Level Set Method Research Articles

Advancing instantaneous detonation prediction of condensed energetic materials based on high-order compressible multiphase fluid dynamics

The instantaneous detonation model (IDM) is widely used in simulating underwater explosions due to its efficiency and ability to ignore the detonation reaction process. In this study, we propose a new IDM to predict the fluid structure in the detonation zone of an RS211 explosive charge. This model is based on high-order solutions provided by the detonation shock dynamics model, where the spatial term is discretized using fifth-order WENO reconstruction in characteristic space and Lax–Friedrichs’s splitting and the temporal terms are discretized using a third-order TVD Runge–Kutta scheme. The interface motion is captured using the level-set method combined with MGFM, and a programmed burn model is provided to describe the generation and propagation of the detonation wave. The self-similarity of detonation wave propagation is validated, and the quantitative calculation formula of the instantaneous detonation model is obtained by averaging or curve fitting the dimensionless results. Consequently, the IDM of the RS211 charge is established using high-order polynomial approximations of the Taylor rarefaction zone and a constant static zone for 1D planar, cylindrical, and spherical RS211 charges. The application of the IDM involves direct mapping from the radial direction to the spatial structured grid for 1D planar, 2D cylindrical, and 3D spherical charges. Numerical results demonstrate that the IDM proposed in this paper shows good accuracy and high computational efficiency.

Mass minimization using the reaction-diffusion level set method by considering local stress constraints in an integral form

Research 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.

Combination of G-Equation and Detailed Chemistry: An application to 3D-CFD hydrogen combustion simulations to predict NOx emissions in reciprocating internal combustion engines

In the recent years, the growing pressure by the European Union to phase out the internal combustion engines has raised the quest for alternative solutions for low-environmental-impact mobility. Nevertheless, concerns on the life-cycle emissions of battery electric vehicles and perplexities on the socio-economic sustainability of the ecological transition suggest that maintaining the interest in internal combustion engines can be strategic, provided that carbon-neutral fuels are adopted. On the basis of the technological neutrality principle, relying on already existing and well-established technologies requires less effort and cost to convert the whole road transport. Moreover, the adoption of bio- or e-fuels obtained from renewable sources widely spread across the globe is not of secondary importance. In fact, cost reduction and worldwide diffusion of the resources are both main promoters of socio-economic sustainability.In this scenario, green hydrogen represents one of the main solutions for the survival of reciprocating engines. Since the production is solely based on renewable energy sources, it is not simply characterized by zero CO2 emissions at the tailpipe, but it can be considered overall carbon neutral. A technical drawback in the use of hydrogen is represented by emissions of nitrogen oxides (NOx), due to the ever-present high temperature combustion process. For this reason, an ad-hoc design is mandatory to minimize NOx production, and CFD can be a valid tool to reduce cost and time to market for the development of hydrogen engines.In this regard, the current work proposes a 3D-CFD numerical methodology, based on the combination of G-Equation and Detailed Chemistry models, for NOx prediction in in-cylinder simulations of reciprocating internal combustion engines fueled with hydrogen. Although the combination of level-set method and chemical kinetics is not a novelty in literature, it is the first time that it is applied to evaluate NOx emissions in H2 engines. The proposed approach is validated against experimental data on a direct injection, spark ignition, hydrogen engine. The methodology is able to properly predict NOx emissions at different mixture qualities, revving speeds and spark times. The total number of investigated cases is 17, which is a large set of simulations compared to the existing literature. Considering the best chemical mechanism (i.e. the one providing the best results among the tested ones), the error in the NOx prediction is always lower than 25% for all the simulations.Once the methodology is validated, the effect of spark and injection timings on NOx is discussed. Such a deepening is useful to emphasize the potential of the CFD to investigate phenomena leading to emission formation and, thus, to optimize engine parameters for NOx reduction.

