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A mathematical model and numerical framework are presented for computing multi-physics multi-layer coating flow dynamics, with applications to the leveling of multi-layer paint films. The algorithm combines finite difference level set methods and high-order accurate sharp-interface implicit mesh discontinuous Galerkin methods to capture a complex set of multi-physics, incorporating Marangoni-driven multi-phase interfacial flow and the transport, mixing, and evaporation of multiple dissolved species. In particular, we develop several numerical methods for this multi-physics problem, including: high-order local discontinuous Galerkin methods for Poisson problems with Robin boundary conditions on implicitly-defined domains, to capture solvent evaporation; finite difference surface gradient methods, to robustly and accurately incorporate Marangoni stresses; and a coupled multi-physics time stepping approach, to incorporate all the different solvers at play including quasi-Newtonian fluid flow. The framework is applicable to an arbitrary number of layers and dissolved species; here, we apply it in a variety of settings, including multi-solvent evaporative paint dynamics, the flow and leveling of multi-layer automobile paint coatings in both 2D and 3D, and an examination of interfacial turbulence within a multi-layer matter cascade. Our results reproduce several phenomena observed in experiment, such as the formation of Marangoni plumes and Bénard cells. We also use the model to study the impact of long-wave deformational surface modes on immersed interfaces as well as the emergence of the final multi-layer film profile.

To reduce the fuel consumption of ships' oceanic voyages, this study incorporates the influence of ocean currents into the traditional level set algorithm and proposes a route planning algorithm capable of identifying energy-efficient routes in complex and variable sea conditions. The approach introduces the influence factor of ocean current to optimize routing in dynamically changing marie environments. First, models for the energy consumption of ships and flow fields are established. The level set curve is then evolved by integrating the flow environment and energy consumption gradient, solving the Hamilton–Jacobi equation with energy consumption parameters. The optimal path is subsequently determined through backtracking along the energy consumption gradient, enabling energy-efficient route planning from the starting point to the endpoint in complex ocean conditions. To verify the effectiveness of the proposed algorithm, its performance is evaluated through two case studies, comparing energy consumption under different environmental conditions. The experimental results demonstrate that, compared to the shortest path method based on the level set algorithm, the proposed approach achieves an energy saving rate of approximately 2.1% in obstacle-free environments and 1.4% in environments with obstacles. [ABSTRACT FROM AUTHOR]

The microstructure of metallic materials plays a crucial role in determining their performance. In order to accurately predict the dynamic recrystallization (DRX) behavior and microstructural evolution during the hot deformation process of GCr15 bearing steel, a microstructural evolution model for the DRX process of GCr15 steel was established by combining the level set (LS) method with the Yoshie–Laasraoui–Jonas dislocation dynamics model. Firstly, hot compression tests were conducted on GCr15 steel using the Gleeble-1500D thermal simulator, and the hardening coefficient k1 and dynamic recovery coefficient k2 of the Yoshie–Laasraoui–Jonas model were derived from the experimental flow stress data. The effects of temperature, strain, and strain rate on DRX behavior and grain size during the hot working process of GCr15 steel were investigated. Through secondary development of the software, the established microstructural evolution model was integrated into the DIGIMU® software. Metallographic images were imported in situ to reconstruct its initial microstructure, enabling GCr15 steel DRX microstructure finite element simulation of the hot compression process. The predicted mean grain size and flow stress demonstrated a strong correlation and excellent agreement with the experimental results. The results demonstrate that the established DRX model effectively predicts the evolution of the DRX fraction and average grain size during the hot forging process and reliably forecasts DRX behavior. [ABSTRACT FROM AUTHOR]

The phase field method (PFM) has emerged as a powerful tool for simulating multiphase flows. With its solid theoretical foundation, this method offers significant potential for further development and application. However, in many cases, interface dispersion can lead to inaccuracies in surface tension calculations, especially when dealing with large density ratio simulations. In this paper, we introduce an optimized PFM that includes profile-corrected, velocity-corrected, and flux-corrected techniques, along with a re-initialization step used in level set method. This method improves the performance of combined PFM corrections through neural networks and optimizes it via the re-initialization process. The present optimized PFM is first tested using the Rayleigh–Taylor instability, and then its performance is evaluated in the context of bubble rising, bubble merging, and falling droplet onto a liquid film. The results obtained show that the proposed method can effectively prevent interface dispersion in complex multiphase flows and capture the tiny interfacial structures. [ABSTRACT FROM AUTHOR]

This study investigates fixed and moving mesh methodologies for modeling liquid metal–free surface deformation during the induction melting process. The numerical method employs robust coupling of magnetic fields with the hydrodynamics of the turbulent stirring of liquid metal. Free surface tracking is implemented using the fixed mesh level set (LS) and the moving mesh arbitrary Lagrangian–Eulerian (ALE) formulation. The model's geometry and operating parameters are designed to replicate a semi-industrial induction melting furnace. Six case studies are analyzed under varying melt masses and coil power levels, with validation performed by comparing experimentally measured free surface profiles and magnetic field distributions. The melt's stirring velocity and recirculation patterns are also examined. The comparative analysis determines an improved performance of the ALE method, convergence, and computational efficiency. Experimental validation confirms that the ALE method reproduces the free surface shape more precisely, avoiding unrealistic topological changes observed in LS simulations. The ALE method faces numerical convergence difficulties for high-power and low-mass filling cases due to mesh element distortion. The proposed ALE-based simulation procedure is a potential numerical optimization tool for enhancing induction melting processes, offering scalable and robust solutions for industrial applications. [ABSTRACT FROM AUTHOR]

