris flow hazards by investigating diverse scenarios in which the debris materials are unknown.

This study focuses on the convection scheme in the vortex particle method. The usual two-step convection procedure for vortex elements, which comprises the convection of vortex elements on each grid point and redistribution of vorticity into each grid point, is extremely difficult to parallelize because of unavoidable memory-write conflictions in the redistribution step, thereby limiting the computational speed. We apply a semi-Lagrangian method called the cubic semi-Lagrangian method, as the convection scheme in the vortex particle method to improve space–time accuracy and accelerate computations. Two test problems, namely the Taylor–Green vortex and double shear flow, are simulated using the semi-Lagrangian vortex particle method proposed in this study to confirm its suitability. The results show that the accuracy of capturing standing vortices and the total amount of kinetic energy conservation are significantly improved. The performance measurements show that the average execution time for the convection of vortex elements is reduced to one-half, thus verifying the semi-Lagrangian method as a suitable convection scheme for the vortex particle method.

Quasi Monte Carlo algorithm is one of the most famous particle method, which is used to solve intersection volume computation problem. Inspired by the quasi Monte Carlo algorithm, a discrete quadrature algorithm is proposed to calculate the intersection volume. First, the three dimensional entity with unknown function is divided into a series of random sequences points using the quasi Monte Carlo algorithm. Second, calculating the common point set in terms of a given function three dimensional entity. Finally, both the intersection volume and irregularity intersection volume are approximated by the number of the common point set. Simulation shows that the proposed method has the advantages in estimation accuracy and computational load.

Cracks in 3D have arbitrary shapes and therefore present difficulties for numerical modelling. A novel adaptive cracking particle method with explicit and accurate description of 3D cracks is described in this paper. In this meshless method, crack surfaces are described by a set of discontinuous segments which are associated with particles. This group of particles are assumed all to be “cracked” and split into two sub-particles with modified support domains. Compared to the original method where the spherical supports at particles are equally divided, the proposed method makes use of non-planar segments to account for changes in crack face direction. The orientations of those segments and the angular changes of cracks during crack propagation steps are recorded using triangular meshes. Supports of weight functions are modified according to those changes so that quasi-continuous crack surfaces can be obtained, avoiding the spurious cracking seen in earlier CPMs. An adaptive approach in 3D is then introduced to capture stress gradients around crack fronts. Several 3D crack problems with reference results have been tested to validate the proposed method with good agreement being achieved using the new method, showing it to be potentially a significant advance for 3D fracture predictions problems.

The nonlinear transfer of mass, momentum, and energy is the main peculiarity of gas dynamics. A discontinuous particle method is proposed for its efficient numerical modeling. The method is described in detail in application to linear and nonlinear transfer processes. The necessary and sufficient monotonicity and stability condition of the discontinuous particle method for the regularized Hopf equation is obtained. On the simplest example of a discontinuous solution, the method’s advantages, which include the discontinuity widening over only one particle and the selfadaptation of the space resolution to the solution’s peculiarities, are shown.

The conventional numerical approximation of Mindlin plate equations can lead to erroneous solutions for thin plates. The so-called shear-locking problem has been well studied in the context of the finite element method (FEM) whereas the development of numerical formulations for its successful elimination in meshfree methods is still a subject of intensive research. This paper studies the effectiveness of some of the most commonly adopted techniques for the reduction of shear-locking and presents the application of a shear-locking-free formulation based on first-order Mindlin plate theory. In this modified formulation, the shear strains are incorporated as degrees of freedom (DOFs) in lieu of the rotational DOFs in the conventional Mindlin theory formulation. A straightforward transformation technique is presented for the enforcement of boundary conditions and comparisons are made with available analytical and numerical solutions. The generalised reproducing kernel particle method (RKPM) is adopted as the numerical tool and a series of numerical examples are presented to demonstrate the accuracy and performance of the presented method.

