Implicit Particle Research Articles

Fluid Implicit Particles on Coadjoint Orbits

We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. We start with a Hamiltonian formulation of the incompressible Euler Equations, and then, using a local, explicit, and high order divergence free interpolation, construct a modified Hamiltonian system that governs our discrete Euler flow. The resulting discretization, when paired with a geometric time integration scheme, is energy and circulation preserving (formally the flow evolves on a coadjoint orbit) and is similar to the Fluid Implicit Particle (FLIP) method. CO-FLIP enjoys multiple additional properties including that the pressure projection is exact in the weak sense, and the particle-to-grid transfer is an exact inverse of the grid-to-particle interpolation. The method is demonstrated numerically with outstanding stability, energy, and Casimir preservation. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions.

An implicit unified gas-kinetic particle method with large time steps for gray radiation transport

For a long time, efficient algorithms for high-dimensional equations, represented by photon radiation transport, have been one important topic in the development of computational methods for particle transport processes. In this paper, we present an implicit unified gas-kinetic particle (IUGKP) method for multiscale gray radiative transfer. Based on the integral solution of the radiative transfer equation, the photon transport processes are categorized into non-equilibrium transport processes with a large photon free path and equilibrium transport processes with a small photon free path. The long-path processes are solved by an implicit Monte Carlo (IMC) method, and the short-path processes are solved by an implicit diffusion system. The closure formulation of photon distribution is derived from the local integral solution of the radiative transfer equation to couple the IMC and diffusion system. The improvement of the proposed IUGKP method over UGKP method is that particles can be tracked continuously instead of just until the first collision, making simulation with large time steps possible. The IUGKP method has the properties of asymptotic-preserving (AP) and regime-adaptive (RA). The AP property states that the IUGKP method converges to the consistent numerical methods for the asymptotic limiting equations of RTE in the limiting regimes. The RA property states that the computational accuracy of the IUGKP method adapts to the regimes. In this paper, the mathematical proof of the AP and RA properties is presented, and the multiscale numerical tests are performed to demonstrate the accuracy and efficiency of the IUGKP method.

An implicit particle code with exact energy and charge conservation for studies of dense plasmas in axisymmetric geometries

A collisional particle code based on implicit energy- and charge-conserving methods in axisymmetric geometries is presented. A new particle pusher for axisymmetric systems is introduced that is compatible with exact energy and charge conservation and yields improved accuracy compared to other methods. How to appropriately treat all aspects of the algorithm near the r=0 axis of symmetry is described in detail. The axisymmetric model is verified by simulating the free expansion of a plasma sphere in 2D cylindrical and 1D spherical geometries. The algorithm's ability to study the dynamic compression of a dense plasma is illustrated by simulating the dynamic Z-pinch in 1D cylindrical geometry.

Deep JKO: Time-implicit particle methods for general nonlinear gradient flows

We develop novel neural network-based implicit particle methods to compute high-dimensional Wasserstein-type gradient flows with linear and nonlinear mobility functions. The main idea is to use the Lagrangian formulation in the Jordan–Kinderlehrer–Otto (JKO) framework, where the velocity field is approximated using a neural network. We leverage the formulations from the neural ordinary differential equation (neural ODE) in the context of continuous normalizing flow for efficient density computation. Additionally, we make use of an explicit recurrence relation for computing derivatives, which greatly streamlines the backpropagation process. Our methodology demonstrates versatility in handling a wide range of gradient flows, accommodating various potential functions and nonlinear mobility scenarios. Extensive experiments demonstrate the efficacy of our approach, including an illustrative example from Bayesian inverse problems. This underscores that our scheme provides a viable alternative solver for the Kalman-Wasserstein gradient flow.

