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Results for “level set methods”
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A continuous surface reconstruction method on point cloud captured from a 3D surface photogrammetry system
Purpose: To accurately and efficiently reconstruct a continuous surface from noisy point clouds captured by a surface photogrammetry system (VisionRT). Methods: The authors have developed a level-set based surface reconstruction method on point clouds captured by a surface photogrammetry system (VisionRT). The proposed method reconstructs an implicit and continuous representation of the underlying patient surface by optimizing a regularized fitting energy, offering extra robustness to noise and missing measurements. By contrast to explicit/discrete meshing-type schemes, their continuous representation is particularly advantageous for subsequent surface registration and motion tracking by eliminating the need for maintaining explicit point correspondences as in discrete models. The authors solve the proposed method with an efficient narrowband evolving scheme. The authors evaluated the proposed method on both phantom and human subject data with two sets of complementary experiments. In the first set of experiment, the authors generated a series of surfaces each with different black patches placed on one chest phantom. The resulting VisionRT measurements from the patched area had different degree of noise and missing levels, since VisionRT has difficulties in detecting dark surfaces. The authors applied the proposed method to point clouds acquired under these different configurations, and quantitatively evaluated reconstructed surfaces by comparing against a high-quality reference surface with respect to root mean squared error (RMSE). In the second set of experiment, the authors applied their method to 100 clinical point clouds acquired from one human subject. In the absence of ground-truth, the authors qualitatively validated reconstructed surfaces by comparing the local geometry, specifically mean curvature distributions, against that of the surface extracted from a high-quality CT obtained from the same patient. Results: On phantom point clouds, their method achieved submillimeter reconstruction RMSE under different configurations, demonstrating quantitatively the faith of the proposed method in preserving local structural properties of the underlying surface in the presence of noise and missing measurements, and its robustness toward variations of such characteristics. On point clouds from the human subject, the proposed method successfully reconstructed all patient surfaces, filling regions where raw point coordinate readings were missing. Within two comparable regions of interest in the chest area, similar mean curvature distributions were acquired from both their reconstructed surface and CT surface, with mean and standard deviation of (μ{sub recon} = − 2.7 × 10{sup −3} mm{sup −1}, σ{sub recon} = 7.0 × 10{sup −3} mm{sup −1}) and (μ{sub CT} = − 2.5 × 10{sup −3} mm{sup −1}, σ{sub CT} = 5.3 × 10{sup −3} mm{sup −1}), respectively. The agreement of local geometry properties between the reconstructed surfaces and the CT surface demonstrated the ability of the proposed method in faithfully representing the underlying patient surface. Conclusions: The authors have integrated and developed an accurate level-set based continuous surface reconstruction method on point clouds acquired by a 3D surface photogrammetry system. The proposed method has generated a continuous representation of the underlying phantom and patient surfaces with good robustness against noise and missing measurements. It serves as an important first step for further development of motion tracking methods during radiotherapy.
The Voronoi Implicit Interface Method for computing multiphase physics
In this paper, we introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. Finally, we test the method’s accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann’s law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.
High-fidelity pool boiling simulations on multiple nucleation sites using interface capturing method
Boiling has proved to be one of the most efficient means for heat transfer and is a very important phenomenon during severe accident scenarios in light water reactors. High-fidelity pool boiling simulations can provide a numerical database for improving mechanistic boiling models by allowing for specific evaluation of interactions among bubbles. Previously published pool boiling simulations investigated two nucleation sites in which bubble growth at one site suppressed nucleation at the other site. Based on previous study results, more complicated interface-capturing simulations on pool boiling were conducted using PHASTA code with locally refined unstructured mesh. First, different boundary conditions (BCs) were assessed to support robustness and reproducibility of the boiling model. Then, a scale study was conducted at a larger domain with nine nucleation sites where either nine or four nucleation sites are activated. Involving more nucleation sites increased the complexity of bubble interactions from surrounding sites. Finally, bubble departure behavior influenced by wall heat flux was investigated. In this work, when heat flux was increased, the order of bubble departure changed, but diagonal bubbles always departed after one another. The departure time interval between the first and second bubble reduced as heat flux increased. The corresponding frequency was almost linearly proportional to the heat flux. In addition, bubble departure behavior was found to be greatly influenced by the nucleation site pattern. Multiple nucleation sites resulted in superimposed inhibitive effects from surrounding sites to each bubble, which extensively delayed the departure. This new observation was not discussed in previously published works. The work presented here provides new insight on the fundamental understanding of boiling phenomena, contributes to the development of a 3D multiphase computational fluid dynamics (M-CFD) model, and provides a more comprehensive database for data-driven pool boiling studies.