Purpose: Although many conventional level-set approaches can be used for segmenting images containing factors such as noise and intensity inhomogeneities, they still can impact the accuracy of the results seriously. To solve this problem, a level-set method for fast image segmentation based on pre-fitting and bilateral filtering is proposed. Design/methodology/approach: Firstly, an improved bilateral filter was investigated for image preprocessing. Secondly, by computing the local average intensity of the preprocessed enhanced picture, two local pre-fitting functions were defined. Thirdly, a new level-set energy functional was defined. Finally, a new distance regularized energy term based on the logarithmic and polynomial functions is proposed to evolve the level-set function in a smooth state. Findings: The experimental results demonstrate that the proposed model has an excellent segmentation capability for images with noise and intensity inhomogeneities and has different degrees of performance improvement compared with the mainstream models. Originality/value: (C1) An improved bilateral filter was investigated and integrated into the model. (C2) Proposing two local pre-fitting functions by computing the local average intensity of the preprocessed enhanced image. (C3) Proposing a new level-set energy functional. (C4) A new distance regularized energy term based on the logarithmic and polynomial functions is proposed to evolve the level set function in a smooth state. (C5) Analyzing and comparing the performance of the proposed model with other similar models. [ABSTRACT FROM AUTHOR]

This paper presents detailed investigations on the free flexural vibration of carbon nanotube-reinforced composite plates with cracks resting on elastic foundations. The higher-order shear deformation theory is implemented in an extended finite element framework to derive the vibration equations of cracked plates. Uniform and graded distribution of carbon nanotubes (CNTs) in the thickness direction of plates are considered. The effective material properties are computed using the Halpin Tsai model and the rule of mixture. The crack in the plate is detected using the level set method. The enrichment of the primary variable is done using enrichment functions to address the crack discontinuity issue. Detailed parametric studies have been performed to explore the effect of cracks, CNT’s volume fraction, gradation pattern of CNTs, thickness ratio of the plate, and the elastic foundations on the frequencies. Comparative results are presented by solving a few numerical examples using in-house MATLAB code to validate and ensure the accuracy and robustness of the proposed model. [ABSTRACT FROM AUTHOR]

In this study, computational fluid dynamics (CFDs) simulation analysis was used to predict the dynamic of crude oil droplets in an American Petroleum Institute (API) oil–water separator unit. To mimic the whole separation process (i.e., the oil droplets rising movement) in the API oil–water separator unit, a single oil droplet rising in a stagnant water column has been used. Three main factors were investigated, namely, crude oil specifications (in terms of specific gravity [S.G.] and viscosity), radius of the oil droplet and the position of the oil droplet. The rising velocity of the droplet of the crude oil was characterized in terms of terminal velocity and the centre of the gravity. Generally, the CFD (COMSOL Multiphysics software) analysis succeeded to visualize the hypothetical bath of the crude oil droplet. The results illustrated that the rising velocity increased with decreasing the S.G. and inversely decreased with increasing the viscosity of the crude oil. In addition, the increase in the crude oil droplet diameter had a direct effect on the increasing of the rising velocity. Moreover, it was found that the terminal velocity increased with decreasing the water column over the oil droplet. [ABSTRACT FROM AUTHOR]

The goal of this numerical study is to get insight into singular solutions of the two-dimensional (2D) Euler equations for nonsmooth initial data, in particular for vortex sheets. To this end, high resolution computations of vortex layers in two-dimensional incompressible Euler flows are performed using the characteristic mapping method (CMM). This semi-Lagrangian method evolves the flow map using the gradient-augmented level set method. The semigroup structure of the flow map allows its decomposition into submaps (each over a finite time interval), and thus, the precision can be controlled by choosing appropriate remapping times. Composing the flow map yields exponential resolution in linear time, a unique feature of CMM, and thus, fine-scale flow structures can be resolved in great detail. Here, the roll-up process of vortex layers is studied varying the thickness of the layer showing its impact on the growth of palinstrophy and possible blow up of absolute vorticity. The curvature of the vortex sheet shows a singular-like behavior. The self-similar structure of the vortex core is investigated in the vanishing thickness limit. Conclusions on the presence of posssible singularities of two-dimensional Euler equations for nonsmooth initial data are drawn by tracking them in the complex plane. [ABSTRACT FROM AUTHOR]

In this work, we develop an approach for the level set based topology optimization of millable 3D structures. We focus on the 3-axis machining with realistic formed milling tools. The basis of the method lies in the identification of surface areas that cannot be reached by a given milling tool during optimization. For this purpose, we present an interpolation method that identifies these areas by an interpolation of the level set function along the outer contours of realistic milling tools, considering available machining directions. To minimize inaccessible surfaces, we define a potential field whose values decrease linearly into the outer normal direction of the structure. The inaccessible boundaries are pushed outward by minimizing their respective potential and therefore become accessible. Manufacturability is integrated into the optimization problem as an explicit constraint. [ABSTRACT FROM AUTHOR]

