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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Perfectly Matched Layers and Characteristic Boundaries in Lattice Boltzmann: Accuracy vs Cost

Artificial boundary conditions (BCs) play a ubiquitous role in numerical simulations of transport phenomena in several diverse fields, such as fluid dynamics, electromagnetism, acoustics, geophysics, and many more. They are essential for accurately capturing the behavior of physical systems whenever the simulation domain is truncated for computational efficiency purposes. Ideally, an artificial BC would allow relevant information to enter or leave the computational domain without introducing artifacts or unphysical effects. Boundary conditions designed to control spurious wave reflections are referred to as nonreflective boundary conditions (NRBCs). Another approach is given by the perfectly matched layers (PMLs), in which the computational domain is extended with multiple dampening layers, where outgoing waves are absorbed exponentially in time. Here, in this work, the definition of PML is revised in the context of the lattice Boltzmann method. The impact of adopting different types of BCs at the edge of the dampening zone is evaluated and compared, in terms of both accuracy and computational costs. It is shown that for sufficiently large buffer zones, PMLs allow stable and accurate simulations even when using a simple zeroth-order extrapolation BC. Moreover, employing PMLs in combination with NRBCs potentially offers significant gains in accuracy at a modest computational overhead, provided the parameters of the BC are properly tuned to match the properties of the underlying fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gaussian process regression constrained by boundary value problems

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

42 ENGINEERING↗
NASA NTRS2006

An Energetic Concept of Habitability for the Deep Subsurface

Universally, life must be characterized by a characteristic level of order and complexity. In the most general sense, habitability could then be defined as the set of factors required to allow the creation and maintenance of molecular complexity. These factors are: chemical raw materials; energy with which to assemble those materials into complex molecules and sustain the resultant state of complexity; a solvent that allows the interaction of complex molecules, promotes tertiary structure, and permits compartmentalization; and environmental conditions that permit the assembly and maintenance of complex molecules. On Earth, these general requirements correspond to the major biogenic elements C, H, O, N, P, S; chemical or light energy; the solvent water; and specific ranges of temperature, pH, radiation, ionic strength, and so forth, which have thus far been determined on and exclusively empirical basis. Importantly, while the complete absence of any of these factors ensures uninhabitable conditions, the mere presence of all four does not guarantee habitability. In each case - even that of water - it is a question of degree. This question can be couched in quantitative terms by considering the impact of each of these factors on cellular energy balance. More "extreme" conditions (e.g., high temperature, high or low pH, etc.), lower water activity, and low concentrations of nutrients incur or have potential to be addressed by increased investment of energy on the part of the cell. This must be balanced by energy conservation in the cell, noting that biochemical, mass transport, and abiotic chemical limitations intervene between environmental energy availability and biological energy capture. Similarly, lower boundary conditions are emplaced on useful environmental energy yields by the "quantized" nature of biological energy conservation, and upper boundary conditions are emplaced by energy levels or fluxes that are destructive with respect to complexity. This energetic framework, with boundary conditions supplied by the specifics of the biochemistry in question, offers a generalized, yet quantitative means of assessing the habitability of any system with respect to complex life.

Hoehler, Tori M.↗
NASA NTRS2004

Deformations of Flat Unsymmetric Laminates Subjected to Inplane Loads

The geometrically nonlinear deformation response of initially flat unsymmetric cross-ply laminates subjected to an inplane compressive load and two sets of boundary conditions is studied. Stability of the deformations is considered. At issue is whether or not the plate remains flat with increased compressive loading, and whether it buckles. A semi-infinite unsymmetric cross-ply laminate is used to show the combined effects of geometric nonlinearities and bending-stretch coupling. Finite element results for finite laminates are then presented, and it is shown that to a large degree the boundary conditions control the character of the deformation response. It appears that clamped boundary conditions support buckling behavior, in the classic sense of bifurcation, whereas simply-supported conditions do not.

Hyer, Michael W.↗
DOE OSTI2022

Bulk and boundary quantum phase transitions in a square Rydberg atom array

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Evaluation of PS 212 Coatings Under Boundary Lubrication Conditions with an Ester-based Oil to 300 C

High friction and wear of turbine engine components occur during high temperature excursions above the oxidation threshold of the liquid lubricant. This paper reports on research to study the use of a high temperature self lubricating coating, PS 212 for back-up lubrication in the event of failure of the liquid lubricant. Pin on disk tests were performed under dry and boundary-lubricated conditions at disk temperatures up to 300 C. The liquid lubricant was a formulated polyol ester qualified under MIL L-23699. At test temperatures above the oil's thermal degradation level, the use of PS 212 reduced wear, providing a back-up lubricant effect.

