Level Set Algorithm Research Articles

An Efficient Framework for Accurate Liver Segmentation in Abdominal CT Images with Low Knowledge Requirement

Liver segmentation from abdominal computed tomography (CT) images is a primary step in the diagnosis and treatment of liver cancer, but previous liver segmentation methods have the problems of excessive demand for prior knowledge, under- and oversegmentation, and boundary leakage. To solve these problems, this paper proposes a new method of liver segmentation to assist doctors in medical judgment. Firstly, a liver reconstruction algorithm is proposed to obtain the approximate initial region of the liver, which reduces the requirement of prior knowledge and can reconstruct the liver region closer to the liver boundary. Then, we refine the edge of the liver region based on the reaction diffusion level set (RD level set). This edge refinement method can effectively deal with the weak boundary problem, prevent under- and oversegmentation, and obtain a more accurate liver region. Our method is verified on the clinical and public datasets, respectively. The segmentation results in terms of mean VOE, RVD, ASD, RMSD, and MSD on dataset Sliver07 are 5.1%, −0.1%, 1.0 mm, 2.0 mm, and 18.2 mm, and on dataset 3Dircadb are 8.1%, −0.2%, 1.5 mm, 2.4 mm, and 20.8 mm, respectively. Compared with the previous algorithms, the experiment results show that this method has a great improvement in accuracy with less prior knowledge. The liver reconstruction algorithm proposed in this paper can obtain a more accurate initial liver region, reduce the requirement for prior knowledge, and reduce time costs compared with the level set algorithm.

Modeling of dynamic bridging of solid particles in multiple propagating fractures

During multi-cluster fracturing, solid particles are widely used to alleviate the non-uniform fluid distribution and fracture growth. Even though diversion technology has been applied and proved effective in numerous field applications, many involved physical mechanisms, such as solid diverters transport, settling, bridging, and packing in multiple propagating fractures, remain unclear. In this work, a computational mechanics system is developed to interpret the coupling process of fluid flow, fracture propagation, and particle transport. The moving fracture front is located using the implicit level set algorithm (ILSA) and tip asymptotic solution. The diverter particle transport model can capture the settling, bridging, and packing of particles; thus the slurry flow in the fracture can transit from Poiseuille flow to Darcy flow naturally. Application of the developed system to simulate a single stage of three equally spaced clusters indicates that it is possible to create multiple fractures with uniform length using diversion technology, but their widths are non-uniform. Instead, they demonstrate pinched or ballooned shapes, because of the stress interference. An extensive parametric study is also performed to investigate how various parameters affect diversion efficiency.

Optimized convolutional neural network for glaucoma detection with improved optic-cup segmentation

Glaucoma is the foremost cause of permanent loss of visioahn; it develops slowly with no discernible sign. Early glaucoma recognition is critical because it might aid to slow the progression of the disease. Customary schemes are less precise and manual. As a result, automatic glaucoma analysis is required to identify glaucoma at the earliest with greater precision. The purpose here is to bring in a new scheme in which pre-processing is done using Gaussian filtering, which aids in the removal of unwanted noise in images. Then Optic Cup segmentation is performed using the Modified Level Set Algorithm. Followed by segmentation, the morphological features (disc area, cup area, and blood vessel), as well as non-morphological features (Color, Shape, and Modified LBP), are derived. The Blood vessel thickness is 5 to 100 micrometers. These features are then classified using the Optimized CNN framework, where the weights get optimized via the Self Adaptive Butterfly Optimization Algorithm (SA-BOA). The precision of the developed approach was 21.16%, 7.35%, 6.62%, 2.98%, 4.29%, 3.89%, 5.67%, 6.23%, 6.79%, and 1.63% better than the values obtained for conservative techniques Similarly, the adopted model's negative metrics show negligible values when compared to other models. Thus, the proposed method supremacy was validated successfully.