In this paper, the semi-floating liquid bridge model with the silicone oil-based ferromagnetic fluid under microgravity was taken as the research object. The enhanced level set method was employed to numerically monitor the free surface flow characteristics, utilizing a staggered grid. The internal flow, temperature, velocity and interface deformation of thermocapillary convection under a uniform axial magnetic field were studied by direct numerical simulation. The results show that the transverse development of thermocapillary convection is suppressed by the axial uniform magnetic field, and the cell flow is controlled near the free surface. The average axial velocity was increased by about three times, and the average radial velocity was increased by about two times. The average axial temperature near the free surface was much higher than that on other radii. The axial temperature level of the surface flow was improved under of the influence of a uniform axial magnetic field. The axial temperature gradient in the central area of the liquid bridge basically showed the same change rule. The closer to the hot disk of the liquid bridge, the larger the axial temperature gradient. In addition, the axial uniform magnetic field effectively suppressed the micro-deformation of the free interface, and the free surface micro-deformation was at an order of magnitude of 10−5 (the deformation of the free surface in thermocapillary convection within a liquid bridge without a magnetic field was at an order of magnitude of 10−4). Therefore, studying the influence of the axial magnetic field on the thermocapillary convection of a high Prandtl number fluid can provide the necessary theoretical support for the development of crystal preparation technology. [ABSTRACT FROM AUTHOR]

We consider an ensemble Kalman inversion scheme for inverse elastic scattering problems in which the unknown quantity is the shape of the scatterer. Assume that the scatterer is a piecewise constant function with known value inside inhomogeneities. The level set method is described as an implicit representation of the scatterer boundary, with Gaussian random fields serving as prior to provide information on the level set functions. The ensemble Kalman filter method is then employed based on the level set functions to reconstruct the shape of the scatterer. We demonstrate the effectiveness of the proposed method using several numerical examples. [ABSTRACT FROM AUTHOR]

In recent years, topology optimization on heat conduction structures has received extensive attention. However, most existing optimization methods focus on steady-state conditions and do not consider the transient effects of heat conduction. We propose a parameterized level set method that offers good stability and smooth boundary representation for solving the topology optimization problem of transient heat conduction structures. The parameterized level set method converts solving a series of partial differential equations into solving ordinary differential equations, thereby improving the efficiency of the optimization process. The interpolation coefficients of the level set functions are updated by sensitivity-driven Lagrange multipliers to facilitate the evolution of the level set functions. By considering heat compliance as the objective function and volume fraction as the constraint, an optimization model is established. This method is applied to various topological optimization problems with different boundary conditions and multi-material, and the efficacy of the proposed method is validated through numerical examples. [ABSTRACT FROM AUTHOR]

Recently, laser energy has been widely utilized from applications ranging from machining to weapon systems. In this study, the objective is to derive a damage modeling that can rapidly predict the damage to metallic materials resulting from continuous-wave laser irradiation. To this end, two materials, steel and aluminum, were subjected to computational analysis, and the analysis techniques were validated by comparing their results to previously published experimental results. Based on the keyhole depths of the specimens, the computational analysis results deviated by 3 %–10 % from the experimental results. The damage to each material was predicted over time by applying laser energies of 15 kW to 80 kW to disk-shaped specimens. Based on the results, a damage modeling was proposed. The proposed damage modeling yielded accuracies of within 4 % for DP600 steel, 7 % for 304 stainless steel, and 9 % for aluminum over a range of laser powers. [ABSTRACT FROM AUTHOR]

This paper constructs a numerical simulation model for the deformation of droplets in a variable cross-section groove of a liquid droplet MEMS switch under different directions, amplitudes, frequencies, and waveforms of acceleration. The numerical simulation utilizes the level set method to monitor the deformation surface boundary of the metal droplets. The simulation outcomes manifest that when the negative impact acceleration on the X-axis is 12.9 m/s2, the negative impact acceleration on the Y-axis is 90 m/s2, the negative impact acceleration on the Z-axis is 34.5 m/s2, and the metal droplet interfaces with the metal electrode. The droplet deformation under the effect of a sine wave acceleration signal in the X and Y directions is lower than that under impact acceleration, while in the Z direction, the deformation is higher than that under impact acceleration. The deformation of metal droplets under square wave acceleration is more pronounced than that under sinusoidal wave acceleration. The deformation escalates with the augmentation in square wave amplitude and dwindles with the reduction in square wave acceleration frequency. Furthermore, there exists a phase difference between the deformation curve of the metal droplet and the continuous acceleration signal curve, and the phase difference is dependent of the material properties of the metal droplet. This work elucidates the deformation of the liquid-metal droplets under continuous acceleration and furnishes the foundation for the continuous operation design of MEMS droplet switches. [ABSTRACT FROM AUTHOR]

Summary: We propose an implicit discontinuous Galerkin (DG) discretization for incompressible two‐phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L‐stable TR‐BDF2 method is adopted for the time discretization of the Navier‐Stokes equations and of the level set method. Adaptive mesh refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks. A specific analysis on the influence of different choices of the mixture viscosity is also carried out. [ABSTRACT FROM AUTHOR]

Reliable interpretation of model tests in geotechnical engineering often is hampered by the limitations of traditional laboratory element testing, especially under low-stress conditions and unconventional stress paths. This paper presents a pragmatic hierarchical multiscale numerical approach that combines the level set discrete-element method (LS-DEM) and continuum-based analysis to improve the interpretation of scaled geotechnical tests. LS-DEM enables high-fidelity simulations of soil behavior, overcoming challenges such as boundary effects and metrological limitations that make accurate assessments under specific conditions in standard laboratory tests difficult. The virtual LS-DEM specimens can be calibrated reliably using traditional laboratory tests, such as oedometer and triaxial tests. This approach was demonstrated and implicitly validated through its application to a study of displacement-dependent earth pressure on retaining walls. Key findings include the identification of additional kinematic constraints under plane strain conditions as the primary factor behind the high peak strength observed in scaled tests, and the observation that the strength of granular materials is negligibly affected by changes in stress level. In addition, the observation of pressure-dependent elastic parameter trends, consistent with previous studies, further validates LS-DEM as a reliable tool for quantitatively capturing the behavior of granular materials. By reducing reliance on semiempirical scaling laws and providing a robust framework for informing continuum-based models, this LS-DEM–based hierarchical approach effectively bridges the gap between small-scale laboratory experiments and large-scale geotechnical applications. Ultimately, this methodology enhances the design and analysis of geotechnical structures with greater confidence and accuracy, providing a practical and effective tool for addressing complex geotechnical engineering challenges. [ABSTRACT FROM AUTHOR]