Sliney, Harold E.↗
NASA NTRS1984

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗
NASA NTRS1977

Turbulent plane Couette flow using probability distribution functions

A numerical scheme employing a combination of the discrete ordinate method and finite differences is developed for solving the one-dimensional form of Lundgren's (1967) model equation for turbulent plane Couette flow. The approach used requires no a priori assumption about the form of the turbulent distribution function, and the numerical solution is obtained directly from the governing differential equations. Two different types of boundary conditions (zero-gradient and Chapman-Enskog) for the distribution function are evaluated by comparing the numerical results with experimental data. It is found that: (1) the present approach gives convergent and stable results over a wide range of Reynolds numbers; (2) Lundgren's equation yields results that compare well with experimental data for mean velocity and skin friction in the case of simple Couette flow; (3) the zero-gradient boundary condition leads to a logarithmic flow profile; and (4) the Chapman-Enskog boundary condition provides very good agreement with experimental data when applied within the near-wall region.

Srinivasan, R.↗
NASA NTRS2000

Description of Panel Method Code ANTARES

Panel method code ANTARES was developed to compute wall interference corrections in a rectangular wind tunnel. The code uses point doublets to represent blockage effects and line doublets to represent lifting effects of a wind tunnel model. Subsonic compressibility effects are modeled by applying the Prandtl-Glauert transformation. The closed wall, open jet, or perforated wall boundary condition may be assigned to a wall panel centroid. The tunnel walls can be represented by using up to 8000 panels. The accuracy of panel method code ANTARES was successfully investigated by comparing solutions for the closed wall and open jet boundary condition with corresponding Method of Images solutions. Fourier transform solutions of a two-dimensional wind tunnel flow field were used to check the application of the perforated wall boundary condition. Studies showed that the accuracy of panel method code ANTARES can be improved by increasing the total number of wall panels in the circumferential direction. It was also shown that the accuracy decreases with increasing free-stream Mach number of the wind tunnel flow field.

Ulbrich, Norbert↗
NASA NTRS2004

The use of NASA GEOS Global Analysis in MM5/WRF Initialization: Current Studies and Future Applications

An effort has been made at NASA/GSFC to use the Goddard Earth Observing system (GEOS) global analysis in generating the initial and boundary conditions for MM5/WRF simulation. This linkage between GEOS global analysis and MM5/WRF models has made possible for a few useful applications. As one of the sample studies, a series of MM5 simulations were conducted to test the sensitivity of initial and boundary conditions to MM5 simulated precipitation over the eastern; USA. Global analyses horn different operational centers (e.g., NCEP, ECMWF, I U ASA/GSFCj were used to provide first guess field and boundary conditions for MM5. Numerical simulations were performed for one- week period over the eastern coast areas of USA. the distribution and quantities of MM5 simulated precipitation were compared. Results will be presented in the workshop. In addition,other applications from recent and future studies will also be addressed.

Pu, Zhao-Xia↗
NASA NTRS1994

Unique determination of solutions to the Burnett equations

Recent success in applying the Burnett equations to the one-dimensional shock-structure problem has raised the issue of whether the full Burnett equations can be used replace the Navier-Stokes equations for solving boundary-value problems in rarefied gasdynamics. As is familiar from the classical rarefied gasdynamics literature, the Burnett equations, if not solved as a successive approximation to the Navier-Stokes equations for a small Knudsen number, would require more boundary conditions than those in the Navier-Stokes system, owing to the presence of the higher-order derivatives. In this paper, this issue is examined with concrete solution examples for the steady Couette flows, addressing specifically whether solutions to the full Burnett equations can be uniquely determined without adding more boundary conditions than those in the Navier-Stokes system. The analysis, supported by detailed numerical solutions, confirms that additional boundary conditions are needed as long as the Knudsen number is not identically zero, lest the solution to the Burnett equations is not unique.