An interior damage free approach for nanosecond pulsed laser ablation of single crystal diamond via metal film induced self-maintaining graphitization

When laser ablation was conducted on an uncoated single-crystal diamond (SCD) substrate, interior damage and random ablation were observed. Metal film-induced self-maintaining graphitization (MISG) was proposed as a generic approach to solve this problem. MISG was realized through coating a ∼ 100-nm-thick metal film on an SCD substrate. Experiments involving laser irradiation of metal films, such as Au-, Al-, Ti-, and Pt-coated SCD substrates, revealed that the material removal depths were the same when the output power was the same and that the surface was covered by graphite after laser irradiation. In addition, the laser-induced damage to the upper or lower surface in the case of the uncoated SCD substrate disappeared. A semitransparent model based on Beer-Lambert law and an opaque model based on modified Level-Set method were built to simulate laser irradiation on uncoated and metal–coated SCD substrates. In the case of the uncoated sample, the laser energy was largely absorbed by the areas with high-concentration defects, leading to preferential graphitization. In the case of the metal-coated sample, a graphite layer was thermally induced on the SCD surface via heat transition during the period of laser irradiation of the metal film. Subsequently, the graphite layer was self-maintaining, and the material removal acted like a graphite piston sinking to the interior of the SCD substrate. This study demonstrates the feasibility of MISG as a universal approach for avoiding interior damage during laser ablation of SCD substrates.

The effect of hydrogen enrichment on the conical premixed methane–air flame response and thermoacoustic modes coupling

This paper investigates the thermoacoustic dynamic responses of hydrogen-enriched laminar premixed conical methane–air flames under dual-mode coupling. Utilizing the level set method and the G-equation model, one meticulously derives the flame describing function (FDF) in relation to variations in hydrogen enrichment levels (ηH). This precisely derived FDF is then integrated into the low-order network model of the Rijke tube to analyze the thermoacoustic unstable modes of the system. Finally, dual-frequencies incoming flow velocity perturbations are reintroduced as inputs to obtain the flame response under thermoacoustic modes coupling. Results show that while keeping the unstretched steady flame aspect ratio constant, an increase in ηH not only raises the FDF’s cut-off frequency but also enhances the FDF gain within the nonlinear frequency region, leading to more unstable modes, especially high frequency modes within the Rijke tube system. Furthermore, the flame response is further altered under the excitation of dual unstable modes. When both modes are within the linear frequency region of the FDF, the flame response is co-controlled by the two modes, predominantly by the mode with a larger velocity perturbation amplitude, with weaker modes coupling leading to the additional frequency perturbation having a suppressive effect on the flame response at the original frequency. Conversely, when one or two modes are within the nonlinear frequency region of the FDF, the flame response is dominated by the lower-frequency mode, with higher nonlinear modes coupling allowing the additional frequency perturbation to both promote and suppress the response at the original frequency and also couple to produce a significant difference frequency response. Novelty and significance The novelty of this paper lies in the determination of the flame describing function (FDF) with varying hydrogen enrichment levels and the stability of thermoacoustic systems, and more significantly, conducting an in-depth and comprehensive investigation into the nonlinear dynamic responses of hydrogen-enriched flames to different types of dual-mode coupling perturbations. The dual-mode perturbations result in either attenuation or amplification of the flame response, depending on whether the corresponding frequencies lie within the linear or nonlinear frequency regions of the FDF, which innovatively incorporates the influence of the FDF phase and examines the responses at the difference frequencies generated by the coupling. This lays a foundation for further exploration into the mechanisms of modes coupling in hydrogen-enriched and other thermoacoustic systems.

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A level-set method for simulating solid-state dewetting in systems with strong crystalline anisotropy

Accurately modeling solid-state dewetting in materials with strong crystalline anisotropy is an open problem in materials science with importance for both the manufacturing and reliability of nano-scale devices. In this work, we propose and demonstrate a level-set method framework for simulating solid-state dewetting which is capable of modeling systems with strongly anisotropic surface energies and diffusivities. Surface energy anisotropy is handled through the use of the Cahn-Hoffman vector construction, and surface self-diffusivity anisotropy is handled through the use of a diffusivity tensor. We benchmark our method against isotropic phenomena with analytical descriptions and go on to demonstrate that our method is capable of reproducing a host of experimentally observed behaviors in strongly anisotropic single-crystal materials.

Heat transfer and fluid flow modeling of steel-Inconel laser welding in an overlap configuration

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.

Study on dynamic imbibition mechanism of matrix-fracture in three dimensions tight sandstone based on level set method

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.