Modeling of solids particle diversion to promote uniform growth of multiple hydraulic fractures

Solid particulate additives are sometimes used to promote the uniform growth of multiple hydraulic fractures in horizontal oil and gas wells. The principle is that solid particulates block, accumulate, and form larger porous plugging zones preferentially at entrances of fracture taking in the most fluid volume. These porous zones create fluid flow resistance or additional pressure loss; thereby, inhibiting the growth of these dominant fractures and diverting fluid to suppressed fractures. While this technology is promising, governing design parameters and ramifications of placing solids diverters inside the fracture remain unclear. This paper models the propagation of multi-fractures with diverter pressure losses induced by the porous plugging zones. The resulting non-linear hydraulic fracturing problem is solved numerically with an Implicit Level Set Algorithm (ILSA) for each time step and the mechanisms of diversion are illustrated by comparing and contrasting cases with and without particle diverter. In both cases, during the fluid ramp-up period (pumping rate gradually increases from 0 to fracturing rate (QT)), the injection can be equally distributed among fractures before the stress interference affects the fluid allocation (Phase I). Then, stress interference starts to partition more fluid into outer fractures and suppress the growth of the middle fracture (Phase II). Once the perforation friction loss is sufficient to counteract the stress interaction, injection begins to shift to the middle fracture, but still gives a significantly non-uniform fracture growth (Phase III). At this point, solid diverter particles are introduced, leading to three additional phases of growth. Phase IV introduces solid diverters to the treatment at a reduced pumping rate. Particles bridge, accumulate and create porous plugging zones at the flow entrance. A higher pressure drop in outer fractures diverts injection fluids to the middle fracture. Phase V resumes the treatment rate to QT without diverter. The increased pump rate in turn increases the pressure drop in outer fractures and diverts more fluids to the middle fracture. This results in a rapid extension velocity for the middle fracture, enabling it to have the chance to catch up with the longer outer fractures (in Phase VI). This process is controlled by the interplay among stress interference, perforation friction loss, and diverting pressure drop. These simulations demonstrate that a model-based optimization could improve the effectiveness of the diverter technology and promote a uniform multi-fracture growth.

Research on laser center positioning under CV model segmentation

Spot positioning accuracy is an important index of laser processing system and ranging system. When the laser spot is noisy or the gray level is not uniform, the positioning accuracy is easily affected. Aiming at the above problems, this paper proposes a laser spot segmentation method based on the Chan-Vese model, which can improve the accuracy of spot center localization in combination with the gray centroid method. Firstly, the laser spot image is decomposed by two-dimensional wavelet, and the high-frequency component is suppressed by soft threshold function to eliminate the noise in the laser spot image. Secondly, the level set algorithm based on Chan-Vese model is used to segment the laser spot image with adaptive improvement of the initial coordinates of the evolution curve. Finally, the center coordinates are calculated inside the segmentation curve using the gray centroid method. Experimental results show that the method is more accurate and robust.

Error-correcting neural networks for semi-Lagrangian advection in the level-set method

We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether we can compute on-the-fly, data-driven corrections to minimize numerical viscosity in the coarse-mesh evolution of an interface. The proposed system's starting point is the semi-Lagrangian formulation. And, to reduce numerical dissipation, we introduce an error-quantifying multilayer perceptron. The role of this neural network is to improve the numerically estimated surface trajectory. To do so, it processes localized level-set, velocity, and positional data in a single time frame for select vertices near the moving front. Our main contribution is thus a novel machine-learning-augmented transport algorithm that operates alongside selective redistancing and alternates with conventional advection to keep the adjusted interface trajectory smooth. Consequently, our procedure is more efficient than full-scan convolutional-based applications because it concentrates computational effort only around the free boundary. Also, we show through various tests that our strategy is effective at counteracting both numerical diffusion and mass loss. In simple advection problems, for example, our method can achieve the same precision as the baseline scheme at twice the resolution but at a fraction of the cost. Similarly, our hybrid technique can produce feasible solidification fronts for crystallization processes. On the other hand, tangential shear flows and highly deforming simulations can precipitate bias artifacts and inference deterioration. Likewise, stringent design velocity constraints can limit our solver's application to problems involving rapid interface changes. In the latter cases, we have identified several opportunities to enhance robustness without forgoing our approach's basic concept. Despite these circumstances, we believe all the above assets make our framework attractive to parallel level-set algorithms. Its appeal resides in the possibility of avoiding further mesh refinement and decreasing expensive communications between computing nodes.

