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In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the macroscopic traffic model: mass is preserved, the mechanical energy is decaying and an energy functional is also decaying. To demonstrate the advantages of the particle method under consideration, a comparison with other numerical methods for viscous compressible fluid models is provided. Since the solutions of the macroscopic traffic model can be approximated by the solutions of a reduced model consisting of a single nonlinear heat-type partial differential equation, the numerical solutions produced by the particle method are also compared with the numerical solutions of the reduced model. Finally, a traffic simulation scenario and a comparison with the Aw-Rascle-Zhang (ARZ) model are provided, illustrating the advantages of the use of automated vehicles. [ABSTRACT FROM AUTHOR]

The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples. [ABSTRACT FROM AUTHOR]

The dynamic interaction between granular flowing masses and rigid obstacles is a complex phenomenon characterised by both large displacements and high strain rates. In case the flowing mass is modelled as a continuum, its numerical simulation requires both advanced computational tools and constitutive relationships capable of predicting the mechanical behaviour of the same material under both fluid and solid regimes. In this paper, the authors employed the open‐source ANURA3D code, based on the Material Point Method (MPM), and a multi‐regime constitutive model. A series of impacts characterised by different velocities, initial void ratios, front inclinations and impacting mass lengths have been simulated. The MPM numerical results are critically compared with those obtained by using a Discrete Element Method (DEM) numerical code. The model capability of simulating material regime transitions, from fluid to solid and vice versa, is shown to be crucial for reproducing the mechanical response of the flowing mass put in evidence by DEM data. [ABSTRACT FROM AUTHOR]

We study the discretisation of generalised Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a Γ-convergence result for the associated discrete metrics as N → ∞ to the continuous one and discuss applications to the approximation of one-dimensional conservation laws (of gradient flow type) via the so-called generalised minimising movements, proving a convergence result of the schemes at any given discrete time step τ > 0 . This the first work of a series aimed at sheding new lights on the interplay between generalised gradient-flow structures, conservation laws, and Wasserstein distances with nonlinear mobilities. [ABSTRACT FROM AUTHOR]

Characteristic dynamics in lava flows, such as the formation processes of lava levees, toe-like tips, and overlapped structures, were reproduced successfully through numerical simulation using the smoothed particle hydrodynamics (SPH) method. Since these specific phenomena have a great influence on the flow direction of lava flows, it is indispensable to elucidate them for accurate predictions of areas where lava strikes. At the first step of this study, lava was expressed using a molten metal with known physical properties. The computational results showed that levees and toe-like tips formed at the fringe of the molten metal flowing down on a slope, which appeared for actual lava flows as well. The dynamics of an overlapped structure formation were also simulated successfully; therein, molten metal flowed down, solidified, and changed the surface shape of the slope, and the second molten metal flowed over the changed surface shape. It was concluded that the computational model developed in this study using the SPH method is applicable for simulating and clarifying lava flow phenomena. [ABSTRACT FROM AUTHOR]

Accomplishing the retrieval of fuel debris from Fukushima Daiichi Nuclear Power Plant (1F) Unit 3 (1F3) requires an understanding of its distribution. In this study, we performed real-scale corium spreading and sedimentation behavior analyses using Lagrangian moving particle hydrodynamics and large eddy simulation methods. These methods allowed us to calculate the spreading of corium with various shear viscosities under water conditions and to propose the best estimation for the fuel debris distribution in 1F3. To minimize uncertainties arising from unknown boundary conditions, we investigated relevant parameters through literature review. Our analyses showed that highly viscous corium tends to pile up within the pedestal region under strong convective vapor and boiling heat transfer, while low-viscosity corium spreads to the outside of the pedestal regions regardless of cooling efficiency. We identified three cooling modes based on initial shear viscosity and cooling efficiency and predicted the fuel debris distribution in 1F3 by comparing our results to those of the Tokyo Electric Power Company (TEPCO) and Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) Benchmark Study of the Accident at the Fukushima Daiichi Nuclear Power Station (BSAF) project. The distribution estimation of highly viscous corium derived from oxidic corium is consistent with the three-dimensional reconstructed image by TEPCO and the calculated results by the OECD/NEA BSAF project. [ABSTRACT FROM AUTHOR]

Characteristic dynamics in lava flows, such as the formation processes of lava levees, toe-like tips, and overlapped structures, were reproduced successfully through numerical simulation using the smoothed particle hydrodynamics (SPH) method. Since these specific phenomena have a great influence on the flow direction of lava flows, it is indispensable to elucidate them for accurate predictions of areas where lava strikes. At the first step of this study, lava was expressed using a molten metal with known physical properties. The computational results showed that levees and toe-like tips formed at the fringe of the molten metal flowing down on a slope, which appeared for actual lava flows as well. The dynamics of an overlapped structure formation were also simulated successfully; therein, molten metal flowed down, solidified, and changed the surface shape of the slope, and the second molten metal flowed over the changed surface shape. It was concluded that the computational model developed in this study using the SPH method is applicable for simulating and clarifying lava flow phenomena.

