Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solution regularity”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗
DOE OSTI2024

Constrained Turret Defense with Fixed Final Time

In this paper, we extend existing turret defense differential game formulations involving a turn-constrained turret and mobile agent to include specified final time and a constraint. For the purposes of this analysis, the specified final time may represent some exogenous input, perhaps representing the time at which some other event will take place. As for the constraint, it represents a no-fly zone for the mobile agent. The scenario is formulated as a two-player, zero-sum differential game and solved via the method of characteristics (i.e., back-propagation of equilibrium trajectories). Three different trajectory types make up the solution: trajectories that end with the turret aligned with the mobile agent, trajectories that end with the mobile agent on the constraint boundary, and regular trajectories.

differential game, game theory↗
DOE OSTI2025

Modeling Sepsis: Establishment and Validation of a 72-Hour Swine Model of Penetrating Abdominal Trauma

Background/Objectives: Fecal peritonitis following penetrating abdominal trauma is a serious condition that often results in sepsis and organ failure. The aim of our study was to develop a novel conscious porcine model of sepsis and organ dysfunction caused by multiple penetrating injuries to the small and large intestines. Methods: Twelve female Yorkshire pigs (average weight 50.6 ± 6.5 kg) were divided into two groups: Penetrating Abdominal Trauma (PAT) (n = 8) and Control (n = 4). All surgical procedures were performed under anesthesia with adequate analgesia. In the PAT group, the small and large intestines were punctured, and feces mixed with saline were introduced into the abdominal cavity to induce peritonitis. The Control group received sham surgery with only saline solution. The animals were observed in a conscious state over a period of 72 h, vital parameters were recorded, and blood samples were taken regularly. We adapted a pig-specific SOFA score and developed pig-specific SIRS criteria and NEWS2 score to assess organ function. The model was validated by independent investigators. Results: The survival rate in the PAT group was 75%, with an average survival time of 58.5 h, while all animals in the Control group survived to euthanasia. Monitoring showed pathophysiological changes, such as tachycardia, leucopenia, and thrombocytopenia, indicative of sepsis and organ dysfunction. Blinded investigators independently confirmed the model’s validity. Conclusions: A new swine model of penetrating abdominal trauma and sepsis has been successfully developed that demonstrates significant physiological and immunologic changes comparable to human sepsis. This new model provides a realistic platform for future research into sepsis, its diagnostics, and the evaluation of therapeutic strategies.

General & Internal Medicine↗
NASA NTRS1985

Nonlinear acoustic wave propagation in atmosphere

A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗
NASA NTRS1986

Nonlinear acoustic wave propagation in atmosphere

In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗
NASA NTRS1987

Nonlinear acoustic wave propagation in atmosphere TLSP - Final report

In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗
NASA NTRS2005

Modeling for Ultrasonic Health Monitoring of Foams with Embedded Sensors

In this report analytical and numerical methods are proposed to estimate the effective elastic properties of regular and random open-cell foams. The methods are based on the principle of minimum energy and on structural beam models. The analytical solutions are obtained using symbolic processing software. The microstructure of the random foam is simulated using Voronoi tessellation together with a rate-dependent random close-packing algorithm. The statistics of the geometrical properties of random foams corresponding to different packing fractions have been studied. The effects of the packing fraction on elastic properties of the foams have been investigated by decomposing the compliance into bending and axial compliance components. It is shown that the bending compliance increases and the axial compliance decreases when the packing fraction increases. Keywords: Foam; Elastic properties; Finite element; Randomness

Wang, L.↗
DOE OSTI2024

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

A large deformation, coupled finite-element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain-rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one-dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. It was discovered that explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time-stepping schemes for shock-like loadings. Here, shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

Engineering↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

Multiresolution With Super-Compact Wavelets

The solution data computed from large scale simulations are sometimes too big for main memory, for local disks, and possibly even for a remote storage disk, creating tremendous processing time as well as technical difficulties in analyzing the data. The excessive storage demands a corresponding huge penalty in I/O time, rendering time and transmission time between different computer systems. In this paper, a multiresolution scheme is proposed to compress field simulation or experimental data without much loss of important information in the representation. Originally, the wavelet based multiresolution scheme was introduced in image processing, for the purposes of data compression and feature extraction. Unlike photographic image data which has rather simple settings, computational field simulation data needs more careful treatment in applying the multiresolution technique. While the image data sits on a regular spaced grid, the simulation data usually resides on a structured curvilinear grid or unstructured grid. In addition to the irregularity in grid spacing, the other difficulty is that the solutions consist of vectors instead of scalar values. The data characteristics demand more restrictive conditions. In general, the photographic images have very little inherent smoothness with discontinuities almost everywhere. On the other hand, the numerical solutions have smoothness almost everywhere and discontinuities in local areas (shock, vortices, and shear layers). The wavelet bases should be amenable to the solution of the problem at hand and applicable to constraints such as numerical accuracy and boundary conditions. In choosing a suitable wavelet basis for simulation data among a variety of wavelet families, the supercompact wavelets designed by Beam and Warming provide one of the most effective multiresolution schemes. Supercompact multi-wavelets retain the compactness of Haar wavelets, are piecewise polynomial and orthogonal, and can have arbitrary order of approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.