Real-time computer assisted measurement of oocyte and embryo volume for assessment of transport parameters

Cryopreservation of gametes has revolutionized both animal agriculture and human reproductive medicine. Although many new technologies have tremendously improved the cryopreservation of oocytes and embryos, osmotic stress encountered during the equilibration process can cause their loss of function. Rational cryoprotective agent (CPA) equilibration strategies can be used to minimize this stress but require trained personnel to monitor the process in individual oocytes or embryos or require the use of suboptimal average transport parameter values in mathematically guided protocols. To enable individually optimized equilibration of CPAs in individual cells, here we establish experimental and computational techniques to track the osmotic behavior of individual bovine oocytes and embryos during CPA equilibration in real time. We designed a microfluidic device to provide a controlled flow of CPA and modified standard image analysis techniques to estimate real-time cell volume changes. In particular, we used a level-set method to define a boundary within a contour plot which could automate the image analysis process. A colour based level set algorithm coupled with contour smoothing not only provided the best fit but also reduced the segmentation time to well under a second per image. The accuracy of the automated method was comparable to human segmented images for both oocytes and embryos. This technology should enable both rapid evaluation of key biophysical parameters in oocytes and embryos undergoing CPA equilibration and the development of real-time feedback-control of CPA equilibration, enabling individual oocyte- and embryo-specific optimal protocols.

Automatic pancreas segmentation using ResNet-18 deep learning approach

The accurate pancreas segmentation process is essential in the early detection of pancreatic cancer. The pancreas is situated in the abdominal cavity of the human body. The abdominal cavity contains the pancreas, liver, spleen, kidney, and adrenal glands. Sharp and smooth detection of the pancreas from this abdominal cavity is a challenging and tedious job in medical image investigation. Top-down approaches like Novel Modified K-means Fuzzy clustering algorithm (NMKFCM), Scale Invariant Feature Transform (SIFT), Kernel Density Estimator (KDE) algorithms were applied for pancreas segmentation in the early days. Recently, Bottom-up method has become popular for pancreas segmentation in medical image analysis and cancer diagnosis. LevelSet algorithm is used to detect the pancreas from the abdominal cavity. The deep learning, bottom-up approach performance is better than another. Deep Residual Network (ResNet-18) deep learning, bottom-up approach is used to detect accurate and sharp pancreas from CT scan medical images. 18 layers are used in the architecture of ResNet-18. The automatic pancreas and kidney segmentation is accurately extracted from CT scan images. The proposed method is applied to the medical CT scan images dataset of 82 patients. 699 images and 150 images with different angles are used for training and testing purposes, respectively. ResNet-18 attains a dice similarity index value up to 98.29±0.63, Jaccard Index value up to 96.63±01.25, Bfscore value up to 84.65±03.96. The validation accuracy of the proposed method is 97.01%, and the loss rate value achieves up to 0.0010. The class imbalance problem is solved by class weight and data augmentation.

Magnetic Resonance Features of Acquired Immune Deficiency Syndrome Involving Central Nervous System Diseases by Intelligent Fuzzy C-Means Clustering (FCM) Algorithm.

This study was aimed to explore the application of fuzzy C-means (FCM) algorithm in MR images of acquired immune deficiency syndrome (AIDS) patients. Sixty AIDS patients with central nervous disease were selected as the research object. A method of brain MR image segmentation based on FCM clustering optimization was proposed, and FCM was optimized based on the neighborhood pixel correlation of gray difference. The correlation was introduced into the objective function to obtain more accurate pixel membership and segmentation features of the image. The segmented image can retain the original image information. The proposed algorithm can clearly distinguish gray matter from white matter in images. The average time of image segmentation was 0.142 s, the longest time of level set algorithm was 2.887 s, and the running time of multithreshold algorithm was 1.708 s. FCM algorithm had the shortest running time, and the average time was significantly better than other algorithms (P < 0.05). FCM image segmentation efficiency was above 90%, and patients can clearly display the location of lesions after MRI imaging examination. In summary, FCM algorithm can effectively combine the spatial neighborhood information of the brain image, segment the BRAIN MR image, analyze the characteristics of AIDS patients from different directions, and provide effective treatment for patients.

