Efficient Simulation Research Articles

Efficient simulation of potential energy operators on quantum hardware: a study on sodium iodide (NaI)

This study introduces a conceptually novel polynomial encoding algorithm for simulating potential energy operators encoded in diagonal unitary forms in a quantum computing machine. The current trend in quantum computational chemistry is effective experimentation to achieve high-precision quantum computational advantage. However, high computational gate complexity and fidelity loss are some of the impediments to the realization of this advantage in a real quantum hardware. In this study, we address the challenges of building a diagonal Hamiltonian operator having exponential functional form, and its implementation in the context of the time evolution problem (Hamiltonian simulation and encoding). Potential energy operators when represented in the first quantization form is an example of such types of operators. Through systematic decomposition and construction, we demonstrate the efficacy of the proposed polynomial encoding method in reducing gate complexity from O(2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(2^n)$$\\end{document} to O∑i=1rnCr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\sum _{i=1}^{r} {} ^nC_r \\right)$$\\end{document} (for some r≪n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r\\ll n$$\\end{document}). This offers a solution with lower complexity in comparison to the conventional Hadamard basis encoding approach. The effectiveness of the proposed algorithm was validated with its implementation in the IBM quantum simulator and IBM quantum hardware. This study demonstrates the proposed approach by taking the example of the potential energy operator of the sodium iodide molecule (NaI) in the first quantization form. The numerical results demonstrate the potential applicability of the proposed method in quantum chemistry problems, while the analytical bound for error analysis and computational gate complexity discussed, throw light on issues regarding its implementation.

PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation

The aim of this paper is to introduce the PLEIADES framework offering a set of services and numerical tools to model and simulate the behavior of nuclear fuels of different concepts of reactors. The framework provides in particular the following features: interfaces to manipulate meshes and fields, services to deal with different physical solvers, setup of coupling trees to realize multiphysics partitioned (accelerated) fixed point couplings, automated time-marching algorithm, checkpoint/restart strategies, capability to realize on-the-fly multiscale couplings. It is built with a permanent concern for sustainability, scalability and maintainability. PLEIADES framework supports multidimensional simulations, typically 1D, 2D and 3D, possibly multilayered. To date, this framework relies on the generic thermomechanical finite elements solver Cast3M to deal with partial derivative problems (mechanical, thermal or diffusion problems) at the scale of the structure or the (heterogeneous) microstructure. It also makes use of so-called point models (mainly based on ODE — ordinary differential equations) to describe the local (mesoscale) evolution of the material through the physics of irradiation. Several software applications are built on the PLEIADES framework, they can use its parallel features to use multiple processors. The multilayered calculation scheme provides a way to loosen the computations and access to a good parallel performance up to hundred cores. It is also possible to achieve efficient scalable concurrent multiscale simulations through finite element square (FE2) computational homogenization algorithms.

An atomic boson sampler.

A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2-12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10-12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16.

A physics and data co-driven surrogate modeling method for high-dimensional rare event simulation

This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical models with data-driven error corrections. The hypothesis is that a well-designed and well-trained simplified physical model can preserve salient features of the original model, while data-fitting techniques can fill the remaining gaps between the surrogate and original model predictions. The coupled physics-data-driven surrogate model is adaptively trained using active learning, aiming to achieve a high correlation and small bias between the surrogate and original model responses in the critical parametric region of a rare event. A final importance sampling step is introduced to correct the surrogate model-based probability estimations. Static and dynamic problems with input uncertainties modeled by random field and stochastic process are studied to demonstrate the proposed method.

Embedded large eddy simulation of boundary layer transition behind a micro-ramp

Boundary layer transition induced by surface roughness elements plays an important role in aerodynamic and aero-thermodynamic design of subsonic/supersonic/hypersonic vehicles. However, the effect of three-dimensional isolated roughness element in the process of promoting/suppressing boundary layer transition is far from being fully understood, particularly in the incompressible laminar flow. In the present study, the laminar-to-turbulent transition induced by a three-dimensional isolated micro-ramp element immersed in an incompressible laminar boundary layer is investigated numerically. The embedded large eddy simulation (ELES) combining the intermittency transition model and the wall-modeled large eddy simulation (WMLES) S − Ω model is employed for the first time. Numerical results on the time-averaged/instantaneous flow field and the statistical flow fluctuations are analysed and validated thoroughly by the existing experimental measurements. It is found that the interaction of the secondary and the tertiary streamwise vortices causes a high level of wall shear and an inflectional velocity distribution in the near-wall region. An additional eddy system that develops nonlinearly from the unstable inflectional flow may trigger the boundary layer transition. The present study validates that the ELES combined with the WMLES S − Ω model is an efficient simulation tool for industrial wall-bounded flows allowing effective compromise between flexibility, cost, and accuracy.