There are abundant complex pores in the coal matrix, which provide a large amount of storage space and migration channels for methane. Diffusion is involved in the gas migration from the pore to the fracture. The scale of the matrix determines to some extent the resistance to diffusion into the fracture, influencing the difficulty of methane diffusion. This study took the intrinsic connection between gas diffusion and coal matrix scale as the starting point, the quantitative relationship between methane concentrations and mass exchange rate within the dual pore structure of coal at different desorption moments was obtained by processing the data of the desorption transient process of particle coal. The matrix shape factor was calculated combined with the time-varying diffusion coefficient. A transient diffusion-based matrix scale calculation method for granular coal was proposed and experimentally validated. The results shown that the initial diffusion coefficients of larger particle coals with intact matrix morphology were essentially unchanged compared to smaller particle coals, so the value of the initial diffusion coefficient can characterize the degree of matrix destruction to some extent. The matrix shape factor decreased with the extension of desorption time and can be divided into sharp-decreasing phase, slow-decreasing phase and stable phase, in which the stable phase matrix shape factor can accurately reflect the matrix shape in the proposed steady state at the late stage of diffusion and is the most suitable for solving matrix scale. The method can reflect the change pattern of matrix scale variation during the damage process of granular coal pulverization and provide a basis for explaining the existence of diffusion-limited particle size. The three experimental particle size matrix scales of the Nuodong coal samples increased with the increasing particle size, 0.059 mm, 0.287 mm and 0.457 mm, respectively, and were non-differential in the large particle size range, proving the accuracy of the method. The particle coal matrix scale can be used to correct the calculation parameters of K1 values, rendering the gas loss calculation model equally applicable in coal samples with a high degree of pulverization.

Total Lagrangian SPH (TLSPH) offers many advantages that can overcome instability and computational time issues. However, it is not naturally applicable to problems with contact. Many problems in solid dynamics and structural analysis require contact definition. In order to use the total Lagrangian formulation, further development for the contact algorithm is required. This research proposes an algorithm to implement inter‐particle contact in TLSPH using an adaptive hybrid‐kernel scheme for the first time. A combination of the updated and total Lagrangian formulations at the contact surface is introduced, in which the kernel type change automatically when particles from a different body are detected. In kernel change from the updated to the total Lagrangian formulation, the gradient correction cannot be performed using a common correction method because different frames of reference are used. Therefore, a hybrid‐kernel correction technique is proposed to maintain the zeroth‐ and first‐order completeness. Then, the contact force is obtained from the inter‐particle force using the conservation of momentum. The proposed method does not require a user‐defined parameter that makes the application straightforward. Based on the test, the proposed method agrees well with the data available in published literature and the finite element method. Compared with the contact method in classical SPH, the proposed TLSPH shows a significant stability improvement. [ABSTRACT FROM AUTHOR]

In this paper, we study three numerical schemes for the McKean-Vlasov equation {dXt=b(t,Xt,μt)dt+σ(t,Xt,μt)dBt,∀t∈[0,T],μt is the probability distribution of Xt, { d X t = b (t , X t , μ t) d t + σ (t , X t , μ t) d B t , ∀ t ∈ [ 0 , T ] , μ t  is the probability distribution of   X t , $ \{ \begin{array}{l}dX_t=b{(t,X_t,\mu_t)}dt+\sigma{(t,X_t,\mu_t)}dB_t,\\ \forall t\in\lbrack 0,T\rbrack,\mu_t\text{is the probability distribution of }X_t,\end{array} $ where X0 : (Ω, F, ℙ) → (ℝd, B(ℝd)) is a known random variable. Under the assumption on the Lipschitz continuity of the coefficients b and σ, our first result proves the convergence rate of the particle method with respect to the Wasserstein distance, which extends previous work [M. Bossy and D. Talay, Math. Comput. 66 (1997) 157–192.] established in a one-dimensional setting. In the second part, we present and analyse two quantization-based schemes, including the recursive quantization scheme (deterministic scheme) in the Vlasov setting, and the hybrid particle-quantization scheme (random scheme inspired by the K-means clustering). Two simulations are presented at the end of this paper: Burgers equation introduced in [M. Bossy and D. Talay, Math. Comput. 66 (1997) 157–192.] and the network of FitzHugh- Nagumo neurons (see [J. Baladron, D. Fasoli, O. Faugeras and J. Touboul, J. Math. Neurosci. 2 (2012) 1–50.] and [M. Bossy, O. Faugeras and D. Talay, J. Math. Neurosci. 5 (2015) 1–23.]) in dimension 3. [ABSTRACT FROM AUTHOR]