An enhancedJ‐integral for hydraulic fracture mechanics

AbstractThis article revisits the formulation of theJ‐integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classicalJ‐integral in finite element models overestimates the length of hydraulic fractures in the viscosity‐dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss in accuracy of theJ‐integral. With this understanding, two novel contributions are presented. The first contribution consists of two variations of theJ‐integral, termed the and ‐integral, that demonstrate an enhanced ability to predict viscosity‐dominated propagation. In particular, such ‐integrals accurately extract stress intensity factors in both viscosity and toughness‐dominated regimes of propagation. The second contribution consists of a methodology to extract the propagation velocity from the energy release rate applicable throughout the toughness‐viscous propagation regimes. Both techniques are combined to form an implicit front‐tracking ‐algorithm capable of quickly converging on the location of the fracture front independently to the toughness‐viscous regime of propagation. The ‐algorithm represents an energy‐based alternative to the aperture‐based methods frequently used with the Implicit Level Set Algorithm to simulate hydraulic fracturing. Simulations conducted at various resolutions of the fracture suggest that the new approach is suitable for hydro‐mechanical finite element simulations at the reservoir scale.

Bladder Wall Segmentation and Characterization on MR Images: Computer-Aided Spina Bifida Diagnosis

(1) Background: Segmentation of the bladder inner’s wall and outer boundaries on Magnetic Resonance Images (MRI) is a crucial step for the diagnosis and the characterization of the bladder state and function. This paper proposes an optimized system for the segmentation and the classification of the bladder wall. (2) Methods: For each image of our data set, the region of interest corresponding to the bladder wall was extracted using LevelSet contour-based segmentation. Several features were computed from the extracted wall on T2 MRI images. After an automatic selection of the sub-vector containing most discriminant features, two supervised learning algorithms were tested using a bio-inspired optimization algorithm. (3) Results: The proposed system based on the improved LevelSet algorithm proved its efficiency in bladder wall segmentation. Experiments also showed that Support Vector Machine (SVM) classifier, optimized by Gray Wolf Optimizer (GWO) and using Radial Basis Function (RBF) kernel outperforms the Random Forest classification algorithm with a set of selected features. (4) Conclusions: A computer-aided optimized system based on segmentation and characterization, of bladder wall on MRI images for classification purposes is proposed. It can significantly be helpful for radiologists as a part of spina bifida study.

Calculating the grain boundary inclination of voxelated grain structures using a smoothing algorithm

We have developed a flexible method for calculating the grain boundary (GB) inclinations of voxelated grain structure data using smoothing algorithms. We compared the performance of four algorithms: the linear interpolation, Allen–Cahn, level-set, and vertex algorithms. We assessed their accuracy using 2D and 3D cases with known inclinations. The vertex algorithm provided the best balance between accuracy and efficiency for 2D structures while the linear interpolation algorithm provided the best balance for 3D structures. We compared the GB inclinations calculated using our smoothing method on a 3D high energy X-ray diffraction microscopy (HEDM) dataset to those determined by meshing the GBs. The two approaches determined similar GB plane distributions, though they varied significantly at triple junctions. Finally, the smoothing method was demonstrated for two sources of 3D voxelated grain structures: HEDM data and results from Monte Carlo Potts grain growth simulations.

