Technology Transfer Automated Retrieval System (TEKTRAN)
Traditionally, it is considered that, under boundary lubrication conditions, the reduction in friction and wear is mostly dependent on Extreme Pressure (EP) additives, rather than the basestock. However, several studies indicate that vegetable oils also contribute to the lubricity under this regime...
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 ...
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.
NHWAVE: Consistent boundary conditions and turbulence modeling
NASA Astrophysics Data System (ADS)
Derakhti, Morteza; Kirby, James T.; Shi, Fengyan; Ma, Gangfeng
2016-10-01
Large-scale σ-coordinate ocean circulation models neglect the horizontal variation of σ in the calculation of stress terms and boundary conditions. Following this practice, the effects of surface and bottom slopes in the dynamic surface and bottom boundary conditions have been usually neglected in the available non-hydrostatic wave-resolving models using a terrain-following grid. In this paper, we derive consistent surface and bottom boundary conditions for the normal and tangential stress fields as well as a Neumann-type boundary condition for scalar fluxes. Further, we examine the role of surface slopes in the predicted near-surface velocity and turbulence fields in surface gravity waves. By comparing the predicted velocity field in a deep-water standing wave in a closed basin, we show that the consistent boundary conditions do not generate unphysical vorticity at the free surface, in contrast to commonly used, simplified stress boundary conditions developed by ignoring all contributions except vertical shear in the transformation of stress terms. In addition, it is shown that the consistent boundary conditions significantly improve predicted wave shape, velocity and turbulence fields in regular surf zone breaking waves, compared with the simplified case. A more extensive model-data comparison of various breaking wave properties in different types of surface breaking waves is presented in companion papers (Derakhti et al., 2016a,b).
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.
Boundary Value Problems With Integral Conditions
NASA Astrophysics Data System (ADS)
Karandzhulov, L. I.; Sirakova, N. D.
2011-12-01
The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of a solution of the posed BVP with integral condition is studied.
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.
Absorbing boundary conditions for exterior problems
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 condition at infinity and be accurate with respect to the interior numerical scheme. Such boundary conditions are commonly referred to as absorbing boundary conditions. A treatment is given of these boundary conditions for wave-like equations.
Determining hydrodynamic boundary conditions from equilibrium fluctuations
NASA Astrophysics Data System (ADS)
Chen, Shuyu; Wang, Han; Qian, Tiezheng; Sheng, Ping
2015-10-01
The lack of a first-principles derivation has made the hydrodynamic boundary condition a classical issue for the past century. The fact that the fluid can have interfacial structures adds additional complications and ambiguities to the problem. Here we report the use of molecular dynamics to identify from equilibrium thermal fluctuations the hydrodynamic modes in a fluid confined by solid walls, thereby extending the application of the fluctuation-dissipation theorem to yield not only the accurate location of the hydrodynamic boundary at the molecular scale, but also the relevant parameter value(s) for the description of the macroscopic boundary condition. We present molecular dynamics results on two examples to illustrate the application of this approach—one on the hydrophilic case and one on the hydrophobic case. It is shown that the use of the orthogonality condition of the modes can uniquely locate the hydrodynamic boundary to be inside the fluid in both cases, separated from the molecular solid-liquid interface by a small distance Δ that is a few molecules in size. The eigenvalue equation of the hydrodynamic modes directly yields the slip length, which is about equal to Δ in the hydrophilic case but is larger than Δ in the hydrophobic case. From the decay time we also obtain the bulk viscosity which is in good agreement with the value obtained from dynamic simulations. To complete the picture, we derive the Green-Kubo relation for a finite fluid system and show that the boundary fluctuations decouple from the bulk only in the infinite-fluid-channel limit; and in that limit we recover the interfacial fluctuation-dissipation theorem first presented by Bocquet and Barrat. The coupling between the bulk and the boundary fluctuations provides both the justification and the reason for the effectiveness of the present approach, which promises broad utility for probing the hydrodynamic boundary conditions relevant to structured or elastic interfaces, as well as
Quantum "violation" of Dirichlet boundary condition
NASA Astrophysics Data System (ADS)
Park, I. Y.
2017-02-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the 'violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
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.
Probability of boundary conditions in quantum cosmology
NASA Astrophysics Data System (ADS)
Suenobu, Hiroshi; Nambu, Yasusada
2017-02-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
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\
Comparative study of boundary conditions with helix
NASA Astrophysics Data System (ADS)
Pillay, Shamini; Kumar, Deepak; Phua, Y. N.
2016-11-01
This paper presents a comparative study of dispersion characteristics of the circular waveguide with helical windings. Our waveguide is doubly unconventional in the choice of reverse boundary condition, in the choice of normal boundary condition and further with the presence of sheath helix between the core and cladding parameters. Two methods of winding the helix between the core and cladding are considered namely from right to left and left to right. Through mathematical analysis using field components and boundary conditions the modal characteristics are derived for both conditions. Normal boundary condition and reverse boundary conditions are used respectively to represent the helical windings. Here the characteristic equation is obtained in the form of Bessel and modified Bessel for both waveguides. Using the modal characteristic equation the dispersion curves are plotted for numerous angles and wavelengths. We find that the method of wrapping the helical material has significant effect on the dispersion properties with regards to the way the modes propagate.
