NASA Astrophysics Data System (ADS)
Yaghjian, A. D.; Silveirinha, M. G.
2016-08-01
Electric quadrupolar continua satisfying a physically reasonable constitutive relation supports both an evanescent and a propagating eigenmode. Thus, three interface boundary conditions, two plus an "additional boundary condition" (ABC), are required to obtain a unique solution to a plane wave incident from free space upon an electric quadrupolar half-space. By generalizing the constitutive relation to hold within the transition layer between the free space and the quadrupolar continuum, we derive these three boundary conditions directly from Maxwell's differential equations. The three boundary conditions are used to determine the unique solution to the boundary value problem of an electric quadrupolar slab. Numerical computations show that for long wavelengths, two previous boundary conditions, derived under the assumption that the electric quadrupolarization contains negligible effective delta functions in the transition layer, produce an accurate solution by neglecting the evanescent eigenmode, that is, by assuming it decays within the transition layer. It appears that the general method used to derive the electric quadrupolar ABC can be applied to obtain the boundary conditions for any other realizable constitutive relation in a Maxwellian multipole continuum.
Reduced Need of Lubricity Additives in Soybean Oil Blends Under Boundary Lubrication Conditions
Technology Transfer Automated Retrieval System (TEKTRAN)
Converging prices of vegetable oils and petroleum, along with increased focus on renewable resources, gave more momentum to vegetable oil lubricants. Boundary lubrication properties of four Extreme Pressure (EP) additive blends in conventional Soy Bean Oil (SBO) and Paraffinic Mineral Oil (PMO) of ...
Magnetohydrodynamic Characteristic Boundary Conditions
NASA Astrophysics Data System (ADS)
Schaffenberger, Werner; Stein, R.
2009-05-01
We implemented MHD characteristic boundary conditions for a non-ideal plasma in the "stagger-code" (Gudiksen and Nordlund, 2005, ApJ 618, 1020). The aim of these boundary conditions is to reduce reflection at the boundaries which is important for the simulation of wave propagation. We present some test simulations of propagating waves demonstrating the capability of these boundary conditions.
Zhang, Ying-Ying; An, Sheng-Bai; Song, Yuan-Hong Wang, You-Nian; Kang, Naijing; Mišković, Z. L.
2014-10-15
We study the wake effect in the induced potential and the stopping power due to plasmon excitation in a metal slab by a point charge moving inside the slab. Nonlocal effects in the response of the electron gas in the metal are described by a quantum hydrodynamic model, where the equation of electronic motion contains both a quantum pressure term and a gradient correction from the Bohm quantum potential, resulting in a fourth-order differential equation for the perturbed electron density. Thus, besides using the condition that the normal component of the electron velocity should vanish at the impenetrable boundary of the metal, a consistent inclusion of the gradient correction is shown to introduce two possibilities for an additional boundary condition for the perturbed electron density. We show that using two different sets of boundary conditions only gives rise to differences in the wake potential at large distances behind the charged particle. On the other hand, the gradient correction in the quantum hydrodynamic model is seen to cause a reduction in the depth of the potential well closest to the particle, and a reduction of its stopping power. Even for a particle moving in the center of the slab, we observe nonlocal effects in the induced potential and the stopping power due to reduction of the slab thickness, which arise from the gradient correction in the quantum hydrodynamic model.
Numerical Boundary Condition Procedures
NASA Technical Reports Server (NTRS)
1981-01-01
Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.
Downstream boundary conditions for viscous flow problems
NASA Technical Reports Server (NTRS)
Fix, G.; Gunzburger, M.
1977-01-01
The problem of the specification of artificial outflow conditions in flow problems is studied. It is shown that for transport type equations incorrect outflow conditions will adversely affect the solution only in a small region near the outflow boundary, while for elliptic equations, e.g. those governing the streamfunction or pressure, a correct boundary specification is essential. In addition, integral outflow boundary conditions for fluid dynamical problems are considered. It is shown that such conditions are well posed, and their effect on the solutions of the Navier-Stokes equations is also considered.
Unified slip boundary condition for fluid flows.
Thalakkottor, Joseph John; Mohseni, Kamran
2016-08-01
Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems. PMID:27627398
Unified slip boundary condition for fluid flows
NASA Astrophysics Data System (ADS)
Thalakkottor, Joseph John; Mohseni, Kamran
2016-08-01
Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems.
Boundary Condition for Modeling Semiconductor Nanostructures
NASA Technical Reports Server (NTRS)
Lee, Seungwon; Oyafuso, Fabiano; von Allmen, Paul; Klimeck, Gerhard
2006-01-01
A recently proposed boundary condition for atomistic computational modeling of semiconductor nanostructures (particularly, quantum dots) is an improved alternative to two prior such boundary conditions. As explained, this boundary condition helps to reduce the amount of computation while maintaining accuracy.
Tidal Boundary Conditions in SEAWAT
Mulligan, Ann E.; Langevin, Christian; Post, Vincent E.A.
2011-01-01
SEAWAT, a U.S. Geological Survey groundwater flow and transport code, is increasingly used to model the effects of tidal motion on coastal aquifers. Different options are available to simulate tidal boundaries but no guidelines exist nor have comparisons been made to identify the most effective approach. We test seven methods to simulate a sloping beach and a tidal flat. The ocean is represented in one of the three ways: directly using a high hydraulic conductivity (high-K) zone and indirect simulation via specified head boundaries using either the General Head Boundary (GHB) or the new Periodic Boundary Condition (PBC) package. All beach models simulate similar water fluxes across the upland boundary and across the sediment-water interface although the ratio of intertidal to subtidal flow is different at low tide. Simulating a seepage face results in larger intertidal fluxes and influences near-shore heads and salinity. Major differences in flow occur in the tidal flat simulations. Because SEAWAT does not simulate unsaturated flow the water table only rises via flow through the saturated zone. This results in delayed propagation of the rising tidal signal inland. Inundation of the tidal flat is delayed as is flow into the aquifer across the flat. This is severe in the high-K and PBC models but mild in the GHB models. Results indicate that any of the tidal boundary options are fine if the ocean-aquifer interface is steep. However, as the slope of that interface decreases, the high-K and PBC approaches perform poorly and the GHB boundary is preferable.
Tidal boundary conditions in SEAWAT.
Mulligan, Ann E; Langevin, Christian; Post, Vincent E A
2011-01-01
SEAWAT, a U.S. Geological Survey groundwater flow and transport code, is increasingly used to model the effects of tidal motion on coastal aquifers. Different options are available to simulate tidal boundaries but no guidelines exist nor have comparisons been made to identify the most effective approach. We test seven methods to simulate a sloping beach and a tidal flat. The ocean is represented in one of the three ways: directly using a high hydraulic conductivity (high-K) zone and indirect simulation via specified head boundaries using either the General Head Boundary (GHB) or the new Periodic Boundary Condition (PBC) package. All beach models simulate similar water fluxes across the upland boundary and across the sediment-water interface although the ratio of intertidal to subtidal flow is different at low tide. Simulating a seepage face results in larger intertidal fluxes and influences near-shore heads and salinity. Major differences in flow occur in the tidal flat simulations. Because SEAWAT does not simulate unsaturated flow the water table only rises via flow through the saturated zone. This results in delayed propagation of the rising tidal signal inland. Inundation of the tidal flat is delayed as is flow into the aquifer across the flat. This is severe in the high-K and PBC models but mild in the GHB models. Results indicate that any of the tidal boundary options are fine if the ocean-aquifer interface is steep. However, as the slope of that interface decreases, the high-K and PBC approaches perform poorly and the GHB boundary is preferable.
Solitons induced by boundary conditions
Zhou, R.L.
1987-01-01
Although soliton phenomena have attracted wide attention since 1965, there are still not enough efforts paid to mixed-boundary - initial-value problems that are important in real physical cases. The main purpose of this thesis is to study carefully the various boundary-induced soliton under different initial conditions. The author states with three sets of nonlinear equations: KdV equations and Boussinesq equations (for water); two-fluid equations for cold-ion plasma. He was interested in four types of problems involved with water solitons: excitation by different time-dependent boundary conditions under different initial conditions; head-on and over-taking collisions; reflection at a wall and the excitation by pure initial conditions. For KdV equations, only cases one and four are conducted. The results from two fully nonlinear KdV and Boussinesq equations are compared, and agree extremely well. The Boussinesq equations permit solition head-on collisions and reflections, studied the first time. The results from take-over collision agree with KdV results. For the ion-acoustic plasma, a set of Boussinesq-type equations was derived from the standard two-fluid equations for the ion-acoustic plasma. It theoretically proves the essential nature of the solitary wave solutions of the cold-ion plasma. The ion acoustic solitons are also obtained by prescribing a potential phi/sub 0/ at one grid point.
Mean Flow Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Nallasamy, M.; Sawyer, S.; Dyson, R.
2003-01-01
In this work, a new type of boundary condition for time-accurate Computational Aeroacoustics solvers is described. This boundary condition is designed to complement the existing nonreflective boundary conditions while ensuring that the correct mean flow conditions are maintained throughout the flow calculation. Results are shown for a loaded 2D cascade, started with various initial conditions.
Boundary Conditions of the Heliosphere
NASA Technical Reports Server (NTRS)
Slavin, Jonathan D.; Frisch, Priscilla C .
2001-01-01
We present new calculations of the ionization of the Local Interstellar Cloud (LIC) by directly observed sources including nearby stellar extreme ultraviolet (EUV) sources and the diffuse emission of the Soft X-ray Background (SXRB). In addition, we model the important, unobserved EUV emission both from the hot gas responsible for the SXRB and from a possible evaporative boundary between the LIC and the hot gas. We show that these ionization sources can provide the necessary ionization and heating of the cloud to match observations. Including the radiation from the conductive boundary, while not required, does improve the agreement with observations of the temperature of the LIC. The ionization predicted in our models shows good agreement with pickup ion results, interstellar absorption line data towards epsilon CMa, and EUV opacity measurements of nearby white dwarf stars. The areas of disagreement point to a possible underabundance (relative to solar abundance) of neon in the LIC. The presence of dust in the cloud, or at least depleted abundances, is necessary to maintain the heating/cooling balance and reach the observed temperature.
Low density gas dynamic wall boundary conditions
NASA Technical Reports Server (NTRS)
Collins, F. G.
1986-01-01
Low density nozzles or large expansion ratio nozzles used in space experience rarefaction effects near their exit in the form of velocity slip and temperature jump at the walls. In addition, the boundary layers become very thick and there is a very strong viscous/inviscid interaction. For these reasons no existing design technique has been found to accurately predict the nozzle flow properties up to the nozzle exit. The objective of this investigation was to examine the slip boundary conditions and formulate them in a form appropriate for use with a full Navier-Stokes numerical code. The viscous/inviscid interaction would automatically be accounted for by using a compressible Navier-Stokes code. Through examination of the interaction of molecules with solid surfaces, a model for the distribution function of the reflected molecules has been determined and this distribution function has been used to develop a new slip boundary condition that can be shown to yield more realistic surface boundary conditions.
Boundary conditions of methamphetamine craving.
Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy
2015-12-01
Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so-the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users' route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications.
Logarithmic minimal models with Robin boundary conditions
NASA Astrophysics Data System (ADS)
Bourgine, Jean-Emile; Pearce, Paul A.; Tartaglia, Elena
2016-06-01
We consider general logarithmic minimal models LM≤ft( p,{{p}\\prime}\\right) , with p,{{p}\\prime} coprime, on a strip of N columns with the (r, s) Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. On the lattice, these models are Yang-Baxter integrable loop models that are described algebraically by the one-boundary Temperley-Lieb algebra. The (r, s) Robin boundary conditions are a class of integrable boundary conditions satisfying the boundary Yang-Baxter equations which allow loop segments to either reflect or terminate on the boundary. The associated conformal boundary conditions are organized into infinitely extended Kac tables labelled by the Kac labels r\\in {Z} and s\\in {N} . The Robin vacuum boundary condition, labelled by ≤ft(r,s-\\frac{1}{2}\\right)=≤ft(0,\\frac{1}{2}\\right) , is given as a linear combination of Neumann and Dirichlet boundary conditions. The general (r, s) Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an (r, s)-type seam consisting of an r-type seam of width w columns and an s-type seam of width d = s - 1 columns. The r-type seam admits an arbitrary boundary field which we fix to the special value ξ =-\\fracλ{2} where λ =\\frac≤ft( {{p}\\prime}-p\\right)π{{{p}\\prime}} is the crossing parameter. The s-type boundary introduces d defects into the bulk. We consider the commuting double-row transfer matrices and their associated quantum Hamiltonians and calculate analytically the boundary free energies of the (r, s) Robin boundary conditions. Using finite-size corrections and sequence extrapolation out to system sizes N+w+d≤slant 26 , the conformal spectrum of boundary operators is accessible by numerical diagonalization of the Hamiltonians. Fixing the parity of N for r\
Charge regulation: A generalized boundary condition?
NASA Astrophysics Data System (ADS)
Markovich, Tomer; Andelman, David; Podgornik, Rudi
2016-01-01
The three most commonly used boundary conditions for charged colloidal systems are constant charge (insulator), constant potential (conducting electrode) and charge regulation (ionizable groups at the surface). It is usually believed that the charge regulation is a generalized boundary condition that reduces in some specific limits to either constant-charge or constant-potential boundary conditions. By computing the disjoining pressure between two symmetric planes for these three boundary conditions, both numerically (for all inter-plate separations) and analytically (for small inter-plate separations), we show that this is not, in general, the case. In fact, the limit of charge regulation is a separate boundary condition, yielding a disjoining pressure with a different characteristic separation scaling. Our findings are supported by several examples demonstrating that the disjoining pressure at small separations for the charge regulation boundary condition depends on the details of the dissociation/association process.
Boundary conditions for viscous vortex methods
Koumoutsakos, P.; Leonard, A.; Pepin, F. )
1994-07-01
This paper presents a Neumann-type vorticity boundary condition for the vorticity formulation of the Navier-Stokes equations. The vorticity creation process at the boundary, due to the no-slip condition, is expressed in terms of a vorticity flux. The scheme is incorporated then into a Lagrangian vortex blob method that uses a particle strength exchange algorithm for viscous diffusion. The no-slip condition is not enforced by the generation of new vortices at the boundary but instead by modifying the strength of the vortices in the vicinity of the boundary. 19 refs., 5 figs.
Evaluation of Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.
1995-01-01
The performance of three boundary conditions for aeroacoustics were investigated, namely, (1) Giles-1990; (2) Tam and Webb-1993, and (3) Thompson-1987. For each boundary condition, various implementations were tested to study the sensitivity of their performance to the implementation procedure. Details of all implementations are given. Results are shown for the acoustic field of a monopole in a uniform freestream.
Boundary conditions for the subdiffusion equation
Shkilev, V. P.
2013-04-15
The boundary conditions for the subdiffusion equations are formulated using the continuous-time random walk model, as well as several versions of the random walk model on an irregular lattice. It is shown that the boundary conditions for the same equation in different models have different forms, and this difference considerably affects the solutions of this equation.
On boundary conditions in lattice Boltzmann methods
Chen, S.; Martinez, D. |; Mei, R.
1996-09-01
A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two-dimensional Poiseuille flow, unsteady Couette flow, lid-driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed. {copyright} {ital 1996 American Institute of Physics.}
Fluid-solid boundary conditions for multiparticle collision dynamics.
Whitmer, Jonathan K; Luijten, Erik
2010-03-17
The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions
NASA Astrophysics Data System (ADS)
Arthur, Robert; Dorey, Patrick; Parini, Robert
2016-04-01
We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering problem associated with the inverse scattering method. We find that an antikink may be reflected into various combinations of an antikink, a kink, and one or more breathers, depending on the values of the initial antikink velocity and a parameter associated with the boundary condition. In addition we observe regions with an intricate resonance structure arising from the creation of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase.
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.
On High-Order Radiation Boundary Conditions
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1995-01-01
In this paper we develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Pade approximants proposed by Engquist and Majda lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.
Boundary Conditions of the Heliosphere
NASA Technical Reports Server (NTRS)
Frisch, Priscilla C.; Slavin, Jonathan D.; Wagner, William (Technical Monitor)
2003-01-01
As described in the Revised Task Statement for this grant (submitted following the award at a reduced budget), my role in these investigations is to focus on the theoretical calculations relevant to the ionization state and dust content of the Local Cloud that surrounds the Solar System. An important motivation for our investigations is to aid in the interpretation of pick-up ion (PUI) and anomalous cosmic ray (ACR) observations which depends on knowledge of the flux of neutral atoms of various elements into the heliosphere. This flux depends on the ionization and elemental abundances of the gas of the Local Cloud. We have made substantial progress in our program to understand the ionization of the Local Cloud. Our steady state photoionization models are remarkably successful in accounting for the ionization observed both by line of sight (column density) observations towards nearby stars and in situ measurements. By lifting some of the simplifying assumptions in our earlier modeling we hope to make further progress in this understanding. In future work on this project we will continue our exploration of photoionization models, focusing on making sense of the differences between the LIC and the BC. In addition we will explore the effects of altered abundances in the hot gas on the ionization and thermal balance in the LIC.
Boundary conditions for the gravitational field
NASA Astrophysics Data System (ADS)
Winicour, Jeffrey
2012-06-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)
Discretely holomorphic parafermions and integrable boundary conditions
NASA Astrophysics Data System (ADS)
Ikhlef, Yacine
2012-07-01
In two-dimensional statistical models possessing a discretely holomorphic parafermion, we introduce a modified discrete Cauchy-Riemann equation on the boundary of the domain, and we show that the solution of this equation yields integrable boundary Boltzmann weights. This approach is applied to (i) the square-lattice O(n) loop model, where the exact locations of the special and ordinary transitions are recovered, and (ii) the Fateev-Zamolodchikov {Z}_N spin model, where a new rotation-invariant, integrable boundary condition is discovered for generic N.
Velocity boundary conditions at a tokamak resistive wall
Strauss, H. R.
2014-03-15
Velocity boundary conditions appropriate for magnetohydrodynamic simulations have been controversial recently. A comparison of numerical simulations of sideways wall force in disruptions is presented for Dirichlet, Neumann, Robin, and DEBS boundary conditions. It is shown that all the boundary conditions give qualitatively similar results. It is shown that Dirichlet boundary conditions are valid in the small Larmor radius limit of electromagnetic sheath boundary conditions.
Coleman-Gurtin type equations with dynamic boundary conditions
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.; Shomberg, Joseph L.
2015-02-01
We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory. As a special case, we investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of Gal (2012). Additionally, we do not assume that the interior and the boundary share the same memory kernel.
Ambarzumyan's theorem for the quasi-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Kıraç, Alp Arslan
2016-09-01
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators Lt(q) with qin L1[0,1] and quasi-periodic boundary conditions, tin [0,2π ), when there is not any additional condition on the potential q.
Boundary conditions in tunneling via quantum hydrodynamics
NASA Technical Reports Server (NTRS)
Nassar, Antonio B.
1993-01-01
Via the hydrodynamical formulation of quantum mechanics, an approach to the problem of tunneling through sharp-edged potential barriers is developed. Above all, it is shown how more general boundary conditions follow from the continuity of mass, momentum, and energy.
Boundary conditions in Chebyshev and Legendre methods
NASA Technical Reports Server (NTRS)
Canuto, C.
1984-01-01
Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.
Radiation (absorbing) boundary conditions for electromagnetic fields
NASA Astrophysics Data System (ADS)
Bevensee, R. M.; Pennock, S. T.
1987-01-01
An important problem in finite difference or finite element computation of the electromagnetic field obeying the space-time Maxwell equations with self-consistent sources is that of truncating the outer numerical boundaries properly to avoid spurious numerical reflection. Methods for extrapolating properly the fields just beyond a numerical boundary in free space have been treated by a number of workers. This report avoids plane wave assumptions and derives boundary conditions more directly related to the source distribution within the region. The Panofsky-Phillips' relations, which enable one to extrapolate conveniently the vector field components parallel and perpendicular to a radial from the coordinate origin chosen near the center of the charge-current distribution are used to describe the space-time fields.
Boundary Conditions for Unsteady Compressible Flows
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Johnson, D. K.
1994-01-01
This paper explores solutions to the spherically symmetric Euler equations. Motivated by the work of Hagstrom and Hariharan and Geer and Pope, we modeled the effect of a pulsating sphere in a compressible medium. The literature available on this suggests that an accurate numerical solution requires artificial boundary conditions which simulate the propagation of nonlinear waves in open domains. Until recently, the boundary conditions available were in general linear and based on nonreflection. Exceptions to this are the nonlinear nonreflective conditions of Thompson, and the nonlinear reflective conditions of Hagstrom and Hariharan. The former are based on the rate of change of the incoming characteristics; the latter rely on asymptotic analysis and the method of characteristics and account for the coupling of incoming and outgoing characteristics. Furthermore, Hagstrom and Hariharan have shown that, in a test situation in which the flow would reach a steady state over a long time, Thompson's method could lead to an incorrect steady state. The current study considers periodic flows and includes all possible types and techniques of boundary conditions. The technique recommended by Hagstrom and Hariharan proved superior to all others considered and matched the results of asymptotic methods that are valid for low subsonic Mach numbers.
NASA Astrophysics Data System (ADS)
Javili, A.; Saeb, S.; Steinmann, P.
2016-10-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Symmetry boundary condition in dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Pal, Souvik; Lan, Chuanjin; Li, Zhen; Hirleman, E. Daniel; Ma, Yanbao
2015-07-01
Dissipative particle dynamics (DPD) is a coarse-grained particle method for modeling mesoscopic hydrodynamics. Most of the DPD simulations are carried out in 3D requiring remarkable computation time. For symmetric systems, this time can be reduced significantly by simulating only one half or one quarter of the systems. However, such simulations are not yet possible due to a lack of schemes to treat symmetric boundaries in DPD. In this study, we propose a numerical scheme for the implementation of the symmetric boundary condition (SBC) in both dissipative particle dynamics (DPD) and multibody dissipative particle dynamics (MDPD) using a combined ghost particles and specular reflection (CGPSR) method. We validate our scheme in four different configurations. The results demonstrate that our scheme can accurately reproduce the system properties, such as velocity, density and meniscus shapes of a full system with numerical simulations of a subsystem. Using a symmetric boundary condition for one half of the system, we demonstrate about 50% computation time saving in both DPD and MDPD. This approach for symmetric boundary treatment can be also applied to other coarse-grained particle methods such as Brownian and Langevin Dynamics to significantly reduce computation time.
Increasing Accuracy in Computed Inviscid Boundary Conditions
NASA Technical Reports Server (NTRS)
Dyson, Roger
2004-01-01
A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number
Advances in Numerical Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.
1997-01-01
Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.
Open Boundary Conditions for Dissipative MHD
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Some observations on boundary conditions for numerical conservation laws
NASA Technical Reports Server (NTRS)
Kamowitz, David
1988-01-01
Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.
Boundary conditions and consistency of effective theories
Polonyi, Janos; Siwek, Alicja
2010-04-15
Effective theories are nonlocal at the scale of the eliminated heavy particles modes. The gradient expansion, which represents such nonlocality, must be truncated to have treatable models. This step leads to the proliferation of the degrees of freedom, which renders the identification of the states of the effective theory nontrivial. Furthermore, it generates nondefinite metric in the Fock space, which in turn endangers the unitarity of the effective theory. It is shown that imposing a generalized Kubo-Martin-Schwinger boundary conditions for the new degrees of freedom leads to reflection positivity for a wide class of Euclidean effective theories, thereby these lead to acceptable theories when extended to real-time.
42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Health Professions Student Loans § 57.217 Additional conditions. The Secretary may with respect to any agreement entered into...
42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Health Professions Student Loans § 57.217 Additional conditions. The Secretary may with respect to any agreement entered into...
42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Health Professions Student Loans § 57.217 Additional conditions. The Secretary may with respect to any agreement entered into...
42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Health Professions Student Loans § 57.217 Additional conditions. The Secretary may with respect to any agreement entered into...
42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Health Professions Student Loans § 57.217 Additional conditions. The Secretary may with respect to any agreement entered into...
A Robust Absorbing Boundary Condition for Compressible Flows
NASA Technical Reports Server (NTRS)
Loh, Ching Y.; orgenson, Philip C. E.
2005-01-01
An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.
42 CFR 67.22 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 67.22 Section 67.22 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING... Research, Evaluation, Demonstration, and Dissemination Projects § 67.22 Additional conditions....
42 CFR 67.22 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 67.22 Section 67.22 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING... Research, Evaluation, Demonstration, and Dissemination Projects § 67.22 Additional conditions....
42 CFR 67.22 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 67.22 Section 67.22 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING... Research, Evaluation, Demonstration, and Dissemination Projects § 67.22 Additional conditions....
42 CFR 67.22 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 67.22 Section 67.22 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING... Research, Evaluation, Demonstration, and Dissemination Projects § 67.22 Additional conditions....
42 CFR 67.22 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 67.22 Section 67.22 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING... Research, Evaluation, Demonstration, and Dissemination Projects § 67.22 Additional conditions....
42 CFR 52e.9 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 52e.9 Section 52e.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL HEART, LUNG, AND BLOOD INSTITUTE GRANTS FOR PREVENTION AND CONTROL PROJECTS § 52e.9 Additional conditions. The...
42 CFR 66.115 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 66.115 Section 66.115 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL RESEARCH SERVICE AWARDS Direct Awards § 66.115 Additional conditions. The Secretary may...
42 CFR 66.115 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 66.115 Section 66.115 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL RESEARCH SERVICE AWARDS Direct Awards § 66.115 Additional conditions. The Secretary may...
42 CFR 66.115 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 66.115 Section 66.115 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL RESEARCH SERVICE AWARDS Direct Awards § 66.115 Additional conditions. The Secretary may...
42 CFR 52c.8 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52c.8 Section 52c.8 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS MINORITY BIOMEDICAL RESEARCH SUPPORT PROGRAM § 52c.8 Additional conditions. The Secretary may with respect to any grant award...
42 CFR 52c.8 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 52c.8 Section 52c.8 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS MINORITY BIOMEDICAL RESEARCH SUPPORT PROGRAM § 52c.8 Additional conditions. The Secretary may with respect to any grant award...
42 CFR 52c.8 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 52c.8 Section 52c.8 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS MINORITY BIOMEDICAL RESEARCH SUPPORT PROGRAM § 52c.8 Additional conditions. The Secretary may with respect to any grant award...
42 CFR 52c.8 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 52c.8 Section 52c.8 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS MINORITY BIOMEDICAL RESEARCH SUPPORT PROGRAM § 52c.8 Additional conditions. The Secretary may with respect to any grant award...
42 CFR 52c.8 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 52c.8 Section 52c.8 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS MINORITY BIOMEDICAL RESEARCH SUPPORT PROGRAM § 52c.8 Additional conditions. The Secretary may with respect to any grant award...
42 CFR 52e.9 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 52e.9 Section 52e.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL HEART, LUNG, AND BLOOD INSTITUTE GRANTS FOR PREVENTION AND CONTROL PROJECTS § 52e.9 Additional conditions. The...
42 CFR 52e.9 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 52e.9 Section 52e.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL HEART, LUNG, AND BLOOD INSTITUTE GRANTS FOR PREVENTION AND CONTROL PROJECTS § 52e.9 Additional conditions. The...
42 CFR 52e.9 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 52e.9 Section 52e.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL HEART, LUNG, AND BLOOD INSTITUTE GRANTS FOR PREVENTION AND CONTROL PROJECTS § 52e.9 Additional conditions. The...
42 CFR 52e.9 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52e.9 Section 52e.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL HEART, LUNG, AND BLOOD INSTITUTE GRANTS FOR PREVENTION AND CONTROL PROJECTS § 52e.9 Additional conditions. The...
42 CFR 52d.9 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52d.9 Section 52d.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL CANCER INSTITUTE CLINICAL CANCER EDUCATION PROGRAM § 52d.9 Additional conditions. The Director, NCI, may with respect to...
42 CFR 52d.9 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 52d.9 Section 52d.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL CANCER INSTITUTE CLINICAL CANCER EDUCATION PROGRAM § 52d.9 Additional conditions. The Director, NCI, may with respect to...
42 CFR 52d.9 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 52d.9 Section 52d.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL CANCER INSTITUTE CLINICAL CANCER EDUCATION PROGRAM § 52d.9 Additional conditions. The Director, NCI, may with respect to...
42 CFR 52d.9 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 52d.9 Section 52d.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL CANCER INSTITUTE CLINICAL CANCER EDUCATION PROGRAM § 52d.9 Additional conditions. The Director, NCI, may with respect to...
42 CFR 52d.9 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 52d.9 Section 52d.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL CANCER INSTITUTE CLINICAL CANCER EDUCATION PROGRAM § 52d.9 Additional conditions. The Director, NCI, may with respect to...
42 CFR 52a.9 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52a.9 Section 52a.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL INSTITUTES OF HEALTH CENTER GRANTS § 52a.9 Additional conditions. The Director may, with respect to any grant...
42 CFR 52b.13 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 52b.13 Section 52b.13 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL INSTITUTES OF HEALTH CONSTRUCTION GRANTS § 52b.13 Additional conditions. The Director may with respect to any...
42 CFR 52b.13 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52b.13 Section 52b.13 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL INSTITUTES OF HEALTH CONSTRUCTION GRANTS § 52b.13 Additional conditions. The Director may with respect to any...
42 CFR 52a.9 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 52a.9 Section 52a.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL INSTITUTES OF HEALTH CENTER GRANTS § 52a.9 Additional conditions. The Director may, with respect to any grant...
Towards Arbitrary Accuracy Inviscid Surface Boundary Conditions
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Hixon, Ray
2002-01-01
Inviscid nonlinear surface boundary conditions are currently limited to third order accuracy in time for non-moving surfaces and actually reduce to first order in time when the surfaces move. For steady-state calculations it may be possible to achieve higher accuracy in space, but high accuracy in time is required for efficient simulation of multiscale unsteady phenomena. A surprisingly simple technique is shown here that can be used to correct the normal pressure derivatives of the flow at a surface on a Cartesian grid so that arbitrarily high order time accuracy is achieved in idealized cases. This work demonstrates that nonlinear high order time accuracy at a solid surface is possible and desirable, but it also shows that the current practice of only correcting the pressure is inadequate.
Conformal counterterms and boundary conditions for open strings
de Beer, W.
1988-03-15
It is explained how Neumann boundary conditions still lead to the mixed boundary conditions required to calculate the functional determinants in the Polyakov model. Neumann boundary conditions on the conformal factor are obtained, thereby negating the need for a finite counterterm in the quantum bare action.
Multicomponent Gas Diffusion and an Appropriate Momentum Boundary Condition
NASA Technical Reports Server (NTRS)
Noever, David A.
1994-01-01
Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e
42 CFR 52.9 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 52.9 Section 52.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR RESEARCH PROJECTS... conditions are necessary to assure or protect advancement of the approved project, the interests of...
42 CFR 52.9 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 52.9 Section 52.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR RESEARCH PROJECTS... conditions are necessary to assure or protect advancement of the approved project, the interests of...
42 CFR 52.9 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 52.9 Section 52.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR RESEARCH PROJECTS... conditions are necessary to assure or protect advancement of the approved project, the interests of...
42 CFR 52.9 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 52.9 Section 52.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR RESEARCH PROJECTS... conditions are necessary to assure or protect advancement of the approved project, the interests of...
42 CFR 52.9 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52.9 Section 52.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR RESEARCH PROJECTS... conditions are necessary to assure or protect advancement of the approved project, the interests of...
A Smoothed Boundary Condition for Reducing Nonphysical Field Effects
NASA Technical Reports Server (NTRS)
Smith, Arlynn W.; Parks, Joseph W., Jr.; Haralson, Joe N., II; Brennan, Kevin F.
1997-01-01
In this paper, we examine the problem associated with abruptly mixing boundary conditions in the context of a two-dimensional semiconductor device simulator. Explicitly, this paper addresses the transition between an ohmic-type Dirichlet condition and a passivated Neumann boundary. In the traditional setting, the details or the transition between the two boundary types are not addressed and an abrupt transition is assumed. Subsequently, the calculated observables (most notably the potential) exhibit discontinuous derivatives near the surface at the point where the boundary type switches. This paper proposes an alternative condition which models the progression between the two boundary types through the use of a finite length, smoothed boundary whereby the numerical discontinuities are eliminated. The physical and mathematical basis for this smoothed boundary condition is discussed and examples of the technique's implementation given. It is found that the proposed boundary condition is numerically efficient and can be implemented in pre-existing device simulators with relative ease.
Long-time behaviour of absorbing boundary conditions
NASA Technical Reports Server (NTRS)
Engquist, B.; Halpern, L.
1990-01-01
A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.
Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Auriault, Laurent
1996-01-01
It is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance. Impedance is a complex quantity. As such, it is designed primarily for frequency-domain analysis. Time-domain boundary conditions that are the equivalent of the frequency-domain impedance boundary condition are proposed. Both single frequency and model broadband time-domain impedance boundary conditions are provided. It is shown that the proposed boundary conditions, together with the linearized Euler equations, form well-posed initial boundary value problems. Unlike ill-posed problems, they are free from spurious instabilities that would render time-marching computational solutions impossible.
Absorbing boundary conditions for second-order hyperbolic equations
NASA Technical Reports Server (NTRS)
Jiang, Hong; Wong, Yau Shu
1989-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
Lateral boundary conditions for the Klein-Gordon-Fock equation
NASA Astrophysics Data System (ADS)
Tulenov, Kanat S.; Dauitbek, Dostilek
2016-08-01
In this paper we consider an initial-boundary value problem for the Klein-Gordon-Fock equation. We prove the uniqueness of the solution and find lateral boundary conditions for the Klein-Gordon-Fock equation.
NASA Astrophysics Data System (ADS)
Kanguzhin, Baltabek; Tokmagambetov, Niyaz
2016-08-01
In this work, we research a boundary inverse problem of spectral analysis of a differential operator with integral boundary conditions in the functional space L2(0, b) where b < ∞. A uniqueness theorem of the inverse boundary problem in L2(0, b) is proved. Note that a boundary inverse problem of spectral analysis is the problem of recovering boundary conditions of the operator by its spectrum and some additional data.