An implicit thermo-mechanical coupling model for heat conduction and thermal cracking in brittle materials

In this paper, an implicit thermo-mechanical coupling model is developed to simulate heat conduction and thermal cracking in brittle materials. In the thermal analysis, an implicit particle heat conduction model (PHCM) is proposed. A linear algebraic system of heat conduction equations is derived based on the temperatures of the particle system and the heat flux among adjacent particles. An analytical expression is introduced for the involved correction coefficient, with which the macroscopic thermal conductivity coefficient can be directly adopted without calibration. Furthermore, a thermal conductivity reduction coefficient is introduced to account for the thermal resistance of the cracks. In the mechanical analysis, particle discontinuous deformation analysis (PDDA), which is an implicit variant of the discrete element method, is employed. The PHCM is first verified against analytical and finite element solutions for transient heat conduction problems. The results show that the PHCM is an effective and accurate heat conduction model that readily reflects the thermal resistance of cracks. Then, the thermo-mechanical coupling model is verified by the expansion of heated specimens under different conditions. Finally, the successful application of the coupling model in the simulation of thermal shock tests demonstrates its effectiveness for thermal cracking problems.

Speeding-up direct implicit particle-in-cell simulations in bounded plasma by obtaining future electric field through explicitly propulsion of particles

The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics. However, it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients. In this work, we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future. The new method retains the form of implicit particle pusher, but the future field is obtained by solving the traditional explicit equation. Several numerical experiments, including the motion of charged particle in electromagnetic field, plasma sheath, and free diffusion of plasma into vacuum, are implemented to evaluate the performance of the method. The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation, while accurately describe low-frequency plasma phenomena, with the price of losing the numerical stability at large time-step. We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.

An implicit particle code with exact energy and charge conservation for electromagnetic studies of dense plasmas

A collisional particle code based on implicit energy- and charge-conserving methods is presented. A modified version of the particle-suppressed Jacobian-Free Newton-Krylov method that can enhance the solver efficiency is introduced. Mathematically, it is shown that this new approach can be viewed as a fixed-point iteration method for the particle positions. The model can exactly conserve global energy and local charge and can efficiently use time steps larger than the plasma period. The algorithm's ability to simulate dense plasmas accurately and efficiently is quantified by simulating the dynamic compression of a plasma slab via a magnetic piston in 1D planar geometry.

Influence of tool rotational speed on mechanical and corrosion behaviour of friction stir processed AZ31/Al2O3 nanocomposite

Nano-sized reinforcements improved the mechanical characteristics efficiently by promoting more implicit particle hardening mechanisms compared to micron-sized reinforcements. Nano-sized particles lessen the critical particle solidification velocity for swamp and thus offers better dispersal. In the present investigation, the friction stir processing (FSP) is utilized to produce AZ31/Al2O3 nanocomposites at various tool rotation speeds (i.e., 900, 1200, and 1500 rpm) with an optimized 1.5% volume alumina (Al2O3) reinforcement ratio. The mechanical and corrosion behavior of AZ31/Al2O3-developed nanocomposites was investigated and compared with that of the AZ31 base alloy. The AZ31 alloy experienced a comprehensive dynamic recrystallization during FSP, causing substantial grain refinement. Grain-size strengthening is the primary factor contributed to the enhancement in the strength of the fabricated nanocomposite. Tensile strength and yield strength values were lower than those for the base metal matrix, although an upward trend in both values has been observed with an increase in tool rotation speed. An 19.72% increase in hardness along with superior corrosion resistance was achieved compared to the base alloy at a tool rotational speed of 1500 rpm. The corrosion currents (Jcorr) of all samples dropped with increase in the rotational speed, in contrast to the corrosion potentials (Ecorr), which increased. The values of Jcorr of AZ31/Al2O3 were 42.3%, 56.8%, and 65.5% lower than those of AZ31 alloy at the chosen rotating speeds of 900, 1200, and 1500 rpm, respectively. The corrosion behavior of friction stir processed nanocomposites have been addressed in this manuscript which has not been given sufficient attention in the existing literature. Further, this work offers an effective choice for the quality assurance of the FSP process of AZ31/Al2O3 nanocomposites. The obtained results are relevant to the development of lightweight automobile and aerospace structures and components.