Lee, Dohyung↗
NASA NTRS2017

Electric Field Conjugation in the Presence of Model Uncertainty

The Wide-Field Infrared Survey Telescope (WFIRST) is a 2.4-meter-diameter space telescope NASA program. The payload will include a coronagraph instrument (CGI). The CGI designs under development use deformable mirrors (DM) to create a point spread function (PSF) with a dark region around the obscured star object. Electric field conjugation (EFC) is an iterative nonlinear optimization procedure that uses measurements of the electric field at the image to determine the DM displacements to modify the PSF to create the region of high contrast in the image. EFC requires a numerical model of the coronagraph to calculate the Jacobian of the system, which is used, along with regularization, to solve for the DM displacements for each iteration of the nonlinear optimization. Ideally, the coronagraph is aligned and calibrated, and the calibration data are used in the numerical model for calculating the Jacobian. However, calibration and alignment measurements always contain uncertainty resulting in calibration error. Therefore, the Jacobian calculated from the numerical model is not an exact representation of the physical coronagraph, and the resulting DM solution for an EFC iteration does not have the exact impact on the electric field of the coronagraph as predicted by the EFC. The result is slow convergence, and, as will be shown, drives the use of more restrictive regularization. Using Monte Carlo trials, we investigate the effect of calibration error on EFC convergence and regulatization. Comparison to results from the High Contrast Imaging Testbed Hybrid Lyot Coronagraph are also presented.

Marx, David↗
NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, Dimitri J.↗
NASA NTRS1990

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗
DOE OSTI2026

Satellite-based Investigation of Power-Line Vegetation Encroachment in the US (SILVANUS)

Rapid wide-area assessments of vegetation encroachment on transmission and distribution line rights-of-way (ROW) is a highly desirable capability for understanding risks to the power grid during severe weather and wildfire events. Conventional assessments are time-consuming and expensive due to the need for in-situ inspections and the use of aerial assets. Performing conventional assessments on a wide area would require immense resources and time that might not be available within the horizon of an expected adverse event. Developing a capability to accurately assess vegetation encroachment into ROWs will enable faster analysis of potential grid vulnerabilities in NAERM. This project sought to develop a prototype capability for rapid ROW vegetation encroachment assessments by using Puerto Rico as a test case. Puerto Rico is a heavily forested island territory frequently impacted by tropical cyclones that threaten the electric grid by downing trees across transmission and distribution lines. Multispectral satellite imagery (MSI) enable very high resolution (i.e., 0.5 - 2 meter) assessment of vegetation conditions at scale and with revisit times appropriate for regular monitoring (e.g., weekly to quarterly, depending on cloud cover) of the entire island. Synthetic aperture radar (SAR) data from satellites was also investigated as solution to the cloud-cover issue as they are active sensors that emit and receive a microwave signal rather than relying on solar illumination, and are therefore unaffected by cloud cover and can collect data during day or night. Finally, MSI-derived digital surface models (DSMs) map the height of objects relative to sea level, and were assessed for their ability to estimate the height of forest canopies relative to coincident transmission lines. The results of the mapping investigation are described in this report.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1978

Sound propagation in a duct of periodic wall structure

A boundary condition, which accounts for the coupling in the sections behind the duct boundary, is given for the sound-absorbing duct with a periodic structure of the wall lining and using regular partition walls. The soundfield in the duct is suitably described by the method of differences. For locally active walls this renders an explicit approximate solution for the propagation constant. Coupling may be accounted for by the method of differences in a clear manner. Numerical results agree with measurements and yield information which has technical applications.

Kurze, U.↗
NASA NTRS1978

A double shooting scheme for certain unstable and singular boundary value problems

A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.

Bayliss, A.↗
NASA NTRS1982

A variational approach to the study of capillary phenomena

The problem of determining the free surface of a liquid in a capillary tube, and of a liquid drop, sitting first on a horizontal plane and then on more general surfaces is considered. With some modifications, the method applies to the study of pendent drops and of rotating drops as well. The standard capillary problem, i.e. the determination of the free surface of a liquid in a thin tube of general cross section, which resuls from the simultaneous action of surface tension, boundary adhesion and gravity is discussed. It turns out that in this case the existence of the solution surface depends heavily on the validity of a simple geometric condition about the mean curvature of the boundary curve of the cross section of the capillary tube. Some particular examples of physical interest are also be discussed. Liquid drops sitting on or hanging from a fixed horizontal plane are discussed. The symmetry of the solutions (which can actually be proved, as consequence of a general symmetrization argument) now plays the chief role in deriving both the existence and the regularity of energy-minimizing configurations. When symmetry fails (this is the case, for example, when the contact angle between the drop and the plate is not constant, or when the supporting surface is not itself symmetric), then more sophisticated methods must be used. Extensions in this direction are outlined.

Emmer, M.↗