Discrete element modeling of 3D irregular concave particles: Transport properties of particle-reinforced composites considering particles and soft interphase effects

Particles of complex morphologies and their surrounding soft interphase are main constituents that play a significant role in the transport properties of particle-reinforced composites (PRCs). It has been a crucial but unresolved issue how to derive the volume fraction of soft interphase around three-dimensional (3D) irregular concave particles, as well as it remains to be virgin to explore the effective transport properties of three-phase PRCs composed of homogeneous matrix, 3D irregular concave particles of a relatively high packing density and their surrounding soft interphase. To this end, this work initially develops a discrete element modeling (DEM) of 3D irregular concave particles with monodispersity in size to generate random dense packing structures, where an innovative mathematical-controllable parameterized method is proposed to devise diverse irregular concave particle shapes. The proposed particle design method is not only universal and controllable to generate a given particle shape, but also can be directly linked with an experimental measurement using digital scanning. In addition, an efficient two-step numerical strategy is presented to check the inter-particle contact detection and collision. Then, the volume fraction of soft interphase around monodisperse concave particles is numerically derived for the first time by using the Monte Carlo random point sampling simulation. The Monte Carlo simulation has good accuracy to obtain the soft interphase volume fraction, which is confirmed by comparing with the theoretical formulae for spherical particle systems. Next, a dual-probability-Brownian motion (DP-BM) scheme along with the level set algorithm is extended to investigate the effective transport properties like thermal conductivity of three-phase PRCs. Comparison against the finite element method (FEM), the proposed DP-BM scheme is more user-friendly and efficient to estimate the effective transport properties of PRCs within an accuracy level. The proposed DP-BM scheme can overcome the two intrinsic limitations of the classical effective medium approximations that one limitation is the ellipsoidal inclusion shape and another is a relative dilute level of inclusion volume fraction. Moreover, the effects of the concave particle shape and packing density, and the interphase dimension on the volume fraction of soft interphase and the effective normalized transport properties of PRCs are evaluated. The results elucidate rigorous component-structure–property relations, which can provide sound guidance for durability evaluation and material design of PRCs.

ANALYSIS OF SPECIFIC PARAMETERS FOR SKIN TUMOR CLASSIFICATION

During the last years, computer vision-based diagnosis systems have been widely used in several hospitals and dermatology clinics, aiming mostly at the early detection of malignant melanoma tumor, which is among the most frequent types of skin cancer, versus other types of nonmalignant cutaneous diseases. They grow in melanocytes, the cells responsible for pigmentation. This type of cancer is increasing rapidly and its related mortality rate is increasing more modestly, and inversely proportional to the tumor’s thickness. The mortality rate can be decreased by earlier detection of suspicious lesions and better prevention. In this work, we are interested in extracting all specific attributes which can be used for computer-aided diagnosis of melanoma. In the first step of the proposed work, we applied the Dull Razor [Lee T et al., Dullrazor: A software approach to hair removal from images, Cancer Control Research, British Columbia Cancer Agency, Vancouver, Canada, Vol. 21, No. 6, pp. 533–543, 1997] technique to images to reduce the influence of small structures, hairs, bubbles, light reflection. In the second step, a new fuzzy level set algorithm is proposed in order to facilitate the medical image segmentation task. It is able to directly evolve from the initial segmentation proposed that uses a spatial fuzzy clustering approach. The controlling parameters of the level set evolution are also estimated from the results of the fuzzy clustering step. This step is essential to characterize the shape of the lesion and also to locate the tumor to be analyzed. In this paper, we have also treated the necessity to extract all the specific attributes used to develop a characterization methodology that enables specialists to take the best possible diagnosis. For this purpose, our proposal relies largely on visual observation of the tumor while dealing with some characteristics as color, texture or form. The method used in this paper is called ABCD. It requires calculating four factors: Asymmetry ([Formula: see text], Border ([Formula: see text], Color ([Formula: see text], and Diversity ([Formula: see text]. Finally, these parameters are used to construct a classification module based on artificial neural network for the recognition of malignant melanoma.

