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Results for “level set method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Identifying attributes of CO 2 leakage zones in shallow aquifers using a parametric level set method: Original Research Article: Identifying attributes of CO 2 leakage zones in shallow aquifers using a parametric level set method

Leakage through abandoned wells and geologic faults poses the greatest risk to CO 2 storage permanence. For shallow aquifers, secondary CO 2 plumes emanating from the leak zones may go undetected for a sustained period of time and has the greatest potential to cause large-scale and long-term environmental impacts. Identification of the attributes of leak zones, including their shape, location, and strength, is required for environmental risk assessment. This study applies a parametric level set (PaLS) method to characterize leak zones. Level set methods are appealing for tracking topological changes and recovering unknown shapes of objects. However, level set evolution using the conventional level set methods is computationally challenging. In PaLS, the level set function is approximated by using a weighted sum of basis functions and the level set evolution problem is replaced by an optimization problem. The efficacy of PaLS is demonstrated by reconstructing attributes of a CO 2 leak zone in a carbonate aquifer. Our results show that PaLS is a robust source identification method that can recover the approximate leak zone locations in the presence of measurement errors, model parameter uncertainty, and inaccurate guesses of source flux strengths. Accurate delineation of source geometry is achievable when a relatively dense observation network is used. The PaLS-based, source recovery framework introduced in this work is generic and can be adapted for any reactive transport model by simply switching the pre- and post-processing routines.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Level set methods for detonation shock dynamics using high-order finite elements

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two- and three-dimensional benchmark problems as well as applications to DSD.

finite element methods↗
DOE OSTI2026

An efficient level set method for tracking many materials

Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

A Cartesian Adaptive Level Set Method for Two-Phase Flows

In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.

Ham, F.↗
NASA NTRS2011

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Kim, Hyoungin↗
DOE OSTI2021

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

42 ENGINEERING↗
DOE OSTI2017

Coalescence Prevention Algorithm for Level Set Method

An algorithm to prevent or delay bubble coalescence for the level set (LS) method is presented. This novel algorithm uses the LS method field to detect when bubbles are in close proximity, indicating a potential coalescence event, and applies a repellent force to simulate the unresolved liquid drainage force. The model is introduced by locally modifying the surface tension force near the liquid film drainage area. The algorithm can also simulate the liquid drainage time of the thin film by controlling the length of time the increased surface tension has been applied. Thus, a new method of modeling bubble coalescence has been developed. Several test cases were designed to demonstrate the capabilities of the algorithm. The simulations, including a mesh study, confirmed the abilities to identify and prevent coalescence as well as implement the time tracking portion, with an additional 10–25% computational cost. Ongoing tests aim to verify the algorithm's functionality for simulations with different flow conditions, a ranging number of bubbles, and both structured and unstructured computational mesh types. Specifically, a bubble rising toward a free surface provides a test of performance and demonstrates the ability to consistently prevent coalescence. In addition, a two bubble case and a seven bubble case provide a more complex demonstration of how the algorithm performs for larger simulations. These cases are compared to much more expensive simulations capable of resolving the liquid film drainage (through very high local mesh resolution) to investigate how the algorithm replicates the liquid film drainage process.

Engineering↗
DOE OSTI2017

Stochastic level-set method for shape optimisation

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical programming. The stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a Boltzmann–Gibbs distribution of structures. In non-convex optimisation problems, the deterministic algorithm can get trapped in local optima: the stochastic generalisation enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of-principle calculation is shown for a simple engineering structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1998

Profile Evolution Simulation in Etching Systems Using Level Set Methods

Semiconductor device profiles are determined by the characteristics of both etching and deposition processes. In particular, a highly anisotropic etch is required to achieve vertical sidewalls. However, etching is comprised of both anisotropic and isotropic components, due to ion and neutral fluxes, respectively. In Ar/Cl2 plasmas, for example, neutral chlorine reacts with the Si surfaces to form silicon chlorides. These compounds are then removed by the impinging ion fluxes. Hence the directionality of the ions (and thus the ion angular distribution function, or IAD), as well as the relative fluxes of neutrals and ions determines the amount of undercutting. One method of modeling device profile evolution is to simulate the moving solid-gas interface between the semiconductor and the plasma as a string of nodes. The velocity of each node is calculated and then the nodes are advanced accordingly. Although this technique appears to be relatively straightforward, extensive looping schemes are required at the profile corners. An alternate method is to use level set theory, which involves embedding the location of the interface in a field variable. The normal speed is calculated at each mesh point, and the field variable is updated. The profile comers are more accurately modeled as the need for looping algorithms is eliminated. The model we have developed is a 2-D Level Set Profile Evolution Simulation (LSPES). The LSPES calculates etch rates of a substrate in low pressure plasmas due to the incident ion and neutral fluxes. For a Si substrate in an Ar/C12 gas mixture, for example, the predictions of the LSPES are identical to those from a string evolution model for high neutral fluxes and two different ion angular distributions.(2) In the figure shown, the relative neutral to ion flux in the bulk plasma is 100 to 1. For a moderately isotropic ion angular distribution function as shown in the cases in the left hand column, both the LSPES (top row) and rude's string method (bottom row) predict tapered profiles. The LSPES uses an AD with a FWHM = 13.5 degrees, and rude's model uses a ratio of sheath voltage to ion temperature of 50. The more anisotropic IADs produce profiles with more vertical sidewalls and a wider bottom surface, as shown in the right hand column. Here, the LSPES has an AD with a FWHM = 2 degrees, and rude's model uses a ratio of 500 of sheath voltage to ion temperature. The agreement between the LSPES and rude's model is excellent in both cases. We will present etching profiles generated by the LSPES, including calculations of the re-emitted fluxes of both neutrals and ions off of the profile walls. In addition, we will show the effect of geometric structures (overhangs, etc.) on the etching profiles. Other physical aspects, such as surface diffusion, will also be included in the model.

Hwang, Helen H.↗
NASA NTRS1997

Etch Profile Simulation Using Level Set Methods

Etching and deposition of materials are critical steps in semiconductor processing for device manufacturing. Both etching and deposition may have isotropic and anisotropic components, due to directional sputtering and redeposition of materials, for example. Previous attempts at modeling profile evolution have used so-called "string theory" to simulate the moving solid-gas interface between the semiconductor and the plasma. One complication of this method is that extensive de-looping schemes are required at the profile corners. We will present a 2D profile evolution simulation using level set theory to model the surface. (1) By embedding the location of the interface in a field variable, the need for de-looping schemes is eliminated and profile corners are more accurately modeled. This level set profile evolution model will calculate both isotropic and anisotropic etch and deposition rates of a substrate in low pressure (10s mTorr) plasmas, considering the incident ion energy angular distribution functions and neutral fluxes. We will present etching profiles of Si substrates in Ar/Cl2 discharges for various incident ion energies and trench geometries.

Hwang, Helen H.↗