Evaluation of Boundary-Enhancement Additives for Perfluoropolyethers
NASA Technical Reports Server (NTRS)
Shogrin, Bradley A.; Jones, William R. , Jr.; Herrera-Fierro, Pilar; Lin, Tzuhn-Yuan; Kawa, Hajimu
1996-01-01
Six additives were synthesized and evaluated as boundary lubrication enhancers for perfluoropolyethers. These additives included a phosphonate, a thiophosphonate, a beta-diketone, a benzothiazole, an amide and a sulfite. These additives were evaluated in a vacuum four-ball apparatus, at a one weight percent concentration in a perfluoropolyether based on hexafluoropropene oxide. Tests were performed in vacuum (less than 5.0 x 10(exp 6) Torr), at room temperature (approx. 23 C), at an initial Hertzian stress of 3.5 GPa (200N load), and a sliding velocity of 28.8 mm/sec (100 rpm). Infrared (IR) and Raman spectroscopies were used to analyze the 440 C specimens after testing. Wear rates for each formulation were determined from the slope of wear volume as a function of sliding distance. All additives yielded reductions in mean wear rates of at least 55 percent, with the exception of the benzothiazole which had no effect. Two of the additives, an amide and a sulfite, reduced the mean wear rate by at least 80 percent. IR and Raman analysis indicated the severity of wear can be correlated to the amount of surface fluorinated polymeric acid species (R(sub f)COOH) and amorphous carbon, in and around the wear scar.
42 CFR 86.20 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES OCCUPATIONAL SAFETY AND HEALTH RESEARCH AND RELATED ACTIVITIES GRANTS FOR EDUCATION PROGRAMS IN OCCUPATIONAL SAFETY AND HEALTH Occupational Safety and Health Training Grants § 86.20 Additional conditions. The Secretary may with respect...
42 CFR 68a.15 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 68a.15 Section 68a.15 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTES OF HEALTH (NIH) CLINICAL RESEARCH LOAN REPAYMENT PROGRAM FOR INDIVIDUALS...
42 CFR 68a.15 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 68a.15 Section 68a.15 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTES OF HEALTH (NIH) CLINICAL RESEARCH LOAN REPAYMENT PROGRAM FOR INDIVIDUALS...
42 CFR 68.16 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... NATIONAL INSTITUTES OF HEALTH (NIH) LOAN REPAYMENT PROGRAMS (LRPs) § 68.16 Additional conditions. (a) When a shortage of funds exists, participants may be funded only partially, as determined by the NIH. However, once an NIH LRP contract has been signed by both parties, the NIH will obligate such funds...
42 CFR 68.16 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... NATIONAL INSTITUTES OF HEALTH (NIH) LOAN REPAYMENT PROGRAMS (LRPs) § 68.16 Additional conditions. (a) When a shortage of funds exists, participants may be funded only partially, as determined by the NIH. However, once an NIH LRP contract has been signed by both parties, the NIH will obligate such funds...
42 CFR 68c.15 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 68c.15 Section 68c.15 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF CHILD HEALTH AND HUMAN DEVELOPMENT CONTRACEPTION AND INFERTILITY RESEARCH...
42 CFR 68c.15 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 68c.15 Section 68c.15 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF CHILD HEALTH AND HUMAN DEVELOPMENT CONTRACEPTION AND INFERTILITY RESEARCH...
42 CFR 68c.15 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 68c.15 Section 68c.15 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF CHILD HEALTH AND HUMAN DEVELOPMENT CONTRACEPTION AND INFERTILITY RESEARCH...
42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 57.317 Section 57.317 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR CONSTRUCTION OF TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Nursing Student Loans §...
42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 57.317 Section 57.317 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR CONSTRUCTION OF TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Nursing Student Loans §...
42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 57.317 Section 57.317 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR CONSTRUCTION OF TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Nursing Student Loans §...
42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 57.317 Section 57.317 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR CONSTRUCTION OF TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Nursing Student Loans §...
42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 57.317 Section 57.317 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS GRANTS FOR CONSTRUCTION OF TEACHING FACILITIES, EDUCATIONAL IMPROVEMENTS, SCHOLARSHIPS AND STUDENT LOANS Nursing Student Loans §...
42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 65.9 Section 65.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES HAZARDOUS WASTE WORKER TRAINING § 65.9...
42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 1 2011-10-01 2011-10-01 false Additional conditions. 65.9 Section 65.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES HAZARDOUS WASTE WORKER TRAINING § 65.9...
42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Additional conditions. 65.9 Section 65.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES HAZARDOUS WASTE WORKER TRAINING § 65.9...
42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Additional conditions. 65.9 Section 65.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES HAZARDOUS WASTE WORKER TRAINING § 65.9...
42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Additional conditions. 65.9 Section 65.9 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES FELLOWSHIPS, INTERNSHIPS, TRAINING NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES HAZARDOUS WASTE WORKER TRAINING § 65.9...
42 CFR 68a.15 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... DISADVANTAGED BACKGROUNDS (CR-LRP) § 68a.15 Additional conditions. When a shortage of funds exists, participants may be funded partially, as determined by the Secretary. However, once a CR-LRP contract has been signed by both parties, the Secretary will obligate such funds as necessary to ensure that...
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
NASA Astrophysics Data System (ADS)
Ehrlacher, V.; Ortner, C.; Shapeev, A. V.
2016-06-01
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.
Absorbing boundary conditions for relativistic quantum mechanics equations
Antoine, X.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A.D.
2014-11-15
This paper is devoted to the derivation of absorbing boundary conditions for the Klein–Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudo-differential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
New boundary conditions for the c=-2 ghost system
Creutzig, Thomas; Quella, Thomas; Schomerus, Volker
2008-01-15
We investigate a novel boundary condition for the bc system with central charge c=-2. Its boundary state is constructed and tested in detail. It appears to give rise to the first example of a local logarithmic boundary sector within a bulk theory whose Virasoro zero modes are diagonalizable.
Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints
NASA Technical Reports Server (NTRS)
Kangro, Urve; Nicolaides, Roy
1997-01-01
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Effect of Far-Field Boundary Conditions on Boundary-Layer Transition
NASA Technical Reports Server (NTRS)
Bertolotti, Fabio P.; Joslin, Ronald D.
1994-01-01
The effect of far-field boundary conditions on the evolution of a finite-amplitude two-dimensional wave in the Blasius boundary layer is assessed. With the use of the parabolized stability equations (PSE) theory for the numerical computations, either asymptotic, Dirichlet, Neumann or mixed boundary conditions are imposed at various distances from the wall. The results indicate that asymptotic and mixed boundary conditions yield the most accurate mean-flow distortion and unsteady instability modes in comparison with the results obtained with either Dirichlet or Neumann conditions.
Effect of Far-Field Boundary Conditions on Boundary-Layer Transition
NASA Technical Reports Server (NTRS)
Bertolotti, Fabio P.; Joslin, Ronald D.
1995-01-01
The effect of far-field boundary conditions on the evolution of a finite-amplitude two-dimensional wave in the Blasius boundary layer is assessed. With the use of the parabolized stability equations (PSE) theory for the numerical computations, either asymptotic, Dirichlet, Neumann or mixed boundary conditions are imposed at various distances from the wall. The results indicate that asymptotic and mixed boundary conditions yield the most accurate mean-flow distortion and unsteady instability modes in comparison with the results obtained with either Dirichlet or Neumann conditions.
Boundary stability under nonequilibrium conditions. Final report
Hackney, S.A.; Lee, J.K.; Plichta, M.R.
1999-08-01
Summaries of research accomplished are given for the following areas: Morphological (Diffusional) Stability; A New Algorithm for Numerical Modeling of Non-equilibrium Materials Behavior; A Unified Treatment of Single and Microcrystalline Film Edge Instabilities; and Validation of the Structure Based Grain Boundary Diffusion/Migration Model.
Quantum Nuclear Pasta Calculations with Twisted Angular Boundary Conditions
NASA Astrophysics Data System (ADS)
Schuetrumpf, Bastian; Nazarewicz, Witold
2015-10-01
Nuclear pasta, expected to be present in the inner crust of neutron stars and core collapse supernovae, can contain a wide spectrum of different exotic shapes such as nuclear rods and slabs. There are also more complicated, network-like structures, the triply periodic minimal surfaces, already known e.g. in biological systems. These shapes are studied with the Hartree-Fock method using modern Skyrme forces. Furthermore twisted angular boundary conditions are utilized to reduce finite size effects in the rectangular simulation boxes. It is shown, that this improves the accuracy of the calculations drastically and additionally more insights into the mechanism of forming minimal surfaces can be gained.
A Poisson-Boltzmann dynamics method with nonperiodic boundary condition
NASA Astrophysics Data System (ADS)
Lu, Qiang; Luo, Ray
2003-12-01
We have developed a well-behaved and efficient finite difference Poisson-Boltzmann dynamics method with a nonperiodic boundary condition. This is made possible, in part, by a rather fine grid spacing used for the finite difference treatment of the reaction field interaction. The stability is also made possible by a new dielectric model that is smooth both over time and over space, an important issue in the application of implicit solvents. In addition, the electrostatic focusing technique facilitates the use of an accurate yet efficient nonperiodic boundary condition: boundary grid potentials computed by the sum of potentials from individual grid charges. Finally, the particle-particle particle-mesh technique is adopted in the computation of the Coulombic interaction to balance accuracy and efficiency in simulations of large biomolecules. Preliminary testing shows that the nonperiodic Poisson-Boltzmann dynamics method is numerically stable in trajectories at least 4 ns long. The new model is also fairly efficient: it is comparable to that of the pairwise generalized Born solvent model, making it a strong candidate for dynamics simulations of biomolecules in dilute aqueous solutions. Note that the current treatment of total electrostatic interactions is with no cutoff, which is important for simulations of biomolecules. Rigorous treatment of the Debye-Hückel screening is also possible within the Poisson-Boltzmann framework: its importance is demonstrated by a simulation of a highly charged protein.
Simulation Study of the Flow Boundary Condition for Rough Surfaces
NASA Astrophysics Data System (ADS)
He, Gang; Robbins, Mark O.
2001-03-01
In order to solve a flow problem with the continuum Navier-Stokes equation, a boundary condition must be assumed. In most cases, a no-slip condition is used, i.e. the velocity of the fluid is set equal to that of a bounding solid at their interface. Deviations from this condition can be quantified by a slip length S that represents the additional width of fluid that would be needed to accomodate any velocity difference at the interface. Previous simulations with atomically flat surfaces show that S can be very large in certain limits. (P. A. Thompson and M. O. Robbins, Phys. Rev. A, 41), 6830(1990). ( J.-L. Barrat and L. Bocquet, Phys. Rev. Lett., 82), 4671(1999). A dramatic divergence with S as shear rate increases has also been seen.( P. A. Thompson and S. M. Troian, Nature, 389), 360(1997) We have extended these simulations to surfaces with random roughness, steps, and angled facets typical of twin boundaries. In all cases, S decreases rapidly as the roughness increases. When peak-to-peak roughness is only two atomic diameters, values of S have dropped from more than 20 diameters to only one or two. In addition, the non-linear regime where S diverges with shear rate is supressed by surface roughness. These results suggest that the experimental behavior of atomically flat surfaces such as mica may be very different than that of more typical rough surfaces.
Attractive and repulsive Casimir vacuum energy with general boundary conditions
NASA Astrophysics Data System (ADS)
Asorey, M.; Muñoz-Castañeda, J. M.
2013-09-01
The infrared behaviour of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth-Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.
Numerical boundary condition procedure for the transonic axisymmetric inverse problem
NASA Technical Reports Server (NTRS)
Shankar, V.
1981-01-01
Two types of boundary condition procedures for the axisymmetric inverse problem are described. One is a Neumann type boundary condition (analogous to the analysis problem) and the other is a Dirichlet type boundary conditon, both requiring special treatments to make the inverse scheme numerically stable. The dummy point concept is utilized in implementing both. Results indicate the Dirichlet type inverse boundary condition is more robust and conceptually simpler to implement than the Neumann type procedure. A few results demonstrating the powerful capability of the newly developed inverse method that can handle both shocked as well as shockless body design are included.
Poynting Flux-Conserving Boundary Conditions for Global MHD Models
NASA Astrophysics Data System (ADS)
Xi, S.; Lotko, W.; Zhang, B.; Brambles, O.; Lyon, J.; Merkin, V. G.; Wiltberger, M. J.
2014-12-01
Poynting Flux-conserving boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the low-altitude (or inner) boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. This method involves the mapping of both the potential from the ionosphere and the perpendicular magnetic field from the inner magnetosphere to the ghost cells of the computational domain. The single fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method. The comparisons of simulations using the standard hardwall boundary conditions of the LFM model and the flux-conserving boundary conditions show that the method reported here improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the field-aligned DC Poynting flux just above the boundary is very nearly equal to the ionospheric Joule heating, as it should be if electromagnetic energy is conserved.
A non-local computational boundary condition for duct acoustics
NASA Technical Reports Server (NTRS)
Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.
1994-01-01
A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.
Accurate boundary conditions for exterior problems in gas dynamics
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.
1988-01-01
The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.
Accurate boundary conditions for exterior problems in gas dynamics
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.
1988-01-01
The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.
Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Zorumski, William E.
1996-01-01
Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.
Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components
NASA Astrophysics Data System (ADS)
Liverts, Evgeny Z.
2016-08-01
The exact values of the presently determined components of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green's-function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in hyperspherical angular coordinates, which follow from the Kato cusp conditions for the two-electron wave function in the natural interparticle coordinates, were derived. The validity of the obtained boundary conditions was verified with examples of all the presently determined components. The additional boundary conditions not arising from the Kato cusp conditions were obtained as well. Wolfram's Mathematica was used extensively to obtain these results.
Electrodynamic boundary conditions for planar arrays of thin magnetic elements
Lisenkov, Ivan; Tyberkevych, Vasyl; Slavin, Andrei; Nikitov, Sergei
2015-08-24
Approximate electrodynamic boundary conditions are derived for an array of dipolarly coupled magnetic elements. It is assumed that the elements' thickness is small compared to the wavelength of an electromagnetic wave in a free space. The boundary conditions relate electric and magnetic fields existing at the top and bottom sides of the array through the averaged uniform dynamic magnetization of the array. This dynamic magnetization is determined by the collective dynamic eigen-excitations (spin wave modes) of the array and is found using the external magnetic susceptibility tensor. The problem of oblique scattering of a plane electromagnetic wave on the array is considered to illustrate the use of the derived boundary conditions.
Improved Boundary Conditions for Cell-centered Difference Schemes
NASA Technical Reports Server (NTRS)
VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.
Development and Preliminary Evaluation of Aryl Ester Boundary Additives for Perfluoropolyethers
NASA Technical Reports Server (NTRS)
Williams, John R.; Feuchter, Debra K.; Jones, William R., Jr.
1994-01-01
A series of additives were developed for evaluation as boundary lubrication enhancers for perfluoropolyethers. They are composed of a hydrocarbon aryl component (for lubrication improvement) and a fluorinated side chain (for solubility enhancement). The two moieties are joined by an ester linkage. Five boundary additives were evaluated in a perfluoropolyether basestock (Fomblin Z25) using a specially designed four-ball apparatus. Additives were evaluated at a one wt percent concentration. Conditions included: an atmosphere of dry air at atmospheric pressure, a 200N load, a speed of 100 rpm, room temperature, and 440C stainless steel specimens. Two monoesters, 2,4,6-trimethyl E2 and H5PDFO yielded wear rate reductions of approximately 60 and 35 percent, respectively. One diester, H4(E2)(sub 2), had no activity, while two other diesters (a diester of bisphenol A and H4(E4)(sub 2)) were pro-wear.
The effects of external conditions in turbulent boundary layers
NASA Astrophysics Data System (ADS)
Brzek, Brian G.
turbulence. However, each scaling for the velocity deficit profiles results in self-similar solutions for fixed experimental conditions. When examining the Reynolds stresses in the inner region, (i.e., 0 < (y + epsilon)+ < 0:1delta +), the < u2 > component shows the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables show self-similarity for fixed experimental conditions. However, as the roughness parameter, k +, increases, all Reynolds stress profiles become similar in shape indicating increased isotropy near the wall. Furthermore, the boundary layer parameters and production terms also show a considerable increase due to roughness. This study of rough wall turbulence was also combined with high freestream turbulence. The freestream turbulence was generated with the use of an active grid, which resulted in freestream turbulence levels of 6.2% and 5.2% at the two downstream measuring locations. The effect of the freestream turbulence on this rough surface significantly alters the mean velocity deficit profiles. In inner variables, the velocity profiles show a significantly reduced wake region, while in outer variables, a more full profile indicates increased momentum transport towards the wall. Furthermore, the effects of freestream turbulence are clearly identifiable in the Reynolds stress profiles. Furthermore, pressure gradient flows are also difficult to generalize, given that a significant difference in the boundary layer structure exists between different external pressure gradients, (i.e., FPG, ZPG, and APG). This was examined through the scaling of the velocity and Reynolds stresses from multiple data sets. (Abstract shortened by UMI.)
Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions
NASA Technical Reports Server (NTRS)
Kane, James H.; Wang, Hua
1991-01-01
Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.
Gonzalez-Lopez, Jennifer; Jansen, Karl; Renner, Dru B.; Shindler, Andrea
2013-02-01
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to non-perturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit.
Exact controllability of partial integrodifferential equations with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Sakthivel, K.; Balachandran, K.; Lavanya, R.
2007-01-01
In this work the exact controllability of linear parabolic integrodifferential equations with mixed boundary conditions are studied. Carleman estimate for the linearized problem providing the observability results is fundamental to the analysis and by duality it provides exact global controllability.
New statistical boundary conditions for argon-tungsten interactions.
Ozhgibesov, M S; Leu, T S; Cheng, C H; Utkin, A V
2012-09-01
In this study, scattering processes of argon beam impinging on tungsten surface are investigated numerically by applying molecular dynamics (MD) simulations. Energy transfer, momentum change, and scattering processes of argon gas atoms from W(110) surface are discussed. A new model of argon-tungsten (Ar-W) interaction is proposed. Based on the new proposed model, one can simplify the boundary conditions of this problem. The new boundary conditions are proved to be in line with previous experimental and theoretical results. This paper demonstrates how to proceed normalization and further conversion of the MD simulation results into boundary conditions. Application of the new proposed boundary conditions for Ar-W interactions provides a significant speedup of computations.
An experiment of rainfall infiltration under different boundary conditions
NASA Astrophysics Data System (ADS)
Hao, Shuang; Tong, Fuguo; Xue, Song
2016-04-01
Rainfall infiltration is a two-phase flow of water and gas, which should be simulated through solving the nonlinear governing equations of gas and water flow. In order to avoid the three main problems, such as convergence, numerical stability and computational efficiency in the solution of the nonlinear governing equations, Richard equation was usually used to simulate rainfall infiltration when the effect of gas phase could be ignored. The purpose of this work is to study the effect of boundary condition on rainfall infiltration, and to know in which cases Richard equation is available for the simulation of rainfall infiltration. The sample of soil has a height of 1200 mm. It is tightly enclosed in a toughened glass sleeve. The gas pressure is equal to the atmospheric pressure on the top surface of the model. The gas tight of its bottom can be controlled by a tap to simulate two different gas boundary conditions, permeable boundary and impermeable boundary. When the bottom of the model is not gas tight, the water infiltration rate is entirely bigger than gas tight. There is a big difference over the long time of rainfall that infiltration rate tends to be stable to 0.05cm/min when permeable but it is only 0.002cm/min when impermeable. The dramatic contrast reflects that gas paly a hindered part during rainfall infiltration. In addition, the gas pressure is obviously lower when the model is not gas tight. Although the pore gas pressure rise a little bit when water block gas, it is still same with atmospheric pressure all time. The situation is different when gas tight, the pore gas pressure increases sharply in the early stage and stable to a higher value, such as 10cm gas pressure on 67cm depth. Therefore, people basically negate the correlation between gas pressure and rainfall infiltration rate, but the evidence points out that the effect of gas pressure is in a significant position and Richard equations are not accurate under gas impermeable condition.
Two Baryons with Twisted Boundary Conditions
Briceno, Raul; Davoudi, Zohreh; Luu, Thomas; Savage, Martin
2014-04-01
The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.
Boundary conditions for direct computation of aerodynamic sound generation
NASA Technical Reports Server (NTRS)
Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz
1992-01-01
A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.
Absorbing Boundary Conditions For Optical Pulses In Dispersive, Nonlinear Materials
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Kwak, Dochan (Technical Monitor)
1995-01-01
This paper will present results in computational nonlinear optics. An algorithm will be described that provides absorbing boundary conditions for optical pulses in dispersive, nonlinear materials. A new numerical absorber at the boundaries has been developed that is responsive to the spectral content of the pulse. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of "light bullet" like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. Comparisons will be shown of calculations that use the standard boundary conditions and the new ones.
Momentum transfer within a porous medium. II. Stress boundary condition
NASA Astrophysics Data System (ADS)
Minale, Mario
2014-12-01
In this paper, we derive a boundary condition at the interface between a free fluid and a porous medium stating that the stress is transferred both to the fluid within the porous medium and to the solid skeleton. A zero stress jump is obtained so that the total stress is preserved at the interface. The boundary condition is obtained with the volume averaging method following the approach of Ochoa-Tapia and Whitaker ["Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development," Int. J. Heat Mass Transfer 38(14), 2635-2646 (1995)], but starting from the momentum balances written on the fluid and on the solid of the porous region, the latter was derived in part I of this paper. In the same way, also the boundary condition at the interface between a porous medium and a homogeneous solid is obtained. Both boundary conditions describe the equilibrium of forces at the interface, where part of the stress is carried by the solid skeleton and part by the fluid within the porous medium. With the derived boundary conditions, together with the stress transfer equation within the solid skeleton, it is now possible to satisfy the overall force equilibrium on a shear cell partially filled with a porous medium.
Formation of an interphase boundary under highly nonequilibrium conditions
Belyaev, A. P.; Rubets, V. P.; Antipov, V. V.
2007-12-15
The results of comparison studies of the CdTe-CdS interphase boundary in Au/CdTe/CdS sandwich structures synthesized on a substrate of artificial fluorophlogopite mica in highly nonequilibrium conditions (with a substrate temperature T{sub s} = 125 K) and in quasi-equilibrium conditions (T{sub s} > 720 K) are reported. The X-ray diffraction patterns and a capacitance-voltage characteristic are also reported. It is shown that highly nonequilibrium conditions allow synthesis of structures with excellent crystalline quality and with an interphase boundary that is no worse than in the structures grown under equilibrium conditions.
Boundary conditions in an integral approach to scattering
NASA Astrophysics Data System (ADS)
Arnoldus, Henk F.
2006-12-01
Scattering of electromagnetic radiation by an object of arbitrary shape or a structured surface, infinite in extent, is considered. When radiation is incident on an interface separating vacuum from a material medium, a current density is induced in the bulk and a surface current density may appear on the boundary surface. The electromagnetic field is then the sum of the incident field and the field generated by the current densities. This concept leads to expressions for the electric and magnetic fields that can easily be shown to be exact integrals of Maxwell's equations both in the vacuum and in the medium. At the boundary surface, the electric and magnetic fields must be discontinuous, with the discontinuity determined by the surface charge and current densities. This is usually referred to as boundary conditions for Maxwell's equations. We show that the integrals for the electric and magnetic fields automatically satisfy these boundary conditions, no matter the origin of the current densities.
Asymptotic boundary conditions for dissipative waves: General theory
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Determination of optical properties by variation of boundary conditions
NASA Astrophysics Data System (ADS)
Nickell, Stephan; Essenpreis, Matthias; Kraemer, U.; Kohl-Bareis, Matthias; Boecker, Dirk
1998-01-01
Propagation of photons in multiple scattering media depends on absorbing and scattering properties as well as the boundary conditions of the semi-infinite medium. A new method is shown that makes use of differences in boundary conditions to determine the optical properties. Induced are these different conditions by varying the reflectivity of a sensor head. We describe the influence of the change in reflectivity with the common diffusion theory. By building a ratio between the spatially-resolved diffuse reflectance under different boundary conditions it is possible to calculate the optical properties of homogeneous phantoms. Due to optical heterogeneities in living tissue, limitations of the method was observed, which restricts the application to in vivo measurements.
Determination of optical properties by variation of boundary conditions
NASA Astrophysics Data System (ADS)
Nickell, Stephan; Essenpreis, Matthias E.; Kraemer, U.; Kohl, Matthias; Boecker, Dirk
1997-12-01
Propagation of photons in multiple scattering media depends on absorbing and scattering properties as well as the boundary conditions of the semi-infinite medium. A new method is shown that makes use of differences in boundary conditions to determine the optical properties. Induced are these different conditions by varying the reflectivity of a sensor head. We describe the influence of the change in reflectivity with the common diffusion theory. By building a ratio between the spatially-resolved diffuse reflectance under different boundary conditions it is possible to calculate the optical properties of homogeneous phantoms. Due to optical heterogeneities in living tissue, limitations of the method was observed, which restricts the application to in vivo measurements.
Influence of boundary condition types on unstable density-dependent flow.
Ataie-Ashtiani, Behzad; Simmons, Craig T; Werner, Adrian D
2014-01-01
Boundary conditions are required to close the mathematical formulation of unstable density-dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density-dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams-Bashford/Backward Trapezoidal time integration approach in comparison to the Euler-Backward/Euler-Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density-dependent flow. PMID:23659688
Modeling sea-water intrusion with open boundary conditions
Padilla, F.; Cruz-Sanjulian, J.
1997-07-01
The present study concerns the application of a new numerical approach to describe the fresh-water/sea-water relationships in coastal aquifers. Essentially, a solution to the partial differential equation governing the regional motion of a phreatic surface and the resulting interface between fresh water and salt water is analyzed by a Galerkin finite-element formulation. A single-phase steady numerical model was applied to approximate, with simple triangular elements, the regional behavior of a coastal aquifer under appropriate sinks, sources, Neumann, outflow face, and open boundary conditions. On the one hand, outflow open boundaries at the coastline were not treated with other classical boundary conditions, but instead with a formal numerical approach for open boundaries inspired in this particular case by the Dupuit approximation of horizontal outflow at the boundary. The solution to this numerical model, together with the Ghyben-Herzberg principle, allows the correct simulation of fresh-water heads and the position of the salt-water interface for a steeply sloping coast. Although the solutions were precise and do not present classical numerical oscillations, this approach requires a previous solution with Dirichlet boundary conditions at the coastline in order to find a good convergence of the solution algorithm. On the other hand, the same precise results were obtained with a more restrictive open boundary condition, similar in a way to the outflow face approach, which required less computer time, did not need a prior numerical solution and could be extended to different coastline conditions. The steady-state problem was solved for different hypothetical coastal aquifers and fresh-water usage through three types of numerical tests.
NASA Astrophysics Data System (ADS)
Maeda, Takuto; Tsushima, Hiroaki; Furumura, Takashi
2016-04-01
We numerically simulated the propagation of tsunami waves with finite difference methods by using perfectly matched layer (PML) boundary conditions to effectively eliminate artificial reflections from model boundaries. The PML method damps the tsunami height and velocity of seawater only in directions perpendicular to the boundary. Although the additional terms required to implement the PML conditions make the use of the PML technique difficult for linear dispersive tsunami waves, we have proposed an empirical extension of the PML method for modeling dispersive tsunami waves. Even for heterogeneous, realistic bathymetries, numerical tests demonstrated that the PML boundary condition dramatically decreased artificial reflections from model boundaries compared to the use of traditional boundary conditions. The use of PML boundary conditions for numerical modeling of tsunamis is especially useful because it facilitates use of the later phases of tsunamis that would otherwise be compromised by artifacts caused by reflections from model boundaries.
Transport synthetic acceleration with opposing reflecting boundary conditions
Zika, M.R.; Adams, M.L.
2000-02-01
The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.
Critical effects of downstream boundary conditions on vortex breakdown
NASA Technical Reports Server (NTRS)
Kandil, Osama; Kandil, Hamdy A.; Liu, C. H.
1992-01-01
The unsteady, compressible, full Navier-Stokes (NS) equations are used to study the critical effects of the downstream boundary conditions on the supersonic vortex breakdown. The present study is applied to two supersonic vortex breakdown cases. In the first case, quasi-axisymmetric supersonic swirling flow is considered in a configured circular duct, and in the second case, quasi-axisymmetric supersonic swirling jet, that is issued from a nozzle into a supersonic jet of lower Mach number, is considered. For the configured duct flow, four different types of downstream boundary conditions are used, and for the swirling jet flow from the nozzle, two types of downstream boundary conditions are used. The solutions are time accurate which are obtained using an implicit, upwind, flux-difference splitting, finite-volume scheme.
Boundary conditions and the simulation of low Mach number flows
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Lorenz, Jens
1993-01-01
The problem of accurately computing low Mach number flows, with the specific intent of studying the interaction of sound waves with incompressible flow structures, such as concentrations of vorticity is considered. This is a multiple time (and/or space) scales problem, leading to various difficulties in the design of numerical methods. Concentration is on one of these difficulties - the development of boundary conditions at artificial boundaries which allow sound waves and vortices to radiate to the far field. Nonlinear model equations are derived based on assumptions about the scaling of the variables. Then these are linearized about a uniform flow and exact boundary conditions are systematically derived using transform methods. Finally, useful approximations to the exact conditions which are valid for small Mach number and small viscosity are computed.
Boundary conditions on internal three-body wave functions
Mitchell, Kevin A.; Littlejohn, Robert G.
1999-10-01
For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.
Viscosity in molecular dynamics with periodic boundary conditions.
Viscardy, S; Gaspard, P
2003-10-01
We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to that developed by Alder, Gass, and Wainwright [J. Chem. Phys. 53, 3813 (1970)]. We apply and verify our method in a fluid composed of N> or =2 hard disks in elastic collisions. We show that the viscosity coefficients already take values in good agreement with Enskog's theory for N=2 hard disks in a hexagonal geometry. PMID:14682933
Boundary conditions in photoacoustic tomography and image reconstruction.
Wang, Lihong V; Yang, Xinmai
2007-01-01
Recently, the field of photoacoustic tomography has experienced considerable growth. Although several commercially available pure optical imaging modalities, including confocal microscopy, two-photon microscopy, and optical coherence tomography, have been highly successful, none of these technologies can penetrate beyond approximately 1 mm into scattering biological tissues because all of them are based on ballistic and quasiballistic photons. Consequently, heretofore there has been a void in high-resolution optical imaging beyond this depth limit. Photoacoustic tomography has filled this void by combining high ultrasonic resolution and strong optical contrast in a single modality. However, it has been assumed in reconstruction of photoacoustic tomography until now that ultrasound propagates in a boundary-free infinite medium. We present the boundary conditions that must be considered in certain imaging configurations; the associated inverse solutions for image reconstruction are provided and validated by numerical simulation and experiment. Partial planar, cylindrical, and spherical detection configurations with a planar boundary are covered, where the boundary can be either hard or soft. Analogously to the method of images of sources, which is commonly used in forward problems, the ultrasonic detectors are imaged about the boundary to satisfy the boundary condition in the inverse problem. PMID:17343502
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-12
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
NASA Astrophysics Data System (ADS)
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-01
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
Compressible turbulent channel flow with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Scalo, Carlo; Bodart, Julien; Lele, Sanjiva K.
2015-03-01
We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, Mb = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Reb = 6900, have been investigated. For each Mb, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju ["Time-domain impedance boundary conditions for computational acoustics and aeroacoustics," Int. J. Comput. Fluid Dyn. 18(6), 503-511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency, ωr, tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ωr = 2πMb (normalized with the speed of sound and channel half-width), reduces the IBCs' free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each Mb. The application of the tuned IBCs results in a drag increase up to 300% for Mb = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, ζ, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength λx, traveling downstream with
Quantum communication through a spin ring with twisted boundary conditions
Bose, S.; Jin, B.-Q.; Korepin, V.E.
2005-08-15
We investigate quantum communication between the sites of a spin ring with twisted boundary conditions. Such boundary conditions can be achieved by a magnetic flux through the ring. We find that a nonzero twist can improve communication through finite odd-numbered rings and enable high-fidelity multiparty quantum communication through spin rings (working near perfectly for rings of five and seven spins). We show that in certain cases, the twist results in the complete blockage of quantum-information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field.
Boundary conditions for hyperbolic systems of partial differentials equations
Guaily, Amr G.; Epstein, Marcelo
2012-01-01
An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids. PMID:25685437
Maxwell boundary condition and velocity dependent accommodation coefficient
Struchtrup, Henning
2013-11-15
A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.
Identification of boundary conditions as a part of model correction
NASA Astrophysics Data System (ADS)
Pabst, U.; Hagedorn, P.
1995-05-01
Experience shows that in mathematical models of elastic systems the boundary conditions, bearings and joints are those parts of the system which are generally much less well known than the main components. The influence of these local parts on the system's dynamic behavior is commonly underestimated. Thus, in model correction, they tend to be modelled in an oversimplified way. Taking this fact into account, the present paper gives a system identification approach that is limited (at least in a first step) to the estimation of boundary conditions by using measured modal data.
Boundary conditions in a meshless staggered particle code
Libersky, L.D.; Randles, P.W.
1998-07-01
A meshless method utilizing two sets of particles and generalized boundary conditions is introduced. Companion sets of particles, one carrying velocity and the other carrying stress, are employed to reduce the undesirable effects of colocation of all field variables and increase accuracy. Boundary conditions implemented within this staggered framework include contact, stress-free, stress, velocity, and symmetry constraints. Several test problems are used to evaluate the method. Of particular importance is the motion of stress particles relative to velocity particles in higher dimensions. Early results show promise, but difficulties remain that must be overcome if the staggered technique is to be successful.
Intermediate boundary conditions for LOD, ADI and approximate factorization methods
NASA Technical Reports Server (NTRS)
Leveque, R. J.
1985-01-01
A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.
Vacuum fluctuations in the presence of nonlinear boundary conditions
NASA Astrophysics Data System (ADS)
Fosco, C. D.; Oxman, L. E.
2015-12-01
We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. These may appear, for example, in metamaterials having nonlinear response functions. The boundary conditions are implemented by nonquadratic interaction vertices, strictly localized on the mirrors. By using the appropriate perturbative expansions, we obtain approximate expressions for the Casimir energy corresponding to weak coupling, regarding the strength of the interaction terms. We also comment on an alternative expansion scheme that may be useful when the weak coupling expansion is not justified.
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
Hoemberg, D. Krumbiegel, K.; Rehberg, J.
2013-02-15
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
Calculation of Multistage Turbomachinery Using Steady Characteristic Boundary Conditions
NASA Technical Reports Server (NTRS)
Chima, Rodrick V.