Fast and realistic 3D feature profile simulation platform for plasma etching process

We present a topographic simulation platform that simultaneously considers 3D surface movement, neutral and ion transport, and surface reactions in plasma high-aspect-ratio (HAR) oxide etching. The hash map data structure is considered for an effective 3D level-set algorithm with parallelized computations to calculate surface moving speed. Neutral and ion transport within nanoscale semiconductor geometry is parallelized with a graphics processing unit (GPU) so that the speedup ratio, as compared to a single central processing unit (CPU), is approximately 200. The surface reaction based on a two-layer model was incorporated into a 3D feature profile simulation platform with CPU parallelization. Finally, our simulation platform demonstrates that adaptive surface meshing can drastically decrease the computational load with a parallelized numerical platform.

Secondary growth and closure behavior of planar hydraulic fractures during shut-in

The evolution of fractures during shut-in after hydraulic fracturing is an important topic in petroleum engineering. Considering the closure and secondary expansion of fractures during shut-in can further improve the accuracy of predicting hydraulic fracture parameters. Based on linear elastic fracture mechanics, elastic mechanics, and the implicit level set algorithm, a numerical model of planar hydraulic fracture propagation was established in this study. In the proposed model, the reservoir was considered as a homogeneous elastic medium, and the fluid loss was characterized using Carter's filtration model. The secondary propagation and fracture closure behavior during shut-in could be simulated by solving the strongly nonlinear system of fluid and stress coupling. Based on this model, the evolution behavior of hydraulic fractures during injection and shut-in was analyzed. According to the variation characteristics of the fracture length, the evolution process could be divided into three stages: fracture propagation during injection, secondary growth, and fracture stopping (but not closing). According to the variation characteristics of the fracture opening and net pressure, the evolution process could be divided into three stages: nonlinear increase, linear decrease, and gradual decrease. For low-permeability reservoirs, fracture closure and secondary propagation may take several times the injection time after shut-in, and the secondary propagation length may reach tens of meters. The results show that the larger the filtration coefficient, the faster the fracture closure will be, and the shorter the secondary propagation distance. The higher the viscosity of the fracturing fluid, the slower the fracture closure will be, while the secondary propagation distance is almost unaffected. The fracture toughness has little effect on the fracture closure and secondary propagation. The crack will close first in the region with large interlayer stress during shut-in. The findings of this study can help for better understanding of the evolution mechanism of fractures during shut-in and closure.

Utilization of Both Machine Vision and Robotics Technologies in Assisting Quality Inspection and Testing

Inspecting the smoothness and durability of the exterior and interior surfaces of manufactured products such as large passenger aircraft requires utilizing manufacturing precision instruments. Manual techniques are mainly adopted in inspections, which are, however, much costly and have low efficiency. Moreover, manual operation is more prone to missing and false inspections. To cope with these issues, effective precision instruments have been needed to devise intelligent inspections for impalpable damages as necessary tools. When many inspection tasks are investigated, very few public datasets are available to recognize the intelligent inspection of precision instruments. On the other hand, precision instruments can be applied to a wide variety of damages. YOLO V3 was proposed based on acquiring and processing the image appearances, which deal with the surface inspection of the precision instrument in this study. The image dataset of the impalpable damage was initially established. More specifically, the YOLO V3 detection network is leveraged to roughly calculate the location of the damage appearances and identify the damage type. Afterward, the designed level set algorithm was employed to obtain more accurate damage locations in the image block utilizing the characteristics of different types of damages. Finally, a quantitative analysis was performed employing the refined detection results. A deep architecture that can intelligently conduct damage detection was proposed. Besides, the proposed method exhibited a strong tolerance for unknown types of damages and excellent flexibility and adaptability. Extensive experimental results demonstrated that the proposed method can alleviate the shortcomings of the traditional inspection methods. Thus, it provided technical guidance for the applications of the intelligent orbital inspection of the robots. The proposed method with a more precise and noninvasive inspection technique remarkably accelerates the inspection time of impalpable damages on surfaces.