An algorithm is proposed for computing the complex stability radius of a linear differential-algebraic system with a single delay and including a neutral term. The exponential factor in the characteristic equation is replaced by its Padé approximant thus reducing the level set method for finding the stability radius to a rational matrix eigenvalue problem. The level set method is coupled with a quadratically convergent iteration. An important condition relating the algebraic constraint and neutral term is introduced to eliminate the presence of characteristic roots approaching the imaginary axis at infinity. The number of iterations of the algorithm is roughly proportional to the numerical value of this condition. Effectiveness of the algorithm is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

We construct a family of singly periodic entire solutions to the Allen–Cahn equation in R 3 . Our approach relies on the relationship between this equation and the two-dimensional Toda lattice, an important integrable system. The level sets of these solutions closely approximate the graphs of suitable scaled lump solutions of the Toda lattice. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid numerical method for simulating the boiling heat transfer in particle-laden fluids. The coupled volume of fluid and level set method, immersed boundary method, and discrete element method are integrated for gas–liquid flow, fluid–solid interaction, and the collision between particles. The energy jump model is adopted to compute mass transfer during phase change. The height-function technique and improved continuum surface force (CSF) model are coupled to decrease the spurious currents. Multiple validation results are provided to test the effectiveness of all sub-models. The test cases include particle sedimentation, stationary droplets without gravity, bubble rise, droplet spreading on particle surfaces, and bubble growth. The test results are in good agreement with analytical results and previous studies. Notably, the average spurious velocity is reduced to less than 10−5 m/s, which is three orders of magnitude smaller than that obtained by traditional CSF model. Moreover, the hybrid method is employed to explore the boiling heat transfer of particle-laden fluids, thereby further validating its reliability. It was found that particles facilitate bubble detachment and enhance heat transfer. [ABSTRACT FROM AUTHOR]

This paper investigates the effects on the behavior of a saturated porous material of an evolving microstructure induced by the mass exchange between the solid and the fluid phases saturating the porous network, using two-scale asymptotic expansions. A thermodynamically consistent model of the fluid physics flowing through the porous network is proposed first, describing microstructure variations to be captured implicitly via the level set method. The two-scale asymptotic expansions method is then applied to obtain an upscaled model capable to account for mass transfer. This last is proven to depend not only on the gradient of the macroscopic forces, such as the fluid pressure and the chemical potential, but also on the average velocity of the solid–fluid interface. Numerical simulations are carried out using the finite element method in order to evaluate the relative weight of the new terms introduced. [ABSTRACT FROM AUTHOR]

We compared the accuracy of volume of fluid (VOF) methods in unstructured solvers using the following five different methods: 1 - the algebraically compressive VOF method, 2 – simple coupled VOF method with Level Set (S-CLSVOF) method, 3 - interface-compressing VOF method incorporated with Laplacian filter (VOFL), 4 - isoAdvector method, and 5 - isoAdvector method incorporated with Laplacian filter (isoAdvectorL) by incorporating them into OpenFOAM®, an open-source software. To evaluate these methods under proper conditions, we compared the calculation accuracy using the optimized parameters, which are explored by Bayesian optimization. The test cases for advection accuracy of volume fraction and for imbalance of surface tension force in static multiphase fluid fields were considered. In this study, we found that the compression parameters and maximum Courant number should be adjusted to obtain high accuracy simulation according to the simulation condition in VOF and S-CLSVOF method. In VOFL and isoAdvectorL methods, the spurious current can be extremely reduced, which means that these methods are suitable for slow flow with higher Laplace number conditions. [ABSTRACT FROM AUTHOR]

The median filter scheme is an elegant, monotone discretization of the level set formulation of motion by mean curvature. It turns out to evolve every level set of the initial condition precisely by another class of methods known as threshold dynamics. Median filters are, in other words, the natural level set versions of threshold dynamics algorithms. Exploiting this connection, we revisit median filters in light of recent progress on the threshold dynamics method. In particular, we give a variational formulation of, and exhibit a Lyapunov function for, median filters, resulting in energy based unconditional stability properties. The connection also yields analogues of median filters in the multiphase setting of mean curvature flow of networks. These new multiphase level set methods do not require frequent redistancing, and can accommodate a wide range of surface tensions. [ABSTRACT FROM AUTHOR]

This paper introduces a multiphysical model for laser welding in a lap joint configuration with dissimilar metals. Initially solved in a 2D axisymmetric configuration for static shots, the model is extended to 3D to simulate laser welding with a weld seam formation. Heat transfer, fluid flow, and species tracking are solved with the level set method to describe dynamically the keyhole and melt pool behavior. Validation against experimental data shows an accurate description of the main phenomena. The paper mainly highlights the need of introducing a thermal contact resistance to correctly predict the melted area dimensions. The study emphasizes the importance of considering imperfect material contact and proposes an effective approach for thermal contact resistance, a phenomenon poorly discussed in the literature. [ABSTRACT FROM AUTHOR]