1998-01-01
A multiblock Navier-Stokes analysis code for turbomachinery has been modified to allow analysis of multistage turbomachines. A steady averaging-plane approach was used to pass information between blade rows. Characteristic boundary conditions written in terms of perturbations about the mean flow from the neighboring blade row were used to allow close spacing between the blade rows without forcing the flow to be axisymmetric. In this report the multiblock code is described briefly and the characteristic boundary conditions and the averaging-plane implementation are described in detail. Two approaches for averaging the flow properties are also described. A two-dimensional turbine stator case was used to compare the characteristic boundary conditions with standard axisymmetric boundary conditions. Differences were apparent but small in this low-speed case. The two-stage fuel turbine used on the space shuttle main engines was then analyzed using a three-dimensional averaging-plane approach. Computed surface pressure distributions on the stator blades and endwalls and computed distributions of blade surface heat transfer coefficient on three blades showed very good agreement with experimental data from two tests.
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
Evaluation of Boundary Conditions for the Gust-Cascade Problem
NASA Technical Reports Server (NTRS)
Hixon, R.; Shih, S.-H.; Mankbadi, R. R.
1998-01-01
Using a high-order accuracy finite-difference time-domain algorithm, the acoustic scattering from a flat-plate cascade is computed. Keeping the grid and time step fixed, the effect of four different boundary conditions on the accuracy and stability of the computed solution is compared.
Investigation of Boundary Conditions for Flexible Multibody Spacecraft Dynamics
NASA Technical Reports Server (NTRS)
MacLean, John R.; Huynh, An; Quiocho, Leslie J.
2007-01-01
In support of both the Space Shuttle and International Space Station programs, a set of generic multibody dynamics algorithms integrated within the Trick simulation environment have addressed the variety of on-orbit manipulator simulation requirements for engineering analysis, procedures development and crew familiarization/training at the NASA Johnson Space Center (JSC). Enhancements to these dynamics algorithms are now being driven by a new set of Constellation program requirements for flexible multibody spacecraft simulation. One particular issue that has been discussed within the NASA community is the assumption of cantilever-type flexible body boundary conditions. This assumption has been commonly utilized within manipulator multibody dynamics formulations as it simplifies the computation of relative motion for articulated flexible topologies. Moreover, its use for modeling of space-based manipulators such as the Shuttle Remote Manipulator System (SRMS) and Space Station Remote Manipulator System (SSRMS) has been extensively validated against flight data. For more general flexible spacecraft applications, however, the assumption of cantilever-type boundary conditions may not be sufficient. This paper describes the boundary condition assumptions that were used in the original formulation, demonstrates that this formulation can be augmented to accommodate systems in which the assumption of cantilever boundary conditions no longer applies, and verifies the approach through comparison with an independent model previously validated against experimental hardware test data from a spacecraft flexible dynamics emulator.
Topological order in Josephson junction ladders with Mobius boundary conditions
NASA Astrophysics Data System (ADS)
Cristofano, Gerardo; Marotta, Vincenzo; Naddeo, Adele
2005-03-01
We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions; in particular we show how such a system can develop topological order. Such a property is crucial for its implementation as a 'protected' solid state qubit.
Outflow boundary conditions for blood flow in arterial trees.
Du, Tao; Hu, Dan; Cai, David
2015-01-01
In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models. PMID:26000782
Outflow Boundary Conditions for Blood Flow in Arterial Trees
Du, Tao; Hu, Dan; Cai, David
2015-01-01
In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models. PMID:26000782
Most general AdS3 boundary conditions
NASA Astrophysics Data System (ADS)
Grumiller, Daniel; Riegler, Max
2016-10-01
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl{(2)}_k current algebras, the levels of which are given by k = ℓ/(4 G N ), where ℓ is the AdS radius and G N the three-dimensional Newton constant.
Free, transverse vibrations of thin plates with discontinuous boundary conditions
NASA Astrophysics Data System (ADS)
Febbo, M.; Vera, S. A.; Laura, P. A. A.
2005-03-01
Vibrations of circular and rectangular plates clamped on part of the boundary and simply supported along the remainder are analyzed by means of a method of perturbation of boundary conditions. This approach appears to be simple and straightforward, giving excellent results for the first mode and its versatility permits to extend it to higher modes of vibration without difficulty. Furthermore, it is shown that the fundamental frequency coefficient can also be determined using a modified Galerkin approach and very simple polynomial coordinate functions which yield good engineering accuracy.
A far-field non-reflecting boundary condition for two-dimensional wake flows
NASA Technical Reports Server (NTRS)
Danowitz, Jeffrey S.; Abarbanel, Saul A.; Turkel, Eli
1995-01-01
Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.
DYNA3D Non-reflecting Boundary Conditions - Test Problems
Zywicz, E
2006-09-28
Two verification problems were developed to test non-reflecting boundary segments in DYNA3D (Whirley and Engelmann, 1993). The problems simulate 1-D wave propagation in a semi-infinite rod using a finite length rod and non-reflecting boundary conditions. One problem examines pure pressure wave propagation, and the other problem explores pure shear wave propagation. In both problems the non-reflecting boundary segments yield results that differ only slightly (less than 6%) during a short duration from their corresponding theoretical solutions. The errors appear to be due to the inability to generate a true step-function compressive wave in the pressure wave propagation problem and due to segment integration inaccuracies in the shear wave propagation problem. These problems serve as verification problems and as regression test problems for DYNA3D.
On the Huygens absorbing boundary conditions for electromagnetics
Berenger, Jean-Pierre
2007-09-10
A new absorbing boundary condition (ABC) is presented for the solution of Maxwell equations in unbounded spaces. Called the Huygens ABC, this condition is a generalization of two previously published ABCs, namely the multiple absorbing surfaces (MAS) and the re-radiating boundary condition (rRBC). The properties of the Huygens ABC are derived theoretically in continuous spaces and in the finite-difference (FDTD) discretized space. A solution is proposed to render the Huygens ABC effective for the absorption of evanescent waves. Numerical experiments with the FDTD method show that the effectiveness of the Huygens ABC is close to that of the PML ABC in some realistic problems of numerical electromagnetics. It is also shown in the paper that a combination of the Huygens ABC with the PML ABC is very well suited to the solution of some particular problems.
Time-domain implementation of an impedance boundary condition with boundary layer correction
NASA Astrophysics Data System (ADS)
Brambley, E. J.; Gabard, G.
2016-09-01
A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.
Boundary element analysis of cavity noise problems with complicated boundary conditions
NASA Astrophysics Data System (ADS)
Suzuki, S.; Maruyama, S.; Ido, H.
1989-04-01
The application of the boundary element method for the numerical solution of noise problems inside a complex-shaped cavity is considered. In particular, a new formulation for complicated boundary conditions to solve practical noise problems inside a vehicle cabin is proposed. This approach makes it possible to treat the acoustic effect of absorbent materials pasted on vibrating surfaces and the effect of leakage through an opening. Furthermore, boundary vibration velocities can be calculated with the structural-acoustic coupling effect. The sound pressure inside a linear duct is calculated to demonstrate the accuracy of the method in comparison with analytically determined solutions. Finally, the transmission of sound through a cavity-backed plate and the characteristics of sound absorption inside a sedan compartment model are discussed.
Nondestructive evaluation of ceramic candle filter with various boundary conditions
Chen, H.L.; Kiriakidis, A.C.
2005-06-01
Nondestructive evaluation (NDE) using a dynamic characterization technique was conducted to study ceramic candle filters. Ceramic candle filters are hollow cylindrical structures made of porous ceramic materials used to protect gas turbine in coal-fired power plants. Deterioration and failure of ceramic filters occurs after being exposed to high-temperature and high-pressure operational environment over a period of time. This paper focuses on the development of an NDE method that can predict the in-situ structural stiffness of the candle filters while still being attached to the plenum. A combination of laboratory testing, theoretical analysis, and finite element method (FEM) simulations are presented. The candle filters were tested using a laser vibrometer/accelerometer setup with variable boundary restraints. A variable end-restraint Timoshenko beam equation was derived to determine the dynamic response of the candle filters with simulated in-situ boundary conditions. Results from the FEM simulation were verified with the analysis to determine the stiffness degradation of the candle filters as well as the boundary conditions. Results from this study show that the vibration characteristics can be used effectively to evaluate both the structural stiffness and the in-situ boundary restraints of the ceramic candle filters during field inspections.
MULTIRESOLUTION REPRESENTATION OF OPERATORS WITH BOUNDARY CONDITIONS ON SIMPLE DOMAINS
Beylkin, Gregory; Fann, George I; Harrison, Robert J; Kurcz, Christopher E; Monzon, Lucas A
2011-01-01
We develop a multiresolution representation of a class of integral operators satisfying boundary conditions on simple domains in order to construct fast algorithms for their application. We also elucidate some delicate theoretical issues related to the construction of periodic Green s functions for Poisson s equation. By applying the method of images to the non-standard form of the free space operator, we obtain lattice sums that converge absolutely on all scales, except possibly on the coarsest scale. On the coarsest scale the lattice sums may be only conditionally convergent and, thus, allow for some freedom in their definition. We use the limit of square partial sums as a definition of the limit and obtain a systematic, simple approach to the construction (in any dimension) of periodized operators with sparse non-standard forms. We illustrate the results on several examples in dimensions one and three: the Hilbert transform, the projector on divergence free functions, the non-oscillatory Helmholtz Green s function and the Poisson operator. Remarkably, the limit of square partial sums yields a periodic Poisson Green s function which is not a convolution. Using a short sum of decaying Gaussians to approximate periodic Green s functions, we arrive at fast algorithms for their application. We further show that the results obtained for operators with periodic boundary conditions extend to operators with Dirichlet, Neumann, or mixed boundary conditions.
Revisiting Johnson and Jackson boundary conditions for granular flows
Li, Tingwen; Benyahia, Sofiane
2012-07-01
In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.
A Boundary Condition for Simulation of Flow Over Porous Surfaces
NASA Technical Reports Server (NTRS)
Frink, Neal T.; Bonhaus, Daryl L.; Vatsa, Veer N.; Bauer, Steven X. S.; Tinetti, Ana F.
2001-01-01
A new boundary condition is presented.for simulating the flow over passively porous surfaces. The model builds on the prior work of R.H. Bush to eliminate the need for constructing grid within an underlying plenum, thereby simplifying the numerical modeling of passively porous flow control systems and reducing computation cost. Code experts.for two structured-grid.flow solvers, TLNS3D and CFL3D. and one unstructured solver, USM3Dns, collaborated with an experimental porosity expert to develop the model and implement it into their respective codes. Results presented,for the three codes on a slender forebody with circumferential porosity and a wing with leading-edge porosity demonstrate a good agreement with experimental data and a remarkable ability to predict the aggregate aerodynamic effects of surface porosity with a simple boundary condition.
Some results for the primitive equations with physical boundary conditions
NASA Astrophysics Data System (ADS)
Evans, Lawrence Christopher; Gastler, Robert
2013-12-01
In this paper, we consider the (simplified) 3-dimensional primitive equations with physical boundary conditions. We show that the equations with constant forcing have a bounded absorbing ball in the H 1-norm and that a solution to the unforced equations has its H 1-norm decay to 0. From this, we argue that there exists an invariant measure (on H 1) for the equations under random kick-forcing.
Slarti: A boundary condition editor for a coupled climate model
NASA Astrophysics Data System (ADS)
Mickelson, S. A.; Jacob, R. L.; Pierrehumbert, R.
2006-12-01
One of the largest barriers to making climate models more flexible is the difficulty in creating new boundary conditions, especially for "deep time" paleoclimate cases where continents are in different positions. Climate models consist of several mutually-interacting component models and the boundary conditions must be consistent between them. We have developed a program called Slarti which uses a Graphical User Interface and a set of consistency rules to aid researchers in creating new, consistent, boundary condition files for the Fast Ocean Atmosphere Model (FOAM). Users can start from existing mask, topography, or bathymetry data or can build a "world" entirely from scratch (e.g. a single island continent). Once a case has been started, users can modify mask, vegetation, bathymetry, topography, and river flow fields by drawing new data through a "paint" interface. Users activate a synchronization button which goes through the fields to eliminate inconsistencies. When the changes are complete and save is selected, Slarti creates all the necessary files for an initial run of FOAM. The data is edited at the highest resolution (the ocean-land surface in FOAM) and then interpolated to the atmosphere resolution. Slarti was implemented in Java to maintain portability across platforms. We also relied heavily on Java Swing components to create the interface. This allowed us to create an object-oriented interface that could be used on many different systems. Since Slarti allows users to visualize their changes, they are able to see areas that may cause problems when the model is ran. Some examples would be lakes from the river flow field and narrow trenches within the bathymetry. Through different checks and options available through its interface, Slarti makes the process of creating new boundary conditions for FOAM easier and faster while reducing the chance for user errors.
Stability analysis of intermediate boundary conditions in approximate factorization schemes
NASA Technical Reports Server (NTRS)
South, J. C., Jr.; Hafez, M. M.; Gottlieb, D.
1986-01-01
The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method.
Artificial Boundary Conditions for Computation of Oscillating External Flows
NASA Technical Reports Server (NTRS)
Tsynkov, S. V.
1996-01-01
In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABC's for oscillating flows is based on an essential assumption: the Navier-Stokes equations can be linearized in the far field against the free-stream back- ground. To actually compute the ABC's, we represent the far-field solution as a Fourier series in time and then apply the Difference Potentials Method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABC's for time-periodic external flows. Based on our experience in implementing analogous ABC's for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.
Dynamic relaxation of a liquid cavity under amorphous boundary conditions.
Cavagna, Andrea; Grigera, Tomás S; Verrocchio, Paolo
2012-05-28
The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set (PTS) correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between mode-coupling theory and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration. PMID:22667566
Maxwell boundary conditions imply non-Lindblad master equation
NASA Astrophysics Data System (ADS)
Bamba, Motoaki; Imoto, Nobuyuki
2016-09-01
From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.
Solitons induced by boundary conditions from the Boussinesq equation
NASA Technical Reports Server (NTRS)
Chou, Ru Ling; Chu, C. K.
1990-01-01
The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.
Inflow/Outflow Boundary Conditions with Application to FUN3D
NASA Technical Reports Server (NTRS)
Carlson, Jan-Renee
2011-01-01
Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.
On the nonlinear Schrodinger equation with nonzero boundary conditions
NASA Astrophysics Data System (ADS)
Fagerstrom, Emily
integral, provided the initial condition satisfies further conditions. Modulational instability (focusing NLS with symmetric nonzero boundary conditions at infinity.) The focusing NLS equation is considered with potentials that are "box-like" piecewise constant functions. Several results are obtained. In particular, it is shown that there are conditions on the parameters of the potential for which there are no discrete eigenvalues. Thus there is a class of potentials for which the corresponding solutions of the NLS equation have no solitons. Hence, solitons cannot be the medium for the modulational instability. This contradicts a recent conjecture by Zakharov. On the other hand, it is shown for a different class of potentials the scattering problem always has a discrete eigenvalue along the imaginary axis. Thus, there exist arbitrarily small perturbations of the constant potential for which solitons exist, so no area theorem is possible. The existence, number and location of discrete eigenvalues in other situations are studied numerically. Finally, the small-deviation limit of the IST is computed and compared with the direct linearization of the NLS equation around a constant background. From this it is shown that there is an interval of the continuous spectrum on which the eigenvalue is imaginary and the scattering parameter is imaginary. The Jost eigenfunctions corresponding to this interval are the nonlinear analogue of the unstable Fourier modes. Defocusing NLS equation with asymmetric boundary conditions at infinity. The defocusing NLS equation with asymmetric boundary conditions is considered. To do so, first the case of symmetric boundary conditions is revisited. While the IST for this case has been formulated in the literature, it is usually done through the use of a uniformization variable. This was done because the eigenvalues of the scattering problem have branching; the uniformization variable allows one to move from a 2-sheeted Riemann surface to the complex
Study on plate silencer with general boundary conditions
NASA Astrophysics Data System (ADS)
Liu, Gongmin; Zhao, Xiaochen; Zhang, Wenping; Li, Shuaijun
2014-09-01
A plate silencer consists of an expansion chamber with two side-branch rigid cavities covered by plates. Previous studies showed that, in a duct, the introduction of simply supported or clamped plates into an air conveying system could achieve broadband quieting from low to medium frequencies. In this study, analytical formulation is extended to the plate silencer with general boundary conditions. A set of static beam functions, which are a combination of sine series and third-order polynomial, is employed as the trial functions of the plate vibration velocity. Greens function and Kirchhoff-Helmholtz integral are used to solve the sound radiation in the duct and the cavity, and then the vibration velocity of the plate is obtained. Having obtained the vibration velocity, the pressure perturbations induced by the plate oscillation and the transmission loss are found. Optimization is carried out in order to obtain the widest stopband. The transmission loss calculated by the analytical method agrees closely with the result of the finite element method simulation. Further studies with regard to the plate under several different classical boundary conditions based on the validated model show that a clamped-free plate silencer has the worst stopband. Attempts to release the boundary restriction of the plate are also made to study its effect on sound reflection. Results show that a softer end for a clamped-clamped plate silencer helps increase the optimal bandwidth, while the same treatment for simply supported plate silencer will result in performance degradation.
Electrostatics of solvated systems in periodic boundary conditions
NASA Astrophysics Data System (ADS)
Andreussi, Oliviero; Marzari, Nicola
2014-12-01
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.
Applying twisted boundary conditions for few-body nuclear systems
NASA Astrophysics Data System (ADS)
Körber, Christopher; Luu, Thomas
2016-05-01
We describe and implement twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twist angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length L ≈8 -14 fm. Of particular importance is our derivation and numerical verification of three-body analogs of "i-periodic" twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.
Nasstrom, J.S.; Ermak, D.L.
1997-04-01
Lagrangian stochastic modeling based on the Langevin equation has been shown to be useful for simulating vertical dispersion of trace material in the convective boundary layer or CBL. This modeling approach can account for the effects of the long velocity correlation time scales, skewed vertical velocity distributions, and vertically inhomogeneous turbulent properties found in the CBL. It has been recognized that Langevin equation models assuming skewed but homogenous velocity statistics can capture the important aspects of diffusion from sources in the CBL, especially elevated sources. We compare three reflection boundary conditions using two different Langevin-equation-based numerical models for vertical dispersion in skewed, homogeneous turbulence. One model, described by Ermak and Nasstrom (1995) is based on a Langevin equation with a skewed random force and a linear deterministic force. The second model, used by Hurley and Physick (1993) is based on a Langevin equation with a Gaussian random force and a non-linear deterministic force. The reflection boundary conditions are all based on the approach described by Thompson and Montgomery (1994).
Impedance-based outflow boundary conditions for human carotid haemodynamics.
Malvè, M; Chandra, S; García, A; Mena, A; Martínez, M A; Finol, E A; Doblaré, M
2014-01-01
In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.
A study of grain boundary sliding in copper with and without an addition of phosphorus
NASA Astrophysics Data System (ADS)
Pettersson, Kjell
2010-10-01
Copper will be used as a corrosion barrier in the storage of high level nuclear waste. In order to improve the creep fracture properties of the material it will contain 30-50 ppm of phosphorus, OFP copper as opposed to OF copper without P. It has been suggested that the phosphorus impedes grain boundary sliding in copper and recently a quantitative theory based on this idea has shown that there is no risk for creep-brittle fracture of OFP copper under waste storage conditions. In order to verify the basis of this theory grain boundary sliding has been investigated in copper with and without a P addition. The method has been to examine intentionally scratched surfaces of tensile specimens tension tested to plastic strains of 1%, 2% and 4% at 150 and 200 °C. After testing specimen surfaces have been examined in SEM and sliding distances have been measured as in-surface displacement of scratches. The results have been plotted as distribution functions where the fraction of slides smaller than a given value is plotted versus sliding distance. The result is that in most cases the distribution functions for OF and OFP copper overlap. In a small number of cases there is a tendency that less sliding has occurred in OFP copper. The overall conclusion is however that although there may be a slight difference between the materials with regard to grain boundary sliding it is not large enough to explain the observed difference in creep brittleness. Tension tests to fracture in the temperature range 100-200 °C show that the tensile properties of the two copper qualities are more or less identical until intergranular cracking starts in the OF copper. Then the flow stress decreases in comparison with OFP. It is suggested that at least part of the observed differences in creep strength between the two coppers may be due to the effect of intergranular cracking.
Three dimensional dynamics of rotating structures under mixed boundary conditions
NASA Astrophysics Data System (ADS)
Bediz, Bekir; Romero, L. A.; Ozdoganlar, O. Burak
2015-12-01
This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method. As a result, mass, damping, and stiffness matrices, as well as a forcing vector, are obtained for a given rotating structure. Several case studies are then performed to demonstrate the application and effectiveness of the 3D-ST solution. For each problem, the natural frequencies and modes shapes from the 3D-ST solution are compared to those from the literature (when available) and to those from a commercial finite elements software. The case studies include rotating/spinning parallelepipeds under free and mixed boundary conditions, and a cantilevered pretwisted beam (i.e., rotating blade) with an airfoil geometry rotating on a hub. It is seen that the natural frequencies and mode shapes from the 3D-ST technique differ from those from the
NASA Astrophysics Data System (ADS)
Livshits, Gideon I.
2014-02-01
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.
Compressible turbulent channel flow with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Scalo, Carlo; Bodart, Julien; Lele, Sanjiva
2014-11-01
We have performed large-eddy simulations of compressible turbulent channel flow at one bulk Reynolds number, Reb = 6900, for bulk Mach numbers Mb = 0.05, 0.2, 0.5, with linear acoustic impedance boundary conditions (IBCs). The IBCs are formulated in the time domain following Fung and Ju (2004) and coupled with a Navier-Stokes solver. The impedance model adopted is a three-parameter Helmholtz oscillator with resonant frequency tuned to the outer layer eddies. The IBC's resistance, R, has been varied in the range, R = 0.01, 0.10, 1.00. Tuned IBCs result in a noticeable drag increase for sufficiently high Mb and/or low R, exceeding 300% for Mb = 0.5 and R = 0.01, and thus represents a promising passive control technique for delaying boundary layer separation and/or enhancing wall heat transfer. Alterations to the turbulent flow structure are confined to the first 15% of the boundary layer thickness where the classical buffer-layer coherent vortical structures are replaced by an array of Kelvin-Helmholtz-like rollers. The non-zero asymptotic value of the Reynolds shear stress gradient at the wall results in the disappearance of the viscous sublayer and very early departure of the mean velocity profiles from the law of the wall.
Artificial Boundary Conditions Based on the Difference Potentials Method
NASA Technical Reports Server (NTRS)
Tsynkov, Semyon V.
1996-01-01
While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then
Reflecting boundary conditions for graded p-n junctions
NASA Technical Reports Server (NTRS)
Schacham, S. E.
1990-01-01
In a graded junction, the formalism for handling reflecting boundary conditions must be modified. Since a significant drift term is present, zero recombination velocity at the surface does not imply a zero excess carrier gradient but rather zero overall flux. A model for analyzing p-n junctions fabricated by implantation or diffusion is presented, assuming the dominant recombination mechanism in the graded region is Auger. The model enables optimization of diode design. By proper selection of parameters, mainly by reducing surface concentration or by increasing the steepness of the dopant profile, it is possible to drastically reduce the saturation current generated by the graded region.
Hawking radiation, covariant boundary conditions, and vacuum states
Banerjee, Rabin; Kulkarni, Shailesh
2009-04-15
The basic characteristics of the covariant chiral current
Hawking radiation, effective actions and covariant boundary conditions
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Kulkarni, Shailesh
2008-01-01
From an appropriate expression for the effective action, the Hawking radiation from charged black holes is derived, using only covariant boundary conditions at the event horizon. The connection of our approach with the Unruh vacuum and the recent analysis [S.P. Robinson, F. Wilczek, Phys. Rev. Lett. 95 (2005) 011303, arxiv:gr-qc/0502074; S. Iso, H. Umetsu, F. Wilczek, Phys. Rev. Lett. 96 (2006) 151302, arxiv:hep-th/0602146; R. Banerjee, S. Kulkarni, arxiv:arXiv: 0707.2449 [hep-th
Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)
NASA Technical Reports Server (NTRS)
Syed, H. H.; Volakis, John L.
1991-01-01
Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.
Boundary conditions for soft glassy flows: slippage and surface fluidization.
Mansard, Vincent; Bocquet, Lydéric; Colin, Annie
2014-09-28
We explore the question of surface boundary conditions for the flow of a dense emulsion. We make use of microlithographic tools to create surfaces with well controlled roughness patterns and measure using dynamic confocal microscopy both the slip velocity and the shear rate close to the wall, which we relate to the notion of surface fluidization. Both slippage and wall fluidization depend non-monotonously on the roughness. We interpret this behavior within a simple model in terms of the building of a stratified layer and the activation of plastic events by the surface roughness.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Reconnection properties in collisionless plasma with open boundary conditions
Sun, H. E.; Ma, Z. W.; Huang, J.
2014-07-15
Collisionless magnetic reconnection in a Harris current sheet with different initial thicknesses is investigated using a 21/2 -D Darwin particle-in-cell simulation with the magnetosonic open boundary condition. It is found that the thicknesses of the ion dissipation region and the reconnection current sheet, when the reconnection rate E{sub r} reaches its first peak, are independent of the initial thickness of the current sheet; while the peak reconnection rate depends on it. The peak reconnection rate increases with decrease of the current sheet thickness as E{sub r}∼a{sup −1/2}, where a is the initial current sheet half-thickness.
General rule for boundary conditions from the action principle
NASA Astrophysics Data System (ADS)
Steiner, Roee
2016-03-01
We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical viewpoint, and it is not in the form of Lagrange multipliers. We show some examples from the past and some new examples that can be useful, where constraint can be obtained from the action principle. Those actions represent physical models. We show that it is possible to use our rule to get those constraints directly.
Eigenmodes of triaxial ellipsoidal acoustical cavities with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Willatzen, M.; Lew Yan Voon, L. C.
2004-12-01
The linear acoustics problem of resonant vibrational modes in a triaxial ellipsoidal acoustic cavity with walls of arbitrary acoustic impedance has been quasi-analytically solved using the Frobenius power-series expansion method. Eigenmode results are presented for the lowest two eigenmodes in cases with pressure-release, rigid-wall, and lossy-wall boundary conditions. A mode crossing is obtained as a function of the specific acoustic impedance of the wall; the degeneracy is not symmetry related. Furthermore, the damping of the wave is found to be maximal near the crossing. .
Implementation of a Blowing Boundary Condition in the LAURA Code
NASA Technical Reports Server (NTRS)
Thompson, Richard a.; Gnoffo, Peter A.
2008-01-01
Preliminary steps toward modeling a coupled ablation problem using a finite-volume Navier-Stokes code (LAURA) are presented in this paper. Implementation of a surface boundary condition with mass transfer (blowing) is described followed by verification and validation through comparisons with analytic results and experimental data. Application of the code to a carbon-nosetip ablation problem is demonstrated and the results are compared with previously published data. It is concluded that the code and coupled procedure are suitable to support further ablation analyses and studies.
Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions
NASA Technical Reports Server (NTRS)
Perkins, A. Louise; Scroggs, Jeffrey S.
1991-01-01
Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups.
Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
NASA Astrophysics Data System (ADS)
Sergeev, V. A.; Chernyaev, I. A.; Angelopoulos, V.; Ganushkina, N. Y.
2015-12-01
Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft during February-March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6-9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs) of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites) to the equatorial magnetosphere (to find the projected isotropy boundary, PIB) and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius) in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1-2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32), with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC) waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.
NASA Astrophysics Data System (ADS)
Abkar, Mahdi; Porte-Agel, Fernando
2011-11-01
Large-eddy simulations are performed to evaluate the performance of the surface boundary condition downwind of a rough-to-smooth surface transition. Two types of boundary conditions are tested: (i) the standard formulation based on local application of Monin-Obukhov similarity (MOS) theory, and (ii) a new model based on a modification of the recently proposed model of Chamorro and Porte-Agel (2009). The new model assumes that the wind velocity downwind of a rough-to-smooth transition can be estimated as a weighted average of two logarithmic profiles. The first log law is recovered above the internal boundary layer height and corresponds to the upwind velocity profile. The second log law is adjusted to the downwind aerodynamic roughness and it is recovered near the surface in the equilibrium sublayer. The performance of the new model is tested with available wind-tunnel measurements and shows improved predictions of surface shear stress and velocity distribution at different positions downwind of the transition. In addition, the prediction of the new model shows very small dependence on the height at which it is applied.
A Kinetic 13-Moment Boundary Conditions Method for Particle Simulations of Viscous Rarefied Flows
NASA Astrophysics Data System (ADS)
Averkin, Sergey; Gatsonis, Nikolaos
2015-11-01
The kinetic 13-moment (Navier-Stokes-Fourrier) boundary condition method is developed for direct simulation Monte Carlo (DSMC) simulations of rarefied gas flows. The particles are injected into the computational domain from the inlet and outlet following the first-order Chapman-Enskog distribution function. The unknown parameters of the Chapman-Enskog distribution function are reconstructed from the full 13-moment (Navier-Stokes-Fourier) equations discretized on the boundaries with the wave amplitudes calculated by the local one dimensional inviscid (LODI) formulation used in compressible (continuous) flow computations. The kinetic-moment boundary conditions are implemented in an unstructured 3D DSMC (U3DSMC) code and are supplemented with a neighboring-cell sampling approach and a time-average smoothing techniques to speed up convergence and reduce fluctuations. Simulations of a pressure-driven viscous subsonic flow in a circular tube are used for verification and validation of the boundary conditions. In addition, the present method is compared to the previously developed kinetic-moment boundary conditions derived from the five-moment (Euler) equations. AFOSR-FA9550-14-1-0366 Computational Mathematics Program.
Solvability of a fourth-order boundary value problem with periodic boundary conditions II
Gupta, Chaitan P.
1991-01-01
Lemore » t f : [ 0 , 1 ] × R 4 → R be a function satisfying Caratheodory's conditions and e ( x ) ∈ L 1 [ 0 , 1 ] . This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d 4 u d x 4 + f ( x , u ( x ) , u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) ) = e ( x ) , 0 < x < 1 , with u ( 0 ) − u ( 1 ) = u ′ ( 0 ) − u ′ ( 1 ) = u ″ ( 0 ) - u ″ ( 1 ) = u ‴ ( 0 ) - u ‴ ( 1 ) = 0 . This problem was studied earlier by the author in the special case when f was of the form f ( x , u ( x ) ) , i.e., independent of u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) . It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problems d 4 u d x 4 = λ 4 u and d 4 u d x 4 = − λ 2 d 2 u d x 2 with periodic boundary conditions.« less
14 CFR 415.11 - Additional license terms and conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 14 Aeronautics and Space 4 2011-01-01 2011-01-01 false Additional license terms and conditions. 415.11 Section 415.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH LICENSE General § 415.11 Additional license terms and conditions. The FAA may modify a...
14 CFR 415.11 - Additional license terms and conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 4 2012-01-01 2012-01-01 false Additional license terms and conditions. 415.11 Section 415.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH LICENSE General § 415.11 Additional license terms and conditions. The FAA may modify a...
14 CFR 415.11 - Additional license terms and conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 4 2014-01-01 2014-01-01 false Additional license terms and conditions. 415.11 Section 415.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH LICENSE General § 415.11 Additional license terms and conditions. The FAA may modify a...
NASA Astrophysics Data System (ADS)
Abkar, M.; Porté-Agel, F.
2012-04-01
Predicting the spatial distribution of surface fluxes over heterogeneous terrains remains a basic challenge in hydrology and the atmospheric sciences. The complexity of such flow, makes it difficult to obtain all the needed information through field experiments alone, and often necessitates high-resolution eddy-resolving numerical tools such as large-eddy simulation (LES). One of the outstanding issues that affect LES performance is the treatment of the surface boundary conditions. Monin-Obukhov similarity (MOS) theory has provided the most common boundary condition formulations for LES of ABL flows. Despite the fact that MOS theory was proposed for homogeneous flat surfaces and applies strictly only to mean quantities, in LES it is used in a wide range of conditions, (including over heterogeneous surfaces and over topography) to compute the fluctuating surface fluxes. Recently, Chamorro and Porté-Agel (2009 and 2010) used wind velocity and surface shear stress data collected in a wind-tunnel experiment and showed direct application of MOS theory over heterogeneous surfaces causes large errors which affect both the average value as well as higher order statistics of the predicted surface shear stress. In this study, Large-eddy simulations are performed to evaluate the performance of the surface boundary condition downwind of a rough-to-smooth surface transition. Two types of boundary conditions are tested: (i) the standard formulation based on local application of Monin-Obukhov similarity (MOS) theory, and (ii) a new model based on a modification of the recently proposed model of Chamorro and Porte-Agel (2009). The new model assumes that the wind velocity downwind of a rough-to-smooth transition can be estimated as a weighted average of two logarithmic profiles. The first log law is recovered above the internal boundary layer height and corresponds to the upwind velocity profile. The second log law is adjusted to the downwind aerodynamic roughness and it is
Boundary conditions on the vapor liquid interface at strong condensation
NASA Astrophysics Data System (ADS)
Kryukov, A. P.; Levashov, V. Yu.
2016-07-01
The problem of the formulation of boundary conditions on the vapor-liquid interface is considered. The different approaches to this problem and their difficulties are discussed. Usually, a quasi-equilibrium scheme is used. At sufficiently large deviations from thermodynamic equilibrium, a molecular kinetics approach should be used for the description of the vapor flow at condensation. The formulation of the boundary conditions at the vapor liquid interface to solve the Boltzmann kinetic equation for the distribution of molecules by velocity is a sophisticated problem. It appears that molecular dynamics simulation (MDS) can be used to provide this solution at the interface. The specific problems occur in the realization of MDS on large time and space scales. Some of these problems, and a hierarchy of continuum, kinetic and molecular dynamic time scales, are discussed in the paper. A description of strong condensation at the kinetic level is presented for the steady one-dimensional problem. A formula is provided for the calculation of the limiting condensation coefficient. It is shown that as the condensation coefficient approaches the limiting value, the vapor pressure rises significantly. The results of the corresponding calculations for the Mach number and temperature at different vapor flows are demonstrated. As a result of the application of the molecular kinetics method and molecular dynamics simulation to the problem of the determination of argon condensation coefficients in the range of temperatures of vapor and liquid ratio 1.0-4.0, it is concluded that the condensation coefficient is close to unity.
On free convection heat transfer with well defined boundary conditions
Davies, M.R.D.; Newport, D.T.; Dalton, T.M.
1999-07-01
The scaling of free convection heat transfer is investigated. The non-dimensional groups for Boussinesq and fully compressible variable property free convection, driven by isothermal surfaces, are derived using a previously published novel method of dimensional analysis. Both flows are described by a different set of groups. The applicability of each flow description is experimentally investigated for the case of the isothermal horizontal cylinder in an air-filled isothermal enclosure. The approach taken to the boundary conditions differs from that of previous investigations. Here, it is argued that the best definition of the boundary conditions is achieved for heat exchange between the cylinder and the enclosure rather than the cylinder and an arbitrarily chosen fluid region. The enclosure temperature is shown both analytically and experimentally to affect the Nusselt number. The previously published view that the Boussinesq approximation has only a limited range of application is confirmed, and the groups derived for variable property compressible free convection are demonstrated to be correct experimentally. A new correlation for horizontal cylinder Nusselt number prediction is presented.