The particle filter is a data assimilation method based on importance sampling for state and parameter estimation. We apply a particle filter in two different quasi-static experiments with models of subsidence caused by a compacting reservoir. The first model considers uncorrelated model state variables and observations, with observed subsidence resulting from a single source of strain. In the second model, subsidence is a summation of subsidence contributions from multiple sources which causes spatial dependencies and correlations in the observed subsidence field. Assimilating these correlated subsidence fields may trigger weight collapse. With synthetic tests, we show in a model of subsidence with 50 independent state variables and spatially correlated subsidence a minimum of 10 13 particles are required to have information in the posterior distribution identical to that in a model with 50 independent and spatially uncorrelated observations. Spatial correlations cause an information loss which can be quantified with mutual information. We illustrate how a stronger spatial correlation results in lower information content in the posterior and we empirically derive the required ensemble size for the importance sampling to remain effective. We furthermore illustrate how this loss of information is reflected in the log likelihood, and how this depends on the number of model state variables. Based on these empirical results, we propose criteria to evaluate the required ensemble size in data assimilation of spatially correlated observation fields. [ABSTRACT FROM AUTHOR]

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A direct-chill (DC) casting simulation model was developed and applied to the authors' particle method simulation to enable three-dimensional thermo-fluid and solidification simulation of DC casting processing, including breakout. DC casting includes the feeding of molten alloy, changes in the direction and speed of molten alloy flow by a floating distributor, cooling of the alloy by the mold and water, state changes and solidification, and motion of an ingot relative to the mold by motion of a starter block. A salient difficulty that might arise with DC casting is breakout, which results from various factors related to these complex processes. The proposed simulation model enabled simulation of DC casting processes, including breakout, under simulation conditions that more closely resemble those of actual phenomena than do conventional methods (such as finite difference method and finite element method): starter block motion, ingot motion relative to the mold, and starter block – ingot interaction was addressed directly and naturally. [ABSTRACT FROM AUTHOR]

Summary: Properties of a cell can determine its deformations, which can aggravate cancer metastasis. In laboratory, microfluidic technology has been adopted to study cell deformations. However, quantifying the effects of cell deformations has remained difficult. To this end, this paper presents a two‐dimensional particle‐based model that can capture flow‐induced cell deformations in a microchannel. The numerical model is validated with an experimental dataset for MCF7 cell. The simulations show that cell deformations are dominantly attributed to flow acceleration. Stress analyses, conducted by inputting the simulated cell deformations as boundary conditions, show that the maximum normal stresses correspond well to high deformations. Shear stress is in general proportional to the cell's distance from a wall. The simulations also suggest a deformed cell shape that apparently may reduce the average normal stresses. This study highlights the potential of the numerical model to relate the measurable cell deformations to the more elusive cell properties. [ABSTRACT FROM AUTHOR]

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate operators by applying our weight functions. The key idea of deriving our error estimates is to divide the integration region into a ring-shaped area and some areas. In the appendix, we give an exemplary application of the main results of this paper. [ABSTRACT FROM AUTHOR]

Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDEconstrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the forward equation and the other for the adjoint. When MC solvers are used, the numerical solutions are Dirac measures. As such, one immediately faces the difficulty in explaining the multiplication of two measures. This suggests that MC solvers are naturally incompatible with gradient-based optimization under PDE constraints. In this paper, we study two different strategies to overcome the difficulty. One is to adopt the discretizethen-optimize technique and conduct the full optimization on the algebraic system, avoiding the Dirac measures. The second strategy stays within the optimize-then-discretize framework. We propose a correlated simulation where, instead of using MC solvers separately for both forward and adjoint problems, we recycle the samples in the forward simulation in the adjoint solver. This frames the adjoint solution as a test function and hence allows a rigorous convergence analysis. The investigation is presented through the lens of the radiative transfer equation, either in the inverse setting from optical imaging or in the optimal control framework. We detail the algorithm development, convergence analysis, and complexity cost. Numerical evidence is also presented to demonstrate the claims. [ABSTRACT FROM AUTHOR]

An enhanced moving particle semi-implicit method for simulation of incompressible fluid flow and FSI (Fluid-Structure Interaction) is developed in the present paper. Based on the recent studies on LSMPS (Least Square Moving Particle Semi-implicit) method [1,2] , the fluid models for FSI are improved, and the elastic structure models and fluid–structure coupling schemes are developed. Many strategies are developed to reduce the influence of mechanical vibration of elastomers on fluid calculation. The models are validated step by step. The improved fluid models with different Dirichlet and Neumann boundary are validated through hydrostatic pool problem, connecting tube problem and dam break problem. The elastic structure models under the velocity boundary and the loading boundary are validated through free oscillation cantilever problem and pressurized ring problem respectively. The fluid-structure coupling schemes are validated by the violent sloshing problem without considering the elastic deformation and the problem of dam break with an elastic gate. The results show a good performance of the developed method on the simulation of incompressible fluid flow and fluid-structure interaction. [ABSTRACT FROM AUTHOR]

Originally developed for solving fluid dynamics problems, a Lagrangian particle method called the consistent particle method (CPM) is expanded to solid mechanics problems in this article. The motions of particles are governed by the mass conservation and dynamics equations which are solved by the second‐order predictor–corrector time stepping scheme. The spatial derivatives of variables required in solving the governing equations and computing strain increments are obtained by Taylor series expansion. Stress components are updated from strain components according to the material constitutive relation. The physical density of material is directly computed without using particle number density. No additional particles are needed for the simulation of boundaries. For boundary surface that is partially loaded, the inverse distance weighting method is applied to deal with the stress singularity problem due to sudden change of stresses. Numerical examples including shock wave propagation and large deformation of footing penetration are presented to demonstrate the capabilities of CPM in solving solid mechanics problems. [ABSTRACT FROM AUTHOR]

In this paper, we study a kinetic model describing the evolution of planetary dust under the action of a planet and its satellites. In particular, we focus our attention on the formation of planetary rings and the role of shepherd moons. The equation describing the considered physical phenomenon is of Vlasov type, posed in an evolutionary domain in time. We first study some theoretical properties of the model. Then, we describe a numerical method, suitable for the study of kinetic equations in evolutionary domains with possibly complicated geometries. Finally, we show and comment some simulations. In particular, our numerical simulations show that shepherd moons play a key role in the formation and maintenance of divisions between rings. [ABSTRACT FROM AUTHOR]

Liquid sloshing is a common phenomenon in ocean engineering, and one which not only affects the stability of ship navigation, but also poses a threat to both the marine environment and human life. Ascertaining how best to reduce the amplitude of liquid sloshing has always been a key problem in ocean engineering. In this study, based on an improved moving-particle semi-implicit method, the BM-MPS method, the damping effect of a vertical slotted screen under rotation excitation was simulated and studied, and the influence of baffle porosity and the rotation amplitude on the resonance period and impact pressure was discussed. The results showed that the porosity had an obvious effect on the resonance period. A significant resonance period transformation happened when the porosity was 0.1, but a porosity of 0.15 was the point at which the maximum impact pressure in the resonance was at its minimum. Meanwhile, the impact duration curve was related to porosity. With the increasing of porosity, the impact duration curve changed from having no peak to a single peak, and then to double peak. In addition, the amplitude of rotation excitation was also one of the factors that affected the resonance period. [ABSTRACT FROM AUTHOR]

This paper develops a novel Hybrid Particle Element Method (HPEM) to model large deformation problems in solid mechanics, combining the strengths of both mesh-based and particle approaches. In the proposed method, the computational domain is discretized into two independent components: a set of finite elements and a set of particles. The finite elements serve as a temporary tool to compute the spatial derivatives of field variables, while the particles are used for storing history variables and establishing equilibrium equations. Spatial derivatives of field variables on particles are obtained by averaging the surrounding Gauss points of finite elements with a smoothing function. When the finite element mesh becomes distorted, it can be arbitrarily adjusted or completely regenerated. No global variable mapping is required when mesh adjustment or regeneration is performed, thus avoiding irreversible interpolation errors. The proposed method is validated through six typical examples, assessing its accuracy, efficiency, and robustness. The superior performance of the proposed method is comprehensively demonstrated through comparisons with several existing numerical methods. [ABSTRACT FROM AUTHOR]