Lee, C. J.↗
DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗
DOE OSTI2021

Upscaling Reactive Transport and Clogging in Shale Microcracks by Deep Learning

Fracture networks in shales exhibit multiscale features. A rock system may contain a few main fractures and thousands of microcracks, whose length and aperture are orders of magnitude smaller than the former. It is computationally prohibitive to resolve all the fractures explicitly for such multiscale fracture networks. One traditional approach is to model the small-scale features (e.g., microcracks in shales) as an effective medium. Although this fracture-matrix conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately upscaled by effective medium approximations, e.g., microcrack clogging during mineral reactions. Here, we employ deep learning in place of effective medium theory to upscale physical processes in small-scale features. Specifically, we consider reactive transport in a fracture-microcrack network where microcracks can be clogged by precipitation. A deep learning multiscale algorithm is developed, in which the microcracks are upscaled as a wall boundary condition of the main fractures. The wall boundary condition is constructed by recurrent neural networks, which take concentration histories as input and predict the solute transport from main fractures to microcracks. The deep learning multiscale algorithm is firstly employed in specific scenarios, then a general model is developed which can work under various conditions. The new approach is validated against fully resolved simulations and an analytical solution, providing a reliable and efficient solution for problems that cannot be upscaled by effective medium models.

58 GEOSCIENCES↗
NASA NTRS1978

Residual-flexibility corrections for transient modal rotordynamic models

A modal residual-flexibility approach due to Schwendler and MacNeal (1962) is adapted to account for the 'static' contribution of higher-frequency modes without requiring their integration. It is assumed that each rotor mode acts as a lightly damped second-order system. The additional accuracy provided by residual-flexibility corrections becomes progressively more important as a modal model's actual boundary conditions are forced to deviate from the boundary conditions used to define the rotor's original structural model (stiffness matrix) and its associated eigendata input to the transient modal model. An analysis of the high-pressure-oxygen turbopump of the Space Shuttle main engine shows that the residual-flexibility approach ensures a substantial improvement in accuracy for a relatively moderate increase in computer-time requirements.

Childs, D. W.↗
NASA NTRS1983

A preconditioned formulation of the Cauchy-Riemann equations

A preconditioning of the Cauchy-Riemann equations which results in a second-order system is described. This system is shown to have a unique solution if the boundary conditions are chosen carefully. This choice of boundary condition enables the solution of the first-order system to be retrieved. A numerical solution of the preconditioned equations is obtained by the multigrid method.

Phillips, T. N.↗
NASA NTRS1991

Time-domain finite elements in optimal control with application to launch-vehicle guidance

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

Bless, Robert R.↗
NASA NTRS1992

Late quaternary time series of Arabian Sea productivity: Global and regional signals

Modern annual floral and faunal production in the northwest Arabian Sea derives primarily from upwelling induced by strong southwest winds during June, July, and August. Indian Ocean summer monsoon winds are, in turn, driven by differential heating between the Asian continent and the Indian ocean to the south. This differential heating produces a strong pressure gradient resulting in southwest monsoon winds and both coastal and divergent upwelling off the Arabian Peninsula. Over geologic time scales (10(exp 4) to 10(exp 6) years), monsoon wind strength is sensitive to changes in boundary conditions which influence this pressure gradient. Important boundary conditions include the seasonal distribution of solar radiation, global ice volume, Indian Ocean sea surface temperature, and the elevation and albedo of the Asian continent. To the extent that these factors influence monsoon wind strength, they also influence upwelling and productivity. In addition, however, productivity associated with upwelling can be decoupled from the strength of the summer monsoon winds via ocean mechanisms which serve to inhibit or enhance the nutrient supply in the intermediate waters of the Indian Ocean, the source for upwelled waters in the Arabian Sea. To differentiate productivity associated with wind-induced upwelling from that associated with other components of the system such as nutrient sequestering in glacial-age deep waters, we employ a strategy which monitors independent components of the oceanic and atmospheric subsystems. Using sediment records from the Owen Ridge, northwest Arabian Sea, we monitor the strength of upwelling and productivity using two independent indicators, percent G. bulloides and opal accumulation. We monitor the strength of southwest monsoon winds by measuring the grain-size of lithogenic dust particles blown into the Arabian Sea from the surrounding deserts of the Somali and Arabian Peninsulas. Our current hypothesis is that the variability associated with the 41 kyr power in the G. bulloides and opal accumulation records derive from nutrient availability in the intermediate waters which are upwelled via monsoon winds. This hypothesis is testable by comparison with Cd records of intermediate and deep waters of the Atlantic and Indian Ocean.

Clemens, Steven C.↗