Boundary conditions for unsteady supersonic inlet analyses
NASA Astrophysics Data System (ADS)
Mayer, David W.; Paynter, Gerald C.
1994-06-01
New bleed and compressor face boundary conditions have been developed to improve the accuracy of unsteady supersonic inlet calculations. The new bleed boundary conditions relate changes in the bleed hole discharge coefficient to changes in the local flow conditions; the local bleed flow rate can more than double as a shock moves forward over a bleed band in response to inlet flow disturbances. The effects of inlet flow disturbances on the flow at the compressor face are represented more realistically with this new boundary condition than with traditional fixed static pressure or mass flow conditions.
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.}
Probing temperature chaos through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut
2015-03-01
Using population annealing Monte Carlo, we numerically study temperature chaos in the three-dimensional Edwards-Anderson Ising spin glass using thermal boundary conditions. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. By studying salient features in the specific heat we show evidence of temperature chaos. Our results suggest that these bumps are mainly caused by system-size excitations where the free energy of two boundary conditions cross. Furthermore, we study the scaling of both entropy and energy at boundary condition crossings and find that the scaling of the energy is very different from the scaling obtained by a simple change of boundary conditions. We attribute this difference to the stronger finite-size effects induced via a simple change of boundary conditions. Finally, we show that temperature chaos occurs more frequently at higher temperatures within the spin-glass phase and for larger system sizes, while the normalized distribution function with respect to temperature is about the same for different system sizes. The work is supported from NSF (Grant No. DMR-1208046).
Stable boundary conditions for Cartesian grid calculations
NASA Technical Reports Server (NTRS)
Berger, M. J.; Leveque, R. J.
1990-01-01
The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.
Experiments on initial and boundary conditions
NASA Technical Reports Server (NTRS)
Moretti, G.
1980-01-01
Effects of three different models for the treatment of subsonic boundary conditions, applied to the problem of flow in a channel with a bump, are discussed. A preliminary discussion of the numerical treatment of the corners is presented.
An outflow boundary condition for aeroacoustic computations
NASA Technical Reports Server (NTRS)
Hayder, M. Ehtesham; Hagstrom, Thomas
1995-01-01
A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.
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 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’)
Spatial periodic boundary condition for MODFLOW.
Laattoe, Tariq; Post, Vincent E A; Werner, Adrian D
2014-01-01
Small-scale hyporheic zone (HZ) models often use a spatial periodic boundary (SPB) pair to simulate an infinite repetition of bedforms. SPB's are common features of commercially available multiphysics modeling packages. MODFLOW's lack of this boundary type has precluded it from being effectively utilized in this area of HZ research. We present a method to implement the SPB in MODFLOW by development of the appropriate block-centered finite-difference expressions. The implementation is analogous to MODFLOW's general head boundary package. The difference is that the terms on the right hand side of the solution equations must be updated with each iteration. Consequently, models that implement the SPB converge best with solvers that perform both inner and outer iterations. The correct functioning of the SPB condition in MODFLOW is verified by two examples. This boundary condition allows users to build HZ-bedform models in MODFLOW, facilitating further research using related codes such as MT3DMS and PHT3D.
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.
Boundary conditions for unsteady supersonic inlet analyses
NASA Astrophysics Data System (ADS)
Mayer, David W.; Paynter, Gerald C.
1994-06-01
New bleed and compresor face boundary conditions have been developed to improve the accuracy of unsteady supersonic inlet calculations. The new bleed boundary condition relates changes in the bleed hole discharge coefficient to change the local flow conditions; the local bleed flow rate can more than double as a shock moves forward over a bleed band in response to inlet flow disturbances. The stability margin of the inlet is strongly dependent on the throat bleed configuration since the locally rapid increase in bleed flow has a stong effect on the motion of the normal shock. The new compressor face boundary condition accounts for changes in the unsteady flow conditions at the compressor face by specifying the compressor face corrected mass flow or Mach number either as a constant or as a linear function of the stagnation conditions. The effects of inlet flow disturbances on the flow at the compressor face are represented more realistically with this new boundary condition than with traditional fixed static pressure or mass flow conditions. Euler calculations of the dynamic response of an inlet flow to a flow disturbance at the compressor face with 20- and 90-deg throat bleed hole angles are reported. These results indicate that an extra margin of stability for the inlet is obtained with 90-deg bleed holes because the increase in bleed flow rate as the shock moves forward over a bleed is much larger for 90-deg holes than for 20-deg holes.