A conservation law consistent updated Lagrangian material point method for dynamic analysis

The Material Point Method (MPM) is well suited to modelling dynamic solid mechanics problems undergoing large deformations with non-linear, history dependent material behaviour. However, the vast majority of existing material point method implementations do not inherit conservation properties (momenta and energy) from their continuum formulations. This paper provides, for the first time, a dynamic updated Lagrangian material point method for elasto-plastic materials undergoing large deformation that guarantees momenta and energy conservation. Sources of energy dissipation during point-to-grid and grid-to-point mappings for FLuid Implicit Particle (FLIP) and Particle In Cell (PIC) approaches are clarified and a novel time-stepping approach is proposed based on an efficient approximation of the Courant-Friedrich-Lewy (CFL) condition. The formulation provided in this paper offers a platform for understanding the energy conservation nature of future/existing features of material point methods, such as contact approaches.

Hierarchical particle optimization for cortical shape correspondence in temporal lobe resection

BackgroundAnterior temporal lobe resection is an effective treatment for temporal lobe epilepsy. The post-surgical structural changes could influence the follow-up treatment. Capturing post-surgical changes necessitates a well-established cortical shape correspondence between pre- and post-surgical surfaces. Yet, most cortical surface registration methods are designed for normal neuroanatomy. Surgical changes can introduce wide ranging artifacts in correspondence, for which conventional surface registration methods may not work as intended. MethodsIn this paper, we propose a novel particle method for one-to-one dense shape correspondence between pre- and post-surgical surfaces with temporal lobe resection. The proposed method can handle partial structural abnormality involving non-rigid changes. Unlike existing particle methods using implicit particle adjacency, we consider explicit particle adjacency to establish a smooth correspondence. Moreover, we propose hierarchical optimization of particles rather than full optimization of all particles at once to avoid trappings of locally optimal particle update. ResultsWe evaluate the proposed method on 25 pairs of T1-MRI with pre- and post-simulated resection on the anterior temporal lobe and 25 pairs of patients with actual resection. We show improved accuracy over several cortical regions in terms of ROI boundary Hausdorff distance with 4.29 mm and Dice similarity coefficients with average value 0.841, compared to existing surface registration methods on simulated data. In 25 patients with actual resection of the anterior temporal lobe, our method shows an improved shape correspondence in qualitative and quantitative evaluation on parcellation-off ratio with average value 0.061 and cortical thickness changes. We also show better smoothness of the correspondence without self-intersection, compared with point-wise matching methods which show various degrees of self-intersection. ConclusionThe proposed method establishes a promising one-to-one dense shape correspondence for temporal lobe resection. The resulting correspondence is smooth without self-intersection. The proposed hierarchical optimization strategy could accelerate optimization and improve the optimization accuracy. According to the results on the paired surfaces with temporal lobe resection, the proposed method outperforms the compared methods and is more reliable to capture cortical thickness changes.

Implicit particle filtering via a bank of nonlinear Kalman filters

The implicit particle filter seeks to mitigate particle degeneracy by identifying particles in the target distribution’s high-probability regions. This study is motivated by the need to enhance computational tractability in implementing this approach. We investigate the connection of the particle update step in the implicit particle filter with that of the Kalman filter and then formulate a novel realization of the implicit particle filter based on a bank of nonlinear Kalman filters. This realization is more amenable and efficient computationally.

The power particle-in-cell method

This paper introduces a new weighting scheme for particle-grid transfers that generates hybrid Lagrangian/Eulerian fluid simulations with uniform particle distributions and precise volume control. At its core, our approach reformulates the construction of Power Particles [de Goes et al. 2015] by computing volume-constrained density kernels. We employ these optimized kernels as particle domains within the Generalized Interpolation Material Point method (GIMP) in order to incorporate Power Particles into the Particle-In-Cell framework, hence the name the Power Particle-In-Cell method. We address the construction of volume-constrained density kernels as a regularized optimal transportation problem and describe an iterative solver based on localized Gaussian convolutions that leads to a significant performance speedup compared to [de Goes et al. 2015]. We also present novel extensions for handling free surfaces and solid obstacles that bypass the need for cell clipping and ghost particles. We demonstrate the advantages of our transfer weights by improving hybrid schemes for fluid simulation such as the Fluid Implicit Particle (FLIP) method and the Affine Particle-In-Cell (APIC) method with volume preservation and robustness to varying particle-per-cell ratio, while retaining low numerical dissipation, conserving linear and angular momenta, and avoiding particle reseeding or post-process relaxations.