In this paper we present numerical simulations of a macroscopic vision-based model (Degond et al. in Kinet Relat Models AIMs 6(4):809–839, 2013) derived from microscopic situation rules described in Ondřej et al. (ACM Trans Graph 29(4):Article 123, 2010). This model describes an approach to collision avoidance between pedestrians by taking decisions of turning or slowing down based on basic interaction rules, where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle and of the time-to-interaction. A meshfree particle method is used to solve the equations of the model. Several numerical cases are considered to compare this model with models established in the field, for example, social force model coupled to an Eikonal equation (Etikyala et al. in Math Models Methods Appl Sci 20(12):2503–2523, 2014). Particular emphasis is put on the comparison of evacuation and computation times.

The 2017 SPHERIC Beijing International Workshop (or SPHERIC Beijing 2017) was held at Peking University, in China, on October 17-20, 2017. This is the first time that the SPHERIC Workshop was held out of Europe. We are delighted to present nine contributions in this Special Column of the Journal of Hydrodynamics, and take this opportunity to announce that the 13th SPHERIC Workshop (or SPHERIC 2018) will be held in Galway, Ireland in 2018 by the National University of Ireland, and the SPHERIC International Workshop in Harbin, China in 2019 by the Harbin Engineering University.

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection–diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

The Fukushima nuclear accident raised the importance of flooding study in nuclear reactor buildings. It is known that the external flooding can be attributed to natural causes, while the internal f...

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.

Summary The conventional SPH method has been frustrated with the low accuracy originated from the particle inconsistency. The finite particle method (FPM) is an improved SPH method with a higher order accuracy. However, the numerical accuracy and stability of FPM depend on the uniformity of particles. Facing the disorder particles, the conventional FPM may suffer from an ill-conditioned corrective matrix and is difficult to carry out long time simulations. A popular and robust particle regularization scheme is the so-called particle shifting technology (PST) which can effectively enhance the accuracy and stability of particle methods. In the context of FPM, PST is analyzed and discussed, and a modified PST (MPST) is proposed. MPST saves great amount of computational cost with respect to the conventional PST, and acquires better features of accuracy and stability. Finally, the coupled FPM method by combining MPST and δ-SPH is developed to simulate a series of viscous flows. The numerical results indicate that, MPST is effective in improving accuracy, stability and efficiency of PST, and the coupled FPM is shown to be robust for simulating viscous flows and has a higher accuracy and stability.

This paper presents a new macroscopic mesh-free particle method in which Darcy’s and Forchheimer’s terms are introduced into the governing equation to ensure the capacity of the particle method in simulating laminar and turbulent porous medium flows. A developed interfacial condition and inflow boundary condition are implemented in the macroscopic particle method to improve the stability of the Particle-based model. The comparisons of channel flow over and within porous bed among the present method, previous mesh-based method, and experimental data show that the macroscopic particle method is capable of simulating flows in both the clear flow region and porous flow region. Finally, two cases of flow over a rigid box and a cylinder lying on porous bed are simulated, and the numerical results are in good agreement with the measured data. The analysis and comparisons indicate that the newly developed particle-based method is reliable and has been successfully extended to macroscopic porous medium sim...

We develop an optimal transportation mesh-free particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle for purposes of time discretization of the diffusive step. This principle characterizes the evolution of the density as a competition between the Wasserstein distance between two consecutive densities and entropy. Exploiting the structure of the Euler–Lagrange equations, we approximate the density as a collection of Diracs. The interpolation of the incremental transport map is effected through mesh-free max-ent interpolation. Remarkably, the resulting update is geometrically exact with respect to advection and volume. We present three-dimensional examples of application that illustrate the scope and robustness of the method.

The Finite Volume Particle Method (FVPM) is a meshless method for simulating fluid flows which includes many of the desirable features of mesh-based finite volume methods. In this paper, we develop a new 3-D FVPM formulation that features spherical kernel supports. The formulation is based on exact integration of interaction vectors constructed from top-hat kernels. The exact integration is obtained by an innovative surface partitioning algorithm as well as precise area computation of the sphere subsurfaces. Spherical-support FVPM improves the recently developed cubic-support version in two main aspects: spherical kernels have no directionality and result in smooth interactions between particles, leading to an improved method. We present three test cases that illustrate the improved accuracy and robustness brought by the spherical kernel. Although computations are 1.5 times slower on spherical support than cubic support, the cost is more than compensated by lower error with a higher convergence rate. (C) 2016 Elsevier B. V. All rights reserved.