We consider the EBT algorithm (a particle method) for the nonlocal equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel, which is not Lipschitz continuous, thus preventing the application of standard arguments. Therefore, we use the radial symmetry of the problem instead and transform it using spherical coordinates. The resulting equation has a Lipschitz kernel with only one singularity at zero. We introduce a new weighted flat norm and prove that the particle method converges in this norm. We also comment on the two-dimensional case that requires the application of the theory of measure spaces on general metric spaces and present numerical simulations confirming the theoretical results. In a companion paper we apply the Bayesian method to fit parameters to this model and study its theoretical properties. [ABSTRACT FROM AUTHOR]

To enable safe operations in applications such as rocket combustion chambers, the materials require cooling to avoid material damage. Here, transpiration cooling is a promising cooling technique. Numerous studies investigate possibilities to simulate and evaluate the complex cooling mechanism. One naturally arising question is the amount of coolant required to ensure a safe operation. To study this, we introduce an approach that determines the posterior probability distribution of the Reynolds number using an inverse problem and constraining the maximum temperature of the system under parameter uncertainties. Mathematically, this chance inequality constraint is dealt with by a generalized polynomial chaos expansion of the system. The posterior distribution will be evaluated by different Markov chain Monte Carlo based methods. A novel method for the constrained case is proposed and tested among others on two‐dimensional transpiration cooling models. [ABSTRACT FROM AUTHOR]

The Smoothed Particle Hydrodynamics (SPH) method is expanding and applied to more and more fields, particularly in engineering. The majority of current SPH developments deal with free-surface and multiphase flows, especially for situations where geometrically complex interface configurations are involved. The present review article covers the last 25 years of development of the method to simulate such flows, discussing the related specific features of the method. A path is drawn to link the milestone articles on the topic, and the main related theoretical and numerical issues are investigated.
In particular, several SPH schemes have been derived over the years, based on different assumptions. The main ones are presented and discussed in this review underlining the different contexts and the ways in which they were derived, resulting in similarities and differences. In addition, a summary is provided of the recent corrections proposed to increase the accuracy, stability and robustness of the SPH schemes in the context of free-surface and multiphase flows, and future perspectives of development are identified placing the method within the panorama of Computational Fluid Dynamics., (Creative Commons Attribution license.)

An implementation of the particle method on a hybrid cluster with graphics processing units (GPU) for modeling bulk generation, propagation, and scattering of electrons in a self-consistent electromagnetic field is presented. For synchronization of recording of results and data exchange in the calculation of particle parameters, solutions are proposed that reduce GPU RAM usage. [ABSTRACT FROM AUTHOR]

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.

Liquid sloshing is a common phenomenon in ocean engineering, and one which not only affects the stability of ship navigation, but also poses a threat to both the marine environment and human life. Ascertaining how best to reduce the amplitude of liquid sloshing has always been a key problem in ocean engineering. In this study, based on an improved moving-particle semi-implicit method, the BM-MPS method, the damping effect of a vertical slotted screen under rotation excitation was simulated and studied, and the influence of baffle porosity and the rotation amplitude on the resonance period and impact pressure was discussed. The results showed that the porosity had an obvious effect on the resonance period. A significant resonance period transformation happened when the porosity was 0.1, but a porosity of 0.15 was the point at which the maximum impact pressure in the resonance was at its minimum. Meanwhile, the impact duration curve was related to porosity. With the increasing of porosity, the impact duration curve changed from having no peak to a single peak, and then to double peak. In addition, the amplitude of rotation excitation was also one of the factors that affected the resonance period.