Accurate and Efficient Simulation Models for Power Electronics Transformers Based on Series-Connected Active Unity Power Factor Rectifier Modules

This paper contributes an efficient simulation technique for input-series output-parallel multilevel power electronics transformers based on active unity-power-factor rectifiers as building blocks. The technical motivation of the work comes from the fact that the computational burden for the simulation of these technologies tends to become unaffordable as the number of modules grows when using commercial software blocksets. This paper presents a new method to drastically reduce the simulation complexity by simplifying the switching rules: in a three-phase circuit, each phase zero-crossing condition is implemented by a single and simple algebraic rule, so the complex calculations for determining the conduction state of each single diode are removed from the model. The computational enhancement and accuracy of the proposed technique are proved by experimental verification using a single-phase single-cell prototype together with multiple simulations of full-scale systems of different sizes.

Hybrid lattice Boltzmann method using Cartesian and body-fitted grids for turbomachinery aeroacoustic simulations

In this study, we developed a hybrid approach using the lattice Boltzmann method (LBM) and finite-volume lattice Boltzmann method (FVLBM) to perform efficient aeroacoustic simulations with moving boundaries. An entire domain, including the flow and acoustic fields, was computed using the standard LBM with a Cartesian grid. Local domains around the moving objects were computed using the FVLBM with body-fitted grids. These simulations were coupled using the direct forcing method to consider moving boundaries. The hybrid method was validated for several problems including turbulent flows and flow-induced sounds under low-Mach-number conditions. These validation problems covered flows with Reynolds numbers up to 2.0×105 and Mach numbers less than 0.2. In the simulations of the aeolian tone generated from stationary and rotating cylinders, the hybrid method results were consistent with those of the conventional methods. In the simulation of the turbulent flow and broadband sound of the isolated airfoil, the hybrid method was 15 times faster than the standard LBM and produced results consistent with the experimental results. Furthermore, the application of a cross-flow fan demonstrated that the hybrid method successfully simulated the flow and acoustic fields around the rotor.

Geometrically Parametrised Reduced Order Models for Studying the Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behavior of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behavior in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

Automated Chemical Reaction Network Generation and Its Application to Exoplanet Atmospheres

With the advent of JWST and the spectroscopic characterization of exoplanet atmospheres in unprecedented detail, there is a demand for more complete pictures of chemical and photochemical reactions and their impacts on atmospheric composition. Traditionally, building reaction networks for (exo)planetary atmospheres involves manually tracking relevant species and reactions, a time-consuming and error-prone process. This approach’s applicability is also often limited to specific conditions, making it less versatile for different planetary types (i.e., photochemical networks for Jupiters may not be directly applicable to water-rich exoplanets). We introduce an automated approach using a computer-aided chemical reaction network generator, combined with a 1D photochemical kinetic-transport model, offering significant advantages. This approach automatically selects reaction rates through a rate-based iterative algorithm and multiple refinement steps, enhancing model reliability. Also, this approach allows for the efficient simulation of diverse chemical environments, from hydrogen to water, carbon dioxide, and nitrogen-dominated atmospheres. Using WASP-39b and WASP-80b as examples, we demonstrate our approach’s effectiveness, showing good agreement with recent JWST data. Our WASP-39b model aligns with prior studies and JWST observations, capturing photochemically produced sulfur dioxide. The WASP-80b model reveals an atmosphere influenced by deep-interior thermochemistry and vertical mixing, consistent with JWST NIRCam observations. Furthermore, our model identifies a novel initial step for the N2–NH3–HCN pathway that enhances the efficiency of the conversion in high-temperature/high-pressure environments. This automated chemical network generation offers a novel, efficient, and precise framework for studying exoplanetary atmospheres, marking a significant advancement over traditional modeling techniques.

Super-localised wave function approximation of Bose-Einstein condensates

This paper presents a novel spatial discretisation method for reliable and efficient simulation of Bose-Einstein condensates modelled by the Gross-Pitaevskii equation and the corresponding nonlinear eigenvector problem. The method combines the high-accuracy properties of numerical homogenisation methods with a novel super-localisation approach for the calculation of the basis functions. A rigorous numerical analysis of the nonlinear eigenvector problem demonstrates superconvergence of the ideal approach compared to classical polynomial and multiscale finite element methods, even in low regularity regimes. Numerical tests show that the super-localised method is competitive with spectral methods, particularly in capturing critical physical effects in extreme conditions, such as vortex lattice formation in fast-rotating potential traps. The method's potential is further highlighted through a dynamic simulation of a phase transition from Mott insulator to Bose-Einstein condensate, emphasising its capability for reliable exploration of physical phenomena.