Sloshing analysis of a two-layered fluid in a tank with baffles using Level Set Method

Sloshing analysis of a two-layered fluid in a tank with baffles using Level Set Method

CMA-ES-based topology optimization accelerated by spectral level-set-boundary modeling

Topology optimization commonly encounters several challenges, such as ill-posedness, grayscale issues, interdependencies among design variables, multimodality, and the curse of dimensionality. Furthermore, addressing the latter two concurrently presents considerable difficulty. In this study, we introduce a framework aimed at mitigating all the above obstacles simultaneously. The objective is to achieve optimal configurations in a notably reduced timeframe eliminating the need for the initial trial-and-error iterations. The topology optimization approach we propose is implemented via precise structural boundary modeling utilizing a body-fitted mesh generated using a Fourier series expanded level-set method. This methodology expedites the exploration of optimal solutions. We employ the covariance matrix adaptation-evolution strategy to address multimodality, thereby enhancing the optimization process. The implementation of the Fourier-series-expanded level-set method reduces the number of design variables while maintaining accuracy in finite-element analyses by replacing design variables from discretized level-set functions with the coefficients of the Fourier series expansion. To facilitate the exploration of optimal solutions, a method is also introduced for handling box constraints through an adaptive penalty function. To demonstrate the effectiveness of the proposed scheme, we address three distinct problems: mean compliance minimization, heat flux manipulation, and the control of electromagnetic wave scattering. Despite each system being governed by different equations, topology optimization method consistently yields notable acceleration in computational efficiency across all scenarios, and remarkably without requiring initial guesses.

A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set

Recently, the high-resolution topology optimization to promote engineering applicability has gained much more attentions. However, an accurate and highly-efficient design framework for implementing shape and topology optimization of engineering structures with integration of CAD model is still in demand. In the current work, the critical intention is to develop a CAD-oriented parallel-computing design framework for arbitrary structures, where the Parametric Level Set Method (PLSM) is employed for shape and topology optimization. Firstly, an implicit identification model is constructed for generating a signed distance field using the vertex and normal information from the ‘STL’ file of engineering structures. The signed distance field is combined with the compactly supported radial basis functions (CSRBFs) to solve the initial level set function with a parametrization. This method is applied to present all domains, including design domains, Neumann boundary domains, Dirichlet boundary domains, and non-design domains. Secondly, the CPU parallel strategy is considered for allocating partitions of structural stiffness matrix in finite element analysis to different CPU cores for the parallel-computing to save computation costs. Thirdly, a parallel-computing design formulation is developed for performing shape and topology optimization of arbitrary structures, in which the partitioned terms of all design variables and stiffness matrix are concurrently computed on each CPU core. Finally, several classic benchmarks and the critical engineering structure of Virtual Reality (VR) glass part with extremely complex geometries, are discussed to demonstrate the effectiveness and efficiency of the proposed design framework.

Advanced image analysis for medical diagnostics: a system for segmentation and classification using level set methods and AI algorithms

This work aims to implement and utilize an advanced computer system for image analysis and processing through artificial intelligence. The system will evaluate images from multiple sources. As a result, a comprehensive e-Medicus system will be developed to capture and analyze X-ray data and classify cancer cells. This innovative tool, with its unique features tailored for medical facilities, will assist them in capturing and analyzing X-ray images and CT scan results. The e-Medicus system offers several benefits for medical facilities, including efficient automation of photo analysis, tracking changes in a patient's condition over time, and facilitating the identification of medical changes and data classification. A multimedia presentation of the change process will use the contour set function, allowing for topological changes in solution properties. The system integrates novel procedures and algorithms from theoretical computer science and numerical mathematics, leveraging neural networks, genetic algorithms, semantic networks, image ontology, rough set theory, contour set methods, and hybrid algorithms. These developed algorithms enhance methods and concepts in image segmentation, gathering, transmitting, storing, extracting, and effectively presenting information.

An implicit DG solver for incompressible two‐phase flows with an artificial compressibility formulation

SummaryWe 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.