Scalar boundary conditions in Lifshitz spacetimes
NASA Astrophysics Data System (ADS)
Keeler, Cynthia
2014-01-01
We investigate the conditions imposable on a scalar field at the boundary of the so-called Lifshitz spacetime which has been proposed as the dual to Lifshitz field theories. For effective mass squared between -( d + z - 1)2 /4 and z 2 - ( d + z - 1)2 /4, we find a one-parameter choice of boundary condition type. The bottom end of this range corresponds to a Breitenlohner-Freedman bound; below it, the Klein-Gordon operator need not be positive, so we cannot make sense of the dynamics. Above the top end of the range, only one boundary condition type is available; here we expect compact initial data will remain compact in the future.
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.
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 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.
2017-01-01
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.
Flux boundary conditions in particle simulations.
Flekkøy, Eirik G; Delgado-Buscalioni, Rafael; Coveney, Peter V
2005-08-01
Flux boundary conditions are interesting in a number of contexts ranging from multiscale simulations to simulations of molecular hydrodynamics in nanoscale systems. Here we introduce, analyze, and test a general scheme to impose boundary conditions that simultaneously control the momentum and energy flux into open particle systems The scheme is shown to handle far from equilibrium simulations. It acquires its main characteristics from the requirement that it fulfills the second law of thermodynamics and thus minimizes the entropy production, when it is applied to reversible processes. It is shown both theoretically and through simulations that the scheme emulates the effect of an extended particle system as far as particle number fluctuations, temperature, and density profiles are concerned. The numerical scheme is further shown to be accurate and stable in both equilibrium and far from equilibrium contexts.
Nonperiodic boundary conditions for solvated systems.
Petraglio, Gabriele; Ceccarelli, Matteo; Parrinello, Michele
2005-07-22
The simulation of charged and/or strongly polar solutes represents a challenge for standard molecular-dynamics techniques. The use of periodic boundary conditions (PBCs) leads to artifacts due to the interaction between two replicas in the presence of the long-range Coulomb forces. A way to avoid these problems is the use of nonperiodic boundary conditions. A possible realization is to consider a finite system, a sphere, embedded in a reaction field described by the method of the images. In the present work the modified image approximation has been implemented in a molecular-dynamics code and optimized for the use of two standard solvents, water and acetonitrile. The methodology has then been applied to investigate the conformational changes in water-solvated alanine dipeptide. The free-energy surface calculated with this method is comparable to that obtained with PBC.
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.
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
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.
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.
42 CFR 67.22 - Additional conditions.
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2010-10-01
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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.
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42 CFR 52b.13 - Additional conditions.
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42 CFR 52b.13 - Additional conditions.
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42 CFR 52a.9 - Additional conditions.
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42 CFR 52a.9 - Additional conditions.
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42 CFR 52a.9 - Additional conditions.
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42 CFR 52b.13 - Additional conditions.
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2010-10-01
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42 CFR 52b.13 - Additional conditions.
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42 CFR 52c.8 - Additional conditions.
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2010-10-01
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2012-10-01
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42 CFR 52c.8 - Additional conditions.
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2011-10-01
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2014-10-01
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2010-10-01
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42 CFR 59.12 - Additional conditions.
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42 CFR 66.115 - Additional conditions.
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42 CFR 66.115 - Additional conditions.
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42 CFR 66.115 - Additional conditions.
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Code of Federal Regulations, 2011 CFR
2011-10-01
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42 CFR 52e.9 - Additional conditions.
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Kac boundary conditions of the logarithmic minimal models
NASA Astrophysics Data System (ADS)
Pearce, Paul A.; Tartaglia, Elena; Couvreur, Romain
2015-01-01
We develop further the implementation and analysis of Kac boundary conditions in the general logarithmic minimal models { {LM}}(p,p\\prime) with 1 ⩽ p < p‧ and p, p‧ coprime. Specifically, working in a strip geometry, we consider the (r, s) Kac boundary conditions. These boundary conditions are organized into infinitely extended Kac tables labeled by the Kac labels r, s = 1, 2, 3, …. They are conjugate to Virasoro Kac representations with conformal dimensions Δr, s given by the usual Kac formula. On a finite strip of width N, built from a square lattice, the associated integrable boundary conditions are constructed by acting on the vacuum (1, 1) boundary with an s-type seam of width s - 1 columns and an r-type seam of width ρ - 1 columns. The r-type seam contains an arbitrary boundary field ξ. While the usual fusion construction of the r-type seam relies on the existence of Wenzl-Jones projectors restricting its application to r ⩽ ρ < p‧, this limitation was recently removed by Pearce et al who further conjectured that the conformal boundary conditions labeled by r are realized, in particular, for ρ=ρ(r)=\\lfloor \\frac{rp\\prime}{p}\\rfloor . In this paper, we confirm this conjecture by performing extensive numerics on the commuting double row transfer matrices and their associated quantum Hamiltonian chains. Letting [x] denote the fractional part, we fix the boundary field to the specialized values ξ=\\fracπ{2} if [\\fracρ{p\\prime}]=0 and ξ=[\\fracρ p}{p\\prime}]\\frac{π{2} otherwise. For these boundary conditions, we obtain the Kac conformal weights Δr, s by numerically extrapolating the finite-size corrections to the lowest eigenvalue of the quantum Hamiltonians out to sizes N ⩽ 32 - ρ - s. Additionally, by solving local inversion relations, we obtain general analytic expressions for the boundary free energies allowing for more accurate estimates of the conformal data. This paper is dedicated to Jean-Bernard Zuber on the occassion
Additive thermochemical effects in turbulent erosive boundary layers
Buckingham, A.C.; Levatin, J.L.