Accelerating the force-coupling method for hydrodynamic interactions in periodic domains

The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for periodic domains involves utilising a compact or exponentially decaying kernel function to spread the force on the structure to a regular grid where the resulting flow and interactions can be computed efficiently using an FFT-based solver. A limitation to this approach is that the grid spacing must be chosen to resolve the kernel and thus, these methods can become inefficient when the separation between the structures is large compared to the kernel width. In this paper, we address this issue for the force-coupling method (FCM) by introducing a modified kernel that can be resolved on a much coarser grid, and subsequently correcting the resulting interactions in a pairwise fashion. The modified kernel is constructed to ensure rapid convergence to the exact hydrodynamic interactions and a positive-splitting of the associated mobility matrix. We provide a detailed computational study of the methodology and establish the optimal choice of the modified kernel width, which we show plays a similar role to the splitting parameter in Ewald summation. Finally, we perform example simulations of rod sedimentation and active filament coordination to demonstrate the performance of fast FCM in application.

Innovative approach to estimate structural damage using linear regression and K-nearest neighbours machine learning algorithms

Conventional structural design methodologies often utilize elastic analysis techniques, such as the equivalent static force method and the response spectrum method. While these methods are known for their simplicity and computational efficiency, they prove inadequate in capturing the extent of structural damage caused by seismic forces. Additionally, employing nonlinear dynamic analysis to estimate structural damage represents a challenging and intricate task, posing difficulties for many structural designers. Consequently, the objective of this paper is to present an innovative methodology for evaluating seismic structural damage of moment-resisting frame structures. This involves the utilization of machine learning algorithms, which have been trained and tested on a large data set generated using a newly developed and numerically efficient simulation procedure. The machine learning algorithms employ both linear regression and K-nearest neighbors approaches to accurately replicate the Park-Ang structural damage index.

Modeling and simulation of pollution transport in the Mediterranean Sea using enriched finite element method

This paper presents a novel numerical method for simulating the transport and dispersion of pollutants in the Mediterranean sea. The governing mathematical equations consist of a barotropic ocean model with friction terms, bathymetric forces, Coriolis and wind stresses coupled to an advection–diffusion equation with anisotropic dispersion tensor and source terms. The proposed numerical solver uses a multilevel adaptive semi-Lagrangian finite element method that combines various techniques, including the modified method of characteristics, finite element discretization, coupled projection scheme based on a rotational pressure correction algorithm, and an adaptive L2-projection. The approach employs the gradient of the concentration as an error indicator for enrichment adaptations and increasing the number of quadrature points where needed without refining the mesh. The method is shown to provide accurate and efficient simulations for pollution transport in the Mediterranean sea. The proposed approach distinguishes itself from the well-established adaptive finite element methods for incompressible viscous flows by retaining the same structure and dimension of linear systems during the adaptation process.

Revealing Interface Polarization Effects on the Electrical Double Layer with Efficient Open Boundary Simulations under Potential Control.

A major challenge in modeling interfacial processes in electrochemical (EC) devices is performing simulations at constant potential. This requires an open-boundary description of the electrons, so that they can enter and leave the computational cell. To enable realistic modeling of EC processes under potential control we have interfaced density functional theory with the hairy probe method in the weak coupling limit (Zauchner et al. Phys. Rev. B 2018, 97, 045116). Our implementation was systematically tested using simple parallel-plate capacitor models with pristine surfaces and a single layer of adsorbed water molecules. Remarkably, our code's efficiency is comparable with a standard DFT calculation. We reveal that local field effects at the electrical double layer induced by the change of applied potential can significantly affect the energies of chemical steps in heterogeneous electrocatalysis. Our results demonstrate the importance of an explicit modeling of the applied potential in a simulation and provide an efficient tool to control this critical parameter.