An Enhanced Approach for Segmentation of Liver from Computed Tomography Images

An accurate segmentation of liver from Computed Tomography (CT) scans is essential for liver tumor research as it offers valuable information for clinical diagnosis and treatment. However, it is challenging to achieve an accurate segmentation of the liver because of the blurred edges, low contrast and similar intensity of the organs in the CT scan. In this paper, an automated model which will segment the liver from CT images using a hybrid algorithm has been used. The segmentation of liver from CT scan is done with the help of Particle Swarm Optimization (PSO) followed by level set algorithm. The ultimate aim of using this hybrid algorithm is to improve the accuracy of liver segmentation. Computer aided classification of liver CT into healthy and tumorous images aids in diagnosis of liver diseases. It can help a great deal in diagnosis of liver disorders. In order to achieve better classification results, it is of high importance to segment the liver accurately without an error of over or under segmentation. The results obtained indicate that the approach used in this work is faster and has 98.62% accuracy, 99.2% specificity, 97.1% sensitivity, 97.8% F-measure, 96.6% Matthews Coefficient Constant (MCC), 99.08% precision, 97.8% dice coefficient and 95.7% jaccard coefficient in segmenting the liver.

A coupled meshless element-free Galerkin and radial basis functions method for level set-based topology optimization

This paper presents a meshless element-free Galerkin method coupled with the radial basis functions (RBFs)-based level set algorithm for topology optimization. The meshless approach provides the structural response and corresponding sensitivities at nodal/grid points, and the solution of RBFs-based level set formulation updates the structural geometry accordingly. Thus, this unique and novel approach allows solution of the optimization problems using a single discretization scheme for both the meshless and the level set methods. A special technique is proposed for the identification of meshless nodal points within the solid and void regions of the structural geometry. The present method handles the appropriate topological modifications, i.e. hole creation, splitting, merging, etc., affectively. Optimal solutions of the benchmark problems suggest reliability and compatibility of the proposed approach versus the mesh-based techniques available within the structural optimization literature.

A massively parallel accurate conservative level set algorithm for simulating turbulent atomization on adaptive unstructured grids

This article presents a massively parallel and robust strategy to perform the simulation of turbulent incompressible two-phase flows on unstructured grids in complex geometries. This strategy relies on a combination of a narrow-band accurate conservative level set (ACLS)/ghost-fluid framework with isotropic adaptive mesh refinement. This combination enables to accurately capture interface dynamics and topology, and the small physical scales at the liquid-gas interface are resolved at an affordable cost. The ACLS method, even if not strictly mass-conserving, ensures the exact conservation of a smoothed phase indicator, which minimizes the liquid mass conservation errors. In the accurate conservative level set framework, presented first in Desjardins et al. (2008) [25], the interface is defined as the iso-contour of a hyperbolic tangent function, which is advected by the fluid, and then reshaped using a reinitialization equation. Several forms of this reinitialization exist: the original ACLS form proposed by Desjardins et al. involves numerical estimation of the hyperbolic tangent gradient, which is difficult to compute accurately on unstructured meshes. It is thus susceptible to induce artificial deformation of the interface. A new form has been recently proposed in Chiodi and Desjardins (2017) [29], which takes advantage of a mapping onto a classical distance level set while much better preserving the interface shape. Nevertheless, the implementation of this new form on unstructured grids requires special care. In this work, a robust implementation of this new form on unstructured meshes is proposed and implemented in the YALES2 low-Mach flow solver. In order to compute interface normals and curvature, the signed-distance function is reconstructed in parallel at nodes in the narrow band around the interface using a Geometric-Projection Marker Method (GPMM). This method relies on the triangulation of the level set iso-contour and exact geometric projection to the closest surface elements. Spatial convergence, robustness and efficiency of the overall procedure are firstly demonstrated through classical interface transport test cases and two-phase flow examples. Eventually, to emphasize the significant computational gain using adaptive mesh refinement and the ability to compute complex turbulent flows with large density ratios, two Large-Eddy Simulations (LES) of atomizing liquid jets in air are presented, each one at various resolutions. The first one is a low-pressure water jet in quiescent air from a compound nozzle with full computation of the internal injector flow, while the latter is a high-pressure kerosene jet in crossflow. Both simulations are validated against experiments, demonstrating the potential of the method to access a deep numerical insight into jet instabilities and internal flow dynamics with 3D unstructured meshes.