Spatial heterogeneity of ocean surface boundary conditions under sea ice
NASA Astrophysics Data System (ADS)
Barthélemy, Antoine; Fichefet, Thierry; Goosse, Hugues
2016-06-01
The high heterogeneity of sea ice properties implies that its effects on the ocean are spatially variable at horizontal scales as small as a few meters. Previous studies have shown that taking this variability into account in models could be required to simulate adequately mixed layer processes and the upper ocean temperature and salinity structures. Although many advanced sea ice models include a subgrid-scale ice thickness distribution, potentially providing heterogeneous surface boundary conditions, the information is lost in the coupling with a unique ocean grid cell underneath. The present paper provides a thorough examination of boundary conditions at the ocean surface in the NEMO-LIM model, which can be used as a guideline for studies implementing subgrid-scale ocean vertical mixing schemes. Freshwater, salt, solar heat and non-solar heat fluxes are examined, as well as the norm of the surface stress. All of the thermohaline fluxes vary considerably between the open water and ice fractions of grid cells. To a lesser extent, this is also the case for the surface stress. Moreover, the salt fluxes in both hemispheres and the solar heat fluxes in the Arctic show a dependence on the ice thickness category, with more intense fluxes for thinner ice, which promotes further subgrid-scale heterogeneity. Our analysis also points out biases in the simulated open water fraction and in the ice thickness distribution, which should be investigated in more details in order to ensure that the latter is used to the best advantage.
Role of the basin boundary conditions in gravity wave turbulence
NASA Astrophysics Data System (ADS)
Berhanu, Michael; Deike, Luc; Miquel, Benjamin; Gutierrez, Pablo; Jamin, Timothee; Semin, Benoit; Falcon, Eric; Bonnefoy, Felicien
2015-11-01
Gravity wave turbulence is studied in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. The wave field properties depend strongly on these boundary conditions. Unidirectional waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4. We have also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation. Using the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated experimentally for the first time.
NASA Astrophysics Data System (ADS)
Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.
2016-10-01
This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.
Influence of Spanwise Boundary Conditions on Slat Noise Simulations
NASA Technical Reports Server (NTRS)
Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.
2015-01-01
The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.
Homogenized boundary conditions and resonance effects in Faraday cages
Hewitt, I. J.
2016-01-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775
Internal friction and boundary conditions in lossy fluid seabeds
Deane, G.B.
1997-01-01
There are two distinct mechanisms associated with compressional wave absorption in lossy media, internal relaxation and internal friction. For the special case of propagation in an homogeneous, unbounded medium, both mechanisms can be modeled by adopting the convention of a complex sound speed and are, in this sense, equivalent. For the more realistic case of propagation in a stratified medium, the convention of complex sound speed does not give a correct description for losses which modify the linearized equation of motion, such as internal friction. In the presence of boundaries, internal friction can be modeled by the introduction of a complex quiescent density in addition to complex sound speed. Propagation models which use complex sound speed only in the presence of boundaries make the tacit assumption that seafloor losses are caused by internal relaxations only. A solution is developed for propagation in a lossy Pekeris channel where absorption in the lower fluid is caused by internal friction. The example that has been considered yields a sound level 3 dB less than the standard description over a 50-km path. {copyright} {ital 1997 Acoustical Society of America.}
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary conditions at infinity and be accurate with respect to the interior numerical scheme. The treatment of these boundary conditions for wave-like equations is discussed.
Dynamic behaviour of thin composite plates for different boundary conditions
Sprintu, Iuliana E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin E-mail: rotaruconstantin@yahoo.com
2014-12-10
In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin. This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.
Equilibrium iron isotope fractionation at core-mantle boundary conditions.
Polyakov, Veniamin B
2009-02-13
The equilibrium iron isotope fractionation between lower mantle minerals and metallic iron at core-mantle boundary conditions can be evaluated from the high-pressure 57Fe partial vibrational density of states determined by synchrotron inelastic nuclear resonant x-ray scattering spectroscopy using a diamond anvil. Ferropericlase [(Mg,Fe)O] and (Fe,Mg)SiO3- post-perovskite are enriched in heavy iron isotopes relative to metallic iron at ultrahigh pressures, as opposed to the equilibrium iron isotope fractionation between these compounds at low pressure. The enrichment of Earth and Moon basalts in heavy iron isotopes relative to those from Mars and asteroid Vesta can be explained by the equilibrium iron isotope fractionation during the segregation of Earth's core and the assumption that Earth was already differentiated before the Moon-forming "giant impact." PMID:19213913
On boundary condition in heat-exchange processes
NASA Astrophysics Data System (ADS)
Stolyarov, E. P.
2016-10-01
This paper describes the numerical study of heat-exchange of solid body with high-temperature external flow. As follows from the Newton's boundary condition, connecting a heat-flux density with temperature difference between the flow and a body, the heat-exchange coefficient is physically equivalent to the body-surface-normal component of the entropy flux from external flow at equilibrium flow regime. The method of determination of the heat-exchange characteristics using the time-history temperature measurements by a thin-film thermocouple sensor is described. As it is shown from the numerical analysis, the asymptotic value of the heat-exchange coefficient that corresponded to equilibrium regime of external flow exists. Implementation time of this value, i.e. relaxation time, may be of some characteristic time scales of the sensor measuring layer.
Estimating Thermal Inertia with a Maximum Entropy Boundary Condition
NASA Astrophysics Data System (ADS)
Nearing, G.; Moran, M. S.; Scott, R.; Ponce-Campos, G.
2012-04-01
Thermal inertia, P [Jm-2s-1/2K-1], is a physical property the land surface which determines resistance to temperature change under seasonal or diurnal heating. It is a function of volumetric heat capacity, c [Jm-3K-1], and thermal conductivity, k [Wm-1K-1] of the soil near the surface: P=√ck. Thermal inertia of soil varies with moisture content due the difference between thermal properties of water and air, and a number of studies have demonstrated that it is feasible to estimate soil moisture given thermal inertia (e.g. Lu et al, 2009, Murray and Verhoef, 2007). We take the common approach to estimating thermal inertia using measurements of surface temperature by modeling the Earth's surface as a 1-dimensional homogeneous diffusive half-space. In this case, surface temperature is a function of the ground heat flux (G) boundary condition and thermal inertia and a daily value of P was estimated by matching measured and modeled diurnal surface temperature fluctuations. The difficulty is in measuring G; we demonstrate that the new maximum entropy production (MEP) method for partitioning net radiation into surface energy fluxes (Wang and Bras, 2011) provides a suitable boundary condition for estimating P. Adding the diffusion representation of heat transfer in the soil reduces the number of free parameters in the MEP model from two to one, and we provided a sensitivity analysis which suggests that, for the purpose of estimating P, it is preferable to parameterize the coupled MEP-diffusion model by the ratio of thermal inertia of the soil to the effective thermal inertia of convective heat transfer to the atmosphere. We used this technique to estimate thermal inertia at two semiarid, non-vegetated locations in the Walnut Gulch Experimental Watershed in southeast AZ, USA and compared these estimates to estimates of P made using the Xue and Cracknell (1995) solution for a linearized ground heat flux boundary condition, and we found that the MEP-diffusion model produced
Modeling solar wind with boundary conditions from interplanetary scintillations
Manoharan, P.; Kim, T.; Pogorelov, N. V.; Arge, C. N.
2015-09-30
Interplanetary scintillations make it possible to create three-dimensional, time- dependent distributions of the solar wind velocity. Combined with the magnetic field observations in the solar photosphere, they help perform solar wind simulations in a genuinely time-dependent way. Interplanetary scintillation measurements from the Ooty Radio Astronomical Observatory in India provide directions to multiple stars and may assure better resolution of transient processes in the solar wind. In this paper, we present velocity distributions derived from Ooty observations and compare them with those obtained with the Wang-Sheeley-Arge (WSA) model. We also present our simulations of the solar wind flow from 0.1 AU to 1 AU with the boundary conditions based on both Ooty and WSA data.
Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes
NASA Astrophysics Data System (ADS)
Sokhan, Vladimir P.; Nicholson, David; Quirke, Nicholas
2002-11-01
Steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon. Building on our previous study of slit carbon nanopores we show that fluid flow in a nanotube is also characterized by a large slip length. By analyzing temporal profiles of the velocity components of particles colliding with the wall we obtain values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall and, for the first time, propose slip boundary conditions for smooth continuum surfaces such that they are equivalent in adsorption, diffusion, and fluid flow properties to fully dynamic atomistic models.
Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions
Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad
2016-01-01
Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208
IFSAR phase unwrapping in the presence of Dirichlet boundary conditions
NASA Astrophysics Data System (ADS)
Rogers, George W.; Mansfield, Arthur W.; Rais, Houra; Poehler, Paul L.
1998-09-01
Phase unwrapping is one of the key computational elements in digital elevation model generation from interferometric SAR. In this paper we present a reformulation of the weighted least squares phase unwrapping approach that incorporates Dirichlet boundary conditions. The application of this formulation to the incorporation of control points into the solution as well as for unwrapping the interferogram in stages is discussed. The ability of the weighted least squares approach to fully unwrap an interferogram can be very dependent on the weight matrix used. This has led us to develop an adaptive approach to updating the weight matrix to be used in conjunction with our weighted least squares approach. Examples along the preliminary results based on ERS data will be presented.
Modeling solar wind with boundary conditions from interplanetary scintillations
Manoharan, P.; Kim, T.; Pogorelov, N. V.; Arge, C. N.; Manoharan, P. K.
2015-09-30
Interplanetary scintillations make it possible to create three-dimensional, time- dependent distributions of the solar wind velocity. Combined with the magnetic field observations in the solar photosphere, they help perform solar wind simulations in a genuinely time-dependent way. Interplanetary scintillation measurements from the Ooty Radio Astronomical Observatory in India provide directions to multiple stars and may assure better resolution of transient processes in the solar wind. In this paper, we present velocity distributions derived from Ooty observations and compare them with those obtained with the Wang-Sheeley-Arge (WSA) model. We also present our simulations of the solar wind flow from 0.1 AUmore » to 1 AU with the boundary conditions based on both Ooty and WSA data.« less
Landauer conductance and twisted boundary conditions for Dirac fermions
NASA Astrophysics Data System (ADS)
Ryu, Shinsei; Mudry, Christopher; Furusaki, Akira; Ludwig, Andreas
2007-03-01
We apply the generating function technique developed by Nazarov to the computation of the density of transmission eigenvalues for a finite graphene sheet in which a two-dimensional freely propagating massless Dirac fermion is realized. By modeling ideal leads attached to the sample as a conformal invariant boundary condition, we relate the generating function for the density of transmission eigenvalues to the twisted chiral partition functions of fermionic (c=1) and bosonic (c=-1) conformal field theories. We also discuss the scaling behavior of the ac Kubo conductivity and compare its different dc limits with results obtained from the Landauer conductance. Finally, we show that the disorder averaged Einstein conductivity is an analytic function of the disorder strength, with vanishing first-order correction, for a tight-binding model on the honeycomb lattice with weak real-valued and nearest-neighbor random hopping.
Final state boundary condition of the Schwarzschild black hole
Ahn, Doyeol
2006-10-15
It is shown that the internal stationary state of the Schwarzschild black hole can be represented by a maximally entangled two-mode squeezed state of collapsing matter and infalling Hawking radiation. The final boundary condition at the singularity is then described by the random unitary transformation acting on the collapsing matter field. The outgoing Hawking radiation is obtained by the final-state projection on the total wave function, which looks like a quantum teleportation process without the classical information transmitted. The black hole evaporation process as seen by the observer outside the black hole is now a unitary process but nonlocal physics is required to transmit the information outside the black hole. It is also shown that the final-state projection by the evaporation process is strongly affected by the quantum state outside the event horizon, which clearly violates the locality principle.
Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.
Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad
2016-01-01
Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208
Gas cushion model and hydrodynamic boundary conditions for superhydrophobic textures.
Nizkaya, Tatiana V; Asmolov, Evgeny S; Vinogradova, Olga I
2014-10-01
Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties. We propose an operator method, which allows us to map the flow in the gas subphase to a local slip boundary condition at the liquid-gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Besides superlubricating Cassie surfaces, our approach is valid for rough surfaces impregnated by a low-viscosity "lubricant," and even for Wenzel textures, where a liquid follows the surface relief. These results provide a framework for the rational design of textured surfaces for numerous applications.
14 CFR 435.11 - Additional license terms and conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING REENTRY OF A REENTRY VEHICLE OTHER THAN A REUSABLE LAUNCH VEHICLE (RLV) General § 435.11 Additional license terms and conditions. The FAA may amend a...
14 CFR 435.11 - Additional license terms and conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING REENTRY OF A REENTRY VEHICLE OTHER THAN A REUSABLE LAUNCH VEHICLE (RLV) General § 435.11 Additional license terms and conditions. The FAA may amend a...
14 CFR 435.11 - Additional license terms and conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING REENTRY OF A REENTRY VEHICLE OTHER THAN A REUSABLE LAUNCH VEHICLE (RLV) General § 435.11 Additional license terms and conditions. The FAA may amend a...
14 CFR 435.11 - Additional license terms and conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING REENTRY OF A REENTRY VEHICLE OTHER THAN A REUSABLE LAUNCH VEHICLE (RLV) General § 435.11 Additional license terms and conditions. The FAA may amend a...
NASA Astrophysics Data System (ADS)
Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.
2015-12-01
Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.
Interstellar Matter and the Boundary Conditions of the Heliosphere
NASA Astrophysics Data System (ADS)
Frisch, Priscilla C.
1998-07-01
The interstellar cloud surrounding the solar system regulates the galactic environment of the Sun, and determines the boundary conditions of the heliosphere. Both the Sun and interstellar clouds move through space, so these boundary conditions change with time. Data and theoretical models now support densities in the cloud surrounding the solar system of n(H0)=0.22±0.06 cm-3, and n(e-)˜0.1 cm-3, with larger values allowed for n(H0) by radiative transfer considerations. Ulysses and Extreme Ultraviolet Explorer satellite He0 data yield a cloud temperature of 6400 K. Nearby interstellar gas appears to be structured and inhomogeneous. The interstellar gas in the Local Fluff cloud complex exhibits elemental abundance patterns in which refractory elements are enhanced over the depleted abundances found in cold disk gas. Within a few parsecs of the Sun, inconclusive evidence for factors of 2-5 variation in Mg+ and Fe+ gas phase abundances is found, providing evidence for variable grain destruction. In principle, photoionization calculations for the surrounding cloud can be compared with elemental abundances found in the pickup ion and anomalous cosmic-ray populations to model cloud properties, including ionization, reference abundances, and radiation field. Observations of the hydrogen pile up at the nose of the heliosphere are consistent with a barely subsonic motion of the heliosphere with respect to the surrounding interstellar cloud. Uncertainties on the velocity vector of the cloud that surrounds the solar system indicate that it is uncertain as to whether the Sun and α Cen are or are not immersed in the same interstellar cloud.
Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions.
Afkari, Damon; Gabaldón, Felipe
2016-01-01
In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder.
Non-disturbing Boundary Conditions for Modeling of Laser Material Processing
NASA Astrophysics Data System (ADS)
Kovaleva, I. O.; Grigoriev, S. N.; Gusarov, A. V.
Surface laser treatment of a massive body is the typical geometry for various laser-assisted processes. The classical mathematical formulation is a heat source moving over the surface of a half-space target. Generally, such problems are numerically solved in a finite calculation domain. The adiabatic or isothermal boundary conditions are often applied at the boundaries of the calculation domain. Such an approach becomes rigorous when the linear size of the calculation domain is much greater than the size of the melt pool. It is time consuming. Economic non-disturbing differential boundary conditions proposed here are derived from the well-known analytical asymptotics for the steady-state temperature distributions around a moving heat source in 2D and 3D. Finite-difference boundary conditions approximating these differential conditions are tested for modeling of additive manufacturing of massive metallic parts and walls by selective laser melting. It is shown that the linear size of the calculation domain can be as small as double the size of the melt pool.
14 CFR 431.11 - Additional license terms and conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Additional license terms and conditions. 431.11 Section 431.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... time by modifying or adding license terms and conditions to ensure compliance with 49 U.S.C....
14 CFR 415.11 - Additional license terms and conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Additional license terms and conditions. 415.11 Section 415.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... and conditions. The FAA may modify a launch license at any time by modifying or adding license...
Experimentally constraining the boundary conditions for volcanic ash aggregation
NASA Astrophysics Data System (ADS)
Kueppers, U.; Auer, B.; Cimarelli, C.; Scolamacchia, T.; Guenthel, M.; Dingwell, D. B.
2011-12-01
Volcanic ash is the primary product of various volcanic processes. Due to its size, ash can remain in the atmosphere for a prolonged period of time. Aggregation processes are a first-order influence on the residence time of ash in the atmosphere and its dispersion from the vent. Due to their internal structure, ash aggregates have been classified as ash pellets or accretionary lapilli. Although several concomitant factors may play a role during aggregation, there is a broad consensus that both 1) particle collision and 2) humidity are required for particles to aggregate. However, direct observation of settling aggregates and record of the boundary conditions favourable to their formation are rare, therefore limiting our understanding of the key processes that determine ash aggregates formation. Here, we present the first results from experiments aimed at reproducing ash aggregation by constraining the required boundary conditions. We used a ProCell Lab System of Glatt Ingenieurtechnik GmbH that is conventionally used for food and chemical applications. We varied the following parameters: 1) air flow speed [40-120 m3/h], 2) air temperature [30-60°C], 3) relative humidity [20-50 %], and 4) liquid droplets composition [water and 25% water glass, Na2SiO3]. The starting material (125-90 μm) is obtained by milling natural basaltic lapilli (Etna, Italy). We found that the experimental duration and the chosen conditions were not favourable for the production of stable aggregates when using water as spraying liquid. Using a 25% water-glass solution as binder we could successfully generate and investigate aggregates of up to 2 mm size. Many aggregates are spherical and resemble ash pellets. In nature, ash pellets and accretionary lapilli are the product of complex processes taking place at very different conditions (temperature, humidity, ash concentration, degree of turbulence). These experiments shed some first light on the ash agglomeration process for which direct
14 CFR 415.11 - Additional license terms and conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 4 2013-01-01 2013-01-01 false Additional license terms and conditions. 415.11 Section 415.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH LICENSE General § 415.11 Additional license...
Stationary flow of non-Newtonian fluid with nonmonotone frictional boundary conditions
NASA Astrophysics Data System (ADS)
Dudek, Sylwia; Kalita, Piotr; Migórski, Stanisław
2015-10-01
We study the stationary two-dimensional incompressible flow of non-Newtonian fluid governed by a nonlinear constitutive law and with a multivalued nonmonotone subdifferential frictional boundary condition. We provide an abstract result on existence of solution to an operator inclusion modeling the flow phenomenon. We prove a theorem on existence and, under additional assumptions, also uniqueness of weak solution to the flow problem.
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.; Warma, Mahamadi
2016-08-01
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.
NASA Astrophysics Data System (ADS)
Mao, Lei; Lu, Yong
2016-07-01
In this paper, the sensitivities of artificial boundary condition (ABC) frequencies to the damages are investigated, and the optimal sensors are selected to provide the reliable structural damage identification. The sensitivity expressions for one-pin and two-pin ABC frequencies, which are the natural frequencies from structures with one and two additional constraints to its original boundary condition, respectively, are proposed. Based on the expressions, the contributions of the underlying mode shapes in the ABC frequencies can be calculated and used to select more sensitive ABC frequencies. Selection criteria are then defined for different conditions, and their performance in structural damage identification is examined with numerical studies. From the findings, conclusions are given.
Tiegs, T.N.; Ploetz, K.L.; Kiggans, J.O.; Yeckley, R.L.
1993-06-01
Microwave annealing of dense Si{sub 3}N{sub 4}-4% Y{sub 2}O{sub 3} materials showed improvements over conventional heating. Increases in fracture toughness were observed for annealing between 1200--1650C. The high temperature strength was related to the residual {alpha}-Si{sub 3}N{sub 4} content which is indicative of a finer average grain size in the specimens. The high temperature dynamic fatigue showed increased stress to failure for specimens microwave annealed between 1400--1550C for periods >5 h. Silicon nitrides with different sintering additives would require different conditions for optimum crystallization. While there were some observed property improvements, they were not so dramatic to justify abandoning conventional over microwave heating. The Si{sub 3}N{sub 4}-4% Y{sub 2}O{sub 3} materials used in the study were developed for elevated temperature use and already posses excellent good high temperature strength, fatigue resistance and creep properties. This is due to the very refractory nature of the grain boundary phases and the small quantity of secondary phase present. However, microwave annealing of these materials may be necessary in applications where the maximum in fracture toughness and fatigue resistance are required and thus justifies its use.
NASA Astrophysics Data System (ADS)
Mayrhofer, Arno; Rogers, Benedict D.; Violeau, Damien; Ferrand, Martin
2013-11-01
Semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in smoothed particle hydrodynamics (SPH) for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which implies exact energy conservation. It will be shown that this property holds only in the limit of the continuous SPH approximation, whereas in the discrete SPH formulation it is only approximately true, leading to numerical noise. This noise, interpreted as a form of "turbulence", is treated using an additional volume diffusion term in the continuity equation which we show is equivalent to an approximate Riemann solver. Subsequently two extensions to the boundary conditions are presented. The first dealing with a variable driving force when imposing a volume flux in a periodic flow and the second showing a generalization of the wall boundary condition to Robin type and arbitrary-order interpolation. Two modifications for free-surface flows are presented for the volume diffusion term as well as the wall boundary condition. In order to validate the theoretical constructs numerical experiments are performed showing that the present volume flux term yields results with an error 5 orders of magnitude smaller then previous methods while the Robin boundary conditions are imposed correctly with an error depending on the order of the approximation. Furthermore, the proposed modifications for free-surface flows improve the behavior at the intersection of free surface and wall as well as prevent free-surface detachment when using the volume diffusion term. Finally, this paper is concluded by a simulation of a dam break over a wedge demonstrating the improvements proposed in this paper.
Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic
NASA Astrophysics Data System (ADS)
Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.
2016-08-01
Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain
Shroud boundary condition characterization experiments at the Radiant Heat Facility.
Suo-Anttila, Jill Marie; Nakos, James Thomas; Gill, Walter
2004-10-01
A series of experiments was performed to better characterize the boundary conditions from an inconel heat source ('shroud') painted with Pyromark black paint. Quantifying uncertainties in this type of experimental setup is crucial to providing information for comparisons with code predictions. The characterization of this boundary condition has applications in many scenarios related to fire simulation experiments performed at Sandia National Laboratories Radiant Heat Facility (RHF). Four phases of experiments were performed. Phase 1 results showed that a nominal 1000 C shroud temperature is repeatable to about 2 C. Repeatability of temperatures at individual points on the shroud show that temperatures do not vary more than 10 C from experiment to experiment. This variation results in a 6% difference in heat flux to a target 4 inches away. IR camera images showed the shroud was not at a uniform temperature, although the control temperature was constant to about {+-}2 C during a test. These images showed that a circular shaped, flat shroud with its edges supported by an insulated plate has a temperature distribution with higher temperatures at the edges and lower temperatures in the center. Differences between the center and edge temperatures were up to 75 C. Phase 3 results showed that thermocouple (TC) bias errors are affected by coupling with the surrounding environment. The magnitude of TC error depends on the environment facing the TC. Phase 4 results were used to estimate correction factors for specific applications (40 and 63-mil diameter, ungrounded junction, mineral insulated, metal-sheathed TCs facing a cold surface). Correction factors of about 3.0-4.5% are recommended for 40 mil diameter TCs and 5.5-7.0% for 63 mil diameter TCs. When mounted on the cold side of the shroud, TCs read lower than the 'true' shroud temperature, and the TC reads high when on the hot side. An alternate method uses the average of a cold side and hot side TC of the same size to
Integrable boundary conditions for multi-species ASEP
NASA Astrophysics Data System (ADS)
Crampe, N.; Finn, C.; Ragoucy, E.; Vanicat, M.
2016-09-01
The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper.
NASA Technical Reports Server (NTRS)
Biringen, S.; Cook, C.
1988-01-01
Pressure boundary conditions satisfying the normal momentum equation at solid boundaries with second-order accuracy are developed. Implementation of these conditions in an explicit numerical procedure for the two-dimensional incompressible Navier-Stokes equations enables convergent and accurate solutions for the driven cavity problem provided that the integral constraint of the Neumann boundary condtions is satisfied.
NASA Astrophysics Data System (ADS)
Pfeiffer, M.; Munz, C.-D.; Fasoulas, S.
2015-08-01
In a numerical solution of the Maxwell-Vlasov system, the consistency with the charge conservation and divergence conditions has to be kept solving the hyperbolic evolution equations of the Maxwell system, since the vector identity ∇ ṡ (∇ × u →) = 0 and/or the charge conservation of moving particles may be not satisfied completely due to discretization errors. One possible method to force the consistency is the hyperbolic divergence cleaning. This hyperbolic constraint formulation of Maxwell's equations has been proposed previously, coupling the divergence conditions to the hyperbolic evolution equations, which can then be treated with the same numerical method. We pick up this method again and show that electrostatic limit may be obtained by accentuating the divergence cleaning sub-system and converging to steady state. Hence, the electrostatic case can be treated by the electrodynamic code with reduced computational effort. In addition, potential boundary conditions as often given in practical applications can be coupled in a similar way to get appropriate boundary conditions for the field equations. Numerical results are shown for an electric dipole, a parallel-plate capacitor, and a Langmuir wave. The use of potential boundary conditions is demonstrated in an Einzel lens simulation.
Influence of boundary conditions on the radiation emitted by an accelerated source
Alves, Danilo T.; Crispino, Luis C. B.; Lima, Marcelo C. de; Higuchi, Atsushi
2010-03-15
We analyze how the radiation emitted by an accelerated source minimally coupled to a massless real scalar field is influenced by the boundary conditions imposed on the field. We find that the response rate of the accelerated source in the presence of nearby boundaries parallel to the direction of the source's motion can be suppressed or enhanced depending on whether Dirichlet or Neumann boundary conditions are imposed on the field. We conclude that the response rate strongly depends on the kind of boundary conditions imposed, just as the sign of the Casimir force depends on the boundary conditions imposed on the field.
Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations
NASA Technical Reports Server (NTRS)
Darmofal, David L.
1998-01-01
An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.
Evaluation of Various Types of Wall Boundary Conditions for the Boltzmann Equation
NASA Astrophysics Data System (ADS)
Wilson, Christopher D.; Agarwal, Ramesh K.; Tcheremissine, Felix G.
2011-05-01
This paper presents the evaluation of several solid wall boundary conditions when used in the numerical solution of the Boltzmann equation using the finite-difference/finite-volume methods. Five solid wall boundary conditions are considered: (a) adsorption, (b) specular reflection, (c) diffuse reflection, (d) Maxwellian reflection, and (e) adsorptive Maxwellian reflection. The boundary conditions are applied on a two-dimensional discretized velocity space mesh. Methods for applying the same boundary conditions on a three-dimensional velocity space grid are also presented. The boundary conditions are implemented for the numerical solution of the hypersonic rarefied flow over a flat plate using a three-dimensional generalized Boltzmann equation (GBE) solver. The derivatives that contribute to heat transfer and skin friction at the solid boundary are calculated and compared. Recommendations for further evaluation of the boundary conditions are made.
Stability of a flexible structure with destabilizing boundary conditions
NASA Astrophysics Data System (ADS)
Shubov, M.; Shubov, V.
2016-07-01
The Euler-Bernoulli beam model with non-dissipative boundary conditions of feedback control type is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivatives of displacement and slope at the right end. The codiagonal matrix depending on two control parameters relates input and observation. The paper contains five results. First, asymptotic approximation for eigenmodes is derived. Second, `the main identity' is established. It provides a relation between mode shapes of two systems: one with non-zero control parameters and the other one with zero control parameters. Third, when one control parameter is positive and the other one is zero, `the main identity' yields stability of all eigenmodes (though the system is non-dissipative). Fourth, the stability of eigenmodes is extended to the case when one control parameter is positive, and the other one is sufficiently small. Finally, existence and properties of `deadbeat' modes are investigated.
Boundary conditions for gas flow problems from anisotropic scattering kernels
NASA Astrophysics Data System (ADS)
To, Quy-Dong; Vu, Van-Huyen; Lauriat, Guy; Léonard, Céline
2015-10-01
The paper presents an interface model for gas flowing through a channel constituted of anisotropic wall surfaces. Using anisotropic scattering kernels and Chapman Enskog phase density, the boundary conditions (BCs) for velocity, temperature, and discontinuities including velocity slip and temperature jump at the wall are obtained. Two scattering kernels, Dadzie and Méolans (DM) kernel, and generalized anisotropic Cercignani-Lampis (ACL) are examined in the present paper, yielding simple BCs at the wall fluid interface. With these two kernels, we rigorously recover the analytical expression for orientation dependent slip shown in our previous works [Pham et al., Phys. Rev. E 86, 051201 (2012) and To et al., J. Heat Transfer 137, 091002 (2015)] which is in good agreement with molecular dynamics simulation results. More important, our models include both thermal transpiration effect and new equations for the temperature jump. While the same expression depending on the two tangential accommodation coefficients is obtained for slip velocity, the DM and ACL temperature equations are significantly different. The derived BC equations associated with these two kernels are of interest for the gas simulations since they are able to capture the direction dependent slip behavior of anisotropic interfaces.
Analytical model of infiltration under constant-concentration boundary conditions
NASA Astrophysics Data System (ADS)
Triadis, D.; Broadbridge, P.
2010-03-01
Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C - 1)/(C - Θ)2, where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant-concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C - 1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C - 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.
Global boundary conditions for a Dirac operator on the solid torus
Klimek, Slawomir; McBride, Matt
2011-06-15
We study a Dirac operator subject to Atiayh-Patodi-Singer-like boundary conditions on the solid torus and shows that the corresponding boundary value problem is elliptic in the sense that the Dirac operator has a compact parametrix.
Evaluating the effects of boundary condition update frequency on CCLMs climate
NASA Astrophysics Data System (ADS)
Pankatz, Klaus; Kerkweg, Astrid
2014-05-01
In regional climate modelling it is common to update the boundary conditions of the model every six hours. This is mainly due to the fact, that reference data sets like ERA are only available every six hours. Additionally, for offline coupling procedures it would be to costly to store boundary data in higher temporal resolution for climate simulations. However, theoretically, the coupling frequency can be as high as the timestep of the driving model. It is however unclear if a more frequent update of the boundary conditions has a significant effect on the climate in the domain of the regional model. This study uses COSMO/MESSy (Kerkweg and Jöckel, 2012) to couple CCLM offline to the GCM ECHAM5. For three update frequencies, namely six hours, one hour and six minutes a 30 year time slice experiment has been performed. The climate is evaluated by comparing means, standard deviations and PDFs of diagnostic and prognostic variables in the whole domain and in subdomains as defined in PRUDENCE. The study shows only small deviations, some stastically significant though, of the means (2m temperature, sea level pressure, precipitaion). The variable stastistics do not defer much. Differences are slightly more pronounced when comparing the PRUDENCE regions. The precipitation bias at the domain borders, especially at the inflow boundary, is more pronounced in higher coupling frequencies. The deviations reach far into the model domain.
Zheng, Lin; Guo, Zhaoli; Shi, Baochang
2012-07-01
The lattice Boltzmann equation (LBE) method has been shown to be a promising tool for microscale gas flows. However, few works focus on the microtube flows, and there still are some fundamental problems for the LBE to such flows. In this paper, a recently proposed axisymmetric LBE with three kinetic boundary conditions, i.e., the combination of bounceback and specular reflection scheme, the combination of the Maxwell and specular-reflection scheme, and the combination of the Maxwell and bounceback scheme, have been investigated in detail. By analyzing the micro-Hagen-Poiseuille flow, we observed the discrete boundary condition effect and provided a revised boundary scheme to overcome such effect near the slip flow regime. Some numerical tests for the micro-Hagen-Poiseuille have been carried out to validate the analysis, and the numerical results of the revised boundary schemes agree well with the analytic solutions which confirmed our theoretical analysis. In addition, we also applied the revised combination of the Maxwell and bounceback scheme to microtube flow with sudden expansion and contraction, the numerical results of the pressure distribution and normalized slip velocity agree well with the theoretical ones. PMID:23005568
Effect of Insolation Boundary Conditions on Type B Package Internal Temperatures
Hovingh, J; Shah, VL
2002-05-30
The prescription of the initial conditions and the final conditions for a thermal accident for Type B packages are different for differing regulations. This paper presents an analytical method for estimating the effect of the boundary conditions on post-fire peak internal package temperatures. Results are given for several boundary conditions for a Type B drum-type package.
Time-dependent density functional theory with twist-averaged boundary conditions
NASA Astrophysics Data System (ADS)
Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.
2016-05-01
Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be
14 CFR 431.11 - Additional license terms and conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 14 Aeronautics and Space 4 2011-01-01 2011-01-01 false Additional license terms and conditions. 431.11 Section 431.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH AND REENTRY OF A REUSABLE LAUNCH VEHICLE...
14 CFR 431.11 - Additional license terms and conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 4 2012-01-01 2012-01-01 false Additional license terms and conditions. 431.11 Section 431.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH AND REENTRY OF A REUSABLE LAUNCH VEHICLE...
14 CFR 431.11 - Additional license terms and conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 4 2013-01-01 2013-01-01 false Additional license terms and conditions. 431.11 Section 431.11 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH AND REENTRY OF A REUSABLE LAUNCH VEHICLE...
High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering
NASA Technical Reports Server (NTRS)
Fibich, Gadi; Tsynkov, Semyon
2000-01-01
When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.