1983-01-18
Previously obtained interior ballistics and wall boundary layer modeling results indicate that significant reduction in erosive heating can be expected when finely divided particles are dispersed through the propellant combustion flow field. Attention was first placed on the particle size influences, together with particle dispersal dynamics in both turbulent combustion core flow and the erosive wall boundary layer region. Submicron thermochemically inert particles were predicted to disperse readily to the near wall region where they were then entrained in the boundary layer. This was estimated to substantially reduce the predicted erosive heat and mass transfer and experimentally confirmed. Examination of the time-averaged turbulent boundary layer macrostructure changes indicated that inertial influences were primarily responsible for this reduction in erosive heating to gun barrel walls. The boundary layers were thickened by the additives and erosive diffusion gradients were correspondingly reduced. The isolated inertial mechanisms are now understood but are difficult to apply in general dimensional analysis scaling or in analytical heat transfer correlation predictions. Three major factors which contribute to these difficulties are: time dependence of both developing mean flow and particle field; turbulence-particle interactions; and thermochemical heat release and exchange between reactive gas components and particles, particles and wall surface, and reactive gas and wall surface. To help illustrate the influence of thes mechanisms and provide a basis for prediction, the influence of submicron additives in unsteady turbulent boundary layer growth and interaction regions adjacent to a model of a chemically active metallic (steel) surface are examined. Equilibrium chemistry is assumed for all phases.
Thermal field theories and shifted boundary conditions
NASA Astrophysics Data System (ADS)
Giusti, L.; Meyer, H.
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.
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.
Statistical tests of additional plate boundaries from plate motion inversions
NASA Technical Reports Server (NTRS)
Stein, S.; Gordon, R. G.
1984-01-01
The application of the F-ratio test, a standard statistical technique, to the results of relative plate motion inversions has been investigated. The method tests whether the improvement in fit of the model to the data resulting from the addition of another plate to the model is greater than that expected purely by chance. This approach appears to be useful in determining whether additional plate boundaries are justified. Previous results have been confirmed favoring separate North American and South American plates with a boundary located beween 30 N and the equator. Using Chase's global relative motion data, it is shown that in addition to separate West African and Somalian plates, separate West Indian and Australian plates, with a best-fitting boundary between 70 E and 90 E, can be resolved. These results are generally consistent with the observation that the Indian plate's internal deformation extends somewhat westward of the Ninetyeast Ridge. The relative motion pole is similar to Minster and Jordan's and predicts the NW-SE compression observed in earthquake mechanisms near the Ninetyeast Ridge.
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.
Slip boundary conditions over curved surfaces
NASA Astrophysics Data System (ADS)
Guo, Lin; Chen, Shiyi; Robbins, Mark O.
2016-01-01
Molecular dynamics simulations are used to investigate the influence of surface curvature on the slip boundary condition for a simple fluid. The slip length is measured for flows in planar and cylindrical geometries with a range of wall-fluid interactions. As wall curvature increases, the slip length decreases dramatically for closely packed surfaces and increases for sparse ones. The magnitude of the changes depends on the crystallographic orientation and differs for flow along and perpendicular to the direction of curvature. These different patterns of behavior are related to the curvature-induced variation in the ratio of the spacing between fluid atoms to the spacing between minima in the potential from the solid surface. The results are consistent with a microscopic theory for the viscous friction between fluid and wall that expresses the slip length in terms of the lateral response of the fluid to the wall potential and the characteristic decay time of this response.
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.
Thermal momentum distribution from shifted boundary conditions
NASA Astrophysics Data System (ADS)
Giusti, L.
At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical potential, for instance, the thermal variance of the total momentum is a direct measure of the entropy. We relate the generating function of the cumulants to the ratio of a path integral with properly shifted boundary conditions in the compact direction over the ordinary partition function. In this form it is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang--Mills theory, and obtain the entropy density at three different temperatures.
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
Characteristic boundary conditions for three-dimensional transonic unsteady aerodynamics
NASA Technical Reports Server (NTRS)
Whitlow, W., Jr.
1984-01-01
Characteristic far-field boundary conditions for the three-dimensional unsteady transonic small disturbance potential equation have been developed. The boundary conditions were implemented in the XTRAN3S finite difference code and tested for a flat plate rectangular wing with a pulse in angle of attack; the freestream Mach number was 0.85. The calculated force response shows that the characteristic boundary conditions reduce disturbances that are reflected from the computational boundaries.
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.