This study investigates the morphology of a free-falling liquid jet by using a computational approach with an experimental validation. Numerical simulations are developed by means of the Finite Element Method (FEM) for solving the viscous fluid flow and the level set method in order to track the interface between the fluid and air. Experiments are conducted in order to capture the shape of a free-falling jet of viscous fluid via circular orifice, where the shape is measured optically. The numerical results are found to be in agreement with the experimental data, demonstrating the validity of the proposed approach. Furthermore, we analyze the role of the surface tension by implementing linear as well as nonlinear surface energy models. All computational codes are developed with the aid of open-source packages from FEniCS and made publicly available. The combination of experimental and numerical techniques provides a comprehensive understanding of the morphology of free-falling jets and may be extended to multiphysics problems rather in a straightforward manner. [ABSTRACT FROM AUTHOR]

In this paper, a novel viscoelastic constitutive model which can reflect the phase transformation mechanism of multi-shape memory polymer (M-SMP) is established. In this model, M-SMP is regarded as an inhomogeneous body composed of different phases, and the rheological representations of each phase are established based on the viscoelastic mechanics theory. Combined with the level set method, the conversion relationships of each adjacent two phases of M-SMP are established, and then the relationships between each phase are obtained. The constitutive model is used to simulate the thermodynamic behavior of dual-shape memory polymer (D-SMP) and triple-shape memory polymer (T-SMP), and the simulation results are compared with the experimental results and models of relevant literature. Meanwhile, the shape memory behaviors under different correlation rates are studied and analyzed considering the influence of rate correlation. The results show that the model can describe the thermodynamic behavior of M-SMP more accurately and effectively, and in shape memory process of M-SMP, there is a strong rate correlation here. The model can provide a theoretical basis for the engineering application of M-SMP. [ABSTRACT FROM AUTHOR]

This study introduces a deep self-organizing map neural network based on level-set (LS-SOM) for the customization of a shoe-last defined from plantar pressure imaging data. To alleviate the over-segmentation problem of images, which refers to segmenting images into more subcomponents, a domain-based segmentation model of plantar pressure images was constructed. The domain growth algorithm was subsequently modified by optimizing its parameters. A SOM with 10, 15, 20, and 30 hidden layers was compared and validated according to domain growth characteristics by using merging and splitting algorithms. Furthermore, we incorporated a level set segmentation method into the plantar pressure image algorithm to enhance its efficiency. Compared to the literature, this proposed method has significantly improved pixel accuracy, average cross-combination ratio, frequency-weighted cross-combination ratio, and boundary F1 index comparison. Using the proposed methods, shoe lasts can be designed optimally, and wearing comfort is enhanced, particularly for people with high blood pressure. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic (EHD) printing enables large-area, ultra-high-resolution manufacturing across a broad range of ink viscosities, but inevitably encounters difficulties when printing on electrically insulating three-dimensional substrates due to unpredictable electric field and surface residual charges. To overcome these obstacles, a novel approach called plasma-induced electrohydrodynamic (PiE) printing has been proposed. PiE printing employs plasma to directly create a controllable local charge region directly on substrate surfaces, which triggers EHD ink ejection and mitigates the effect of residual charges. However, the underlying mechanisms of the jetting behavior with respect to printing parameters, such as the charge-induced electric field, remain unexplored. Here, we conduct a numerical investigation, based on the Taylor–Melcher leaky dielectric model and the level set method, on the jetting behavior of substrate surface charge-induced EHD printing. We first introduce the dynamics behavior throughout the entire printing process. Then, we carry out a comprehensive investigation on surface charge-induced EHD printing under four crucial parameters: the amount of preset surface charge, the radius of preset surface charge, the duration of preset surface charge, and liquid electrical conductivity. By analyzing the induced electric field, induced charge density, fluid velocity, jet diameters, and deposited droplet sizes obtained from the numerical results, we elucidate the influence of these parameters on the dynamic behavior, durations of jetting process, and printing quality. These findings offer valuable insights into surface charge-induced EHD jetting, advancing the understanding and optimization methods for this useful micro-/nano-manufacturing technology. [ABSTRACT FROM AUTHOR]

Intensity inhomogeneity often appears in medical images and causes great difficulties in image segmentation. Most active contour models perform poorly when applied to intensity inhomogeneous images because their energy functions use local intensity information in a fixed-size domain, causing the contour to evolve in the wrong direction. To overcome the difficulties caused by intensity inhomogeneity, we propose an adaptive multi-scale Gaussian kernel function based on image local entropy, which can determine the appropriate scale for each local region. Choosing the small scale and large scale for inhomogeneous and homogeneous areas respectively make the contour move toward the target boundary accurately. We also propose three adaptive multi-scale (AMS) models, AMS-region scalable fitting (AMS-RSF) model, AMS-local image fitting (AMS-LIF) model, AMS-local and global intensity fitting (AMS-LGIF) model, to segment medical images with intensity inhomogeneity and noise, including left atrial MR images and breast ultrasound images. The experimental results show that the adaptive multi-scale Gaussian kernel function enables the active contour model to effectively segment intensity inhomogeneous images and has a certain robustness to the initial contour and noise, which achieves good performance on MR left atrial images and ultrasound images of breast cancer. The AMS-LGIF model obtained the highest DICE coefficient of 0.9532, which was better than the 0.9429 obtained by the second-ranked LGIF model to segment left atrial MR images. For segmenting breast ultrasound images, the DICE coefficient is increased by 16% than that of the U-Net++ model. • An adaptive multi-scale Gaussian kernel function based on image local entropy is proposed. • Adaptive multi-scale RSF, LIF, and LGIF models are proposed. • The proposed adaptive multi-scale model is robust to initial contours and noise. • Numerical results such as DICE, JS, Precision, and Recall values are given. • The experimental results show that our adaptive multi-scale model is better than the other methods. [ABSTRACT FROM AUTHOR]