Implicit iterative particle shifting for meshless numerical schemes using kernel basis functions

A novel particle shifting technique (PST) for meshless numerical methods is presented. The proposed methodology uses an implicit iterative particle shifting (IIPS) technique aiming to reduce the spatial particle’ anisotropy, which is associated with the discretization error in meshless numerical schemes based on kernel basis functions. The algorithm controls the particle spatial distribution through an implicit minimization problem, related to the particle concentration gradient and therefore, to the particles’ anisotropy. This results in accurate particle distributions, to demonstrate the effectiveness of the proposed method, the IIPS algorithm is tested within a smoothed particle hydrodynamics (SPH) framework, with static and kinematic cases, by examining the particle distributions and the corresponding spatial accuracy. Further, the computational cost of the proposed methodology is reported and it is shown that it introduces minimal overhead. Moreover, the simulations of the Taylor–Green vortex (TGV), employing a weakly-compressible SPH Navier–Stokes solver, confirmed the superior accuracy of the IIPS in comparison to existing explicit shifting approaches, in simulating internal flows.

A drift homotopy implicit particle filter method for nonlinear filtering problems

<p style='text-indent:20px;'>In this paper, we develop a drift homotopy implicit particle filter method. The methodology of our approach is to adopt the concept of drift homotopy in the resampling procedure of the particle filter method for solving the nonlinear filtering problem, and we introduce an implicit particle filter method to improve the efficiency of the drift homotopy resampling procedure. Numerical experiments are carried out to demonstrate the effectiveness and efficiency of our drift homotopy implicit particle filter.</p>

Research on 3D Simulation Method of Nearshore Storm Surge Based on FLIP

This paper proposes a FLIP-based three-dimensional storm surge simulation method. Based on the Fluid Implicit Particle (FLIP) method, the flow field is calculated by FLIP fluid, and finally through the standard coloring based on PBR in the Unity engine. The device renders the fluid state model generated at each moment. The experimental results show that the method in this paper not only meets the realistic requirements of nearshore storm surge simulation, but also effectively improves the efficiency of scene rendering. The result can be used not only in game production and movie special effects, but also in engineering simulations such as ocean engineering and environmental engineering, and has a wide range of application prospects and application values.

Kinetic studies for adsorption of anumber of food coloring dyes by using activated carbon

The research included the application of some kinematic models to study the adsorption process, such as the pseudo-first order (Lacquerine) and the second false (Hood and Mickey) model, the wafer kinematic model and the implicit particle diffusion model, and then applying the experimental results of the adsorption process to some food dyes through which color is given to juices, soft drinks and pastries. And foodstuffs such as jams, medicines and others that bear the following codes: E110, E122, E102, E133, E123, E124 and E127. Commercial activated carbon was used as an adsorbent for these dyes, which constitute a very wide sector of important industries for humans everywhere in the world. The kinematic study is indicated by obtaining important information that helps in designing a simple and economical adsorption system in order to get rid of these pigments and treat them. After using different kinematic models, the study found the applicability of the experimental results of the adsorption of colored dyes of juices, foodstuffs and soft drinks to a second-order pseudo kinetic model. Obtain the constant adsorption velocity of those pigments with good and high linear relationship and match the practical values of adsorption capacity with the theoretical values, as well as the values of the initial velocity of adsorption.