• A new solid body formation model in particle method was developed. • The solid bodies in the new model are formed by inter-particle attraction force. • The new model can simulate creation, formation, and motion of solid bodies. • The solid bodies by the new model can diminish and disappear by melting. • The mechanism based on the inter-particle attraction force is common with that in real world. In severe accidents of SFRs, molten core materials can discharge from the core, and the jet can impinge on the lower structure plate. After the jet impingement, fragmented discharged materials can form ring-shape solidification. A fundamental experiment was conducted to simulate the behavior. In order to simulate the behavior of solid body creation and motion, a new solid body formation model by inter-particle attraction force in particle method was developed. The advantage of the new model is that it can simulate creation, formation, and motion of solid bodies without any artificial treatment as solid bodies. The movable solid bodies by the new model have any size, shape, and number, and they are created and grown by solidification, and diminish and disappear by melting. The mechanism based on the inter-particle attraction force is common with that in real world where interatomic attraction force is the cause of solid body formation. [ABSTRACT FROM AUTHOR]

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted at particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) function, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that given moments up to the heat flux—that is, information equivalent to that contained in the Chapman-Enskog distribution—the proposed methodology provides a reliable closure in the collision-dominated and early transition regimes. Applications to greater rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure. • Generate samples from distribution defined by small number of its moments. • Solution based on entropic optimal transport. • Resulting distribution is well defined for all realizable moments. • Samples generated using efficient Monte Carlo algorithm. • Validated using DSMC simulations of rarefied gas hydrodynamics. [ABSTRACT FROM AUTHOR]

Discretization corrected particle strength exchange (DC PSE) is a particle based spatial differential operator designed to solve meshless continuum mechanics problems. DC PSE is a spatial gradient operator that can discretize a computational domain with randomly distributed particles, provided that each particle has enough neighboring particles. In contrast, conventional methods such as the standard finite difference method require the computational domain to be discretized into a Cartesian grid. In linear elasticity simulations, especially steady state cases, this domain is mostly discretized using mesh-based methods such as finite element. However, while particle methods such as smoothed particle hydrodynamics (SPH) have been widely applied to solve dynamic elasticity problems, they have rarely been used in steady state simulations. In this study, a DC PSE operator was used to solve steady linear elasticity problems in a twodimensional domain. The result of the DC PSE numerical simulation was compared to numerical results, empirical formula results, and results from conventional commercial finite element software, respectively. [ABSTRACT FROM AUTHOR]

We study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As we deal with the planning problem, we prescribe initial and terminal distributions for the transport equation. The particle approximation builds on a semi-discrete variational problem. First, we address the existence and uniqueness of a solution to the semi-discrete variational problem. Next, we show that our discretization preserves some previously identified conserved quantities. Finally, we prove that the approximation by particle systems preserves displacement convexity. We use this last property to establish uniform estimates for the discrete problem. We illustrate our results for the discrete problem with numerical examples. [ABSTRACT FROM AUTHOR]

A steel/aluminum alloy dissimilar resistance spot welding process was simulated by a three-dimensional smoothed particle hydrodynamics method. Furthermore, the time-dependent increase in the intermetallic compound thickness at the joint interface was estimated using the obtained numerical data of temperature history. As a result, the steel sheet started to melt from the center of the sheet in the thickness direction. The convection in the molten aluminum alloy caused by the electromagnetic force promoted the heat transfer at the solid-liquid interface because the temperature gradient becomes steeper. Moreover, the maximum thickness of the intermetallic compound was estimated to be approximately 1 µm. These results support the validity of the computational model developed in this study for simulating the nugget formation process during dissimilar resistance spot welding and estimating the intermetallic compound thickness. [ABSTRACT FROM AUTHOR]

Numerical simulation based on an incompressible smoothed particle hydrodynamics method was performed to clarify dominant factors of slag transfer and deposition processes in a metal active gas welding. The computational model considered the effects of a shielding gas flow on a slag floating on a weld pool surface. The computational result showed that the slags were generated on the weld pool surface near the centre of a heat source and were transferred to the edge of the pool. Those tendencies were similar to those observed in an experiment. The slags stayed at the trailing region of the pool and then deposited on a weld bead. These behaviours supported the validity of the present computational result. To identify the dominant factors of the slag behaviour on the weld pool, numerical experiments were conducted with individually acting forces due to the Marangoni effect, the shearing force, the Lorentz force, and the drag by the shielding gas flow. The computational results suggested that the shearing force and the drag due to the shielding gas were dominant near the centre of the heat source, and the slag was transferred from the vicinity of the heat source to the end of the weld pool. On the other hand, the force due to the Marangoni effect was dominant in the trailing region of the weld pool, and consequently, the slag was transferred from there to the front region in the welding direction. [ABSTRACT FROM AUTHOR]