To improve the efficiency of topology optimization for piezoelectric energy harvesters (PEHs), this paper proposes a discrete level set method enhanced by conformal mapping. By mapping the PEH onto a 2D regular domain, the original 3D topology optimization problem is simplified as a 2D problem by using a scalar function. Then re-meshing and barycentric interpolation theory are used to simplify the solution of the driving equation and resolve the issue of inconsistent discretization between the level set function and the finite element model. Moreover, based on the proposed method, the finite element expression of the piezoelectric shell element is derived, taking into account the piezoelectric material coupling effect and polarization direction. This leads to an accurate numerical solution for the optimization process. Resultantly, numerical examples demonstrate that proposed method enables the optimization using a simple discretization, while effectively preserving surface characteristics of PEHs. Hence, this method offers a new approach for the structural optimization of PEHs. [ABSTRACT FROM AUTHOR]

Structural optimization problems are often associated with the so-called shape functionals depending on a shape through its geometry and the state being a solution of given partial differential equation. In such a framework it is convenient to work with the gradient-like method based on a concept of a shape derivative and level set method. The key idea of level set method is to represent the structural boundary with zero level set of given function (level set function—LSF). Now, changing the shape of a structure under optimization is equivalent to transport the LSF in such a direction that ensures decreasing the value of the objective functional. To this end, we make use of coercive bilinear form taken from the weak formulation of elasticity problem to obtain descent direction at each iteration. This descent direction is a solution of an additional variational problem, involving the bilinear form mentioned above and the volumetric expression of the shape derivative plays the role of a linear form. In this paper, we combine level set method with radial basis functions (RBFs) used to approximate LSF. We focus on the so-called multiquadric RBFs, but other classes of RBFs are also briefly considered. This eventually leads to transformation of partial differential equation (linear transport equation governing the evolution of shapes) to a system of linear ordinary differential equations which admits analytical formula for the solution. We apply our method to compliance minimization of a cantilever problem as well as to total potential energy minimization of a structure with kinematic loading. To run all the numerical experiments, we wrote our own code in Wolfram Mathematica environment. [ABSTRACT FROM AUTHOR]

As a method of lightweight design, multi-material design aims to make targeted use of materials in order to reduce CO2 emissions. In this context, it can be described as one of the product development methods used to meet the challenges of climate change. However, since the design of structures in multi-material design is complex, topology optimization can be used to support the product developer. In this article, a multi-material topology optimization method is developed that combines the Velocity Field Level Set method with the Reconciled Level Set method. Furthermore, the current design is explicitly resolved in each iteration by means of multi-material remeshing. The edge collapse phase in the remeshing process is achieved by applying the producer consumer pattern. The developed method is then validated using known examples from the state of research, and the influence of the parameters of the method on the result is analyzed by means of studies. [ABSTRACT FROM AUTHOR]

This study proposes a computational method for estimating in vivo mechanical properties of tissues using clinical imaging data. In particular, a new level-set-based objective functional to compare a target and estimated shape of a tissue structure is introduced, along with its integration into an optimization-based approach for inverse material parameter estimation. The approach employs a continuous shape comparison metric using signed distance functions and combines the adjoint method for efficient gradient-based optimization. Simulated inverse problems based upon estimating cardiac ventricular wall stiffness from untagged imaging and hemodynamic data are used to assess the capability of the proposed approach. The results show that the proposed method is able to consistently and effectively minimize the shape-based objective functional to estimate material parameters. The minimization of this shape difference is capable of providing relatively accurate estimates of material parameters, although naturally depending on the sensitivity of the shape change to the particular parameters, and the process is tolerant to the inclusion of model error. Thus, the approach has the potential capability to provide estimates of in vivo mechanical properties of tissues from the shape of the tissue structure as can be directly estimated from imaging data. [ABSTRACT FROM AUTHOR]

Topology optimization has demonstrated its effectiveness in generating lightweight and structurally efficient designs. This study focuses on refining the geometry of an automatic coupler body for trains using solid isotropic material with penalization and a level set method. These optimization methods are applied to the numerical model of the automatic coupler, and their results are compared to select the optimal design. The tensile strength of the automatic coupler is examined through numerical simulations and validated by experimental tensile tests conducted on a 1:1 scale prototype. The optimization outcomes reveal a remarkable 46.41% reduction in the mass of the automatic coupler body compared to the initial model. An evaluation of the tensile strength of the prototype demonstrates the ability of the automatic coupler to withstand the primary load without undergoing plastic deformation. Furthermore, a strong correlation is observed between the numerical and experimental results. This research contributes to advancing the design of next-generation automatic couplers, emphasizing the crucial aspects of lightweight design and structural performance. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the evolution of rock fracture slug structures and decongestion strategies for natural gas extraction processes. For this purpose, the level set method was used to simulate the evolution of the slug structure under the effect of different flow ratios, fracture surface wettability, and fracture tortuosity. The results show that an increase in the water-to-gas flow ratio and fracture tortuosity leads to a significant increase in the proportion of slug structures in the fracture, while an increase in the surface contact angle leads to a decrease in the proportion of slug structures in the fracture. Based on the above slug structure evolution law, a quantitative characterization method for the slug structure of two-phase fluids considering the combined effects of the water–gas flow ratio, average wall contact angle, and flow channel tortuosity was developed. Subsequently, we engage in further discussion on the optimization of the extraction and decongestion process in natural gas extraction. [ABSTRACT FROM AUTHOR]