Surface Tension Estimation of Steel above Boiling Temperature

Surface tension is an important characteristic of materials. In particular at high temperatures, surface tension values are often unknown. However, for metals, these values are highly relevant in order to enable efficient industrial processing or simulation of material behavior. Plasma, electron or laser beam processes can induce such high energy inputs, which increase the metal temperatures to, and even above, boiling temperatures, e.g., during deep penetration welding or remote cutting. Unfortunately, both theoretical and experimental methods experience challenges in deriving surface tension values at high temperatures. Material models of metals have limitations in explaining complex ion interactions, and experimentally measuring temperature and surface tension at high temperatures is a challenge for methods and equipment. Therefore, surface wave analysis was conducted in this work to derive surface tension values around the boiling temperature of steel and identify trends. In addition, a simple ion interaction calculation was used to simulate the impacting parameters that define the surface tension. Since both the experimental values and simulation results indicate an increasing trend in surface tension above the boiling temperature, it is concluded that the dominating attractive forces above this temperature should increase with increasing temperature and lead to increasing surface tension forces in the surface layers of liquid metal.

QuadWire: An extended one dimensional model for efficient mechanical simulations of bead-based additive manufacturing processes

This paper presents the basis of a new mechanical model named QuadWire dedicated to efficient simulations of bead-based additive manufacturing processes in which elongated beads undergoing significant cooling and eigenstrain are assembled to form 3D parts. The key contribution is to use a multi-particular approach containing 4 particles per material point to develop an extended 1D model capable of capturing complex 3D mechanical states, while significantly reducing computation time with respect to conventional approaches. Indeed, 3D models usually require at least 3 to 4 elements across the bead section, which results in fine discretization along the tangential direction to avoid conditioning issues, and therefore very fine mesh of the entire 3D part. In the QuadWire model, the bead height and thickness are internal dimensions, enabling a significantly coarser mesh along the tangential direction. Thus, although the QuadWire has 12 degrees of freedom per material point instead of 3 for classical models, the total number of degrees of freedom is reduced by several orders of magnitude for large parts. The proposed model is classically developed within the framework of the principle of virtual power and standard generalized hyperelastic media (i.e., finite strain theory), which necessitates a thermodynamic analysis. Furthermore, the proposed approach includes native and manageable kinematic constraints between successive beads so that the stress state properly evolves during fabrication. Finite element analysis is used for numerical implementation under infinitesimal strain assumption for the sake of simplicity, and the QuadWire stiffness parameters are optimized so that the mechanical response fit conventional 3D approaches. To validate and demonstrate the capabilities of the proposed strategy, the evolution of displacements and stresses in fused deposition modeling of polylactide is simulated.

Flat-Histogram Monte Carlo Simulation of Water Adsorption in Metal-Organic Frameworks.

Molecular simulations of water adsorption in porous materials often converge slowly due to sampling bottlenecks that follow from hydrogen bonding and, in many cases, the formation of water clusters. These effects may be exacerbated in metal-organic framework (MOF) adsorbents, due to the presence of pore spaces (cages) that promote the formation of discrete-size clusters and hydrophobic effects (if present), among other reasons. In Grand Canonical Monte Carlo (MC) simulations, these sampling challenges are typically manifested by low MC acceptance ratios, a tendency for the simulation to become stuck in a particular loading state (i.e., macrostates), and the persistence of specific clusters for long periods of the simulation. We present simulation strategies to address these sampling challenges, by applying flat-histogram MC (FHMC) methods and specialized MC move types to simulations of water adsorption. FHMC, in both Transition-matrix and Wang-Landau forms, drives the simulation to sample relevant macrostates by incorporating weights that are self-consistently adjusted throughout the simulation and generate the macrostate probability distribution (MPD). Specialized MC moves, based on aggregation-volume bias and configurational bias methods, separately address low acceptance ratios for basic MC trial moves and specifically target water molecules in clusters; in turn, the specialized MC moves improve the efficiency of generating new configurations which is ultimately reflected in improved statistics collected by FHMC. The combined strategies are applied to study the adsorption of water in CuBTC and ZIF-8 at 300 K, through examination of the MPD and the adsorption isotherm generated by histogram reweighting. A key result is the appearance of nontrivial oscillations in the MPD, which we show to be associated with water clusters in the adsorption system. Additionally, we show that the probabilities of certain clusters become similar in value near the boundaries of the isotherm hysteresis loop, indicating a strong connection between cluster formation/destruction and the thermodynamic limits of stability. For a hydrophobic MOF, the FHMC results show that the phase transition from low density to high density is suppressed to water pressure far above the bulk-fluid saturation pressure; this is consistent with results presented elsewhere. We also compare our FHMC simulation isotherm to one measured by a different technique but with ostensibly the same molecular interactions and comment on observed differences and the need for follow-up work. The simulation strategies presented here can be applied to the simulation of water in other MOFs using heuristic guidelines laid out in our text, which should facilitate the more consistent and efficient simulation of water adsorption in porous materials in future applications.