NASA Astrophysics Data System (ADS)
Zhang, Tiangang; Koshizuka, Seiichi; Murotani, Kohei; Shibata, Kazuya; Ishii, Eiji; Ishikawa, Masanori
2016-02-01
The boundary conditions represented by polygons in moving particle semi-implicit (MPS) method (Koshizuka and Oka, Nuclear Science and Engineering, 1996) have been widely used in the industry simulations since it can simply simulate complex geometry with high efficiency. However, the inaccurate particle number density near non-planar wall boundaries dramatically affects the accuracy of simulations. In this paper, we propose an initial boundary particle arrangement technique coupled with the wall weight function method (Zhang et al. Transaction of JSCES, 2015) to improve the particle number density near slopes and curved surfaces with boundary conditions represented by polygons in three dimensions. Two uniform grids are utilized in the proposed technique. The grid points in the first uniform grid are used to construct boundary particles, and the second uniform grid stores the same information as in the work by Zhang et al. The wall weight functions of the grid points in the second uniform grid are calculated by newly constructed boundary particles. The wall weight functions of the fluid particles are interpolated from the values stored on the grid points in the second uniform grid. Because boundary particles are located on the polygons, complex geometries can be accurately represented. The proposed method can dramatically improve the particle number density and maintain the high efficiency. The performance of the previously proposed wall weight function (Zhang et al.) with the boundary particle arrangement technique is verified in comparison with the wall weight function without boundary particle arrangement by investigating two example geometries. The simulations of a water tank with a wedge and a complex geometry show the general applicability of the boundary particle arrangement technique to complex geometries and demonstrate its improvement of the wall weight function near the slopes and curved surfaces.
Interface Conditions for Wave Propagation Through Mesh Refinement Boundaries
NASA Technical Reports Server (NTRS)
Choi, Dae-II; Brown, J. David; Imbiriba, Breno; Centrella, Joan; MacNeice, Peter
2002-01-01
We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells eliminates these spurious signals.
Interface conditions for wave propagation through mesh refinement boundaries
NASA Astrophysics Data System (ADS)
Choi, Dae-Il; David Brown, J.; Imbiriba, Breno; Centrella, Joan; MacNeice, Peter
2004-01-01
We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells suppresses these spurious signals.
NASA Astrophysics Data System (ADS)
Hung, K. C.; Liew, K. M.; Lim, M. K.; Leong, S. L.
An investigation on the effects of boundary constraints on the vibratory characteristics of symmetrically laminated rectangular plates is carried out. The research findings are reported in a two-part paper. Vibration frequency parameters and mode shapes for symmetric laminates with classical boundary conditions are reported in Part I and elastically restrained boundaries in Part II. The analysis is performed based on the use of admissible beam characteristics orthonormal polynomial functions in the Rayleigh-Ritz method to derive the governing eigenvalue equation. In this paper, several examples for laminates with different combinations of free, simply supported and clamped edges are solved to demonstrate the accuracy and flexibility of the present method. Discussion on the effects of boundary conditions, fiber orientations and stacking sequences on the vibrational response is included.
A device adaptive inflow boundary condition for Wigner equations of quantum transport
Jiang, Haiyan; Lu, Tiao; Cai, Wei
2014-02-01
In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.
A device adaptive inflow boundary condition for Wigner equations of quantum transport
NASA Astrophysics Data System (ADS)
Jiang, Haiyan; Lu, Tiao; Cai, Wei
2014-02-01
In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi-Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.
Revisit boundary conditions for the self-adjoint angular flux formulation
Wang, Yaqi; Gleicher, Frederick N.
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
Implementation of C* Boundary Conditions in the Hybrid Monte Carlo Algorithm
NASA Astrophysics Data System (ADS)
Carmona, José Manuel; D'elia, Massimo; Di Giacomo, Adriano; Lucini, Biagio
In the study of QCD dynamics, C* boundary conditions are physically relevant in certain cases. In this paper, we study the implementation of these boundary conditions in the lattice formulation of full QCD with staggered fermions. In particular, we show that the usual even-odd partition trick to avoid the redoubling of the fermion matrix is still valid in this case. We give an explicit implementation of these boundary conditions for the Hybrid Monte Carlo algorithm.
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
NASA Technical Reports Server (NTRS)
Baker, A. J.
1986-01-01
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
Phase-modulated solitary waves controlled by a boundary condition at the bottom.
Mukherjee, Abhik; Janaki, M S
2014-06-01
A forced Korteweg-de Vries (KdV) equation is derived to describe weakly nonlinear, shallow-water surface wave propagation over nontrivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced KdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition, whereas amplitude remains constant. PMID:25019847
Critical deflagration waves leading to detonation onset under different boundary conditions
NASA Astrophysics Data System (ADS)
Lin, Wei; Zhou, Jin; Fan, Xiao-Hua; Lin, Zhi-Yong
2015-01-01
High-speed turbulent critical deflagration waves before detonation onset in H2-air mixture propagated into a square cross section channel, which was assembled of optional rigid rough, rigid smooth, or flexible walls. The corresponding propagation characteristic and the influence of the wall boundaries on the propagation were investigated via high-speed shadowgraph and a high-frequency pressure sampling system. As a comprehensive supplement to the different walls effect investigation, the effect of porous absorbing walls on the detonation propagation was also investigated via smoke foils and the high-frequency pressure sampling system. Results are as follows. In the critical deflagration stage, the leading shock and the closely following turbulent flame front travel at a speed of nearly half the CJ detonation velocity. In the preheated zone, a zonary flame arises from the overlapping part of the boundary layer and the pressure waves, and then merges into the mainstream flame. Among these wall boundary conditions, the rigid rough wall plays a most positive role in the formation of the zonary flame and thus accelerates the transition of the deflagration to detonation (DDT), which is due to the boost of the boundary layer growth and the pressure wave reflection. Even though the flexible wall is not conducive to the pressure wave reflection, it brings out a faster boundary layer growth, which plays a more significant role in the zonary flame formation. Additionally, the porous absorbing wall absorbs the transverse wave and yields detonation decay and velocity deficit. After the absorbing wall, below some low initial pressure conditions, no re-initiation occurs and the deflagration propagates in critical deflagration for a relatively long distance. Project supported by the National Natural Science Foundation of China (Grant No. 51206182).
Conditions at the downstream boundary for simulations of viscous incompressible flow
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.
NASA Astrophysics Data System (ADS)
Borjan, Z.
2016-09-01
We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.
Incorporation of a boundary condition to numerical solution of POISSON's equation
Caspi, S.; Helm, M.; Laslett, L.J.
1988-10-01
Two-dimensional and axially-symmetric problems in electrostatics, magnetostatics or potential fluid flow frequently are solved numerically by means of relaxation techniques -- employing, for example, the finite-difference program POISSON. In many such problems, the ''sources'' (charges or currents, vorticity, and regions of permeable material) lie exclusively within a finite closed boundary curve and the relaxation process, in principle, then can be confined to the region interior to such a boundary -- provided that a suitable boundary condition is imposed on the solution at the boundary. This paper is a review and illustration of a computational method that uses a boundary condition of such a nature as to avoid the inaccuracies and more extensive meshes present when, alternatively, a simple Dirichlet or Neumann boundary condition is specified on a somewhat more remote outer boundary. 2 refs., 5 figs., 1 tab.
Additional Results of Ice-Accretion Scaling at SLD Conditions
NASA Technical Reports Server (NTRS)
Bond, Thomas H. (Technical Monitor); Anderson, David N.; Tsao, Jen-Ching
2005-01-01
To determine scale velocity an additional similarity parameter is needed to supplement the Ruff scaling method. A Weber number based on water droplet MVD has been included in several studies because the effect of droplet splashing on ice accretion was believed to be important, particularly for SLD conditions. In the present study, ice shapes recorded at Appendix-C conditions and recent results at SLD conditions are reviewed to show that droplet diameter cannot be important to main ice shape, and for low airspeeds splashing does not appear to affect SLD ice shapes. Evidence is presented to show that while a supplementary similarity parameter probably has the form of a Weber number, it must be based on a length proportional to model size rather than MVD. Scaling comparisons were made between SLD reference conditions and Appendix-C scale conditions using this Weber number. Scale-to-reference model size ratios were 1:1.7 and 1:3.4. The reference tests used a 91-cm-chord NACA 0012 model with a velocity of approximately 50 m/s and an MVD of 160 m. Freezing fractions of 0.3, 0.4, and 0.5 were included in the study.
Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition
NASA Astrophysics Data System (ADS)
Yang, Xin; Zhou, Zhengfang
2016-09-01
This paper estimates the blow-up time for the heat equation ut = Δu with a local nonlinear Neumann boundary condition: The normal derivative ∂ u / ∂ n =uq on Γ1, one piece of the boundary, while on the rest part of the boundary, ∂ u / ∂ n = 0. The motivation of the study is the partial damage to the insulation on the surface of space shuttles caused by high speed flying subjects. We show the finite time blow-up of the solution and estimate both upper and lower bounds of the blow-up time in terms of the area of Γ1. In many other work, they need the convexity of the domain Ω and only consider the problem with Γ1 = ∂ Ω. In this paper, we remove the convexity condition and only require ∂Ω to be C2. In addition, we deal with the local nonlinearity, namely Γ1 can be just part of ∂Ω.
NASA Technical Reports Server (NTRS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Green's function of a heat problem with a periodic boundary condition
NASA Astrophysics Data System (ADS)
Erzhanov, Nurzhan E.
2016-08-01
In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
NASA Astrophysics Data System (ADS)
Esmaili Sikarudi, M. A.; Nikseresht, A. H.
2016-01-01
Smoothed particle hydrodynamics is a robust Lagrangian particle method which is widely used in various applications, from astrophysics to hydrodynamics and heat conduction. It has intrinsic capabilities for simulating large deformation, composites, multiphysics events, and multiphase fluid flows. It is vital to use reliable boundary conditions when boundary value problems like heat conduction or Poisson equation for incompressible flows are solved. Since smoothed particle hydrodynamics is not a boundary fitted grids method, implementation of boundary conditions can be problematic. Many methods have been proposed for enhancing the accuracy of implementation of boundary conditions. In the present study a new approach for facilitating the implementation of Robin and Neumann boundary conditions is proposed and proven to give accurate results. Also there is no need to use complicated preprocessing as in virtual particle method. The new method is compared to an equivalent one dimensional moving least square scheme and it is shown that the present method is less sensitive to particle disorder.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
NASA Astrophysics Data System (ADS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-07-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
NASA Astrophysics Data System (ADS)
Alcubierre, Miguel; Torres, Jose M.
2015-02-01
We introduce a set of constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing eigenfields are left to propagate freely off the numerical grid, boundary conditions are set to enforce that the incoming eigenfields don't introduce spurious reflections and, more importantly, that there are no fields introduced at the boundary that violate the constraint equations. In order to do this we adopt two different approaches to set boundary conditions for the extrinsic curvature, by expressing either the radial or the time derivative of its associated ingoing eigenfield in terms of the constraints. We find that these boundary conditions are very robust in practice, allowing us to perform long lasting evolutions that remain accurate and stable, and that converge to a solution that satisfies the constraints all the way to the boundary.
Experimental verification of free-space singular boundary conditions in an invisibility cloak
NASA Astrophysics Data System (ADS)
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile
2016-04-01
A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.
B. Arnold; T. Corbet
2001-12-18
The purpose of the flow boundary conditions analysis is to provide specified-flux boundary conditions for the saturated zone (SZ) site-scale flow and transport model. This analysis is designed to use existing modeling and analysis results as the basis for estimated groundwater flow rates into the SZ site-scale model domain, both as recharge at the upper (water table) boundary and as underflow at the lateral boundaries. The objective is to provide consistency at the boundaries between the SZ site-scale flow model and other groundwater flow models. The scope of this analysis includes extraction of the volumetric groundwater flow rates simulated by the SZ regional-scale flow model to occur at the lateral boundaries of the SZ site-scale flow model and the internal qualification of the regional-scale model for use in this analysis model report (AMR). In addition, the scope includes compilation of information on the recharge boundary condition taken from three sources: (1) distributed recharge as taken from the SZ regional-scale flow model, (2) recharge below the area of the unsaturated zone (UZ) site-scale flow model, and (3) focused recharge along the Fortymile Wash channel.
Do-It-Yourself Additives Recharge Auto Air Conditioning
NASA Technical Reports Server (NTRS)
2010-01-01
In planning for a return mission to the Moon, NASA aimed to improve the thermal control systems that keep astronauts comfortable and cool while inside a spacecraft. Goddard Space Flight Center awarded a Small Business Innovation Research (SBIR) contract to Mainstream Engineering Corporation, of Rockledge, Florida, to develop a chemical/mechanical heat pump. IDQ Inc., of Garland, Texas, exclusively licensed the technology and incorporates it into its line of Arctic Freeze products for automotive air conditioning applications. While working on the design, Mainstream Engineering came up with a unique liquid additive called QwikBoost to enhance the performance of the advanced heat pump design.
NASA Astrophysics Data System (ADS)
Ghosh, Somnath; Kubair, Dhirendra V.
2016-10-01
Statistically equivalent representative volume elements or SERVEs are representations of the microstructure that are used for micromechanical simulations to generate homogenized material constitutive responses and properties (Swaminathan et al., 2006a; Ghosh, 2011). Typically, a SERVE is generated from the parent microstructure as a statistically equivalent region, whose size is determined from the requirements of convergence of macroscopic properties. Standard boundary conditions, such as affine transformation-based displacement boundary conditions (ATDBCs), uniform traction boundary conditions (UTBCs) or periodic boundary conditions (PBCs) are conventionally applied on the SERVE boundary for micromechanical simulations. However, when the microstructure is characterized by arbitrary, nonuniform distributions of heterogeneities, these simple boundary conditions do not represent the effect of regions exterior to the SERVE. Improper boundary conditions can result in significantly larger than optimal SERVE domains, needed for converged properties. In an attempt to overcome the limitations of the conventional boundary conditions on the SERVE, this paper explores the effect of boundary conditions that incorporate the statistics of the exterior region on the SERVE of elastic composites. Using Green's function based interaction kernels, coupled with statistical functions of the microstructural characteristics like one-point and two-point correlation functions, a novel exterior statistics-based boundary condition or ESBC is derived for the SERVE. The advantages of the ESBC are established by comparing with results of simulations using conventional boundary conditions. Results of the SERVE simulations subjected to ESBCs are also compared with those from other popular methods like statistical volume element (SVE) and weighted statistical volume element (WSVE). The proposed ESBCs offer significant advantages over other methods in the SERVE-based analysis of heterogeneous
General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures
Higuchi, Takuya
2011-08-19
When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II-VI' for semiconductors. As we will review, interfaces between
Hydromagnetic conditions near the core-mantle boundary
NASA Technical Reports Server (NTRS)
Backus, George E.
1995-01-01
The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.
On the Boundary Condition Between Two Multiplying Media
DOE R&D Accomplishments Database
Friedman, F. L.; Wigner, E. P.
1944-04-19
The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.
Poynting flux-conserving low-altitude boundary conditions for global magnetospheric models
NASA Astrophysics Data System (ADS)
Xi, S.; Lotko, W.; Zhang, B.; Brambles, O. J.; Lyon, J. G.; Merkin, V. G.; Wiltberger, M.
2015-01-01
A method for specifying low-altitude or inner boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. The single-fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method, with comparisons between simulations using LFM's standard hardwall boundary conditions and the new flux-conserving boundary conditions. Identical idealized upstream solar wind and interplanetary magnetic field conditions and the same constant ionospheric conductance are used in both runs. The results show that, compared to LFM's standard hardwall boundary conditions, the flux-conserving method improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the hemispheric integrated field-aligned DC Poynting flux just above the boundary is close to the hemispheric total Joule heating of the ionosphere, as it should be if electromagnetic energy is conserved. The MHD velocity and perpendicular currents are well-behaved near the inner boundary for the flux conserving boundary conditions.
Boundary lubrication of formulated C-ethers in air to 300 C. 2: Organic acid additives
NASA Technical Reports Server (NTRS)
Jones, W. R., Jr.
1973-01-01
Friction and wear measurements were made on CVM M-50 steel lubricated with three C-ether (modified polyphenyl ether) formulations in dry and moist air. Results were compared to those obtained with a formulated Type 2 ester and the C-ether base fluid. A ball-on-disk sliding friction apparatus was used. Experimental conditions were a 1-kilogram load, a 17-meter/minute surface speed, and a 25 to 300 C (77 to 572 F) disk temperature range. The three C-ether formulations yielded better boundary lubricating characteristics than the Type 2 ester under most test conditions. All C-ether formulations exhibited higher friction coefficients than the ester from 150 to 300 C (302 to 572 F) and similar or lower values from 25 to 150 C (77 to 302 F).
Technology Transfer Automated Retrieval System (TEKTRAN)
Transient unsaturated horizontal column experiments were conducted with a loam soil, under variable boundary conditions, to obtain added insight on anion exclusion processes that impact nitrate transport in soil. The boundary conditions evaluated were column inlet soil water content, initial soil w...
Open boundary conditions for ISPH and their application to micro-flow
NASA Astrophysics Data System (ADS)
Hirschler, Manuel; Kunz, Philip; Huber, Manuel; Hahn, Friedemann; Nieken, Ulrich
2016-02-01
Open boundary conditions for incompressible Smoothed Particle Hydrodynamics (ISPH) are rare. For stable simulations with open boundary conditions, one needs to specify all boundary conditions correctly in the pressure force as well as in the linear equation system for pressure calculation. Especially for homogeneous or non-homogeneous Dirichlet boundary conditions for pressure there exist several possibilities but only a few lead to stable results. However, this isn't trivial for open boundary conditions. We introduce a new approach for open boundary conditions for ISPH to enable stable simulations. In contrast to existing models for weakly-compressible SPH, we can specify open pressure boundary conditions because in ISPH, pressure can be calculated independently of the density. The presented approach is based on the mirror particle approach already introduced for solid wall boundary conditions. Here we divide the mirror axis in several segments with time-dependent positions. We validate the presented approach for the example of Poiseuille flow and flow around a cylinder at different Reynolds numbers and show that we get good agreement with references. Then, we demonstrate that the approach can be applied to free surface flows. Finally, we apply the new approach to micro-flow through a random porous medium with a different number of in- and outlets and demonstrate its benefits.
The effect of external boundary conditions on condensation heat transfer in rotating heat pipes
NASA Technical Reports Server (NTRS)
Daniels, T. C.; Williams, R. J.
1979-01-01
Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.
NASA Technical Reports Server (NTRS)
Chiavassa, G.; Liandrat, J.
1996-01-01
We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.
Guo, Zhaoli; Shi, Baochang; Zhao, T S; Zheng, Chuguang
2007-11-01
The lattice Boltzmann equation (LBE) has shown its promise in the simulation of microscale gas flows. One of the critical issues with this advanced method is to specify suitable slip boundary conditions to ensure simulation accuracy. In this paper we study two widely used kinetic boundary conditions in the LBE: the combination of the bounce-back and specular-reflection scheme and the discrete Maxwell's scheme. We show that (i) both schemes are virtually equivalent in principle, and (ii) there exist discrete effects in both schemes. A strategy is then proposed to adjust the parameters in the two kinetic boundary conditions such that an accurate slip boundary condition can be implemented. The numerical results demonstrate that the corrected boundary conditions are robust and reliable.
Structural acoustic control of plates with variable boundary conditions: design methodology.
Sprofera, Joseph D; Cabell, Randolph H; Gibbs, Gary P; Clark, Robert L
2007-07-01
A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties. PMID:17614487
Stability of basis property of a periodic problem with nonlocal perturbation of boundary conditions
NASA Astrophysics Data System (ADS)
Imanbaev, Nurlan; Sadybekov, Makhmud
2016-08-01
The present work is the continuation of authors' researchers on stability (instability) of basis property of root vectors of a differential operator with nonlocal perturbation of one of boundary conditions. In this paper a spectral problem for a multiple differentiation operator with an integral perturbation of boundary conditions of one type, which are regular, but not strongly regular, is devoted. For this type of the boundary conditions it is known that the unperturbed problem has an asymptotically simple spectrum, and its system of normalized eigenfunctions creates the Riesz basis. We construct the characteristic determinant of the spectral problem with an integral perturbation of the boundary conditions. It is shown that the Riesz basis property of a system of eigen and adjoint functions is stable with respect to integral perturbations of the boundary condition. In the paper requirements of smoothness to the kernel of the integral perturbation are also reduced (unlike our previous researchers).
Open boundary conditions for the Diffuse Interface Model in 1-D
NASA Astrophysics Data System (ADS)
Desmarais, J. L.; Kuerten, J. G. M.
2014-04-01
New techniques are developed for solving multi-phase flows in unbounded domains using the Diffuse Interface Model in 1-D. They extend two open boundary conditions originally designed for the Navier-Stokes equations. The non-dimensional formulation of the DIM generalizes the approach to any fluid. The equations support a steady state whose analytical approximation close to the critical point depends only on temperature. This feature enables the use of detectors at the boundaries switching between conventional boundary conditions in bulk phases and a multi-phase strategy in interfacial regions. Moreover, the latter takes advantage of the steady state approximation to minimize the interface-boundary interactions. The techniques are applied to fluids experiencing a phase transition and where the interface between the phases travels through one of the boundaries. When the interface crossing the boundary is fully developed, the technique greatly improves results relative to cases where conventional boundary conditions can be used. Limitations appear when the interface crossing the boundary is not a stable equilibrium between the two phases: the terms responsible for creating the true balance between the phases perturb the interior solution. Both boundary conditions present good numerical stability properties: the error remains bounded when the initial conditions or the far field values are perturbed. For the PML, the influence of its main parameters on the global error is investigated to make a compromise between computational costs and maximum error. The approach can be extended to multiple spatial dimensions.
NASA Astrophysics Data System (ADS)
Park, Hyunwook; Pan, Xiaomin; Lee, Changhoon; Choi, Jung-Il
2016-06-01
A novel immersed boundary (IB) method based on an implicit direct forcing (IDF) scheme is developed for incompressible viscous flows. The key idea for the present IDF method is to use a block LU decomposition technique in momentum equations with Taylor series expansion to construct the implicit IB forcing in a recurrence form, which imposes more accurate no-slip boundary conditions on the IB surface. To accelerate the IB forcing convergence during the iterative procedure, a pre-conditioner matrix is introduced in the recurrence formulation of the IB forcing. A Jacobi-type parameter is determined in the pre-conditioner matrix by minimizing the Frobenius norm of the matrix function representing the difference between the IB forcing solution matrix and the pre-conditioner matrix. In addition, the pre-conditioning parameter is restricted due to the numerical stability in the recurrence formulation. Consequently, the present pre-conditioned IDF (PIDF) enables accurate calculation of the IB forcing within a few iterations. We perform numerical simulations of two-dimensional flows around a circular cylinder and three-dimensional flows around a sphere for low and moderate Reynolds numbers. The result shows that PIDF yields a better imposition of no-slip boundary conditions on the IB surfaces for low Reynolds number with a fairly larger time step than IB methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the IB forcing. Finally, we demonstrate the robustness of the present PIDF scheme by numerical simulations of flow around a circular array of cylinders, flows around a falling sphere, and two sedimenting spheres in gravity.
Evaluation of Far-Field Boundary Conditions for the Gust Response Problem
NASA Technical Reports Server (NTRS)
Scott, James R.; Kreider, Kevin L.; Heminger, John A.
2002-01-01
This paper presents a detailed situ dy of four far-field boundary conditions used in solving the single airfoil gust response problem. The boundary conditions, examined are the partial Sommerfeld radiation condition with only radial derivatives, the full Sommerfeld radiation condition with both radial and tangential derivatives, the Bayliss-Turkel condition of order one, and the Hagstrom-Hariharan condition of order one. The main objectives of the study were to determine which far-field boundary condition was most accurate, which condition was least sensitive to changes in grid. and which condition was best overall in terms of both accuracy and efficiency. Through a systematic study of the flat plate gust response problem, it was determined that the Hagstrom-Hariharan condition was most accurate, the Bayliss-Turkel condition was least sensitive to changes in grid, and Bayliss-Turkel was best in terms of both accuracy and efficiency.
On the effects of downstream boundary conditions on diffusive flood routing
NASA Astrophysics Data System (ADS)
Chung, Wei-Hao; Aldama, Alvaro A.; Smith, James A.
The advection-diffusion (AD) equation is widely used to represent flood wave propagation in waterways. Laplace transform methods are employed to obtain the exact solution of a nonhomogeneous AD equation with spatially varied initial condition and time dependent Dirichlet boundary conditions. Numerical inversion of the Laplace transform is employed to solve the AD equation with Neumann and Robin boundary conditions specified at the downstream end of a finite reach of channel. The Neumann boundary condition is specified by the assumption that water level remains constant at the downstream boundary, that is, by a mass conservation version. This is a special case of the general condition that is obtained by plugging a steady rating curve into the continuity equation. Backwater effects are assessed by analyzing response functions of flood wave movement in a semi-infinite channel and of a finite channel with the general condition prescribed as the downstream boundary condition. The Robin boundary condition, however, is derived on the basis of momentum conservation through the stage-discharge relationship. To investigate backwater effects a simple parameterized inflow hydrograph, based on Hermite polynomials, is introduced. The inflow flood hydrograph is completely determined, given three parameters: the time to peak tp, the base time tb, and the peak discharge Qp. Comparisons between backwater effects associated with the Neumann and the Robin boundary conditions are made.
A note on the loop thermosyphon with mixed boundary conditions
NASA Technical Reports Server (NTRS)
Hart, J. E.
1985-01-01
This paper presents a one-dimensional model for flow in a toroidal fluid loop in which the wall heat transfer coefficient is constant over one half of the loop, and zero over the other. A mathematically low-dimensional form of the model gives reasonably accurate predictions of the steady state mass flow, stability, and the nature of nonsteady motions. Numerical computations with a high-dimensional model illustrate the effects of mixed boundaries and axial heat conduction on the chaotic solutions. Comparisons are made with previous low-dimensional models that are exact only for a spatially uniform heat transfer coefficient.
A note on the loop thermosyphon with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Hart, J. E.
1985-05-01
This paper presents a one-dimensional model for flow in a toroidal fluid loop in which the wall heat transfer coefficient is constant over one half of the loop, and zero over the other. A mathematically low-dimensional form of the model gives reasonably accurate predictions of the steady state mass flow, stability, and the nature of nonsteady motions. Numerical computations with a high-dimensional model illustrate the effects of mixed boundaries and axial heat conduction on the chaotic solutions. Comparisons are made with previous low-dimensional models that are exact only for a spatially uniform heat transfer coefficient.
Towards Perfectly Absorbing Boundary Conditions for Euler Equations
NASA Technical Reports Server (NTRS)
Hayder, M. Ehtesham; Hu, Fang Q.; Hussaini, M. Yousuff
1997-01-01
In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.
Liquid Crystals under Photo-patterned Spatially Varying Boundary Conditions
NASA Astrophysics Data System (ADS)
Jiang, Miao; Guo, Yu-Bing; Wei, Qi-Huo
2015-03-01
Liquid crystals under geometric confinements are of not only fundamental interest but also practical importance to applications such as chemical sensing and smart windows. Orientations of liquid crystal molecules in most geometric confinements are uniform at the boundaries and not highly controllable. In this paper, we will present a novel photoalignment technique to pattern spatially varying complex orientation fields, and discuss experimental studies on nematic liquid crystals under confinements of two parallel plates with various well designed molecular orientation fields. Work supported by NSF CMMI-1436565.
Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2011-09-01
The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.
Nordström, Jan Wahlsten, Markus
2015-02-01
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.
Comparison of Methods for Determining Boundary Layer Edge Conditions for Transition Correlations
NASA Technical Reports Server (NTRS)
Liechty, Derek S.; Berry, Scott A.; Hollis, Brian R.; Horvath, Thomas J.
2003-01-01
Data previously obtained for the X-33 in the NASA Langley Research Center 20-Inch Mach 6 Air Tunnel have been reanalyzed to compare methods for determining boundary layer edge conditions for use in transition correlations. The experimental results were previously obtained utilizing the phosphor thermography technique to monitor the status of the boundary layer downstream of discrete roughness elements via global heat transfer images of the X-33 windward surface. A boundary layer transition correlation was previously developed for this data set using boundary layer edge conditions calculated using an inviscid/integral boundary layer approach. An algorithm was written in the present study to extract boundary layer edge quantities from higher fidelity viscous computational fluid dynamic solutions to develop transition correlations that account for viscous effects on vehicles of arbitrary complexity. The boundary layer transition correlation developed for the X-33 from the viscous solutions are compared to the previous boundary layer transition correlations. It is shown that the boundary layer edge conditions calculated using an inviscid/integral boundary layer approach are significantly different than those extracted from viscous computational fluid dynamic solutions. The present results demonstrate the differences obtained in correlating transition data using different computational methods.
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmed I.
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Evaluation of general non-reflecting boundary conditions for industrial CFD applications
NASA Astrophysics Data System (ADS)
Basara, Branislav; Frolov, Sergei; Lidskii, Boris; Posvyanskii, Vladimir
2007-11-01
The importance of having proper boundary conditions for the calculation domain is a known issue in Computational Fluid Dynamics (CFD). In many situations, it is very difficult to define a correct boundary condition. The flow may enter and leave the computational domain at the same time and at the same boundary. In such circumstances, it is important that numerical implementation of boundary conditions enforces certain physical constraints leading to correct results which then ensures a better convergence rate. The aim of this paper is to evaluate recently proposed non-reflecting boundary conditions (Frolov et al., 2001, Advances in Chemical Propulsion) on industrial CFD applications. Derivation of the local non-reflecting boundary conditions at the open boundary is based on finding the solution of linearized Euler equations vanishing at infinity for both incompressible and compressible formulations. This is implemented into the in-house CFD package AVL FIRE and some numerical details will be presented as well. The key applications in this paper are from automotive industry, e.g. an external car aerodynamics, an intake port, etc. The results will show benefits of using effective non-reflecting boundary conditions.
Noisy contact interactions of multi-layer mechanical structures coupled by boundary conditions
NASA Astrophysics Data System (ADS)
Awrejcewicz, J.; Krysko, V. A., Jr.; Yakovleva, T. V.; Krysko, V. A.
2016-05-01
In this work mathematical models of temporal part of chaos at chosen spatial locations of a plate locally reinforced by ribs taking into account an interplay of their interactions are derived and studied numerically for the most relevant dynamical parameters. In addition, an influence of the additive external noise on chaotic vibrations of multi-layer beam-plate structures coupled only by boundary conditions is investigated. We illustrate and discuss novel nonlinear phenomena of the temporal regular and chaotic contact/no-contact dynamics with the help of Morlet wavelets and Fourier analysis. We show how the additive white noise cancels deterministic chaos close to the boundary of chaotic region in the space of parameters, and we present windows of on/off switching of the frequencies during the contact dynamics between structural members. In order to solve the mentioned design type nonlinear problem we apply methods of qualitative theory of differential equations, the Bubnov-Galerkin method in higher approximations, the Runge-Kutta methods of 4th, 6th and 8th order, as well as the computation and analysis of the largest Lyapunov exponent (Benettin's and Wolf's algorithms are used). The agreement of outcomes of all applied qualitatively different numerical approaches validate our simulation results. In particular, we have illustrated that the Fourier analysis of the studied mechanical structures may yield erroneous results, and hence the wavelet-based analysis is used to investigate chaotic dynamics in the system parameter space.
On the asymptotic behaviour for an electromagnetic system with a dissipative boundary condition
NASA Astrophysics Data System (ADS)
Amendola, Giovambattista
2005-04-01
In this work we study some properties of solutions for the system describing a three-dimensional non-homogeneous non-conducting dielectric with a general boundary condition with memory. We first show the existence of the inverse of this boundary condition, which allows us to introduce a boundary free energy, similar to the one considered by Fabrizio & Morro (1996, Arch. Rat. Mech. Anal., 136, 359-381). Then, we prove existence and uniqueness theorems for weak and strong solutions of the evolutive problem in a finite time interval. Moreover, following Rivera & Olivera (1997, Boll. U.M.I., 11-A, 115-127), we examine some dissipative properties of the boundary condition and of its inverse and we give a useful energy estimate. Finally, when there is no memory in the boundary condition the exponential decay of the solution is proved.
An implicit-iterative solution of the heat conduction equation with a radiation boundary condition
NASA Technical Reports Server (NTRS)
Williams, S. D.; Curry, D. M.
1977-01-01
For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.
NASA Astrophysics Data System (ADS)
Lee, Sanghyun; Salgado, Abner J.
2016-09-01
We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A. Bonito, J.-L. Guermond, and S. Lee. Modified pressure-correction projection methods: Open boundary and variable time stepping. In Numerical Mathematics and Advanced Applications - ENUMATH 2013, volume 103 of Lecture Notes in Computational Science and Engineering, pages 623-631. Springer, 2015]. This scheme turns out to be unconditionally stable, provided the stabilization parameter is suitably chosen. We also establish a conditional stability result for the boundary correction scheme presented in [E. Bansch. A finite element pressure correction scheme for the Navier-Stokes equations with traction boundary condition. Comput. Methods Appl. Mech. Engrg., 279:198-211, 2014]. These results are shown by employing the equivalence between stabilized gauge Uzawa methods and rotational pressure correction schemes with traction boundary conditions.
Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations
NASA Astrophysics Data System (ADS)
Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping
2016-07-01
We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical boundary may not coincide with grid points in a Cartesian mesh and may intersect with the mesh in an arbitrary fashion. For purely convection equations, the so-called inverse Lax-Wendroff procedure [28], in which we convert the normal derivatives into the time derivatives and tangential derivatives along the physical boundary by using the equations, has been quite successful. In this paper, we extend this methodology to convection-diffusion equations. It turns out that this extension is non-trivial, because totally different boundary treatments are needed for the diffusion-dominated and the convection-dominated regimes. We design a careful combination of the boundary treatments for the two regimes and obtain a stable and accurate boundary condition for general convection-diffusion equations. We provide extensive numerical tests for one- and two-dimensional problems involving both scalar equations and systems, including the compressible Navier-Stokes equations, to demonstrate the good performance of our numerical boundary conditions.
Sharapov, T F
2014-10-31
We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.
Exploring the Boundary Conditions of the Redundancy Principle
ERIC Educational Resources Information Center
McCrudden, Matthew T.; Hushman, Carolyn J.; Marley, Scott C.
2014-01-01
This experiment investigated whether study of a scientific text and a visual display that contained redundant text segments would affect memory and transfer. The authors randomly assigned 42 students from a university in the southwestern United States in equal numbers to 1 of 2 conditions: (a) a redundant condition, in which participants studied a…
Control of functional differential equations with function space boundary conditions.
NASA Technical Reports Server (NTRS)
Banks, H. T.
1972-01-01
The results of various authors dealing with problems involving functional differential equations with terminal conditions in function space are reviewed. The review includes not only very recent results, but also some little known results of Soviet mathematicians prior to 1970. Particular attention is given to results concerning controllability, existence of optimal controls, and necessary and sufficient conditions for optimality.
Time dependent inflow-outflow boundary conditions for 2D acoustic systems
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Myers, Michael K.