Retraction Note: Segmentation of spinal cord from computed tomography images based on level set method with gaussian kernel

Retraction Note: Segmentation of spinal cord from computed tomography images based on level set method with gaussian kernel

NUMERICAL SIMULATION OF UNSTEADY SIGNAL TRANSDUCTION DURING THE FORMATION OF INVADOPODIA USING LEVEL SET METHOD

The finger-like protrusions formed by an invasive cancer cell known as invadopodia is actively observed recently because of this formation on the cancer invasion. The signal on the interface which is stimulated upon contact between epidermal growth factor receptor and ligand, is investigated to be the start of invadopodia formation. In this research, a model of invadopodia formation with signal variable is formulated in two dimensions. The plasma membrane is assumed to be free boundary. The signal is in an unsteady state. The equation of signal is represented by heat-like equation with time-dependent boundary condition. Trigonometry types of the boundary condition which are sine and cosine function are tested to identify the most suitable boundary condition represented the free boundary. The plasma membrane is considered as zero level set function. The membrane moves by the velocity of the signal inside the cell. To handle the free boundary problem, the level set method combining features of ghost method, interpolation and extrapolation method is applied to solve the model numerically. Our result shows that the free boundary is moved at different positions and seen to move inward meaning that the boundary has shrunk. Cosine function is discovered to fit the boundary conditions since the boundary solutions are stable across the time. The computation of the signal density profiles displayed highest density on the membrane.

Properties and Model of Pore-Scale Methane Displacing Water in Hydrate-Bearing Sediments

The flow characteristics of methane and water in sedimentary layers are important factors that affect the beneficial exploitation of marine hydrates. To study the influencing factors of methane drive-off water processes in porous media, we constructed nonhomogeneous geometric models using MATLAB 2020a random distribution functions. We developed a mathematical model of gas–water two-phase flow based on the Navier–Stokes equation. The gas-driven water processes in porous media were described using the level-set method and solved through the finite element method. We investigated the effects of the nonhomogeneous structure of pore media, wettability, and repulsion rate on gas-driven water channeling. The nonhomogeneity of the pore medium is the most critical factor influencing the flow. The size of the throat within the hydrophilic environment determines the level of difficulty of gas-driven water flow. In regions with a high concentration of narrow passages, the formation of extensive air-locked areas is more likely, leading to a decrease in the efficiency of the flow channel. In the gas–water drive process, water saturation changes over time according to a negative exponential function relationship. The more hydrophilic the pore medium, the more difficult the gas-phase drive becomes, and this correlation is particularly noticeable at higher drive rates. The significant pressure differentials caused by the high drive-off velocities lead to quicker methane breakthroughs. Instantaneous flow rates at narrow throats can be up to two orders of magnitude higher than average. Additionally, there is a susceptibility to vortex flow in the area where the throat connects to the orifice. The results of this study can enhance our understanding of gas–water two-phase flow in porous media and help commercialize the exploitation of clean energy in the deep ocean.

Evaluation on different volume of fluid methods in unstructured solver under the optimized condition

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.

Shell topology optimization based on level set method

Shell topology optimization based on level set method

Computational simulation-based comparative analysis of standard 3D printing and conical nozzles for pneumatic and piston-driven bioprinting.

Bioprinting is an application of additive manufacturing that can deliver promising results in regenerative medicine. Hydrogels, as the most used materials in bioprinting, are experimentally analyzed to assure printability and suitability for cell culture. Besides hydrogel features, the inner geometry of the microextrusion head might have an equal impact not only on printability but also on cellular viability. In this regard, standard 3D printing nozzles have been widely studied to reduce inner pressure and get faster printings using highly viscous melted polymers. Computational fluid dynamics is a useful tool capable of simulating and predicting the hydrogel behavior when the extruder inner geometry is modified. Hence, the objective of this work is to comparatively study the performance of a standard 3D printing and conical nozzles in a microextrusion bioprinting process through computational simulation. Three bioprinting parameters, namely pressure, velocity, and shear stress, were calculated using the level-set method, considering a 22G conical tip and a 0.4 mm nozzle. Additionally, two microextrusion models, pneumatic and piston-driven, were simulated using dispensing pressure (15 kPa) and volumetric flow (10 mm3/s) as input, respectively. The results showed that the standard nozzle is suitable for bioprinting procedures. Specifically, the inner geometry of the nozzle increases the flow rate, while reducing the dispensing pressure and maintaining similar shear stress compared to the conical tip commonly used in bioprinting.