Molecular dynamics simulations of heat transport using machine-learned potentials: A mini-review and tutorial on GPUMD with neuroevolution potentials

Molecular dynamics (MD) simulations play an important role in understanding and engineering heat transport properties of complex materials. An essential requirement for reliably predicting heat transport properties is the use of accurate and efficient interatomic potentials. Recently, machine-learned potentials (MLPs) have shown great promise in providing the required accuracy for a broad range of materials. In this mini-review and tutorial, we delve into the fundamentals of heat transport, explore pertinent MD simulation methods, and survey the applications of MLPs in MD simulations of heat transport. Furthermore, we provide a step-by-step tutorial on developing MLPs for highly efficient and predictive heat transport simulations, utilizing the neuroevolution potentials as implemented in the GPUMD package. Our aim with this mini-review and tutorial is to empower researchers with valuable insights into cutting-edge methodologies that can significantly enhance the accuracy and efficiency of MD simulations for heat transport studies.

Efficient EndoNeRF reconstruction and its application for data-driven surgical simulation.

The healthcare industry has a growing need for realistic modeling and efficient simulation of surgical scenes. With effective models of deformable surgical scenes, clinicians are able to conduct surgical planning and surgery training on scenarios close to real-world cases. However, a significant challenge in achieving such a goal is the scarcity of high-quality soft tissue models with accurate shapes and textures. To address this gap, we present a data-driven framework that leverages emerging neural radiance field technology to enable high-quality surgical reconstruction and explore its application for surgical simulations. We first focus on developing a fast NeRF-based surgical scene 3D reconstruction approach that achieves state-of-the-art performance. This method can significantly outperform traditional 3D reconstruction methods, which have failed to capture large deformations and produce fine-grained shapes and textures. We then propose an automated creation pipeline of interactive surgical simulation environments through a closed mesh extraction algorithm. Our experiments have validated the superior performance and efficiency of our proposed approach in surgical scene 3D reconstruction. We further utilize our reconstructed soft tissues to conduct FEM and MPM simulations, showcasing the practical application of our method in data-driven surgical simulations. We have proposed a novel NeRF-based reconstruction framework with an emphasis on simulation purposes. Our reconstruction framework facilitates the efficient creation of high-quality surgical soft tissue 3D models. With multiple soft tissue simulations demonstrated, we show that our work has the potential to benefit downstream clinical tasks, such as surgical education.

Shape deformation, disintegration, and coalescence of suspension drops: Efficient simulation enabled by graph neural networks

Understanding the behaviors of suspension drops (particle swarms) as they settle in a viscous fluid holds significant importance across various applications. Due to hydrodynamic interactions (HIs), suspension drops would undergo a series of intricate behaviors, including shape deformation, disintegration, and coalescence. This work presents the hydrodynamic interaction graph neural network (HIGNN), developed in our prior work (Ma et al., 2022), as an efficient and accurate modeling framework for simulating the dynamics of suspension drops and investigating the various behaviors they exhibit. The HIGNN effectively incorporates the many-body nature of HIs, a feature lacking in most previous simulations that employ the Stokeslet assumption. In the meanwhile, the HIGNN achieves superior computational efficiency compared to traditional, high-fidelity numerical tools such as Stokesian dynamics and PDE solvers. Moreover, the HIGNN, once trained, is applicable to predicting suspension drops across a range of particle concentrations and under diverse forces (such as gravity and Coulombic interactions). Training the HIGNN only requires the data containing a small number of particles, leading to low training cost. Our results demonstrate that the HIGNN can effectively reproduce the various behaviors of suspension drops that were previously reported in literature. More specifically, a single, initially spherical drop slowly evolves into a torus-shaped drop, as particles escape from its rear and form a tail along the sedimenting direction. Subsequently, the torus breaks into secondary droplets, each undergoing a similar transition (deformation into a torus followed by disintegration), thereby leading to a repeating cascade. Further, we quantitatively analyze the correlation between the drop’s sedimentation velocity and volume fraction. We also propose new scaling laws for evaluating both the leakage rate of particles and the expansion rate of the horizontal radius of a suspension drop. For single suspension drops, we also systematically investigate how their dynamics is affected by their initial shapes and the formed tori’s aspect ratios, as well as with or without Coulombic interactions between particles. For a pair of suspension drops, we study the process of coalescence of two vertically aligned particles and examine the effect of introducing a horizontal offset on the subsequent breakup of the coalesced drop. All simulations were executed on a single GPU, with the computation of velocities for several thousand particles requiring less than five seconds per time step. This computational efficiency enables fast and resource-saving simulations of large suspension drops over extended time scales.