1989-01-01
An analysis of the number and form of the required inflow-outflow boundary conditions for the full two-dimensional time-dependent nonlinear acoustic system in subsonic mean flow is performed. The explicit predictor-corrector method of MacCormack (1969) is used. The methodology is tested on both uniform and sheared mean flows with plane and nonplanar sources. Results show that the acoustic system requires three physical boundary conditions on the inflow and one on the outflow boundary. The most natural choice for the inflow boundary conditions is judged to be a specification of the vorticity, the normal acoustic impedance, and a pressure gradient-density gradient relationship normal to the boundary. Specification of the acoustic pressure at the outflow boundary along with these inflow boundary conditions is found to give consistent reliable results. A set of boundary conditions developed earlier, which were intended to be nonreflecting is tested using the current method and is shown to yield unstable results for nonplanar acoustic waves.
NASA Astrophysics Data System (ADS)
Rahman, R.; Foster, J. T.
2015-08-01
In this paper we have investigated the ripples in graphenes under thermal agitation. It is known that as temperature increases ripples originate in the flat landscape of a graphene sheet which is responsible for changing its properties. Among a limited number of works available in literature the role of length scales and temperature on the characteristics of the ripples has been investigated. However it is important to include the boundary conditions with other parameters in order to get a broader picture. In this work graphenes with three different sizes (2 nm, 10 nm and 50 nm) were considered under both simply supported and free-opposite-sides boundary conditions at different temperatures (e.g. 10 K, 100 K and 500 K) using molecular dynamics simulations. The variation in natural frequencies and their dependency on the boundary condition, length scale and temperature was thoroughly studied. Change in the boundary condition can introduce new modes of vibrations in graphenes. A combined effect of length scale, boundary condition and temperature was shown to be responsible for developing the geometrical patterns in the ripples. With free-opposite-sides boundary conditions the ripples are more harmonic in larger graphene than other cases. It was also noticed that the probability distribution for the off-plane displacements of the carbon atoms in graphene is typically non-stationary at small length scales. Variation in boundary conditions and length scales may affect the kurtosis of the distribution. The results showed adequate agreement with available data in the literature.
Unified boundary conditions and Casimir forces for fields with arbitrary spin
NASA Astrophysics Data System (ADS)
Bennett, Robert; Stokes, Adam
The electromagnetic Casimir effect is well-known and has been extensively studied for the last half-century. This attractive force between parallel plates arises from the imposition of boundary conditions upon the fluctuating spin-1 photon field, so a natural further question is wether fields of different spin can cause similar forces when confined in the same way. However, so far it has not been clear what the appropriate boundary conditions for physically-confined spinor fields may be. Here we present work that generalises the physically well-motivated electromagnetic boundary conditions to fields of arbitrary spin, thus arriving at physically reasonable boundary conditions and Casimir forces for a selection of interesting fields. For example, the so-called `bag model' boundary conditions from nuclear physics emerge from our generalised boundary condition as a special case, as do the linearised gravity boundary conditions suggested in a remarkable recent proposal concerning possible measurement of gravitonic Casimir forces. Supported by the UK Engineering and Physical Sciences Research Council (EPSRC).
NASA Astrophysics Data System (ADS)
Ramesh, G. K.; Gireesha, B. J.; Gorla, Rama Subba Reddy
2015-08-01
The steady two-dimensional boundary layer flow of a viscous dusty fluid over a stretching sheet with the bottom surface of the sheet heated by convection from a hot fluid is considered. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg fourth-fifth order method (RKF45 Method) with the help of MAPLE. The effects of convective Biot number, fluid particle interaction parameter, and Prandtl number on the heat transfer characteristics are discussed. It is found that the temperature of both fluid and dust phase increases with increasing Biot number. A comparative study between the previous published and present results in a limiting sense is found in an excellent agreement.
NASA Technical Reports Server (NTRS)
Ghil, M.; Balgovind, R.
1979-01-01
The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.
A comparison of time domain boundary conditions for acoustic waves in wave guides
NASA Technical Reports Server (NTRS)
Banks, H. T.; Propst, G.; Silcox, R. J.
1991-01-01
Researchers consider several types of boundary conditions in the context of time domain models for acoustic waves. Experiments with four different duct terminations (hard wall, free radiation, foam, and wedge) were carried out in a wave duct from which reflection coefficients over a wide frequency range were measured. These reflection coefficients were used to estimate parameters in the time domain boundary conditions. A comparison of the relative merits of the models in describing the data is presented. Boundary conditions which yield a good fit of the model to the experimental data were found for all duct terminations except the wedge.
Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S.; Ingber, M.S.
1995-03-01
Velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations are presented. Vorticity is created on boundaries to simultaneously satisfy the tangential and normal components of the velocity boundary condition. The newly created vorticity is specified by a kinematical formulation which is a generalization of Helmholtz decomposition of a vector field. Related forms of the decomposition were developed by Bykhovskiy and Smirnov in 1983, and Wu and Thompson in 1973. Though it has not been generally recognized as such, these formulations resolve the over-specification issues associated with determining a velocity field from velocity boundary conditions and a vorticity field. The generalized decomposition has not been widely used, however, apparently due to a general lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition for the normal and tangential velocity boundary conditions is discussed in detail. As an example of the use of this boundary condition, the flow in a lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRE. ALEGRE`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.
NASA Astrophysics Data System (ADS)
Ge, Wenjun; Modest, Michael F.; Roy, Somesh P.
2016-03-01
The high-order spherical harmonics (PN) method for 2-D Cartesian domains is extracted from the 3-D formulation. The number of equations and intensity coefficients reduces to (N + 1)2 / 4 in the 2-D Cartesian formulation compared with N(N + 1) / 2 for the general 3-D PN formulation. The Marshak boundary conditions are extended to solve problems with nonblack and mixed diffuse-specular surfaces. Additional boundary conditions for specified radiative wall flux, for symmetry/specular reflection boundaries have also been developed. The mathematical details of the formulations and their implementation in the OpenFOAM finite volume based CFD software platform are presented. The accuracy and computational cost of the 2-D Cartesian PN are compared with that of the 3-D PN solver and a Photon Monte Carlo solver for a square enclosure, as well as a 45° wedge geometry with variable radiative properties. The new boundary conditions have been applied for both test cases, and the boundary condition for mixed diffuse-specular surfaces is further illustrated by numerical examples of a rectangular geometry enclosed by walls with different surface characteristics.
Boundary conditions for General Relativity on AdS3 and the KdV hierarchy
NASA Astrophysics Data System (ADS)
Pérez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-06-01
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer k. Gravitational excitations are then described by "boundary gravitons" that fulfill the equations of the k-th element of the KdV hierarchy. In particular, k = 0 corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers. In the case of k = 1, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy ( k > 1). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent z = 2 k + 1. Remarkably, despite spacetimes solving the field equations are locally AdS, they possess anisotropic scaling being induced by the choice of boundary conditions. As an application, the entropy of a rotating BTZ black hole is precisely recovered from a suitable generalization of the Cardy formula that is compatible with the anisotropic scaling of the chiral KdV movers at the boundary, in which the energy of AdS spacetime with our boundary conditions depends on z and plays the role of the central charge. The extension of our boundary conditions to the case of higher spin gravity and its link with different classes of integrable systems is also briefly addressed.
Alsaedi, Ahmed; Ntouyas, Sotiris K.; Ahmad, Bashir
2015-01-01
By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example. PMID:25629085
Nonequilibrium kinetic boundary condition at the vapor-liquid interface of argon.
Ishiyama, Tatsuya; Fujikawa, Shigeo; Kurz, Thomas; Lauterborn, Werner
2013-10-01
A boundary condition for the Boltzmann equation (kinetic boundary condition, KBC) at the vapor-liquid interface of argon is constructed with the help of molecular dynamics (MD) simulations. The KBC is examined at a constant liquid temperature of 85 K in a wide range of nonequilibrium states of vapor. The present investigation is an extension of a previous one by Ishiyama, Yano, and Fujikawa [Phys. Rev. Lett. 95, 084504 (2005)] and provides a more complete form of the KBC. The present KBC includes a thermal accommodation coefficient in addition to evaporation and condensation coefficients, and these coefficients are determined in MD simulations uniquely. The thermal accommodation coefficient shows an anisotropic behavior at the interface for molecular velocities normal versus tangential to the interface. It is also found that the evaporation and condensation coefficients are almost constant in a fairly wide range of nonequilibrium states. The thermal accommodation coefficient of the normal velocity component is almost unity, while that of the tangential component shows a decreasing function of the density of vapor incident on the interface, indicating that the tangential velocity distribution of molecules leaving the interface into the vapor phase may deviate from the tangential parts of the Maxwell velocity distribution at the liquid temperature. A mechanism for the deviation of the KBC from the isotropic Maxwell KBC at the liquid temperature is discussed in terms of anisotropic energy relaxation at the interface. The liquid-temperature dependence of the present KBC is also discussed.
Nonequilibrium kinetic boundary condition at the vapor-liquid interface of argon.
Ishiyama, Tatsuya; Fujikawa, Shigeo; Kurz, Thomas; Lauterborn, Werner
2013-10-01
A boundary condition for the Boltzmann equation (kinetic boundary condition, KBC) at the vapor-liquid interface of argon is constructed with the help of molecular dynamics (MD) simulations. The KBC is examined at a constant liquid temperature of 85 K in a wide range of nonequilibrium states of vapor. The present investigation is an extension of a previous one by Ishiyama, Yano, and Fujikawa [Phys. Rev. Lett. 95, 084504 (2005)] and provides a more complete form of the KBC. The present KBC includes a thermal accommodation coefficient in addition to evaporation and condensation coefficients, and these coefficients are determined in MD simulations uniquely. The thermal accommodation coefficient shows an anisotropic behavior at the interface for molecular velocities normal versus tangential to the interface. It is also found that the evaporation and condensation coefficients are almost constant in a fairly wide range of nonequilibrium states. The thermal accommodation coefficient of the normal velocity component is almost unity, while that of the tangential component shows a decreasing function of the density of vapor incident on the interface, indicating that the tangential velocity distribution of molecules leaving the interface into the vapor phase may deviate from the tangential parts of the Maxwell velocity distribution at the liquid temperature. A mechanism for the deviation of the KBC from the isotropic Maxwell KBC at the liquid temperature is discussed in terms of anisotropic energy relaxation at the interface. The liquid-temperature dependence of the present KBC is also discussed. PMID:24229188
Flow boundary conditions for fluid mixtures at solid walls and moving contact lines
NASA Astrophysics Data System (ADS)
Robbins, Mark
2005-11-01
Molecular simulations of slip at solid surfaces have focused on single component systems, but polymers are frequently blended to optimize performance. This talk will examine counterintuitive behavior that can arise when binary fluid mixtures flow past stationary solid walls in simple shear and at moving contact lines. In general the velocities of the two species do not go to zero at the walls. In addition to the slip found for single fluids, there may be velocity discontinuities due to diffusive fluxes and to interfacial forces when there is a concentration gradient.^1 Cases where the fluid velocity is largest near the wall and where the apparent slip length diverges will be shown, and a general boundary condition for multi-phase flow presented. The no-slip boundary condition leads to singular dissipation when the contact line between a fluid interface and solid moves, but it was suggested that a diffusive flux could remove this singularity.^2 The flow and stress near moving contact lines are analyzed for a range of interfacial widths, velocities and interactions. A significant diffusive flux is only observed in the layer closest to the solid and is not sufficient to remove the singularity. Instead, the finite molecular size and non-Newtonian effects cutoff the singularity.1. C. Denniston and M. O. Robbins, Phys. Rev. Lett. 87, 178302 (2001).2. H.-Y. Chen and D. Jasnow and J. Vinals, Phys. Rev. Lett. 85, 1686 (2000).
A dynamic slip boundary condition for wall-modeled large-eddy simulation
NASA Astrophysics Data System (ADS)
Bose, S. T.; Moin, P.
2014-01-01
Wall models for large-eddy simulation (LES) are a necessity to remove the prohibitive resolution requirements of near-wall turbulence in high Reynolds turbulent flows. Traditional wall models often rely on assumptions about the local state of the boundary layer (e.g., logarithmic velocity profiles) and require a priori prescription of tunable model coefficients. In the present study, a slip velocity boundary condition for the filtered velocity field is obtained from the derivation of the LES equations using a differential filter. A dynamic procedure for the local slip length is additionally formulated making the slip velocity wall model free of any a priori specified coefficients. The accuracy of the dynamic slip velocity wall model is tested in a series of turbulent channel flows at varying Reynolds numbers and in the LES of a National Advisory Committee for Aeronautics (NACA) 4412 airfoil at near-stall conditions. The wall-modeled simulations are able to accurately predict mean flow characteristics, including the formation of a trailing-edge separation bubble in NACA 4412 configuration. The validation cases demonstrate the effectiveness of this wall-modeling approach in both attached and separated flow regimes.
Sensitivity of Pliocene climate simulations in MRI-CGCM2.3 to respective boundary conditions
NASA Astrophysics Data System (ADS)
Kamae, Youichi; Yoshida, Kohei; Ueda, Hiroaki
2016-08-01
Accumulations of global proxy data are essential steps for improving reliability of climate model simulations for the Pliocene warming climate. In the Pliocene Model Intercomparison Project phase 2 (PlioMIP2), a part project of the Paleoclimate Modelling Intercomparison Project phase 4, boundary forcing data have been updated from the PlioMIP phase 1 due to recent advances in understanding of oceanic, terrestrial and cryospheric aspects of the Pliocene palaeoenvironment. In this study, sensitivities of Pliocene climate simulations to the newly archived boundary conditions are evaluated by a set of simulations using an atmosphere-ocean coupled general circulation model, MRI-CGCM2.3. The simulated Pliocene climate is warmer than pre-industrial conditions for 2.4 °C in global mean, corresponding to 0.6 °C warmer than the PlioMIP1 simulation by the identical climate model. Revised orography, lakes, and shrunk ice sheets compared with the PlioMIP1 lead to local and remote influences including snow and sea ice albedo feedback, and poleward heat transport due to the atmosphere and ocean that result in additional warming over middle and high latitudes. The amplified higher-latitude warming is supported qualitatively by the proxy evidences, but is still underestimated quantitatively. Physical processes responsible for the global and regional climate changes should be further addressed in future studies under systematic intermodel and data-model comparison frameworks.
Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation
NASA Technical Reports Server (NTRS)
Ryabenkii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels,' nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces, It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.
A Boundary Mixture Approach to Violations of Conditional Independence
ERIC Educational Resources Information Center
Braeken, Johan
2011-01-01
Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of…
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
NASA Astrophysics Data System (ADS)
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
NASA Astrophysics Data System (ADS)
Bencheva, G.
2012-10-01
A mathematical model for haematopoietic stem cells migration towards their niche in the bone marrow has been proposed in the literature. It consists of a chemotaxis system of partial differential equations with nonlinear boundary conditions and an additional ordinary differential equation on a part of the computational boundary. The aim in the current paper is first to answer some of the open questions of a recently introduced finite volume scheme for this chemotaxis system of differential equations and second to investigate the influence of the boundary conditions on the choice of flux limiters (the generalized minmod, Koren, van Leer limiters are investigated) used to ensure positivity and non-oscillating nature of the numerical solution.
Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji
2014-07-01
A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.
White, D; Fasenfest, B; Rieben, R; Stowell, M
2006-09-08
We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law.
Implementation of a Compressor Face Boundary Condition Based on Small Disturbances
NASA Technical Reports Server (NTRS)
Slater, John W.; Paynter, Gerald C.
2000-01-01
A compressor-face boundary condition that models the unsteady interactions of acoustic and convective velocity disturbances with a compressor has been implemented into a three-dimensional computational fluid dynamics code. Locally one-dimensional characteristics along with a small-disturbance model are used to compute the acoustic response as a function of the local stagger angle and the strength and direction of the disturbance. Simulations of the inviscid flow in a straight duct, a duct coupled to a compressor, and a supersonic inlet demonstrate the behavior of the boundary condition in relation to existing boundary conditions. Comparisons with experimental data show a large improvement in accuracy over existing boundary conditions in the ability to predict the reflected disturbance from the interaction of an acoustic disturbance with a compressor.
Influence of Boundary Conditions on Simulated U.S. Air Quality
One of the key inputs to regional-scale photochemical models frequently used in air quality planning and forecasting applications are chemical boundary conditions representing background pollutant concentrations originating outside the regional modeling domain. A number of studie...
Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations
Li, Tingwen; Benyahia, Sofiane
2013-10-01
Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.
X. Z. Tang
2000-12-18
Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given.
Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems
NASA Astrophysics Data System (ADS)
Alves, M. S.; Jorge Silva, M. A.; Ma, T. F.; Muñoz Rivera, J. E.
2016-06-01
This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233-1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate {t^{-1/2}} for mixed Dirichlet-Neumann boundary condition and rate {t^{-1/4}} for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate {t^{-1/2}} (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.
PRESBC: pressure boundary conditions for the K-FIX code. Supplement III
Travis, J.R.; Rivard, W.C.
1980-07-01
Recommended pressure boundary condition modifications are described for the computer code K-FIX, which has been published in the report LA-NUREG-6623 and released to the National Energy Software Center in April 1977.
Hintermueller, M.; Kao, C.-Y.; Laurain, A.
2012-02-15
This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this threshold value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.
On a regular problem for an elliptic-parabolic equation with a potential boundary condition
NASA Astrophysics Data System (ADS)
Arepova, Gauhar
2016-08-01
In this paper, we construct a lateral boundary condition for an elliptic-parabolic equation in a finite domain. Theorem on existence and uniqueness of a solution of the considered problem is proved by method of theory potential.
NASA Astrophysics Data System (ADS)
Otelbaev, Mukhtarbay; Koshanov, Bakytbek D.
2016-08-01
This paper describes the correct narrowing of the Navier-Stokes equations in a stationary three-dimensional cube and clarified the correct formulation of the boundary conditions for the pressure in the environment.
NASA Astrophysics Data System (ADS)
Hübler, G.; Parrish, D. D.; Aikin, K. C.; Oltmans, S. J.; Johnson, B. J.; Ives, M.; Thouret, V.; Nédélec, P.; Cammas, J.; Team, A.
2009-12-01
Most detailed photochemical modeling must be carried out at regional or air basin scales in order to achieve the spatial resolution and detailed treatment of the chemical mechanisms required for realistic treatment of local air quality. Consequently these models must define upwind boundary conditions at the edge of the model domain. Uncertainty in the appropriate boundary conditions contributes significantly to the overall uncertainty of the photochemical modeling in California. Here we will investigate the available data sets to define to the extent possible the average summertime oceanic boundary conditions, the variability about that average, and the horizontal and vertical variability of the boundary conditions. The data sets considered will include ozone sondes launched from Trinidad Head CA, ozone and carbon monoxide profiles measured by MOZAIC aircraft flights into 4 west coast US cities, and the many chemical species measured on four aircraft flights conducted during the CARB-ARCTAS campaign during summer 2008
Boundary conditions on faster-than-light transportation systems
NASA Technical Reports Server (NTRS)
Bennett, Gary L.; Knowles, H. B.
1993-01-01
In order to be consistent with current physical theories, any proposal of a faster-than light (FTL) transportation system must satisfy several critical conditions. It must predict the mass, space, and time dimensional changes predicted by relativity physics when velocity falls below the speed of light. It must also not violate causality, and remain consistent with quantum physics in the limit of microscopic systems. It is also essential that the proposal conserve energy.
A bridging technique to analyze the influence of boundary conditions on instability patterns
Hu Heng; Damil, Noureddine; Potier-Ferry, Michel
2011-05-10
In this paper, we present a new numerical technique that permits to analyse the effect of boundary conditions on the appearance of instability patterns. Envelope equations of Landau-Ginzburg type are classically used to predict pattern formation, but it is not easy to associate boundary conditions for these macroscopic models. Indeed, envelope equations ignore boundary layers that can be important, for instance in cases where the instability starts first near the boundary. In this work, the full model is considered close to the boundary, an envelope equation in the core and they are bridged by the Arlequin method . Simulation results are presented for the problem of buckling of long beams lying on a non-linear elastic foundation.
NASA Technical Reports Server (NTRS)
Wada, B. K.; Kuo, C.-P.; Glaser, R. J.
1986-01-01
A major challenge to the structural dynamicist is to validate mathematical models of large space structures which cannot be ground tested because of its size and/or flexibility. The paper presents a Multiple Boundary Condition Test (MBCT) approach which allows a systematic validation of the mathematical model by performing a number of ground tests on a large structure with variable boundary conditions. A numerical simulation is presented which illustrates the validity of the MBCT including some of the potential limitations.
NASA Astrophysics Data System (ADS)
Gasymov, E. A.; Guseinova, A. O.; Gasanova, U. N.
2016-07-01
One of the methods for solving mixed problems is the classical separation of variables (the Fourier method). If the boundary conditions of the mixed problem are irregular, this method, generally speaking, is not applicable. In the present paper, a generalized separation of variables and a way of application of this method to solving some mixed problems with irregular boundary conditions are proposed. Analytical representation of the solution to this irregular mixed problem is obtained.
Unsteady Validation of a Mean Flow Boundary Condition for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Zhen, F.; Nallasamy, M.; Sawyer, S>
2004-01-01
In this work, a previously developed mean flow boundary condition will be validated for unsteady flows. The test cases will be several reference benchmark flows consisting of vortical gusts convecting in a uniform mean flow, as well as the more realistic case of a vortical gust impinging on a loaded 2D cascade. The results will verify that the mean flow boundary condition both imposes the desired mean flow as well as having little or no effect on the instantaneous unsteady solution.
Boundary mass-exchange conditions in the form of the Newton and Dalton laws
NASA Astrophysics Data System (ADS)
Afanas'ev, A. M.; Siplivyi, B. N.
2007-01-01
It has been established that the linear boundary mass-exchange conditions in the form of the Newton law are unsuitable for description of the initial period of drying and the constant-rate period. The nonlinear boundary conditions of the third kind based on the Dalton evaporation law have been proposed. A numerical algorithm for investigation of the temperature and moisture-content fields up to the dropping-rate period has been developed.
A hybrid FEM-BEM unified boundary condition with sub-cycling for electromagnetic radiation
Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N; Rockway, J; Champagne, N J; Jandhyala, V; Pingenot, J
2006-01-12
Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique.
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
NASA Astrophysics Data System (ADS)
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions
NASA Technical Reports Server (NTRS)
Hesthaven, J. S.; Gottlieb, D.
1994-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.
A truncated implicit high-order finite-difference scheme combined with boundary conditions
NASA Astrophysics Data System (ADS)
Chang, Suo-Liang; Liu, Yang
2013-03-01
In this paper, first we calculate finite-difference coefficients of implicit finitedifference methods (IFDM) for the first- and second-order derivatives on normal grids and firstorder derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition (ABC) to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.
ALmost EXact boundary conditions for transient Schrödinger-Poisson system
NASA Astrophysics Data System (ADS)
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016-05-01
For the Schrödinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
NASA Technical Reports Server (NTRS)
Haywood, A. M.; Dowsett, H. J.; Robinson, M. M.; Stoll, D. K.; Dolan, A. M.; Lunt, D. J.; Otto-Bliesner, B.; Chandler, M. A.
2011-01-01
The Palaeoclimate Modelling Intercomparison Project has expanded to include a model intercomparison for the mid-Pliocene warm period (3.29 to 2.97 million yr ago). This project is referred to as PlioMIP (the Pliocene Model Intercomparison Project). Two experiments have been agreed upon and together compose the initial phase of PlioMIP. The first (Experiment 1) is being performed with atmosphere only climate models. The second (Experiment 2) utilizes fully coupled ocean-atmosphere climate models. Following on from the publication of the experimental design and boundary conditions for Experiment 1 in Geoscientific Model Development, this paper provides the necessary description of differences and/or additions to the experimental design for Experiment 2.
Haywood, A.M.; Dowsett, H.J.; Robinson, M.M.; Stoll, D.K.; Dolan, A.M.; Lunt, D.J.; Otto-Bliesner, B.; Chandler, M.A.
2011-01-01
The Palaeoclimate Modelling Intercomparison Project has expanded to include a model intercomparison for the mid-Pliocene warm period (3.29 to 2.97 million yr ago). This project is referred to as PlioMIP (the Pliocene Model Intercomparison Project). Two experiments have been agreed upon and together compose the initial phase of PlioMIP. The first (Experiment 1) is being performed with atmosphere-only climate models. The second (Experiment 2) utilises fully coupled ocean-atmosphere climate models. Following on from the publication of the experimental design and boundary conditions for Experiment 1 in Geoscientific Model Development, this paper provides the necessary description of differences and/or additions to the experimental design for Experiment 2.
Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)
NASA Technical Reports Server (NTRS)
Ricoy, Mark A.; Volakis, John L.
1990-01-01
The diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's). The sheet currents are then formulated and solved via the standard dual integral equation approach. This yields the diffracted field in terms of unknown constants which underscore the non-uniqueness of the GSTC current sheet representation. The constants are dependent on the geometry and properties of the discontinuity and are determined by enforcing field continuity across the material junction. This requires the field internal to the slab which are determined from the external ones via analytic continuity. Results are given which validate the solution and demonstrate the importance of the constants.
Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation
NASA Technical Reports Server (NTRS)
Kwak, D.
1981-01-01
The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.
An energy absorbing far-field boundary condition for the elastic wave equation
Petersson, N A; Sjogreen, B
2008-07-15
The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
NASA Astrophysics Data System (ADS)
Yakushev, Evgeniy
2013-04-01
Climate Change affects oxygen depletion and leads to spreading of the bottom areas with hypoxic and anoxic conditions in the coastal areas of the seas and inland waters. This work aimed in estimation of a role of changes of redox conditions in the biogeochemical structure there. We use a 1-dimensional C-N-P-Si-O-S-Mn-Fe vertical transport-reaction model describing the water column, bottom boundary layer and benthic boundary layer with biogeochemical block simulating redox conditions changeability. A biogeochemical block is based on ROLM (RedOx Layer Model), that was constructed to simulate basic features of the water column biogeochemical structure changes in oxic, anoxic and changeable conditions (Yakushev et al., 2007). Organic matter formation and decay, reduction and oxidation of species of nitrogen, sulfur, manganese, iron, and the transformation of phosphorus species are parameterized in the model. ROLM includes a simplified ecological model with phytoplankton, zooplankton, aerobic autotrophic and heterotrophic bacteria, anaerobic autotrophic and heterotrophic bacteria. We simulate changes in the parameters distributions and fluxes connected with the vertical displacement of redox interface from the sediments to the water.
A direct approach to finding unknown boundary conditions in steady heat conduction
NASA Technical Reports Server (NTRS)
Martin, Thomas J.; Dulikravich, George S.
1993-01-01
The capability of the boundary element method (BEM) in determining thermal boundary conditions on surfaces of a conducting solid where such quantities are unknown was demonstrated. The method uses a non-iterative direct approach in solving what is usually called the inverse heat conduction problem (IHCP). Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on a surface where such data is readily available, the algorithm computes the temperature field within the object and any unknown thermal boundary conditions on surfaces where thermal boundary values are unavailable. A two-dimensional, steady-state BEM program was developed and was tested on several simple geometries where the analytic solution was known. Results obtained with the BEM were in excellent agreement with the analytic values. The algorithm is highly flexible in treating complex geometries, mixed thermal boundary conditions, and temperature-dependent material properties and is presently being extended to three-dimensional and unsteady heat conduction problems. The accuracy and reliability of this technique was very good but tended to deteriorate when the known surface conditions were only slightly over-specified and far from the inaccessible surface.
A direct approach to finding unknown boundary conditions in steady heat conduction
NASA Astrophysics Data System (ADS)
Martin, Thomas J.; Dulikravich, George S.
1993-11-01
The capability of the boundary element method (BEM) in determining thermal boundary conditions on surfaces of a conducting solid where such quantities are unknown was demonstrated. The method uses a non-iterative direct approach in solving what is usually called the inverse heat conduction problem (IHCP). Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on a surface where such data is readily available, the algorithm computes the temperature field within the object and any unknown thermal boundary conditions on surfaces where thermal boundary values are unavailable. A two-dimensional, steady-state BEM program was developed and was tested on several simple geometries where the analytic solution was known. Results obtained with the BEM were in excellent agreement with the analytic values. The algorithm is highly flexible in treating complex geometries, mixed thermal boundary conditions, and temperature-dependent material properties and is presently being extended to three-dimensional and unsteady heat conduction problems. The accuracy and reliability of this technique was very good but tended to deteriorate when the known surface conditions were only slightly over-specified and far from the inaccessible surface.
Fluid flow in nanopores: An examination of hydrodynamic boundary conditions
NASA Astrophysics Data System (ADS)
Sokhan, V. P.; Nicholson, D.; Quirke, N.
2001-08-01
Steady-state Poiseuille flow of a simple fluid in carbon slit pores under a gravity-like force is simulated using a realistic empirical many-body potential model for carbon. In this work we focus on the small Knudsen number regime, where the macroscopic equations are applicable, and simulate different wetting conditions by varying the strength of fluid-wall interactions. We show that fluid flow in a carbon pore is characterized by a large slip length even in the strongly wetting case, contrary to the predictions of Tolstoi's theory. When the surface density of wall atoms is reduced to values typical of a van der Waals solid, the streaming velocity profile vanishes at the wall, in accordance with earlier findings. From the velocity profiles we have calculated the slip length and by analyzing temporal profiles of the velocity components of particles colliding with the wall we obtained values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall.
Characterizing summertime chemical boundary conditions for airmasses entering the US West Coast
NASA Astrophysics Data System (ADS)
Pfister, G. G.; Parrish, D.; Worden, H.; Emmons, L. K.; Edwards, D. P.; Wiedinmyer, C.; Diskin, G. S.; Huey, G.; Oltmans, S. J.; Thouret, V.; Weinheimer, A.; Wisthaler, A.
2010-11-01
The objective of this study is to analyze the pollution inflow into California during summertime and how it impacts surface air quality through combined analysis of a suite of observations and global and regional models. The focus is on the transpacific pollution transport investigated by the NASA Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) mission in June 2008. Additional observations include satellite retrievals of carbon monoxide and ozone by the EOS Aura Tropospheric Emissions Spectrometer (TES), aircraft measurements from the MOZAIC program and ozonesondes. We compare chemical boundary conditions (BC) from the MOZART-4 global model, which are commonly used in regional simulations, with measured concentrations to quantify both the accuracy of the model results and the variability in pollution inflow. Both observations and model reflect a large variability in pollution inflow on temporal and spatial scales, but the global model captures only about half of the observed free tropospheric variability. Model tracer contributions show a large contribution from Asian emissions in the inflow. Recirculation of local US pollution can impact chemical BC, emphasizing the importance of consistency between the global model simulations used for BC and the regional model in terms of emissions, chemistry and transport. Aircraft measurements in the free troposphere over California show similar concentration range, variability and source contributions as free tropospheric air masses over ocean, but caution has to be taken that local pollution aloft is not misinterpreted as inflow. A flight route specifically designed to sample boundary conditions during ARCTAS-CARB showed a prevalence of plumes transported from Asia and thus may not be fully representative for average inflow conditions. Sensitivity simulations with a regional model with altered BCs show that the temporal variability in the pollution inflow does impact modeled
Characterizing summertime chemical boundary conditions for airmasses entering the US West Coast
NASA Astrophysics Data System (ADS)
Pfister, G. G.; Parrish, D. D.; Worden, H.; Emmons, L. K.; Edwards, D. P.; Wiedinmyer, C.; Diskin, G. S.; Huey, G.; Oltmans, S. J.; Thouret, V.; Weinheimer, A.; Wisthaler, A.
2011-02-01
The objective of this study is to analyze the pollution inflow into California during summertime and how it impacts surface air quality through combined analysis of a suite of observations and global and regional models. The focus is on the transpacific pollution transport investigated by the NASA Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) mission in June 2008. Additional observations include satellite retrievals of carbon monoxide and ozone by the EOS Aura Tropospheric Emissions Spectrometer (TES), aircraft measurements from the MOZAIC program and ozonesondes. We compare chemical boundary conditions (BC) from the MOZART-4 global model, which are commonly used in regional simulations, with measured concentrations to quantify both the accuracy of the model results and the variability in pollution inflow. Both observations and model reflect a large variability in pollution inflow on temporal and spatial scales, but the global model captures only about half of the observed free tropospheric variability. Model tracer contributions show a large contribution from Asian emissions in the inflow. Recirculation of local US pollution can impact chemical BC, emphasizing the importance of consistency between the global model simulations used for BC and the regional model in terms of emissions, chemistry and transport. Aircraft measurements in the free troposphere over California show similar concentration ranges, variability and source contributions as free tropospheric air masses over ocean, but caution has to be taken that local pollution aloft is not misinterpreted as inflow. A flight route specifically designed to sample boundary conditions during ARCTAS-CARB showed a prevalence of plumes transported from Asia and thus may not be fully representative for average inflow conditions. Sensitivity simulations with a regional model with altered BCs show that the temporal variability in the pollution inflow does impact modeled
On the Nature of Boundary Conditions for Flows with Moving Free Surfaces
NASA Astrophysics Data System (ADS)
Renardy, Michael; Renardy, Yuriko
1991-04-01
We consider small perturbations of plane parallel flow between a wall and a moving free surface. The problem is posed on a rectangle with inflow and outflow boundaries. The usual boundary conditions are posed at the wall and the free surface, and the fluid satisfies the Navier-Stokes equations. We examine the nature of boundary conditions which can be imposed at the inflow and outflow boundaries in order to yield a well-posed problem. This question turns out to be more delicate than is generally appreciated. Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed. For example, we show that if the velocities at te inflow and outflow boundaries are prescribed, then the position of the free surface at the inflow boundary can be prescribed, but not at the outflow if an H1-solution is desired. Numerical simulations with the FIDAP package are used to illustrate our analytical results.
Lozenge Tilings with Gaps in a 90° Wedge Domain with Mixed Boundary Conditions
NASA Astrophysics Data System (ADS)
Ciucu, Mihai
2015-02-01
We consider a triangular gap of side two in a 90° angle on the triangular lattice with mixed boundary conditions: a constrained, zig-zag boundary along one side, and a free lattice line boundary along the other. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its three images in the sides of the angle. This provides evidence for a unified way of understanding the interaction of gaps with the boundary under mixed boundary conditions, which we present as a conjecture. Our conjecture is phrased in terms of the steady state heat flow problem in a uniform block of material in which there are a finite number of heat sources and sinks. This new physical analogy is equivalent in the bulk to the electrostatic analogy we developed in previous work, but arises as the correct one for the correlation with the boundary. The starting point for our analysis is an exact formula we prove for the number of lozenge tilings of certain trapezoidal regions with mixed boundary conditions, which is equivalent to a new, multi-parameter generalization of a classical plane partition enumeration problem (that of enumerating symmetric, self-complementary plane partitions).