AbstractResearch in topology optimization with stress constraints has shown that defining the stress constraint locally yields better performance compared to global methods. However, an examination of the formulas for local stress constraints reveals a limitation - the constraint is only satisfied at points where it is explicitly defined, failing to guarantee satisfaction across the entire design domain. To address this shortcoming, this paper proposes utilizing an integral form of the stress constraint. The integral formulation theoretically ensures that the stress constraint is satisfied over whole design domain. The objective is to minimize the mass of plane stress structures using reaction-diffusion level set method while incorporating local stress constraints in this integral form. The methodology utilizes finite element approximations for geometry and displacements, defining local stress constraints through an integral formulation. A Lagrangian function combines objective and constraint functions, with sensitivity analysis performed during optimization based on level set function changes. Structural boundaries are updated using the Hamilton-Jacobi equation. The paper presents numerical examples with varying loads and support conditions to demonstrate the effectiveness of this integral stress constraint approach. Results illustrate the capability of the proposed method to generate optimal topologies while satisfying stress constraints across the entire design space. [ABSTRACT FROM AUTHOR]

The analysis of the psoas muscle in morphological and functional imaging has proved to be an accurate approach to assess sarcopenia, i.e. a systemic loss of skeletal muscle mass and function that may be correlated to multifactorial etiological aspects. The inclusion of sarcopenia assessment into a radiological workflow would need the implementation of computational pipelines for image processing that guarantee segmentation reliability and a significant degree of automation. The present study utilizes three-dimensional numerical schemes for psoas segmentation in low-dose X-ray computed tomography images. Specifically, here we focused on the level set methodology and compared the performances of two standard approaches, a classical evolution model and a three-dimension geodesic model, with the performances of an original first-order modification of this latter one. The results of this analysis show that these gradient-based schemes guarantee reliability with respect to manual segmentation and that the first-order scheme requires a computational burden that is significantly smaller than the one needed by the second-order approach. [ABSTRACT FROM AUTHOR]

In order to better handle images with intensity inhomogeneity and noise, an adaptive multi-level set active contour model based on block search is proposed in this paper. This model first defines a multiple edge extension criterion for the input image to block the image and avoid the loss of image edge information; Then, the proposed adaptive block search method is used to find the level set that is considered redundant, and the remaining parts are fused to obtain a rough binary mask; Finally, the target is extracted by using the newly defined energy functional and the edge contours of the extracted binary mask. The experimental results show that the average jaccard similarity coefficients of the proposed model for segmenting images with intensity inhomogeneity and real images are 97.81% and 98.41%, respectively, and the accuracy of the segmentation results is higher than that of other models participating in the comparison. Similarly, the results of the ablation experiment once again validated the robustness of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we propose an anti-diffusion method to effectively prevent flotsams (non-physical tiny droplets and bubbles) and/or diffusion of the VOF (volume of fluid) function that occur in CLSVOF (coupled level set and volume of fluid), VOF (volume of fluid), and THINC (tangent of hyperbola for interface capturing) methods. In the proposed method, VOF functions that are not 1 or 0 and exist at a certain distance from the interface are identified as flotsams and/or diffusion ( C a d ), and these VOF functions ( C a d ) are moved to the transition region around the interface, where the VOF value is between 0 and 1, using a conservative advection method to prevent flotsams and/or diffusion. Additionally, the proposed method allows for some control over the position to which C a d is moved within the transition region. As a result of applying the proposed anti-diffusion method to various benchmark tests and droplet problems, it was found that the proposed method effectively suppresses flotsams and/or diffusion while ensuring conservation. In some cases, the anti-diffusion method even improves interface capture accuracy. Furthermore, investigating the impact of the position to which C a d is moved revealed that when handling C a d occurring on the gas side (liquid side), moving C a d as far as possible from the gas side (liquid side) increases the effectiveness of flotsams suppression. [ABSTRACT FROM AUTHOR]

Tight oil reservoirs require fracturing techniques to create complex fracture networks for efficient development. It is frequently accompanied by a dynamic matrix-fracture imbibition process, promoting enhanced recovery. At present, the mechanism of three dimensions (3D) matrix-fracture dynamic imbibition at the pore scale has not been fully elucidated. In this paper, the dynamic imbibition process of oil-water two phases in matrix-fracture was simulated based on the Navier–Stokes equations, and the level set method was used to capture the real-time interfacial changes between the two phases. It was found that during matrix-fracture dynamic imbibition process, oil-phase droplets in a single pore remain in the pore mainly due to the "stuck" effect. Cluster residual oil in the pore space is mainly retained due to the "flow around" effect. Continuous residual oil in the deeper regions of the matrix is due to insufficient capillary force. Water phase in the micro-confinement space of a tight reservoir intrudes into the pore space along the pore corners, forming the "fingering" phenomenon is beneficial for enhancing the efficiency of micro-dynamic imbibition. It differs from cognition obtained in the micro-view space during conventional water flooding. The enhancement of imbibition efficiency is often accompanied by the occurrence of fluctuations in the average pressure within the matrix. Therefore, a method involving impulse type of high-frequency and short-period for supplemental energy and imbibition is suggested to enhance recovery in tight sandstone reservoirs. This study reveals the detailed mechanisms of oil-water two-phase transport at different stages in the dynamic imbibition process and holds significant guiding implications for enhancing recovery in this type of reservoirs. [ABSTRACT FROM AUTHOR]