Non-local model for surface tension in fluid-fluid simulations
We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5e added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pe,in - Pe,out satisfies the Young-Laplace law for droplet radius greater than 3.5e and other- wise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non- local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.
High-order quadrature on multi-component domains implicitly defined by multivariate polynomials
Not Available
High-resolution computational algorithms for simulating offshore wind turbines and farms: Model development and validation
The present project involves the development of modeling and analysis design tools for assessing offshore wind turbine technologies. The computational tools developed herein are able to resolve the effects of the coupled interaction of atmospheric turbulence and ocean waves on aerodynamic performance and structural stability and reliability of offshore wind turbines and farms. Laboratory scale experiments have been carried out to derive data sets for validating the computational models.
A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows.
Abstract Not Provided
A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows.
Abstract not provided.
CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.
Hierarchical median narrow band for level set segmentation of cervical cell nuclei
This paper presents a novel hierarchical nuclei segmentation algorithm for isolated and overlapping cervical cells based on a narrow band level set implementation. Our method applies a new multiscale analysis algorithm to estimate the number of clusters in each image region containing cells, which turns into the input to a narrow band level set algorithm. We assess the nuclei segmentation results on three public cervical cell image databases. Overall, our segmentation method outperformed six state-of-the-art methods concerning the number of correctly segmented nuclei and the Dice coefficient reached values equal to or higher than 0.90. We also carried out classification experiments using features extracted from our segmentation results and the proposed pipeline achieved the highest average accuracy values equal to 0.89 and 0.77 for two-class and three-class problems, respectively. Furthermore, these results demonstrated the suitability of the proposed segmentation algorithm to integrate decision support systems for cervical cell screening.
A Level Set Model for Structured Mesh Representation of Fibrous Preforms used in Composites Manufacturing
Here, a model for implicit representation of fibrous and woven preforms used for composites manufacturing is described. The method is based on a level set function defined on a structured mesh to implicitly capture the complex fiber and weave geometries. Since most software packages used to model woven preforms are based on unstructured mesh, a numerical model for transforming a discretized surface to a structured mesh representation and vice-a-versa is presented. Specific emphasis is on scalable computation of a level set function for large and complex 3D woven structures from a triangulated surface of the smallest unit (yarn). The model is applied to capture a periodic 3D layered 5-harness satin (5HS) weave geometry on a structured mesh. Geometric transformations needed to efficiently compute the level set function for the 3D structure on a high resolution mesh are described. Effects of mesh resolution on the geometric features such as number of resolved fibers, effective fiber size, and the surface area to volume ratio of the iso-surface are analyzed. Using the distance property of the level set function, an approach to evaluate the structure function resulting from transient evolving topology representing densification due to matrix phase depositions is also presented. The approach captures transition of the geometric characteristic from fiber governed at early stages of densification to yarn governed at the terminal stage.
Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.
Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation
A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.