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
NASA Technical Reports Server (NTRS)
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
Derivation and application of a class of generalized impedance boundary conditions, part 2
NASA Technical Reports Server (NTRS)
Volakis, J. L.; Senior, T. B. A.; Jin, J.-M.
1989-01-01
Boundary conditions involving higher order derivatives are presented by simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to non-planar surfaces. As an illustration, the simulation of metal-backed uniform and three-layer dielectric coatings is given. It is shown that fourth order conditions are capable of providing an accurate simulation for the uniform coating at least a quarter of a wavelength in thickness. Provided, though, some compromise in accuracy is acceptable, it is also shown that a third order condition may be sufficient for practical purposes when simulating uniform coatings.
Evaluation of several non-reflecting computational boundary conditions for duct acoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Zorumski, William E.; Hodge, Steve L.
1994-01-01
Several non-reflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each non-reflecting boundary conditions. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other non-reflecting conditions.
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1991-01-01
Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary.
On the formulation of open boundary conditions at the mouth of a bay
NASA Astrophysics Data System (ADS)
Greatbatch, Richard J.; Otterson, Timm
1991-10-01
We describe our experience in formulating open boundary conditions to apply at the mouth of a reduced-gravity model of a bay. Our objective is to find a way to calculate the response of the bay to wind forcing over the bay itself, without being concerned about the influence of regions beyond. We show that open boundaries from which Kelvin waves can propagate along the coast into the model domain ("upstream" boundaries) must be treated with care. We begin by considering an "upstream" boundary which runs perpendicular to the coast. We find that if a radiation condition is applied on such a boundary, then spurious Kelvin waves of near-inertial period can propagate in from the boundary and contaminate the solution in the interior of the model domain. Also, if there is Ekman transport at the "upstream" boundary away from (toward) the coast, then upwelling (downwelling) will occur indefinitely and completely swamp the model solution in the bay. This is similar to the solution we expect when the coastline is straight and extends to infinity in the "upstream" direction. However, it is not the same, since the rate of upwelling (downwelling) is roughly half the theoretical value for that case. For the problem of a bay we suggest that the way to deal with this is to extend the coastline out to sea on the "upstream" side of the mouth and apply a condition on the artificial stretch of the boundary which suppresses Kelvin wave propagation but is also not prohibitively reflective to outgoing Poincaré waves. For our problem a condition of zero normal gradient in interface displacement seems to be sufficient. This condition also captures reasonably well the near-inertial Kelvin waves that are generated by the northwest corner of the bay (which are a genuine part of the solution) as long as the other boundaries are sufficiently far from the bay. We have also experimented with using sponge layers rather than radiation conditions on the other boundaries. We find that sponging only
Tam, C.K.W.; Webb, J.C. )
1994-07-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompatibility between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevitably introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. 15 refs., 15 figs.
Effect of thermal boundary condition on wall-bounded, stably-stratified turbulence
NASA Astrophysics Data System (ADS)
Flores, Oscar; Garcia-Villalba, Manuel
2012-11-01
The dynamics of stably stratified wall-bounded turbulent flows are of great importance for many engineering and geophysical problems. In some cases, like the stably stratified atmospheric boundary layer, it is unclear which is the most appropriate thermal boundary condition, i.e. constant temperature or constant flux at the ground. Here, we analyze the effect that this boundary condition has on the dynamics of turbulent motions in the near-wall region in the case of strong stable stratification. Two Direct Numerical Simulations of turbulent channels will be used, at Reτ =uτ h / ν = 560 and Riτ = Δρgh /ρ0uτ2 = 600 - 900 , which are described in detail in Flores & Riley (2011, Boundary-Layer Meteorol) and Garcia-Villalba & del Alamo (2011, Phys.Fluids). For this range of Reynolds and Richardson numbers, the near-wall region is intermittent, with patches of laminar flow embedded in the otherwise turbulent flow. It is in this regime where the differences between the constant temperature and the constant flux boundary conditions are expected to be larger, with the thermal boundary condition affecting how the local relaminarization of the flow takes place. This research has been supported by ARO, NSF and the German Research Foundation.
Poisson-Nernst-Planck model with Chang-Jaffe, diffusion, and ohmic boundary conditions
NASA Astrophysics Data System (ADS)
Lelidis, I.; Macdonald, J. Ross; Barbero, G.
2016-01-01
Using the linear Poisson-Nernst-Planck impedance-response continuum model, we investigate the possible equivalences of three different types of boundary conditions previously proposed to model the electrode behavior of an electrolytic cell in the shape of a slab. We show analytically that the boundary conditions proposed long ago by Chang-Jaffe are fully equivalent to the ohmic boundary conditions only if the positive and negative ions have the same mobility, or when only ions of a single polarity are mobile. In the case where the ions have different and non-zero mobilities, we fit exact impedance spectra created for ohmic boundary conditions by using the Chang-Jaffe Poisson-Nernst-Planck response model, one that is dominated by diffusion effects. These fits yield conditions for essentially exact or approximate numerical correspondence for the complex impedance between the two models even in the unequal mobility case. Finally, diffusion type boundary conditions are shown to be fully equivalent to the ohmic one. Some limiting cases of the model parameters are investigated.
Additional Results of Glaze Icing Scaling in SLD Conditions
NASA Technical Reports Server (NTRS)
Tsao, Jen-Ching
2016-01-01
New guidance of acceptable means of compliance with the super-cooled large drops (SLD) conditions has been issued by the U.S. Department of Transportation's Federal Aviation Administration (FAA) in its Advisory Circular AC 25-28 in November 2014. The Part 25, Appendix O is developed to define a representative icing environment for super-cooled large drops. Super-cooled large drops, which include freezing drizzle and freezing rain conditions, are not included in Appendix C. This paper reports results from recent glaze icing scaling tests conducted in NASA Glenn Icing Research Tunnel (IRT) to evaluate how well the scaling methods recommended for Appendix C conditions might apply to SLD conditions. The models were straight NACA 0012 wing sections. The reference model had a chord of 72 in. and the scale model had a chord of 21 in. Reference tests were run with airspeeds of 100 and 130.3 kn and with MVD's of 85 and 170 micron. Two scaling methods were considered. One was based on the modified Ruff method with scale velocity found by matching the Weber number WeL. The other was proposed and developed by Feo specifically for strong glaze icing conditions, in which the scale liquid water content and velocity were found by matching reference and scale values of the nondimensional water-film thickness expression and the film Weber number Wef. All tests were conducted at 0 deg AOA. Results will be presented for stagnation freezing fractions of 0.2 and 0.3. For nondimensional reference and scale ice shape comparison, a new post-scanning ice shape digitization procedure was developed for extracting 2-D ice shape profiles at any selected span-wise location from the high fidelity 3-D scanned ice shapes obtained in the IRT.
On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws
NASA Technical Reports Server (NTRS)
Loh, Ching Y.
2003-01-01
A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.
On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws
NASA Technical Reports Server (NTRS)
Loh, Ching Y.
2003-01-01
A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.
NASA Astrophysics Data System (ADS)
Pan, Ke-Qi; Liu, Jin-Yang
2012-02-01
The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation. The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Numerical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free-free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time. The project was supported by the National Natural Science Foundation of China (10872126) and the Research Fund of the Doctoral Program of Higher Education of China (20100073110007).
Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons
Elizalde, E.; Odintsov, S. D.; Saharian, A. A.
2009-03-15
We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a (D+1)-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.
Supersonic far-field boundary conditions for transonic small-disturbance theory
NASA Technical Reports Server (NTRS)
Gibbons, Michael D.; Batina, John T.
1989-01-01
Characteristic far-field boundary conditions for supersonic freestream flow have been developed and implemented within a transonic small-disturbance code. The boundary conditions have been implemented within the CAP-TSD code which has been developed recently for aeroelastic analysis of complete aircraft configurations. These boundary conditions improve the accuracy of the solutions for supersonic freestream applications. They also allow the extent of the grid to be much smaller, thus providing savings in the computational time required to obtain solutions. Comparisons are shown between surface pressures computed using large and small grid extents for the NACA 0012 airfoil and the F-5 wing at various Mach numbers and angles of attack. Both steady and unsteady results are presented and comparisons are made with Euler results and with experimental data to assess the accuracy of the new far-field boundary conditions. Comparisons of these results show that the supersonic boundary conditions allow a much smaller grid to be used without losing accuracy.
Konikow, L.F.; Sanford, W.E.; Campbell, P.J.
1997-01-01
In a solute-transport model, if a constant-concentration boundary condition is applied at a node in an active flow field, a solute flux can occur by both advective and dispersive processes. The potential for advective release is demonstrated by reexamining the Hydrologic Code Intercomparison (HYDROCOIN) project case 5 problem, which represents a salt dome overlain by a shallow groundwater system. The resulting flow field includes significant salinity and fluid density variations. Several independent teams simulated this problem using finite difference or finite element numerical models. We applied a method-of-characteristics model (MOCDENSE). The previous numerical implementations by HYDROCOIN teams of a constant-concentration boundary to represent salt release by lateral dispersion only (as stipulated in the original problem definition) was flawed because this boundary condition allows the release of salt into the flow field by both dispersion and advection. When the constant-concentration boundary is modified to allow salt release by dispersion only, significantly less salt is released into the flow field. The calculated brine distribution for case 5 depends very little on which numerical model is used, as long as the selected model is solving the proper equations. Instead, the accuracy of the solution depends strongly on the proper conceptualization of the problem, including the detailed design of the constant-concentration boundary condition. The importance and sensitivity to the manner of specification of this boundary does not appear to have been recognized previously in the analysis of this problem.
The Additional Error of Inertial Sensors Induced by Hypersonic Flight Conditions.
Karachun, Volodimir; Mel'nick, Viktorij; Korobiichuk, Igor; Nowicki, Michał; Szewczyk, Roman; Kobzar, Svitlana
2016-01-01
The emergence of hypersonic technology pose a new challenge for inertial navigation sensors, widely used in aerospace industry. The main problems are: extremely high temperatures, vibration of the fuselage, penetrating acoustic radiation and shock N-waves. The nature of the additional errors of the gyroscopic inertial sensor with hydrostatic suspension components under operating conditions generated by forced precession of the movable part of the suspension due to diffraction phenomena in acoustic fields is explained. The cause of the disturbing moments in the form of the Coriolis inertia forces during the transition of the suspension surface into the category of impedance is revealed. The boundaries of occurrence of the features on the resonance wave match are described. The values of the "false" angular velocity as a result of the elastic-stress state of suspension in the acoustic fields are determined. PMID:26927122
The Additional Error of Inertial Sensors Induced by Hypersonic Flight Conditions
Karachun, Volodimir; Mel’nick, Viktorij; Korobiichuk, Igor; Nowicki, Michał; Szewczyk, Roman; Kobzar, Svitlana
2016-01-01
The emergence of hypersonic technology pose a new challenge for inertial navigation sensors, widely used in aerospace industry. The main problems are: extremely high temperatures, vibration of the fuselage, penetrating acoustic radiation and shock N-waves. The nature of the additional errors of the gyroscopic inertial sensor with hydrostatic suspension components under operating conditions generated by forced precession of the movable part of the suspension due to diffraction phenomena in acoustic fields is explained. The cause of the disturbing moments in the form of the Coriolis inertia forces during the transition of the suspension surface into the category of impedance is revealed. The boundaries of occurrence of the features on the resonance wave match are described. The values of the “false” angular velocity as a result of the elastic-stress state of suspension in the acoustic fields are determined. PMID:26927122
The Additional Error of Inertial Sensors Induced by Hypersonic Flight Conditions.
Karachun, Volodimir; Mel'nick, Viktorij; Korobiichuk, Igor; Nowicki, Michał; Szewczyk, Roman; Kobzar, Svitlana
2016-02-26
The emergence of hypersonic technology pose a new challenge for inertial navigation sensors, widely used in aerospace industry. The main problems are: extremely high temperatures, vibration of the fuselage, penetrating acoustic radiation and shock N-waves. The nature of the additional errors of the gyroscopic inertial sensor with hydrostatic suspension components under operating conditions generated by forced precession of the movable part of the suspension due to diffraction phenomena in acoustic fields is explained. The cause of the disturbing moments in the form of the Coriolis inertia forces during the transition of the suspension surface into the category of impedance is revealed. The boundaries of occurrence of the features on the resonance wave match are described. The values of the "false" angular velocity as a result of the elastic-stress state of suspension in the acoustic fields are determined.
The Navier-Stokes Equations Under a Unilateral Boundary Condition of Signorini's Type
NASA Astrophysics Data System (ADS)
Zhou, Guanyu; Saito, Norikazu
2016-09-01
We propose a new outflow boundary condition, a unilateral condition of Signorini's type, for the incompressible Navier-Stokes equations. The condition is a generalization of the standard free-traction condition. Its variational formulation is given by a variational inequality. We also consider a penalty approximation, a kind of the Robin condition, to deduce a suitable formulation for numerical computations. Under those conditions, we can obtain energy inequalities that are key features for numerical computations. The main contribution of this paper is to establish the well-posedness of the Navier-Stokes equations under those boundary conditions. Particularly, we prove the unique existence of strong solutions of Ladyzhenskaya's class using the standard Galerkin's method. For the proof of the existence of pressures, however, we offer a new method of analysis.
NASA Astrophysics Data System (ADS)
Alpert, P.; Krichak, S. O.; Krishnamurti, T. N.; Stein, U.; Tsidulko, M.
1996-07-01
The contributions of boundary factors, which may be considered to be independent of the physics or the dynamics of the mesoscale model, are explored in a consistent approach for a widely investigated Alpine Experiment (AL-PEX) lee cyclogenesis case. The roles of the lateral boundaries and the initial fields in conjunction with that of the topography, as well as their possible nonlinear interactions in various model settings, are calculated with the aid of the recently developed factor separation method. Focus is given to the influences of the extent of the model domain and of the running period prior to the climax of the lee cyclone development during 3 6 March 1982. It is shown that the initial conditions are dominant in the first 9 15 h, during which time the topography and lateral boundaries play negative roles because of the adjusting processes. The nonlinear interaction BI between lateral boundaries (B) and the initial conditions (I) was found to be the major contributor to the cyclone deepening during the adjustment period. For longer running periods, some equilibrium is reached in which both the BI interaction and the lateral boundary dominate. The topographic contribution to the lee cyclone deepening in this ALPEX case was indeed limited to about 20% only, as already indicated by earlier studies. Testing several distances of the western lateral boundary suggests the existence of an optimal distance for good results. Both too distant and too close lateral boundaries yield worse results. Testing with frozen boundary conditions shows that the update of the lateral boundaries at a specific time of +36 h was crucial to the development. The results are clearly dependent to some extent on the model type and the particular case under investigation, as well as on the boundary conditions, the initialization procedures, and other model characteristics. The current experiments, however, provide a quantitative approach for estimating the relative roles of the
Dynamic modeling of beams with non-material, deformation-dependent boundary conditions
NASA Astrophysics Data System (ADS)
Humer, Alexander
2013-02-01
In conventional problems of structural mechanics, both kinematic boundary conditions and external forces are prescribed at fixed material points that are known in advance. If, however, a structure may move relative to its supports, the position of the imposed constraint relations generally changes in the course of motion. A class of problems which inherently exhibits this particular type of non-material boundary conditions is that of axially moving continua. Despite varying in time, the positions of the supports relative to the material points of the body have usually assumed to be known a priori throughout the deformation process in previous investigations. This requirement is abandoned in the present paper, where the dynamic behavior of a structure is studied, which may move freely relative to one of its supports. As a consequence, the position of such a non-material boundary relative to the structure does not only change in time but also depends on the current state of deformation of the body. The variational formulation of the equilibrium relations of a slender beam that may undergo large deformations is presented. To this end, a theory based on Reissner's geometrically exact relations for the plane deformation of beams is adopted, in which shear deformation is neglected for the sake of brevity. Before a finite element scheme is developed, a deformation-dependent transformation of the beam's material coordinate is introduced, by which the varying positions of the constraint relations are mapped onto fixed points with respect to the new non-material coordinate. By means of this transformation, additional convective terms emerge from the virtual work of the inertia forces, whose symmetry properties turn out to be different from what has previously been presented in the literature. In order to obtain approximate solutions, a finite element discretization utilizing absolute nodal displacements as coordinates is subsequently used in characteristic numerical examples
Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S.; Ingber, M.S.
1995-04-01
formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.
Fang, Angbo; Qian, Tiezheng; Sheng, Ping
2008-12-01
Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable pi -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times.
Li, Chenxi; Cazzolato, Ben; Zander, Anthony
2016-01-01
The classic analytical model for the sound absorption of micro perforated materials is well developed and is based on a boundary condition where the velocity of the material is assumed to be zero, which is accurate when the material vibration is negligible. This paper develops an analytical model for finite-sized circular micro perforated membranes (MPMs) by applying a boundary condition such that the velocity of air particles on the hole wall boundary is equal to the membrane vibration velocity (a zero-slip condition). The acoustic impedance of the perforation, which varies with its position, is investigated. A prediction method for the overall impedance of the holes and the combined impedance of the MPM is also provided. The experimental results for four different MPM configurations are used to validate the model and good agreement between the experimental and predicted results is achieved. PMID:26827008
NASA Astrophysics Data System (ADS)
Su, Zhu; Jin, Guoyong; Ye, Tiangui
2016-06-01
The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier series which consists of standard Fourier cosine series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt’s rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.
Boundary condition handling approaches for the model reduction of a vehicle frame
NASA Astrophysics Data System (ADS)
Xie, Qingxi; Zhang, Nong; Zhang, Bangji; Ji, Jinchen
2016-06-01
In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, 'constraint first' is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one.
Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions
NASA Astrophysics Data System (ADS)
Colangelo, Gilberto; Vaghi, Alessio
2016-07-01
We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae à la Lüscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.
Jiang Haiyan; Cai Wei; Tsu, Raphael
2011-03-01
In this paper, the accuracy of the Frensley inflow boundary condition of the Wigner equation is analyzed in computing the I-V characteristics of a resonant tunneling diode (RTD). It is found that the Frensley inflow boundary condition for incoming electrons holds only exactly infinite away from the active device region and its accuracy depends on the length of contacts included in the simulation. For this study, the non-equilibrium Green's function (NEGF) with a Dirichlet to Neumann mapping boundary condition is used for comparison. The I-V characteristics of the RTD are found to agree between self-consistent NEGF and Wigner methods at low bias potentials with sufficiently large GaAs contact lengths. Finally, the relation between the negative differential conductance (NDC) of the RTD and the sizes of contact and buffer in the RTD is investigated using both methods.
Influence of Boundary Conditions on Metastable Lifetimes for The Ising Model on the Hyperbolic Plane
NASA Astrophysics Data System (ADS)
Richards, Howard L.; Sharma Chapagain, Dipendra; Molchanoff, James
2012-02-01
Some corals grow in shapes that resemble 3D models of the hyperbolic plane, since this allows them to have greater area for a given growth radius. Each polyp could be represented by an Ising site, with ``feeding'' = ``up'' and ``retracted'' = ``down''. The mechanisms of metastable decay could be interpreted as how the coral as a whole reacts to changing conditions of food availability or predation. Previous studies have shown that there is a spinodal field for the Ising model on a regular lattice in the hyperbolic plane if it is infinite or has periodic or mean-field boundary conditions. This happens because the size of the boundary grows asymptotically at the same rate as the droplet volume, in clear contrast with droplets in the Euclidean plane. Our simulations show, however, that the spinodal field disappears if more physically relevant open boundary conditions are used instead.
Friction-term response to boundary-condition type in flow models
Schaffranek, R.W.; Lai, C.
1996-01-01
The friction-slope term in the unsteady open-channel flow equations is examined using two numerical models based on different formulations of the governing equations and employing different solution methods. The purposes of the study are to analyze, evaluate, and demonstrate the behavior of the term in a set of controlled numerical experiments using varied types and combinations of boundary conditions. Results of numerical experiments illustrate that a given model can respond inconsistently for the identical resistance-coefficient value under different types and combinations of boundary conditions. Findings also demonstrate that two models employing different dependent variables and solution methods can respond similarly for the identical resistance-coefficient value under similar types and combinations of boundary conditions. Discussion of qualitative considerations and quantitative experimental results provides insight into the proper treatment, evaluation, and significance of the friction-slope term, thereby offering practical guidelines for model implementation and calibration.
Effects of uncertainty in boundary-conditions on flood hazard assessment
NASA Astrophysics Data System (ADS)
Domeneghetti, A.; Vorogushyn, S.; Castellarin, A.; Merz, B.; Brath, A.
2012-04-01
Comprehensive flood-risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of utmost importance, especially in the case of flood hazard assessments along dike-protected reaches, where dike failures have to be considered. This paper focuses on a 50km reach of River Po (Italy) and three major sources of uncertainty in inundation mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in the dike-failure location and breach morphology. We derive confidence bounds for flood hazard maps by means of the Inundation Hazard Assessment Model (IHAM) - a hybrid probabilistic-deterministic model. IHAM couples in a dynamic way a 1D hydrodynamic model and a 2D raster-based hydraulic model through a probabilistic dike-breaching analysis that considers three different failure mechanisms: overtopping, piping and micro-instability due to seepage. To address the randomness resulting from the variability in boundary conditions and dike-failures the system is run in a Monte Carlo framework. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed by applying different bivariate copula families to model the frequency of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterized by associating the rating-curve used as boundary condition with confidence intervals which reflect discharge measurements errors and interpolation errors. The results of the study are presented in terms of the Monte Carlo-based flood hazard mapping for different flood-intensity indicators (e.g., inundation depth, flow velocity, inundation duration, etc.) together with the corresponding uncertainty bounds. We conclude on the influence of uncertainty in boundary conditions and provide decision makers with an important piece of information
The influence of upstream boundary conditions on swirling flows undergoing vortex breakdown
NASA Astrophysics Data System (ADS)
Rukes, Lothar; Sieber, Moritz; Oberleithner, Kilian; Paschereit, Oliver
2014-11-01
Swirling jets undergoing vortex breakdown are common in research and technology. In part this is because swirling jets are widely used to anchor the flame position in gas turbines. Recently, the benefit in terms of flashback safety of axial air injection via a center body in the upstream mixing tube of a simplified premixed burner was demonstrated, Reichel (ASME Turbo Expo 2014). However, the presence of a center body alone alters the upstream boundary conditions for the downstream swirling flow. This study investigates how different upstream conditions modify the downstream swirling jet in a more generic setup. A swirling jet facility is used, consisting of a swirler, a pipe, a nozzle and an unconfined part. The focus lies on two large-scale flow features: the precessing vortex core (PVC) and the recirculation bubble. The flow field is measured with Particle Image Velocimetry and proper orthogonal decomposition is conducted to extract the dominant coherent structures. Additionally, a feature tracking approach is used to track the instantaneous shape and position of the recirculation bubble. We find that different center bodies modify the inflow profiles of the unconfined part of the flow in a specific way. This leads to significant differences in the large scale dynamics. Financial support from the German Science Foundation is gratefully acknowledged.
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies. PMID:27322600
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies. PMID:27322600
The specification of distributed boundary conditions in numerical simulation of the ionosphere
NASA Technical Reports Server (NTRS)
Waldman, H.
1973-01-01
The approach described makes it possible to use boundary conditions which do not have to be associated with any particular point of the solution interval. The approach was applied in a program which solves simultaneously the coupled differential equations describing the concentrations of the O(+) ions, their temperature, the electron temperature and the concentrations of O2(+), NO(+) and N2(+) ions. Several versions of the proposed scheme are described for various kinds of boundary conditions. Attention is given to a given columnar ionic content, a given incoming or outgoing flux, or a given height of the peak concentration.
On the choice of boundary conditions in continuum models of continental deformation
NASA Technical Reports Server (NTRS)
Wdowinski, Shimon; O'Connell, Richard J.
1990-01-01
Recent studies of continental deformation have treated the lithosphere as a viscous medium and investigated the time evolution of the deformation caused by tectonic and buoyancy forces. This paper examines the differences between (1) continuum models that keep velocity boundary conditions constant with time and (2) models that keep stress boundary conditions constant with time. These differences are demonstrated by using a simple example of a continental lithosphere that is subjected to horizontal compression. The results show that in (2) the indentation velocity decreases with time, while in (1) the indentation velocity remains constant with time.
Free vibrations of thermally stressed orthotropic plates with various boundary conditions
NASA Technical Reports Server (NTRS)
Bailey, C. D.; Greetham, J. C.
1973-01-01
An analytical investigation of the vibrations of thermally stressed orthotropic plates in the prebuckled region is presented. The investigation covers the broad class of trapezoidal plates with two opposite sides parallel. Each edge of the plate may be subjected to different uniform boundary conditions. variable thickness and arbitrary temperature distributions (analytical or experimental) for any desired combination of boundary conditions may be prescribed. Results obtained using this analysis are compared to experimental results obtained for isotropic plates with thermal stress, and to results contained in the literature for orthotropic plates without thermal stress. Good agreement exists for both sets of comparisons.
Boundary conditions at closed edge of bilayer graphene and energy bands of collapsed nanotubes
NASA Astrophysics Data System (ADS)
Nakanishi, Takeshi; Ando, Tsuneya
2016-10-01
Band structure is systematically studied in an effective-mass scheme in collapsed armchair and zigzag nanotubes based on the model in which collapsed tubes are regarded as bilayer ribbons with closed edges. Boundary conditions at closed edges, describing the connection of the envelope wave functions between the bottom and top layers, are derived. Among electronic states in bilayers, which change sensitively depending on the relative displacement of two layers, those having wave functions matching well with the obtained boundary conditions, i.e., unaffected by the presence of closed edges, constitute important states near the Fermi level in collapsed nanotubes.
The sensitivity of numerically simulated climates to land-surface boundary conditions
NASA Technical Reports Server (NTRS)
Mintz, Y.
1982-01-01
Eleven sensitivity experiments that were made with general circulation models to see how land-surface boundary conditions can influence the rainfall, temperature, and motion fields of the atmosphere are discussed. In one group of experiments, different soil moistures or albedos are prescribed as time-invariant boundary conditions. In a second group, different soil moistures or different albedos are initially prescribed, and the soil moisture (but not the albedo) is allowed to change with time according to the governing equations for soil moisture. In a third group, the results of constant versus time-dependent soil moistures are compared.
Topological quantum scattering under the influence of a nontrivial boundary condition
NASA Astrophysics Data System (ADS)
Mota, Herondy
2016-04-01
We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein-Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov-Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov-Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
NASA Technical Reports Server (NTRS)
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
Air Flow Path Dynamics In The Vadose Zone Under Various Land Surface Climate Boundary Conditions
NASA Astrophysics Data System (ADS)
Illangasekare, T. H.; Sakaki, T.; Schulte, P. E.; Cihan, A.; Christ, J.
2010-12-01
Vapor intrusion (VI) refers to the transport of volatile chemical vapors from subsurface sources to surface and subsurface structures through the vadose zone. Because of the difference in pressure between the inside of the building and the subsurface soil pores, vapor can enter the building through cracks in the foundation, slab and walls and utility openings. The processes that govern the vapor transport in the heterogeneous subsurface “outside the home” are complex, and the sampling to assess potential pathways is subjected to spatial and temporal variability. Spatial variability is a result of a number of factors that include changing soil and soil moisture conditions. Temporal variability is a result of transient heat, wind, ambient pressure and a water flux boundary conditions at the land-atmospheric interface. Fluctuating water table conditions controlled by recharge, pumping, and stream-aquifer interactions will also contribute to the transient vapor flux generation at the sources. When the soil moisture changes as a result of precipitation events and other soil surface boundary conditions, the soil moisture content changes and hence the air permeability. Therefore, the primary pathways for the vapor are preferential channels that change with the transient soil moisture distribution. Both field and laboratory studies have shown that heterogeneity has a significant influence on soil moisture conditions in unsaturated soils. Uncertainties in vapor transport predictions have been attributed to heterogeneity and spatial variability in hydraulic properties. In this study, our goal was to determine the role of soil moisture variability on vapor transport and intrusion as affected by the climate driven boundary conditions on the land surface. A series of experiments were performed to generate a comprehensive data set to understand and evaluate how the spatial and temporal variability of soil moisture affected by the mass and heat flux boundary conditions on the
NASA Astrophysics Data System (ADS)
Kushwaha, Hari Mohan; Sahu, Santosh Kumar
2016-06-01
This paper reports the hydrodynamically and thermally fully developed, laminar, incompressible, forced convective heat transfer characteristics of gaseous flows through a parallel plate microchannel with different constant heat flux boundary conditions. The first order velocity slip and viscous dissipation effects are considered in the analysis. Here, three different thermal boundary conditions such as: both plates kept at different constant heat fluxes, both plates kept at equal constant heat fluxes and one plate kept at constant heat flux and other one insulated are considered for the analysis. The deviation in Nusselt number between the model that considers both first order velocity slip and temperature jump and the one that considers only velocity slip is reported. Also, the effect of various heat flux ratios on the Nusselt number is reported in this analysis. In addition, the deviation in Nusselt number between first and second order slip model is discussed in this study.
Turbulance boundary conditions for shear flow analysis, using the DTNS flow solver
NASA Technical Reports Server (NTRS)
Mizukami, M.
1995-01-01
The effects of different turbulence boundary conditions were examined for two classical flows: a turbulent plane free shear layer and a flat plate turbulent boundary layer with zero pressure gradient. The flow solver used was DTNS, an incompressible Reynolds averaged Navier-Stokes solver with k-epsilon turbulence modeling, developed at the U.S. Navy David Taylor Research Center. Six different combinations of turbulence boundary conditions at the inflow boundary were investigated: In case 1, 'exact' k and epsilon profiles were used; in case 2, the 'exact' k profile was used, and epsilon was extrapolated upstream; in case 3, both k and epsilon were extrapolated; in case 4, the turbulence intensity (I) was 1 percent, and the turbulent viscosity (mu(sub t)) was equal to the laminar viscosity; in case 5, the 'exact' k profile was used and mu(sub t) was equal to the laminar viscosity; in case 6, the I was 1 percent, and epsilon was extrapolated. Comparisons were made with experimental data, direct numerical simulation results, or theoretical predictions as applicable. Results obtained with DTNS showed that turbulence boundary conditions can have significant impacts on the solutions, especially for the free shear layer.
Effects of boundary conditions on thermomechanical calculations: Spent fuel test - climax
Butkovich, T.R.
1982-10-01
The effects of varying certain boundary conditions on the results of finite-element calculations were studied in relation to the Spent Fuel Test - Climax. The study employed a thermomechanical model with the ADINA structural analysis. Nodal temperature histories were generated with the compatible ADINAT heat flow codes. The boundary conditions studied included: (1) The effect of boundary loading on three progressively larger meshes. (2) Plane strain vs plane stress conditions. (3) The effect of isothermal boundaries on a small mesh and on a significantly larger mesh. The results showed that different mesh sizes had an insignificant effect on isothermal boundaries up to 5 y, while on the smallest and largest mesh, the maximum temperature difference in the mesh was <1{sup 0}C. In the corresponding ADINA calculation, these different mesh sizes produce insignificant changes in the stress field and displacements in the region of interest near the heat sources and excavations. On the other hand, plane stress produces horizontal and vertical stress differences approx. 9% higher than does plane strain.
Sankaran, Sethuraman; Kim, Hyun Jin; Choi, Gilwoo; Taylor, Charles A
2016-08-16
Computational fluid dynamic methods are currently being used clinically to simulate blood flow and pressure and predict the functional significance of atherosclerotic lesions in patient-specific models of the coronary arteries extracted from noninvasive coronary computed tomography angiography (cCTA) data. One such technology, FFRCT, or noninvasive fractional flow reserve derived from CT data, has demonstrated high diagnostic accuracy as compared to invasively measured fractional flow reserve (FFR) obtained with a pressure wire inserted in the coronary arteries during diagnostic cardiac catheterization. However, uncertainties in modeling as well as measurement results in differences between these predicted and measured hemodynamic indices. Uncertainty in modeling can manifest in two forms - anatomic uncertainty resulting in error of the reconstructed 3D model and physiologic uncertainty resulting in errors in boundary conditions or blood viscosity. We present a data-driven framework for modeling these uncertainties and study their impact on blood flow simulations. The incompressible Navier-Stokes equations are used to model blood flow and an adaptive stochastic collocation method is used to model uncertainty propagation in the Navier-Stokes equations. We perform uncertainty quantification in two geometries, an idealized stenosis model and a patient specific model. We show that uncertainty in minimum lumen diameter (MLD) has the largest impact on hemodynamic simulations, followed by boundary resistance, viscosity and lesion length. We show that near the diagnostic cutoff (FFRCT=0.8), the uncertainty due to the latter three variables are lower than measurement uncertainty, while the uncertainty due to MLD is only slightly higher than measurement uncertainty. We also show that uncertainties are not additive but only slightly higher than the highest single parameter uncertainty. The method presented here can be used to output interval estimates of hemodynamic indices
Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC
NASA Technical Reports Server (NTRS)
Liu, Nan-Suey; Shih, Tsan-Hsing
2009-01-01
This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The
Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation.
Renou, Ygaäl; Aurégan, Yves
2011-07-01
This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aurégan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications. PMID:21786877
Navier-Stokes equations in 3D thin domains with Navier friction boundary condition
NASA Astrophysics Data System (ADS)
Hu, Changbing
In this article we study the 3D Navier-Stokes equations with Navier friction boundary condition in thin domains. We prove the global existence of strong solutions to the 3D Navier-Stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small. We generalize the techniques developed to study the 3D Navier-Stokes equations in thin domains, see [G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains I: Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993) 503-568; G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains II: Global regularity of spatially periodic conditions, in: Nonlinear Partial Differential Equations and Their Application, College de France Seminar, vol. XI, Longman, Harlow, 1994, pp. 205-247; R. Temam, M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996) 499-546; R. Temam, M. Ziane, Navier-Stokes equations in thin spherical shells, in: Optimization Methods in Partial Differential Equations, in: Contemp. Math., vol. 209, Amer. Math. Soc., Providence, RI, 1996, pp. 281-314], to the Navier friction boundary condition by introducing a new average operator M in the thin direction according to the spectral decomposition of the Stokes operator A. Our analysis hinges on the refined investigation of the eigenvalue problem corresponding to the Stokes operator A with Navier friction boundary condition.