Ocean satellite data assimilation using the implicit equal-weights variational particle smoother

The implicit equal-weights variational particle smoother (IEWVPS) is a combination of the particle filter (PF) and weak-constraint 4-dimensional variational (4D-Var) method, that inherits the merits of both. The IEWVPS avoids the filter degeneracy of particle filters through an implicit equal-weights scheme and reduces the root mean square deviations (RMSDs) by introducing the 4D-Var method. This method has been tested using the Lorenz 96 model in a previous study, and we now implement it in the Regional Ocean Model System (ROMS), which is a realistic and complex ocean model. Two key problems, the representation of the analysis error covariance and the choice of the parameter α, were solved during this implementation. With an eddy-permitting model, satellite-based sea surface height (SSH) and sea surface temperature (SST) observations were assimilated with a set of 40 particles IEWVPS scheme. Compared with the ensemble 4D-Var method, the IEWVPS can reduce the bias introduced by perturbed atmospheric forcing, effectively improving temperature simulations in the upper 50 m while maintaining the RMSD of SSH at the same level. Therefore, the cooling effect caused by typhoons in the upper ocean is better characterized under the IEWVPS scheme than with previously used method. The ratio of RMSD to the ensemble spread indicates that the ensemble quality of the IEWVPS is much better than that of the ensemble 4D-Var. In addition, the computational cost of the IEWVPS is only slightly larger than that of the ensemble 4D-Var. One additional tangent linear model integration, one additional nonlinear model integration, and perturbation fields inputs/outputs are still needed.

Small-Scale Condensation Simulation on Complicated Surface

<p indent=0mm>Vapor condensation is a typical phenomenon in the nature, whose realistic simulation is of great significance to virtual reality, video effects, game entertainment, etc. Traditional physically-based methods failed to preserve the small-scale details during condensation. A novel hybrid framework combining smoothed particle hydrodynamics and adaptive fluid implicit particle method is proposed. The heat transfer of air is modeled with smoothed particle hydrodynamics, with phase transition controlled by relative humidity and dew point. The fluid implicit particle method is combined with an octree-based adaptive grid to achieve high-resolution details of small-scale drops. Finally, surface tension, adhesion and resistance are introduced to simulate the motion of drops on complicated surfaces realistically. It is demonstrated that proposed method provides plausible results of condensation on intricate surfaces efficiently through several experiments.

Affine particle-in-cell method for two-phase liquid simulation

BackgroundThe interaction of gas and liquid can produce many interesting phenomena, such as bubbles rising from the bottom of the liquid. The simulation of two-phase fluids is a challenging topic in computer graphics. To animate the interaction of a gas and liquid, MultiFLIP samples the two types of particles, and a Euler grid is used to track the interface of the liquid and gas. However, MultiFLIP uses the fluid implicit particle (FLIP) method to interpolate the velocities of particles into the Euler grid, which suffer from additional noise and instability. MethodsTo solve the problem caused by fluid implicit particles (FLIP), we present a novel velocity transport technique for two individual particles based on the affine particle-in-cell (APIC) method. First, we design a weighed coupling method for interpolating the velocities of liquid and gas particles to the Euler grid such that we can apply the APIC method to the simulation of a two-phase fluid. Second, we introduce a narrowband method to our system because MultiFLIP is a time-consuming approach owing to the large number of particles. ResultsExperiments show that our method is well integrated with the APIC method and provides a visually credible two-phase fluid animation. ConclusionsThe proposed method can successfully handle the simulation of a twophase fluid.

An advanced hybrid smoothed particle hydrodynamics–fluid implicit particle method on adaptive grid for condensation simulation

AbstractIn this article, we propose a novel hybrid framework by combining smoothed particle hydrodynamics and adaptive narrow band fluid implicit particle method (NB‐FLIP) to faithfully model the multiphysical processes involving heat transfer and phase transition, and to precisely simulate the dynamics of condensed droplets moving along intricate objects. We first formulate a governing physical model built upon an improved phase transition model and an augmented on‐surface drop analysis method to achieve realistic condensation effects over intricate hydrophilic/hydrophobic interface. To achieve both high‐fidelity interactions and high‐resolution visual effects, we further develop an adaptive NB‐FLIP solver with octree‐dictated background grid in order to further enhance the performance of our framework. Experimental results have shown that our approach can be used to efficiently and realistically simulate the small‐scale interaction details between condensed drops and complex objects with arbitrary geometry.