NASA Astrophysics Data System (ADS)
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka
2010-07-01
We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ-convergence arguments, and identify a general class of boundary conditions.
Measuring the entropy from shifted boundary conditions
NASA Astrophysics Data System (ADS)
Giusti, L.; Pepe, M.
We explore a new computational strategy for determining the equation of state of the SU(3) Yang-Mills theory. By imposing shifted boundary conditions, the entropy density is computed from the vacuum expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor. A step-scaling function is introduced to span a wide range in temperature values. We present preliminary numerical results for the entropy density and its step-scaling function obtained at eight temperature values in the range T_c - 15 T_c. At each temperature, discretization effects are removed by simulating the theory at several lattice spacings and by extrapolating the results to the continuum limit. Finite-size effects are always kept below the statistical errors. The absence of ultraviolet power divergences and the remarkably small discretization effects allow for a precise determination of the step-scaling function in the explored temperature range. These findings establish this strategy as a viable solution for an accurate determination of the equation of state in a wide range of temperature values.
42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
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42 CFR 57.317 - Additional conditions.
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2013-10-01
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42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
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42 CFR 68a.15 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
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42 CFR 68a.15 - Additional conditions.
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42 CFR 68a.15 - Additional conditions.
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42 CFR 67.22 - Additional conditions.
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42 CFR 67.22 - Additional conditions.
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42 CFR 67.22 - Additional conditions.
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42 CFR 67.22 - Additional conditions.
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42 CFR 68c.15 - Additional conditions.
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42 CFR 68c.15 - Additional conditions.
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42 CFR 57.317 - Additional conditions.
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2012-10-01
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42 CFR 57.217 - Additional conditions.
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42 CFR 57.317 - Additional conditions.
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2011-10-01
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42 CFR 57.217 - Additional conditions.
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2011-10-01
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42 CFR 57.217 - Additional conditions.
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2012-10-01
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42 CFR 57.317 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
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42 CFR 57.217 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
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42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2010 CFR
2010-10-01
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42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
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42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
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42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2011 CFR
2011-10-01
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42 CFR 65.9 - Additional conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
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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.
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
NASA Astrophysics Data System (ADS)
Ehrlacher, V.; Ortner, C.; Shapeev, A. V.
2016-12-01
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.
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.
Incorporation of a circular boundary condition into the program POISSON
Caspi, S.; Helm, M.; Laslett, L.J.
1984-03-02
Two-dimensional problems in electrostatics or magnetostatics frequently are solved numerically by means of relaxation techniques. In many such problems the ''sources'' (charges or currents, and regions of permeable material) lie exclusively within a finite closed boundary curve and the relaxation process in principle then could be confined to the region interior to such a boundary - provided a suitable boundary condition is imposed onto the solution at that boundary. The present notes discuss and illustrate the use of a boundary condition of such a nature as to imply the absence of external sources, in order thereby 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.
NASA Astrophysics Data System (ADS)
Boerstoel, J. W.
1987-04-01
A numerical method to obtain the additional equations in Euler-flow calculations based on cell-centered schemes when the number of equations required to determine the flow-state evaluation at grid points half a mesh outside the flow domain exceeds the number of boundary-condition equations provided by characteristic theory, is presented. A layer of auxiliary cells on flow boundaries is introduced, and semidiscrete conservation equations for these cells are defined. The time variations of the state in these auxiliary cells at the boundary are transformed into characteristic form, and time variations of characteristic variables corresponding to incoming information from the boundary into the flow are replaced by boundary conditions for these time variations. The boundary equations so obtained are mapped back into a form with primitive variables, and numerically integrated in time. The characteristic boundary conditions are first-order differential equations for time variations at boundary points of characteristic variables. These equations may be chosen to express that given functions of the flow state on the boundary should asymptotically tend with time to prescribed steady-state values.
Boundary conditions and generalized functions in a transition radiation problem
NASA Astrophysics Data System (ADS)
Villavicencio, M.; Jiménez, J. L.
2017-03-01
The aim of this work is to show how all the components of the electromagnetic field involved in the transition radiation problem can be obtained using distribution functions. The handling of the products and derivatives of distributions appearing in the differential equations governing transition radiation, allows to obtain the necessary boundary conditions, additional to those implied by Maxwell's equations, in order to exactly determine the longitudinal components of the electromagnetic field. It is shown that this method is not only useful but it is really convenient to achieve a full analysis of the problem.
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.
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.
Implementation of nonreflecting boundary conditions for the nonlinear Euler equations
NASA Astrophysics Data System (ADS)
Atassi, Oliver V.; Galán, José M.
2008-01-01
Computationally efficient nonreflecting boundary conditions are derived for the Euler equations with acoustic, entropic and vortical inflow disturbances. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of Fourier-Bessel modes. This leads to an 'exact' nonreflecting boundary condition, local in space but nonlocal in time, for each Fourier-Bessel mode of the perturbation pressure. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. Extension of the boundary conditions to nonuniform swirling flows is presented for the narrow annulus limit which is relevant to many aeroacoustic problems. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Two test problems are carried out: propagation of acoustic waves in an annular duct and the scattering of a vortical wave by a cascade. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that, unlike the local boundary conditions whose accuracy depends on the group velocity of the scattered waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities. Results also show that this approach leads to a significant savings in computational time and memory by obviating the need to store the pressure field and calculate the nonlocal convolution integral at each point in the inlet and exit boundaries.