A level set approach for the computational study of a yield stress fluid filling a thin mold
Many important engineering and scientific applications such as cement slurries, foams, crude oil, and granular avalanches involve the concept of yield stress. Therefore, modeling yield stress fluids in different flow configurations, including the accurate prediction of the yield surface, is important. In this paper, we present a computational model based on the finite element method to study the flow of yield stress fluids in a thin mold and compare the results with data from flow visualization experiments. Here, we use the level set method to describe the interface between the filling fluid and air. We use polypropylene glycol as a model Newtonian fluid and Carbopol for the model yield stress fluid, as the Carbopol solution demonstrates yielding without thixotropy. To describe the yielding and shear-thinning behavior, we use a generalized Newtonian constitutive equation with a Bingham–Carreau–Yasuda form. We compare the results obtained from the mold filling experiments with the results from the three-dimensional (3D) model and from a reduced-order Hele-Shaw (HS) model that is two-dimensional, including the effect of shear-thinning along the thin direction only approximately. We show that both the 3D and the HS model can capture the experimental meniscus shape reasonably well for all the fluids considered at three different flow rates. This indicates that the shape evolution is insensitive to the dimensionality of the model. However, the viscosity and yield surfaces predicted by the 3D and HS models are different. The HS model underestimates the high viscosity and unyielded regions compared to the estimation by the 3D model.
Learning nonlinear level sets for dimensionality reduction in function approximation
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.
Interface tracking simulations of bubbly flows in PWR relevant geometries
[en] Highlights: • Simulations were performed for turbulent bubbly flows in PWR subchannel geometry. • Liquid turbulence is fully resolved by direct numerical simulation approach. • Bubble behavior is captured using level-set interface tracking method. • Time-averaged single- and two-phase turbulent flow statistical quantities are obtained. - Abstract: The advances in high performance computing (HPC) have allowed direct numerical simulation (DNS) approach coupled with interface tracking methods (ITM) to perform high fidelity simulations of turbulent bubbly flows in various complex geometries. In this work, we have chosen the geometry of the pressurized water reactor (PWR) core subchannel to perform a set of interface tracking simulations (ITS) with fully resolved liquid turbulence. The presented research utilizes a massively parallel finite-element based code, PHASTA, for the subchannel geometry simulations of bubbly flow turbulence. The main objective for this research is to demonstrate the ITS capabilities in gaining new insight into bubble/turbulence interactions and assisting the development of improved closure laws for multiphase computational fluid dynamics (M-CFD). Both single- and two-phase turbulent flows were studied within a single PWR subchannel. The analysis of numerical results includes the mean gas and liquid velocity profiles, void fraction distribution and turbulent kinetic energy profiles. Two sets of flow rates and bubble sizes were used in the simulations. The chosen flow rates corresponded to the Reynolds numbers of 29,079 and 80,775 based on channel hydraulic diameter (D_h) and mean velocity. The finite element unstructured grids utilized for these simulations include 53.8 million and 1.11 billion elements, respectively. This has allowed to fully resolve all the turbulence scales and the deformable interfaces of individual bubbles. For the two-phase flow simulations, a 1% bubble volume fraction was used which resulted in 17 bubbles in the smaller case and 262 bubbles in the larger case. In the larger simulation case the size of the resolved bubbles is 0.65 mm in diameter, and the bulk mesh cell size is about 30 microns. Those large-scale simulations provide new level of details previously unavailable and were enabled by the excellent scaling performance of our two-phase flow solver and access to the state-of-the-art supercomputing resources. The presented simulations used up to 256 thousand processing threads on the IBM BG/Q supercomputer “Mira” (Argonne National Laboratory).
Search for the decay modes D⁰→e⁺e⁻, D⁰→μ⁺μ⁻, and D⁰→e ± μ∓
We present searches for the rare decay modes D⁰→e⁺e⁻, D0→μ⁺μ⁻, and D⁰→e ± μ ∓ in continuum e⁺e⁻→cc¯ events recorded by the BABAR detector in a data sample that corresponds to an integrated luminosity of 468 fb⁻¹. These decays are highly Glashow–Iliopoulos–Maiani suppressed but may be enhanced in several extensions of the standard model. Our observed event yields are consistent with the expected backgrounds. An excess is seen in the D⁰→μ⁺μ⁻ channel, although the observed yield is consistent with an upward background fluctuation at the 5% level. Using the Feldman–Cousins method, we set the following 90% confidence level intervals on the branching fractions: B(D⁰→e⁺e⁻)<1.7×10⁻⁷, B(D⁰→μ⁺μ⁻) within [0.6,8.1]×10⁻⁷, and B(D⁰→e ± μ ∓ )<3.3×10⁻⁷.