In this study, a numerical framework based on the material point method is presented for the simulation of material extrusion (MEX)-based 3-D printing processes. The melt flow during material extrusion is assumed to be viscous flow including phase changes. To apply the free surface boundary conditions, the framework utilizes the level set method to track the free surface and the ghost fluid method for the application of the boundary conditions. For validation, three representative problems are first investigated to show the versatility of the model. Then, the numerical framework is adapted for the simulation of material extrusion (MEX) based 3-D printing processes. An in-depth parametric study is presented to show how printing parameters affect the overall extruded printing material. [ABSTRACT FROM AUTHOR]

The proposed paper uses Taguchi design of experiments and topology optimization to design a low throat angle and lightweight structure of an open gap (C-frame) stamping press. First, finite element analysis was used for discussing the effects of frame structure deformation by various parameters, such as upper round corner (R1), eccentric distance of upper round corner (L1), throat depth (K), lower round corner of throat (R2), and eccentric distance of lower round corner of throat (L2). With throat angle as the quality objective, we conducted single-objective optimization using Taguchi's smaller-the-better formula. The optimal values of the quality objectives were as follows: R1 was 60 mm, L1 was 30 mm, L2 was 340 mm, and R2 was 48 mm, the resulting throat angle of which was 0°1′18.99″. The throat angle resulting from this parameter combination in the static analysis with 44% force area was 0°1′18.50″. The weight of the frame was approximately 5971 kg. We also confirmed the influence of the four process parameters on the quality objectives and their mathematical relationships using analysis of variance (ANOVA) and multiple regression analysis. Next, LSM (level set method) topology optimization was used to create an optimized structure. The analysis of the optimized structure using LSM showed that the deformation with 100% force area increased by 2.6%. However, the throat angle decreased by 0°0′0.78″, and the mass of the machine dropped by 444 kg. The proposed paper shows the process of using a combination of optimization methodologies to create an optimal structure, and the results show that the proposed methodology can improve not only throat angle but also structure weight. [ABSTRACT FROM AUTHOR]

We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in combination with a Discontinuous Galerkin finite element approximation, provides an ideal setting to model physical problems characterized by embedded or evolving complex geometries, since it allows us skipping any mesh post-processing in terms of grid quality. The proposed methodology is firstly assessed on the linear elasticity equation, by verifying the approximation capability of the level set-fitted approach when dealing with configurations with heterogeneous material properties. Successively, we combine the level set-fitted methodology with a minimum compliance topology optimization technique, in order to deliver optimized layouts exhibiting crisp boundaries and reliable mechanical performances. An extensive numerical test campaign confirms the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study numerically the motion of a pair of double-emulsion (DE) droplets in a two-dimensionally singly constricted capillary tube. The momentum and continuity equations are solved using the finite element method, and the interface is tracked via the level set method. The influence of interfacial tension, viscosity and density ratios, droplet size, pore throat size, and geometrical shape on the droplets' local extra pressure drop and instantaneous velocities are calculated. It is found that at higher interfacial tension, DE droplets are difficult to deform and lead to coalescence at the constriction throat. At low interfacial tension, droplets do not coalesce and can be easily deformed. Higher interfacial tension gives a larger pressure drop and reduces fluid flow mobility. More viscous oil drops pass through the constriction without coalescence and create larger pressure drops. Changing the inner drop size does not result in oil drop coalescence. However, the local pressure drop elevates as the inner water drop size decreases and vice versa. Small pores reduce the droplet and fluid flow mobility. Among the geometrical shape effects, the rectangular shape is more responsible for larger local pressure drop. [ABSTRACT FROM AUTHOR]

SUMMARY: Reconciling rock unit boundary geometry is crucial for geological and geophysical studies aiming to achieve a comprehensive 3-D subsurface model. To create a unified 3-D parametrization suitable for both geological modelling and geophysical inversion, an integrated approach utilizing implicit modelling is essential. However, a key challenge lies in encapsulating all pertinent information within the 3-D model, ensuring compatibility with the utilized data sets and existing constraints. In this study, we present a workflow that enables the generation of an integrated 3-D subsurface model primarily using gravity and reflection seismic data sets. Our approach involves a cooperative geophysical inversion workflow, which incorporates the inverted model from the reflection seismic data while leveraging sparse petrophysical information. Despite advances in integrated modelling, the incorporation of implicit modelling approaches in cooperative inversion workflows remains unexplored. In our gravity inversion process, we use a generalized level set method to refine the boundaries of rock units in the prior model. We integrate the inverted model, derived from seismic and other sparse petrophysical data sets, to create a comprehensive 3-D prior model. To enhance the integration of reflection seismic data sets in the level set inversion, we introduce a weighting uncertainty matrix containing constraint terms. This step refines the model's accuracy and ensures greater consistency. Finally, we search for any missing rock units within inverted model through nucleation investigations. The introduced methodology has undergone successful testing in the Boulia region (Southern Mount Isa, Queensland), utilizing two 2-D reflection seismic profiles and regional gravity data sets. This study primarily aims to reconstruct the geometry of major structures within the basement units and the basin at a regional scale. By combining seismic profiles and gravity data sets with constraining information, we are able to create a 3-D model of the area that accurately represents distinct rock units and their boundary geometries. Additionally, relevant legacy data sets and prior modelling results from the region have been incorporated and refined, ensuring that the final model aligns with all available knowledge about the area. [ABSTRACT FROM AUTHOR]