Effects of initial and boundary conditions on thermal explosion development
NASA Astrophysics Data System (ADS)
Novozhilov, Vasily
2017-01-01
The paper investigates effects of non-uniform initial conditions, as well as oscillatory boundary conditions on critical conditions for thermal explosion. It is shown that natural convection plays significant role in case of initial non-uniformities in the temperature distribution. The role of convection is quantified considering critical Frank-Kamenetskii parameters at different Rayleigh numbers, relative to the same parameter at no-convection conditions. Preliminary results are presented for the effect of oscillatory boundary conditions. It is demonstrated that the system may develop thermal explosion if oscillations are imposed at the boundaries of otherwise thermally stable medium.
Chaos in spin glasses revealed through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.
2015-09-01
We study the fragility of spin glasses to small temperature perturbations numerically using population annealing Monte Carlo. We apply thermal boundary conditions to a three-dimensional Edwards-Anderson Ising spin glass. In thermal boundary conditions all eight combinations of periodic versus antiperiodic boundary conditions in the three spatial directions are present, each appearing in the ensemble with its respective statistical weight determined by its free energy. We show that temperature chaos is revealed in the statistics of crossings in the free energy for different boundary conditions. By studying the energy difference between boundary conditions at free-energy crossings, we determine the domain-wall fractal dimension. Similarly, by studying the number of crossings, we determine the chaos exponent. Our results also show that computational hardness in spin glasses and the presence of chaos are closely related.
Finite difference time domain implementation of surface impedance boundary conditions
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a 2-D demonstration. Extensions to 3-D should be straightforward.
Finite difference time domain implementation of surface impedance boundary conditions
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.
Boundary conditions for direct simulations of compressible viscous flows
NASA Technical Reports Server (NTRS)
Poinsot, T. J.; Lele, S. K.
1992-01-01
The present consideration of procedures for the definition of boundary conditions for the Navier-Stokes equations emphasizes the derivation of boundary conditions that are compatible with nondissipative algorithms applicable to direct simulations of turbulent flows. A novel formulation for the Euler equations is derived on the basis of characteristic wave relations through boundaries; this formulation is generalized to the Navier-Stokes equations. The method, which applies to both sub- and supersonic flows, is used in reflecting and nonreflecting boundary-condition treatments. Attention is given to practical implementations involving inlet and outlet boundaries and slip and nonslip walls, as well as the test cases of a ducted shear layer, vortices propagating through boundaries, and Poiseuille flow.
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.
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.
QCT/FEA predictions of femoral stiffness are strongly affected by boundary condition modeling
Rossman, Timothy; Kushvaha, Vinod; Dragomir-Daescu, Dan
2015-01-01
Quantitative computed tomography-based finite element models of proximal femora must be validated with cadaveric experiments before using them to assess fracture risk in osteoporotic patients. During validation it is essential to carefully assess whether the boundary condition modeling matches the experimental conditions. This study evaluated proximal femur stiffness results predicted by six different boundary condition methods on a sample of 30 cadaveric femora and compared the predictions with experimental data. The average stiffness varied by 280% among the six boundary conditions. Compared with experimental data the predictions ranged from overestimating the average stiffness by 65% to underestimating it by 41%. In addition we found that the boundary condition that distributed the load to the contact surfaces similar to the expected contact mechanics predictions had the best agreement with experimental stiffness. We concluded that boundary conditions modeling introduced large variations in proximal femora stiffness predictions. PMID:25804260
Boundary condition effects on maximum groundwater withdrawal in coastal aquifers.
Lu, Chunhui; Chen, Yiming; Luo, Jian
2012-01-01
Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.
Hydrodynamic boundary conditions and dynamic forces between bubbles and surfaces.
Manor, Ofer; Vakarelski, Ivan U; Tang, Xiaosong; O'Shea, Sean J; Stevens, Geoffrey W; Grieser, Franz; Dagastine, Raymond R; Chan, Derek Y C
2008-07-11
Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.
Hydrodynamic Boundary Conditions and Dynamic Forces between Bubbles and Surfaces
NASA Astrophysics Data System (ADS)
Manor, Ofer; Vakarelski, Ivan U.; Tang, Xiaosong; O'Shea, Sean J.; Stevens, Geoffrey W.; Grieser, Franz; Dagastine, Raymond R.; Chan, Derek Y. C.
2008-07-01
Dynamic forces between a 50μm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.
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.
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.)
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.
On dualities for SSEP and ASEP with open boundary conditions
NASA Astrophysics Data System (ADS)
Ohkubo, J.
