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Results for “boundary value problem”

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 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch

The evolution of magnetic energy, helicity, and hybrid helicity during nonlinear relaxation of a driven-damped plasma pinch is compared in visco-resistive magnetohydrodynamics and two-fluid models with and without the ion gyroviscous stress tensor. Magnetic energy and helicity are supplied via a boundary electric field which initially balances the resistive dissipation, and the plasma undergoes multiple relaxation events during the nonlinear evolution. The magnetic helicity is well conserved relative to the magnetic energy over each event, which is short compared with the global resistive diffusion time. The magnetic energy decreases by roughly 1.5% of its initial value over a relaxation event, while the magnetic helicity changes by at most 0.2% of the initial value. The hybrid helicity is dominated by magnetic helicity in low-β pinch conditions and is also well conserved. Differences of less than 1% between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution. The cross helicity is found to change appreciably due to the first-order finite Larmor radius effects which have not been included in contemporary relaxation theories. The plasma current evolves towards the flat parallel current state predicted by Taylor relaxation theory but does not achieve it. Plasma flow develops significant structure for two-fluid models, and the flow perpendicular to the magnetic field is much more substantial than the flow along it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Structure of cyano-anion ionic liquids: X-ray scattering and simulations

Ionic liquids with cyano anions have long been used because of their unique combination of low-melting temperatures, reduced viscosities, and increased conductivities. Recently we showed that cyano anions in ionic liquids are particularly interesting for their potential use as electron donors to excited state photo-acceptors [B. Wu et al., J. Phys. Chem. B 119, 14790–14799 (2015)]. Here we report on bulk structural and quantum mechanical results for a series of ionic liquids based on the 1-ethyl-3-methylimidazolium cation, paired with the following five cyano anions: SeCN - , SCN - , N(CN) $-\atop{2}$ , C(CN) $-\atop{3}$ , and B(CN) $-\atop{4}$ . By combining molecular dynamics simulations, high-energy X-ray scattering measurements, and periodic boundary condition DFT calculations, we are able to obtain a comprehensive description of the liquid landscape as well as the nature of the HOMO-LUMO states for these ionic liquids in the condensed phase. Features in the structure functions for these ionic liquids are somewhat different than the commonly observed adjacency, charge-charge, and polarity peaks, especially for the bulkiest B(CN) $-\atop{4}$ anion. While the other four cyano-anion ionic liquids present an anionic HOMO, the one for Im $+\atop{2,1}$ /B(CN) $-\atop{4}$ is cationic.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Plasma electron hole kinematics. II. Hole tracking Particle-In-Cell simulation

The kinematics of a 1-D electron hole is studied using a novel Particle-In-Cell simulation code. A hole tracking technique enables us to follow the trajectory of a fast-moving solitary hole and study quantitatively hole acceleration and coupling to ions. We observe a transient at the initial stage of hole formation when the hole accelerates to several times the cold-ion sound speed. Artificially imposing slow ion speed changes on a fully formed hole causes its velocity to change even when the ion stream speed in the hole frame greatly exceeds the ion thermal speed, so there are no reflected ions. The behavior that we observe in numerical simulations agrees very well with our analytic theory of hole momentum conservation and the effects of “jetting.”.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Real-space pseudopotential method for computing the vibrational Stark effect

The vibrational Stark shift is an important effect in determining the electrostatic environment for molecular or condensed matter systems. However, accurate ab initio calculations of the vibrational Stark effect are a technically demanding challenge. In this paper, we make use of density functional theory constructed on a real-space grid to expedite the computation of this effect. Our format is especially advantageous for the investigation of small molecules in finite fields as cluster boundary conditions eliminate spurious supercell interactions and allow for charged systems, while convergence is controlled by a single parameter, the grid spacing. The Stark tuning rate is highly sensitive to the interaction between anharmonicity in a vibrational mode and the applied field. To ensure this subtle interaction is fully captured, we apply three parallel approaches: a direct finite field, a perturbative method, and a molecular dynamics method. Finally, we illustrate this method by applying it to several small molecules containing C–O and C–N bonds and show that a consistent result can be obtained.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Assessment of Horizontal External Stresses in the Vorkuta Mine Field Using Seismic Tomography Data

3D geomechanical model of the Vorkuta Mine, Pechora Coal Basin, has been developed and implemented numerically. By the data on dynamic events recorded by stationary seismic stations, tomography of the study object is performed, and velocity of elastic waves is recovered in the illuminated area of the object. The boundary value inverse problem on horizontal external stresses by stress distribution found using empirical relations between elastic wave velocities and stresses determined in the laboratoryscale experiments is formulated and solved.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2015

Fractional diffusion on bounded domains

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

University of Miami Coupled Model (UMCM) for Hurricanes Ike and Sandy

The University of Miami Coupled Model (UMCM) is a coupled model that integrates atmospheric, wave, and ocean components to produce wind, wave, and current data. Atmospheric data is produced using the [Weather Research and Forecasting model](https://www.mmm.ucar.edu/weather-research-and-forecasting-model) (WRF), Wave data is produced using the [University of Miami Wave Model](https://umwm.org/) (UMWM), While ocean current data is produced using the [HYbrid Coordinate Ocean Model](https://www.hycom.org/) (HYCOM). The time resolution for each model run is as follows: Hurricane Ike -> 1 sample/hour from 9/8/2008 12:00:00 UTC to 9/12/2008 6:00:00 UTC -> 1 sample/10 minutes from 9/12/2008 6:00:00 UTC to 9/13/2008 9:00:00 UTC Hurricane Sandy -> 1 sample/10 minutes from 10/28/2012 00:10:00 UTC to 10/31/2012 00:00:00 UTC

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