Shifted periodic boundary conditions for large-eddy simulation of wind farms
NASA Astrophysics Data System (ADS)
Munters, Wim; Meneveau, Charles; Meyers, Johan
2015-11-01
In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. In the context of wind-farm large-eddy simulations, this effect induces artificial spanwise inhomogeneities in the time-averaged local wind conditions as seen by the wind turbines, leading to spurious differences in power prediction between otherwise equivalent columns of wind turbines in a wind farm (a column is defined here as a set of turbines parallel to the mean flow direction). We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. Instead of straightforwardly reintroducing the velocity from the outlet plane back at the inlet, as in classic periodic boundary conditions, this plane is first shifted in the spanwise direction by a predefined and constant distance. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. Finally, we apply the method in a precursor simulation, generating inlet conditions for a spatially developing wind-farm boundary layer. WM and JM are supported by the ERC (ActiveWindFarms, grant no: 306471). CM acknowledges support by the NSF (grant IIA-1243482, the WINDINSPIRE project).
NASA Astrophysics Data System (ADS)
Allaerts, Dries; Meyers, Johan
2014-05-01
Atmospheric boundary layers (ABL) are frequently capped by an inversion layer limiting the entrainment rate and boundary layer growth. Commonly used analytical models state that the entrainment rate is inversely proportional to the inversion strength. The height of the inversion turns out to be a second important parameter. Conventionally neutral atmospheric boundary layers (CNBL) are ABLs with zero surface heat flux developing against a stratified free atmosphere. In this regime the inversion-filling process is merely driven by the downward heat flux at the inversion base. As a result, CNBLs are strongly dependent on the heating history of the boundary layer and strong inversions will fail to erode during the course of the day. In case of large wind farms, the power output of the farm inside a CNBL will depend on the height and strength of the inversion above the boundary layer. On the other hand, increased turbulence levels induced by wind farms may partially undermine the rigid lid effect of the capping inversion, enhance vertical entrainment of air into the farm, and increase boundary layer growth. A suite of large eddy simulations (LES) is performed to investigate the effect of the capping inversion on the conventionally neutral atmospheric boundary layer and on the wind farm performance under varying initial conditions. For these simulations our in-house pseudo-spectral LES code SP-Wind is used. The wind turbines are modelled using a non-rotating actuator disk method. In the absence of wind farms, we find that a decrease in inversion strength corresponds to a decrease in the geostrophic angle and an increase in entrainment rate and geostrophic drag. Placing the initial inversion base at higher altitudes further reduces the effect of the capping inversion on the boundary layer. The inversion can be fully neglected once it is situated above the equilibrium height that a truly neutral boundary layer would attain under the same external conditions such as
Zunger, A.
2005-11-01
New theoretical studies reveal the way that grain boundaries lead to a reduction in electron-hole recombination in CIS, and how Ga addition leads to cell deterioration largely because of grain-interior (not boundary) effects.
NASA Astrophysics Data System (ADS)
Shao, J. Y.; Shu, C.; Chew, Y. T.
2013-02-01
The implementation of Neumann boundary condition in the framework of immersed boundary method (IBM) is presented in this paper to simulate contact line dynamics using a phase field-lattice Boltzmann method. Immersed boundary method [10] is known as an efficient algorithm for modelling fluid-solid interaction. Abundance of prominent works have been devoted to refine IBM [1,11,12]. However, they are mainly restricted to problems with Dirichlet boundary condition. Research that implements the Neumann boundary condition in IBM is very limited to the best of our knowledge. This deficiency significantly limits the application of IBM in computational fluid dynamics (CFD) since physical phenomena associated with Neumann boundary conditions are extremely diverse. The difficulty is attributed to the fact that implementation of Neumann boundary condition is much more complex than that of Dirichlet boundary condition. In the present work, we initiate the first endeavour to implement Neumann boundary condition in IBM with assistance of its physical interpretation rather than simple mathematical manipulation. Concretely speaking, rooted from physical conservation law, the Neumann boundary condition is considered as contribution of flux from the boundary to its relevant physical parameter in a control volume. Moreover, the link between the flux and its corresponding flow field variable is directly manipulated through the immersed boundary concept. In this way, the Neumann boundary conditions can be implemented in IBM. The developed method is applied together with phase field-lattice Boltzmann method to study contact line dynamics. The phase field method [27,39], which becomes increasingly popular in multiphase flow simulation, can efficiently capture complex interface topology and naturally resolve the contact line singularity. Meanwhile, the lattice Boltzmann method is known as an alternative to model fluid dynamics and holds good prospect to simulate multiphase flows with
NASA Astrophysics Data System (ADS)
Bardhan, Jaydeep P.; Knepley, Matthew G.
2014-10-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
Elasto visco-plastic flow with special attention to boundary conditions
NASA Technical Reports Server (NTRS)
Shimazaki, Y.; Thompson, E. G.
1981-01-01
A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.
NASA Astrophysics Data System (ADS)
Brasiello, Antonio; Crescitelli, Silvestro; Giona, Massimiliano
2016-05-01
We consider the one-dimensional Cattaneo equation for transport of scalar fields such as solute concentration and temperature in mass and heat transport problems, respectively. Although the Cattaneo equation admits a stochastic interpretation-at least in the one-dimensional case-negative concentration values can occur in boundary-value problems on a finite interval. This phenomenon stems from the probabilistic nature of this model: the stochastic interpretation provides constraints on the admissible boundary conditions, as can be deduced from the wave formulation here presented. Moreover, as here shown, energetic inequalities and the dissipative nature of the equation provide an alternative way to derive the same constraints on the boundary conditions derived by enforcing positivity. The analysis reported is also extended to transport problems in the presence of a biasing velocity field. Several general conclusions are drawn from this analysis that could be extended to the higher-dimensional case.
Tang, M; Kubin, L P
2001-05-01
In order to study the dislocation density evolution of body centered cubic (bcc) crystals at low temperature by dislocation dynamics (DD) simulations, we investigated carefully three different boundary conditions (BC) for DD, i.e., the quasi-free surface BC, the flux-balanced BC, and the periodic BC. The latter two BCs can account for the dislocation loss from the boundary of the finite simulation box. PBC can also eliminate the influence of surfaces and improve the line connectivity. We have found that the PBC provides a convenient and effective boundary condition for DD simulations and have applied it to the study of dislocation density evolution of bcc metals during stage 0 deformation at low temperature.
Mixed boundary conditions for FFT-based homogenization at finite strains
NASA Astrophysics Data System (ADS)
Kabel, Matthias; Fliegener, Sascha; Schneider, Matti
2016-02-01
In this article we introduce a Lippmann-Schwinger formulation for the unit cell problem of periodic homogenization of elasticity at finite strains incorporating arbitrary mixed boundary conditions. Such problems occur frequently, for instance when validating computational results with tensile tests, where the deformation gradient in loading direction is fixed, as is the stress in the corresponding orthogonal plane. Previous Lippmann-Schwinger formulations involving mixed boundary can only describe tensile tests where the vector of applied force is proportional to a coordinate direction. Utilizing suitable orthogonal projectors we develop a Lippmann-Schwinger framework for arbitrary mixed boundary conditions. The resulting fixed point and Newton-Krylov algorithms preserve the positive characteristics of existing FFT-algorithms. We demonstrate the power of the proposed methods with a series of numerical examples, including continuous fiber reinforced laminates and a complex nonwoven structure of a long fiber reinforced thermoplastic, resulting in a speed-up of some computations by a factor of 1000.
Bardhan, Jaydeep P; Knepley, Matthew G
2014-10-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776
NASA Astrophysics Data System (ADS)
Yaghjian, Arthur D.
2010-08-01
Generalized electromagnetic boundary conditions are derived for interfaces containing surface layers of electric and magnetic polarization. Next, the singularities in the fields and polarization densities at the inner surfaces of spherical and circular cylindrical cloaks illuminated by sources inside the cavities of the cloaks are determined from a plane-wave analysis of fields incident on a half space of material characterized by a relative permittivity-permeability dyadic equal to that of the inner material surfaces of the cloaks. Lastly, these singular fields and polarization densities are shown to satisfy the generalized boundary conditions. For sources inside the cloak cavities, it is found that the inner surfaces of spherical cloaks, unlike the inner surfaces of cylindrical cloaks, behave as "DB boundaries" at which nˆṡD and nˆṡB are zero.
Boundary conditions and partition functions in higher spin AdS3/CFT2
NASA Astrophysics Data System (ADS)
de Boer, Jan; Jottar, Juan I.
2016-04-01
We discuss alternative definitions of the semiclassical partition function in two-dimensional CFTs with higher spin symmetry, in the presence of sources for the higher spin currents. Theories of this type can often be described via Hamiltonian reduction of current algebras, and a holographic description in terms of three-dimensional Chern-Simons theory with generalized AdS boundary conditions becomes available. By studying the CFT Ward identities in the presence of sources, we determine the appropriate choice of boundary terms and boundary conditions in Chern-Simons theory for the various types of partition functions considered. In particular, we compare the Chern-Simons description of deformations of the field theory Hamiltonian versus those encoding deformations of the CFT action. Our analysis clarifies various issues and confusions that have permeated the literature on this subject.
Bardhan, Jaydeep P.; Knepley, Matthew G.
2014-10-07
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
NASA Astrophysics Data System (ADS)
Mantile, Andrea; Posilicano, Andrea; Sini, Mourad
2016-07-01
The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the "free" operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.
NASA Astrophysics Data System (ADS)
Kim, Do Wan; Liu, Wing Kam; Yoon, Young-Cheol; Belytschko, Ted; Lee, Sang-Ho
2007-10-01
Conclusions on the General Circulation Models (GCMs) horizontal and temporal optimum resolution for dynamical downscaling of rainfall in Mediterranean Spain are derived based on the statistical analysis of mesoscale simulations of past events. These events correspond to the 165 heavy rainfall days during 1984 1993, which are simulated with the HIRLAM mesoscale model. The model is nested within the European Centre for Medium-Range Weather Forecasts atmospheric grid analyses. We represent the spectrum of GCMs resolutions currently applied in climate change research by using varying horizontal and temporal resolutions of these analyses. Three sets of simulations are designed using input data with 1°, 2° and 3° horizontal resolutions (available at 6 h intervals), and three additional sets are designed using 1° horizontal resolution with less frequent boundary conditions updated every 12, 24 and 48 h. The quality of the daily rainfall forecasts is verified against rain-gauge observations using correlation and root mean square error analysis as well as Relative Operating Characteristic curves. Spatial distribution of average precipitation fields are also computed and verified against observations. For the whole Mediterranean Spain, model skill is not appreciably improved when using enhanced spatial input data, suggesting that there is no clear benefit in using high resolution data from General Circulation Model for the regional downscaling of precipitation under the conditions tested. However, significant differences are found in verification scores when boundary conditions are interpolated less frequently than 12 h apart. The analysis is particularized for six major rain bearing flow regimes that affect the region, and differences in model performance are found among the flow types, with slightly better forecasts for Atlantic and cold front passage flows. A remarkable spatial variability in forecast quality is found in the domain, with an overall tendency for higher
Fatigue crack damage detection using subharmonic component with nonlinear boundary condition
Wu, Weiliang Qu, Wenzhong E-mail: xiaoli6401@126.com; Xiao, Li E-mail: xiaoli6401@126.com; Shen, Yanfeng Giurgiutiu, Victor
2015-03-31
In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from
Fatigue crack damage detection using subharmonic component with nonlinear boundary condition
NASA Astrophysics Data System (ADS)
Wu, Weiliang; Shen, Yanfeng; Qu, Wenzhong; Xiao, Li; Giurgiutiu, Victor
2015-03-01
In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from
In-plane vibration analysis of annular plates with arbitrary boundary conditions.
Shi, Xianjie; Shi, Dongyan; Qin, Zhengrong; Wang, Qingshan
2014-01-01
In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.
Monopole modes in a finite Fermi system with diffuse reflection boundary conditions
NASA Astrophysics Data System (ADS)
Kolomietz, V. M.; Magner, A. G.; Strutinsky, V. M.; Vydrug-Vlasenko, S. M.
1994-04-01
At semi-classical response function for a finite system of Fermi particles on which acts a spherical external perturbation is obtained assuming a boundary condition with diffuse reflection which takes into account particle correlation interaction within the nuclear surface region.
NASA Astrophysics Data System (ADS)
Lazauskas, Rimantas
2015-12-01
A formalism based on the complex-scaling method is used to solve a four-nucleon scattering problem above the breakup threshold using the realistic nuclear Hamiltonians. This method allows to solve diverse scattering problems based on very trivial boundary conditions and is compatible with the techniques used to solve bound state problems.
Effects of physical boundary conditions on the transverse vibration of single-layer graphene sheets
NASA Astrophysics Data System (ADS)
Sadeghzadeh, S.; Khatibi, M. M.
2016-09-01
The effects of various approaches for a comprehensive application of boundary conditions on the molecular dynamics of graphene nanosheets were studied in this paper. Fixing more than two rows of carbon atoms was tested for satisfaction of clamped boundary condition in dynamics problems, and it was demonstrated that a completely different view should be taken for clamped boundary conditions. To do this, through the frequency domain decomposition approach, operational modal analysis has been developed to carry out the Laboratory of Nanometric Operational Modal Analysis on a molecular dynamics platform. The theory of the mentioned approach was introduced, and some comparisons were made with experimental works. The modeling results have shown that for graphene sheets with simply supported edges, fixing two or more rows leads to the same response as fixing one row. For clamped edges, the use of a flexible base as a substrate satisfies the boundary condition with the best possible. At the end, as an example, it has been demonstrated that the second and third natural vibration frequencies increase with the increase in aspect ratio, while the first frequency remains unchanged.
In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions
Qin, Zhengrong; Wang, Qingshan
2014-01-01
In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions. PMID:24688416
On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population
NASA Astrophysics Data System (ADS)
Boulanouar, Mohamed
2013-04-01
In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.
NASA Astrophysics Data System (ADS)
F. N., Fagundes; R. O., Francisco; B. B., Dilem; J. A., Nogueira
2010-12-01
In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman—Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough (a = e2 M-1varphi, where Mvarphi is the mass of the scalar field generated by the Coleman—Weinberg mechanism).
Burgers equation with no-flux boundary conditions and its application for complete fluid separation
NASA Astrophysics Data System (ADS)
Watanabe, Shinya; Matsumoto, Sohei; Higurashi, Tomohiro; Ono, Naoki
2016-09-01
Burgers equation in a one-dimensional bounded domain with no-flux boundary conditions at both ends is proven to be exactly solvable. Cole-Hopf transformation converts not only the governing equation to the heat equation with an extra damping but also the nonlinear mixed boundary conditions to Dirichlet boundary conditions. The average of the solution v bar is conserved. Consequently, from an arbitrary initial condition, solutions converge to the equilibrium solution which is unique for the given v bar. The problem arises naturally as a continuum limit of a network of certain micro-devices. Each micro-device imperfectly separates a target fluid component from a mixture of more than one component, and its input-output concentration relationships are modeled by a pair of quadratic maps. The solvability of the initial boundary value problem is used to demonstrate that such a network acts as an ideal macro-separator, separating out the target component almost completely. Another network is also proposed which leads to a modified Burgers equation with a nonlinear diffusion coefficient.
Franke, O. Lehn; Reilly, Thomas E.; Bennett, Gordon D.
1987-01-01
Accurate definition of boundary and initial conditions is an essential part of conceptualizing and modeling ground-water flow systems. This report describes the properties of the seven most common boundary conditions encountered in ground-water systems and discusses major aspects of their application. It also discusses the significance and specification of initial conditions and evaluates some common errors in applying this concept to ground-water-system models. An appendix is included that discusses what the solution of a differential equation represents and how the solution relates to the boundary conditions defining the specific problem. This report considers only boundary conditions that apply to saturated ground-water systems.
Improving bottom-boundary conditions for SVAT simulations in shallow-groundwater systems
NASA Astrophysics Data System (ADS)
Morris, Paul J.; Verhoef, Anne; Macdonald, David M. J.; Gardner, Cate M.; Punalekar, Suvarna M.; Tatarenko, Irina; Gowing, David
2013-04-01
A well documented disparity exists between models that simulate: i) groundwater hydrological processes; and ii) soil-vegetation-atmosphere transfers (SVAT) of water and energy. This is particularly pertinent in shallow groundwater systems, such as lowland floodplains, where the domains of surface water and groundwater necessarily overlap. Consideration of either SVAT or groundwater processes in shallow groundwater systems necessitates a robust understanding of their bi-directional interactions. The hydrological bottom-boundary conditions of SVAT models can be driven using continuous groundwater data from dipwells. However, where such data are not available the bottom boundary must be simulated. We sought to develop a simple empirical model of subsurface fluxes of water between a floodplain soil column and its adjoining river, without the additional cost and complication of a fully linked surface water-groundwater model. We conducted our research at Yarnton Mead, a floodplain meadow on the River Thames in Oxfordshire, UK. We used in-situ soil-physical, hydrological and meteorological data to generate an empirical relationship between floodplain water-table position, and rate and direction of subsurface water fluxes between the floodplain soil and the river. We estimated rates of subsurface water flux into and out of our instrumented soil column as the residual term of a water balance equation. We then fitted a linear model to describe the rate and direction of subsurface flux as a function of water-table position. Although the level of explanation of the linear model is not high (r-squared = 0.39), the relationship is highly significant (p < 0.001). When water tables are close to the ground surface the soil column loses water rapidly to the groundwater store and ultimately to the river and other local drainage features. When water tables are low the soil column receives water. This negative feedback leads to a water-table attractor, which our model suggests is
Grid resolution and turbulent inflow boundary condition recommendations for NPARC calculations
NASA Technical Reports Server (NTRS)
Georgiadis, Nicholas J.; Dudek, Julianne C.; Tierney, Thomas P.
1995-01-01
The effects of grid resolution and specification of turbulent inflow boundary conditions were examined using the NPARC code with the Baldwin-Lomax and Chien k-e turbulence models. Three benchmark turbulent test cases were calculated: two were wall bounded flows and the third was a compressible mixing layer. The wall bounded flows were essentially insensitive to axial grid density; however, the location of the first point off the wall had a substantial effect on flow solutions. It was determined that the first point off the wall must be in the laminar sublayer (y+ less than or equal to 5) for the entire boundary layer. For the compressible mixing layer cases, the axial grid density affected the capturing of oblique shock waves in the mixing region, but the overall mixing rate was not strongly dependent on grid resolution. In specifying the inflow turbulent boundary conditions, it was very important to match the boundary layer and momentum thicknesses of the two flows entering the mixing region; calculations obtained with smaller or no boundary layers resulted in substantially reduced mixing. The solutions were relatively insensitive to freestream turbulence level.
NASA Astrophysics Data System (ADS)
Volino, Ralph John
1995-01-01
Measurements from transitional, heated boundary layers along a concave-curved test wall are presented and discussed. A boundary layer subject to low free-stream turbulence intensity (FSTI), which contains stationary streamwise (Gortler) vortices, is documented. The low FSTI measurements are followed by measurements in boundary layers subject to high (initially 8%) free-stream turbulence intensity and moderate to strong (K = {nuover U_sp{infty} {2}}{dUinftyover dx} as high as 9times 10^{ -6}) acceleration. The high FSTI experiments are the main focus of the work. Conditions were chosen to simulate those present on the downstream half of the pressure side of a gas turbine airfoil. The high FSTI boundary layers undergo transition from a strongly disturbed non-turbulent state to a fully-turbulent state. Due to the stabilizing effect of strong acceleration, the transition zones are of extended length in spite of the high FSTI. Transitional values of skin friction coefficients and Stanton numbers drop below flat-plate, low FSTI, turbulent flow correlations, but remain well above laminar flow values. Mean velocity and temperature profiles exhibit clear changes in shape as the flow passes through transition. Turbulence statistics, including the turbulent shear stress, turbulent heat flux, and turbulent Prandtl number, are documented. Turbulent transport is strongly suppressed below values in unaccelerated turbulent boundary layers. A technique called "octant analysis" is introduced and applied to several cases from the literature as well as to data from the present study. Octant analysis shows a fundamental difference between transitional and fully-turbulent boundary layers. Transitional boundary layers are characterized by incomplete mixing compared to fully-turbulent boundary layers. Similar octant analysis results are observed in both low and high FSTI cases. Spectral analysis suggests that the non-turbulent zone of the high FSTI flow is dominated by large scale
NASA Technical Reports Server (NTRS)
Wilson, Jack; Paxson, Daniel E.
2002-01-01
In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.
Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method
NASA Technical Reports Server (NTRS)
Watson, W. R.; Jones, M. G.
2012-01-01
The accuracy of the Ingard-Myers boundary condition and a recently proposed modified Ingard-Myers boundary condition is evaluated for use in impedance eduction under the assumption of uniform mean flow. The evaluation is performed at three centerline Mach numbers, using data acquired in a grazing flow impedance tube, using both upstream and downstream propagating sound sources, and on a database of test liners for which the expected behavior of the impedance spectra is known. The test liners are a hard-wall insert consisting of 12.6 mm thick aluminum, a linear liner without a facesheet consisting of a number of small diameter but long cylindrical channels embedded in a ceramic material, and two conventional nonlinear liners consisting of a perforated facesheet bonded to a honeycomb core. The study is restricted to a frequency range for which only plane waves are cut on in the hard-wall sections of the flow impedance tube. The metrics used to evaluate each boundary condition are 1) how well it educes the same impedance for upstream and downstream propagating sources, and 2) how well it predicts the expected behavior of the impedance spectra over the Mach number range. The primary conclusions of the study are that the same impedance is educed for upstream and downstream propagating sources except at the highest Mach number, that an effective impedance based on both the upstream and downstream measurements is more accurate than an impedance based on the upstream or downstream data alone, and that the Ingard-Myers boundary condition with an effective impedance produces results similar to that achieved with the modified Ingard-Myers boundary condition.
NASA Astrophysics Data System (ADS)
Janssen, R. H. H.; Vilà-Guerau de Arellano, J.; Ganzeveld, L. N.; Kabat, P.; Jimenez, J. L.; Farmer, D. K.; van Heerwaarden, C. C.; Mammarella, I.
2012-08-01
We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the model for a case study in Hyytiälä, Finland, and find that it is able to satisfactorily reproduce the observed dynamics and gas-phase chemistry. We show that the exchange of organic aerosol between the free troposphere and the boundary layer (entrainment) must be taken into account in order to explain the observed diurnal cycle in organic aerosol (OA) concentration. An examination of the budgets of organic aerosol and terpene concentrations show that the former is dominated by entrainment, while the latter is mainly driven by emission and chemical transformation. We systematically investigate the role of the land surface, which governs both the surface energy balance partitioning and terpene emissions, and the large-scale atmospheric process of vertical subsidence. Entrainment is especially important for the dilution of organic aerosol concentrations under conditions of dry soils and low terpene emissions. Subsidence suppresses boundary layer growth while enhancing entrainment. Therefore, it influences the relationship between organic aerosol and terpene concentrations. Our findings indicate that the diurnal evolution of secondary organic aerosols (SOA) in the boundary layer is the result of coupled effects of the land surface, dynamics of the atmospheric boundary layer, chemistry, and free troposphere conditions. This has potentially some consequences for the design of both field campaigns and large-scale modeling studies.
Singh, V.; Mukhopadhyay, A.K.; Prasad, K.S.
1997-11-15
In this paper results using transmission electron microscopy (TEM), electron diffraction and energy dispersive x-ray spectroscopy on the influence of small additions of Zn({approximately}0.25 at%) on the nature of the grain boundary precipitates in an AA 8090 alloy are presented to show that Zn is indeed detected in enhanced concentrations in association with both {delta} (AlLi) and T{sub 2}(Al{sub 6}CuLi{sub 3}) precipitates formed at the grain boundary. An addition of 0.6 wt% of Zn to an al-2.2Li-1.2Cu-0.8Mg-0.10Zr alloy does not either change the type of the coarse grain boundary precipitates, i.e., {delta} (AlLi) and T{sub 2} (Al{sub 6}CuLi{sub 3}) or reduce the width of the precipitate free zones (PFZs) adjacent to the grain boundary, while, it does change the chemistry of both {delta} and T{sub 2} via incorporation of Zn into these phases.
Periodic two-dimensional cavity flow: Effect of linear horizontal thermal boundary condition
Jones, D.N. ); Briggs, D.G. )
1989-02-01
A two-dimensional air-filled cavity with isothermal vertical walls adiabatic top and bottom surfaces has been extensively studied both numerically and experimentally. When the aspect ratio is of order one and the Rayleigh number is less than about 10{sup 9} this geometry produces a highly stable and reproducible laminar flow. The result is quite different when the upper and lower surfaces are subjected to a destabilizing boundary condition, i.e., a linear temperature variation between the hot and cold vertical walls. At a critical Rayleigh number between 10{sup 6} and 10{sup 7} the flow becomes periodic and thus appears to fall into the category of instability of the type known as Hopf bifurcation. Briggs and Jones (1985) report velocity variations measured ner the vertical surfaces that vary by nearly {plus minus} 20% about the mean. Other unexplained behavior reported by Briggs and Jones (1985) consisted of jumps exhibited hysteresis effect, which resulted in some overlap between regimes. This paper presents the results of additional measurements, which indicate that the periodic flow is characterized by the convection of hot and cold pairs of thermals around the enclosure.
NASA Astrophysics Data System (ADS)
Greenshields, Christopher J.; Reese, Jason M.
2012-07-01
This paper investigates the use of Navier-Stokes-Fourier equations with non-equilibrium boundary conditions (BCs) for simulation of rarefied hypersonic flows. It revisits a largely forgotten derivation of velocity slip and temperature jump by Patterson, based on Grad's moment method. Mach 10 flow around a cylinder and Mach 12.7 flow over a flat plate are simulated using both computational fluid dynamics using the temperature jump BCs of Patterson and Smoluchowski and the direct simulation Monte-Carlo (DSMC) method. These flows exhibit such strongly non-equilibrium behaviour that, following Patterson's analysis, they are strictly beyond the range of applicability of the BCs. Nevertheless, the results using Patterson's temperature jump BC compare quite well with the DSMC and are consistently better than those using the standard Smoluchowski temperature jump BC. One explanation for this better performance is that an assumption made by Patterson, based on the flow being only slightly non-equilibrium, introduces an additional constraint to the resulting BC model in the case of highly non-equilibrium flows.
NASA Astrophysics Data System (ADS)
Adesanya, S. O.; Oluwadare, E. O.; Falade, J. A.; Makinde, O. D.
2015-12-01
In this paper, the free convective flow of magnetohydrodynamic fluid through a channel with time periodic boundary condition is investigated by taking the effects of Joule dissipation into consideration. Based on simplifying assumptions, the coupled governing equations are reduced to a set of nonlinear boundary valued problem. Approximate solutions are obtained by using semi-analytical Adomian decomposition method. The effect of pertinent parameters on the fluid velocity, temperature distribution, Nusselt number and skin friction are presented graphically and discussed. The result of the computation shows that an increase in the magnetic field intensity has significant influence on the fluid flow.
Boundary conditions for arbitrarily shaped and tightly focused laser pulses in electromagnetic codes
NASA Astrophysics Data System (ADS)
Thiele, Illia; Skupin, Stefan; Nuter, Rachel
2016-09-01
Investigation of laser matter interaction with electromagnetic codes requires to implement sources for the electromagnetic fields. A way to do so is to prescribe the fields at the numerical box boundaries in order to achieve the desired fields inside the numerical box. Here we show that the often used paraxial approximation can lead to unexpected field profiles with strong impact on the laser matter interaction results. We propose an efficient numerical algorithm to compute the required laser boundary conditions consistent with the Maxwell's equations for arbitrarily shaped, tightly focused laser pulses.
A forced fractional Schrödinger equation with a Neumann boundary condition
NASA Astrophysics Data System (ADS)
Esquivel, L.; Kaikina, Elena I.
2016-07-01
We study the initial-boundary value problem for the nonlinear fractional Schrödinger equation {ut+i(uxx+12π∫0∞sign(x-y)|x-y|12uy( y)dy)+i|u|2u=0, t>0, x>0u(x,0)=u0(x), x>0,ux(0,t)=h(t), t>0. We prove the global-in-time existence of solutions for a nonlinear fractional Schrödinger equation with inhomogeneous Neumann boundary conditions. We are also interested in the study of the asymptotic behaviour of the solutions.
NASA Astrophysics Data System (ADS)
Narita, Y.
This work presents a method of analysis for solving the free vibration of symmetrically laminated composite rectangular plates having any combination of free, simply supported and clamped edges along four sides. This approach uses a Ritz method for the energy functional, and trial functions used for deflections are introduced so as to automatically include geometric boundary conditions for a prescribed boundary. A computer code was developed to calculate natural frequencies and mode shapes for the problem, and was used to demonstrate the effectiveness and accuracy of the present approach.
Stable boundary conditions and difference schemes for Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Dutt, P.
1985-01-01
The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.
A forced fractional Schrödinger equation with a Neumann boundary condition
NASA Astrophysics Data System (ADS)
Esquivel, L.; Kaikina, Elena I.
2016-07-01
We study the initial-boundary value problem for the nonlinear fractional Schrödinger equation {ut+i(uxx+12π∫0∞sign(x‑y)|x‑y|12uy( y)dy)+i|u|2u=0, t>0, x>0u(x,0)=u0(x), x>0,ux(0,t)=h(t), t>0. We prove the global-in-time existence of solutions for a nonlinear fractional Schrödinger equation with inhomogeneous Neumann boundary conditions. We are also interested in the study of the asymptotic behaviour of the solutions.
NASA Astrophysics Data System (ADS)
Rauf, A.; Siddiq, M. K.; Abbasi, F. M.; Meraj, M. A.; Ashraf, M.; Shehzad, S. A.
2016-10-01
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge-Kutta-Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs.
Mikolajewicz, U.; Maier-reimer, E.
1994-11-01
When driven under `mixed boundary conditions` coarse resolution ocean general circulation models (OGCMs) generally show a high sensitivity of the present-day thermohaline circulation against perturbations. We will show that an alternative formulation of the boundary condition for temperature, a mixture of prescribed heat fluxes and additional restoring of the sea surface temperature to a climatological boundary temperature with a longer time constant, drastically alters the stability of the modes of the thermohaline circulation. The results from simulations with the Hamburg large-scale geostrophic OGCM indicate that the stability of the mode of the thermohaline circulation with formation of North Atlantic deepwater increases, if the damping of sea surface temperature anomalies is reduced, whereas the opposite is true for the mode without North Atlantic deep water formation. It turns out that the formulation of the temperature boundary condition also affects the variability of the model.
Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea
NASA Astrophysics Data System (ADS)
Silalahi, Fitriani Tupa R.; Budhi, Wono Setya; Adytia, Didit; van Groesen, E.
2015-09-01
One interesting phenomena is investigating the movement of ships at the sea. To start with the investigation in modelling of this problem, we will assume that the ship is only a one-dimensional object that is floating on the sea surface. Similarly, we assume that the water flow is uniform in parallel directions to the ship. Therefore, we simply use the two-dimensional Laplace equation in this problem. In the section that describes the surface of sea, Neumann boundary condition is imposed in part related to the ship and the Dirichlet boundary condition for others. Then on the other three boundaries, we imposed the Neumann boundary condition by assuming that the water does not flow on the bottom, and both end. The model is solved by numerical solution using the finite element method. Velocity potential solution on the whole domain is demonstrated as a result of the implementation of the finite element method. In this paper, we initiate an investigation with assuming that the ship is on the water so that the domain of the Laplace equation is rectangular. Then we assume the drift ship. Furthermore, we also study the dependence of width and depth of the domain to the velocity potential.
Slugs and Plugs: the Role of Conduit Boundary Conditions in Shaping Strombolian Explosive Activity
NASA Astrophysics Data System (ADS)
Llewellin, E. W.; Del Bello, E.; Mathias, S.; Lane, S. J.; James, M. R.; Taddeucci, J.; Capponi, A.; Scarlato, P.
2015-12-01
Strombolian activity is characterized by quasi-periodic, short-lived explosions, which vary greatly in magnitude. The explosions are understood to be driven by the bursting of large, overpressured 'slugs' of magmatic gas, which have ascended the conduit. We use scaled laboratory analogue experiments and numerical modelling to investigate the impact of varying the boundary conditions at the top and bottom of the volcanic conduit, and find that they strongly influence the character and explosivity of strombolian explosions. The presence of a viscous plug at the top of the conduit has been inferred from recent studies of strombolian pyroclasts, which indicate that degassed, crystal-rich magma, and gas-rich, crystal-poor magma co-exist and mingle in the shallow part of the volcanic conduit. We investigate the impact of the plug on eruptive behaviour experimentally, and find that the presence of a viscous plug enhances explosivity by increasing the overpressure within the ascending gas slug. We also find that the plug is prone to fluid-dynamic instability as the gas slug passes through it, causing the low and high viscosity magma analogues to intermingle, explaining the origin of the mingled pyroclasts observed in nature. The instabilities can also cause the slug to break into smaller pockets of gas, providing an explanation for pulsations in strombolian explosions, recently revealed by high-speed videography. Separate analogue experiments, and numerical modelling, are used to investigate slug ascent under contrasting lower boundary conditions: zero-flux; and constant-pressure. Analogue conduit experiments typically use a zero-flux lower boundary (i.e. the base of the pipe is sealed). We show that a more-realistic constant-pressure boundary condition dramatically changes slug ascent velocity and the development of overpressure. Together these two studies constitute a new framework for understanding the role of the boundary conditions in shaping strombolian explosive
Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira
2015-01-01
Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to
Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira
2015-01-01
Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to
NASA Astrophysics Data System (ADS)
Curiac, Daniel-Ioan; Volosencu, Constantin
2014-10-01
The path-planning algorithm represents a crucial issue for every autonomous mobile robot. In normal circumstances a patrol robot will compute an optimal path to ensure its task accomplishment, but in adversarial conditions the problem is getting more complicated. Here, the robot’s trajectory needs to be altered into a misleading and unpredictable path to cope with potential opponents. Chaotic systems provide the needed framework for obtaining unpredictable motion in all of the three basic robot surveillance missions: area, points of interests and boundary monitoring. Proficient approaches have been provided for the first two surveillance tasks, but for boundary patrol missions no method has been reported yet. This paper addresses the mentioned research gap by proposing an efficient method, based on chaotic dynamic of the Hénon system, to ensure unpredictable boundary patrol on any shape of chosen closed contour.
NASA Astrophysics Data System (ADS)
Angoshtari, Arzhang; Yavari, Arash
2015-12-01
We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first Piola-Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work done by the prescribed boundary displacements. This condition is very similar to the classical compatibility equations for the linear strain. Since these compatibility equations for linear and nonlinear strains involve infinite-dimensional spaces and consequently are not easy to use in practice, we derive alternative compatibility equations, which are written in terms of some finite-dimensional spaces and are more useful in practice. Using these new compatibility equations, we present some non-trivial examples that show that compatible strains may become incompatible in the presence of prescribed boundary displacements.