2017-03-01
Duality relations for simple exclusion processes with general open boundaries are discussed. It is shown that a combination of spin operators and bosonic operators enables us to have a unified discussion about duality relations with open boundaries. As for the symmetric simple exclusion process (SSEP), more general results than those from previous studies are obtained. It is clarified that not only the absorbing sites, but also additional sites—called copying sites— are needed for the boundaries in the dual process for the SSEP. The role of the copying sites is to conserve information about the particle states on the boundary sites. Similar discussions are applied to the asymmetric simple exclusion process (ASEP), in which the q-analogues are employed, and it is clarified that the ASEP with open boundaries has a complicated dual process on the boundaries.
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.
Inflow/outflow with Dirichlet boundary conditions for pressure in ISPH
NASA Astrophysics Data System (ADS)
Kunz, P.; Hirschler, M.; Huber, M.; Nieken, U.
2016-12-01
In the present work we propose a new algorithm for open boundary treatment in ISPH. In the literature a few models for open boundary conditions are available, but most of them are applied to weakly compressible SPH (WCSPH) only. In our method the inflow/outflow is driven by true Dirichlet boundary conditions of the projected pressure field. We ensure the Dirichlet boundary condition by a particle mirroring technique at the open boundary to compute the pressure field. This procedure enables us to handle variable inlet velocities across the open boundary. The Dirichlet boundary conditions are introduced for the projected pressure matrix. We apply an error analysis for a Hagen-Poiseuille flow driven by a pressure gradient and demonstrate the robustness and accuracy with a flow around a cylinder and an oscillating flow, where inlet and outlet conditions periodically change. Additionally, a volume flux controller is presented in combination with variable pressure boundary conditions. Finally, the new open boundary treatment is applied to a bubble formation process during gas injection and validated with experimental results.
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.
Effect of boundary conditions on thermal plume growth
NASA Astrophysics Data System (ADS)
Kondrashov, A.; Sboev, I.; Rybkin, K.
2016-07-01
We have investigated the influence of boundary conditions on the growth rate of convective plumes. Temperature and rate fields were studied in a rectangular convective cell heated by a spot heater. The results of the full-scale test were compared with the numerical data calculated using the ANSYS CFX software package. The relationship between the heat plume growth rate and heat boundary conditions, the width and height of the cell, size of heater for different kinds of liquid was established.
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.
Optimal control problem for impulsive systems with integral boundary conditions
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Sharifov, Y. A.
2012-08-01
In the present work the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
NASA Astrophysics Data System (ADS)
Dong, S.
2014-06-01
We present an effective outflow boundary condition, and an associated numerical algorithm, within the phase-field framework for dealing with two-phase outflows or open boundaries. The set of two-phase outflow boundary conditions for the phase-field and flow variables are designed to prevent the un-controlled growth in the total energy of the two-phase system, even in situations where strong backflows or vortices may be present at the outflow boundaries. We also present an additional boundary condition for the phase field function, which together with the usual Dirichlet condition can work effectively as the phase-field inflow conditions. The numerical algorithm for dealing with these boundary conditions is developed on top of a strategy for de-coupling the computations of all flow variables and for overcoming the performance bottleneck caused by variable coefficient matrices associated with variable density/viscosity. The algorithm contains special constructions, for treating the variable dynamic viscosity in the outflow boundary condition, and for preventing a numerical locking at the outflow boundaries for time-dependent problems. Extensive numerical tests with incompressible two-phase flows involving inflow and outflow boundaries demonstrate that, the two-phase outflow boundary conditions and the numerical algorithm developed herein allow for the fluid interface and the two-phase flow to pass through the outflow or open boundaries in a smooth and seamless fashion, and that our method produces stable simulations when large density ratios and large viscosity ratios are involved and when strong backflows are present at the outflow boundaries.
Time-domain boundary conditions for outdoor ground surfaces
NASA Astrophysics Data System (ADS)
Collier, Sandra L.; Ostashev, Vladimir E.; Wilson, D. Keith; Marlin, David H.
2003-10-01
Finite-difference time-domain techniques are promising for detailed dynamic simulations of sound propagation in complex atmospheric environments. Success of such simulations requires the development of new techniques to accurately handle the reflective and absorptive properties of a porous ground. One method of treating the ground boundary condition in the time domain [Salomons et al., Acta Acust. 88, 483-492 (2002)] is to use modified fluid dynamic equations, where the ground is considered as a porous medium described by its physical properties. However, this approach significantly increases computation time, as the domain must be extended into the ground and a large number of grid points are needed. Standard impedance models for the ground boundary condition are frequency-domain models, which generally are non-causal [Y. H. Berthelot, J. Acoust. Soc. Am. 109, 1736-1739 (2001)]. The development of a time-domain boundary condition from these models requires removing the singularity from the impedance equation when transforming from the frequency domain to the time domain. Alternatively, as the impedance boundary condition is a flux equation, a time-domain boundary condition can be derived from first principles, using the physical properties of the ground. We report on our development of a time-domain ground boundary condition.
Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites
Wysocki, Aleksander L.; Antropov, Vladimir P.
2016-12-01
Here, we developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hard phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.
Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites
NASA Astrophysics Data System (ADS)
Wysocki, Aleksander L.; Antropov, Vladimir P.
2017-04-01
We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hard phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.
Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites
Wysocki, Aleksander L.; Antropov, Vladimir P.
2016-12-01
Here, we developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hardmore » phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.« less
A novel periodic boundary condition for computational hemodynamics studies.
Bahramian, Fereshteh; Mohammadi, Hadi
2014-07-01
In computational fluid dynamics models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. For major cardiovascular models, the realistic boundary conditions are not available. In order to address this issue, the whole computational domain needs to be modeled, which is practically impossible. For simulating fully developed turbulent flows using the large eddy simulation and dynamic numerical solution methods, which are very popular in hemodynamics studies, periodic boundary conditions are suitable. This is mainly because the computational domain can be reduced considerably. In this study, a novel periodic boundary condition is proposed, which is based on mass flow condition. The proposed boundary condition is applied on a square duct for the sake of validation. The mass-based condition was shown to obtain the solution in 15% less time. As such, the mass-based condition has two decisive advantages: first, the solution for a given Reynolds number can be obtained in a single simulation because of the direct specification of the mass flow, and second, simulations can be made more quickly.
Scattering through a straight quantum waveguide with combined boundary conditions
Briet, Ph. Soccorsi, E.; Dittrich, J.
2014-11-15
Scattering through a straight two-dimensional quantum waveguide R×(0,d) with Dirichlet boundary conditions on (R{sub −}{sup *}×(y=0))∪(R{sub +}{sup *}×(y=d)) and Neumann boundary condition on (R{sub −}{sup *}×(y=d))∪(R{sub +}{sup *}×(y=0)) is considered using stationary scattering theory. The existence of a matching conditions solution at x = 0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.
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.
Vibration of thermally stressed plates with various boundary conditions.
NASA Technical Reports Server (NTRS)
Bailey, C. D.
1973-01-01
By discarding Lurie's (1952) assumption of mode identity, it is shown that linear theory correctly predicts the frequency of all modes of a thermally stressed cantilever plate as well as the frequency and modes of plates with other boundary conditions. The thermal stress distribution is obtained for whatever temperature distribution and boundary conditions that may be specified. Experimental results are compared to calculated results for several different plates. Boundary conditions for the plates range from a plate with edges completely clamped to a plate with edges completely free with various other combinations of mixed and uniform edge conditions. Comparison of calculated data to experimental data shows that accurate, quantitative results can be obtained from linear theory for 'as cut' real plates for a significant range of heating when the assumption of mode identity is discarded.
Exponential dichotomy for hyperbolic systems with periodic boundary conditions
NASA Astrophysics Data System (ADS)
Klyuchnyk, R.; Kmit, I.; Recke, L.
2017-02-01
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the existence of exponential dichotomies on R in the space of continuous periodic functions.
Boundary conditions for electropositive and electronegative radio-frequency sheaths
NASA Astrophysics Data System (ADS)
Sobolewski, Mark
2016-09-01
Plasma sheaths play a dominant role in determining ion bombardment energies. To optimize plasma processes, sheaths must be understood and carefully controlled, which requires predictive models. One very efficient approach is to only model the sheath, excluding the bulk plasma. This approach, however, requires boundary conditions at the plasma/sheath boundary. Models that use the step approximation for electron density require initial ion velocities. More exact models with Boltzmann electrons (and, for electronegative discharges, negative ions) require the electron temperature (and the temperature and relative density of negative ions). It is often assumed that these boundary conditions have negligible effects on ion energies, but, for certain conditions in radio-frequency sheaths, this is not true. Analytic models as well as numerical simulations show that, at low frequencies (<= 1 MHz) and high bias voltages, the amplitude of the low-energy peak in ion energy distributions (IEDs) at the electrode is very sensitive to the boundary conditions. By measuring IEDs and sheath voltage waveforms, we obtain the most appropriate values of the boundary conditions for electropositive (Ar) as well as electronegative (CF4) discharges and insight into their presheath dynamics.
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.
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.
Magnetic Boundary Conditions at Non-Conducting Planetary Bodies: Applications to Ganymede
NASA Astrophysics Data System (ADS)
Saur, J.; Duling, S.; Seufert, M.; Wicht, J.
2013-12-01
The interaction of planetary bodies with their surrounding magnetized plasma can often be described with the magneto-hydrodynamic (MHD) equations, which are commonly solved by numerical models. For these models it is necessary to define physically correct boundary conditions. Many planetary bodies have electrically non-conductive surfaces, which do not allow electric current to penetrate their surfaces. Magnetic boundary conditions, which correctly consider that the associated radial electric current at the planetary surface is zero, are however difficult to implement because they include the curl of the magnetic field. Here we derive new boundary conditions for the magnetic field at non-conducting surfaces by a decomposition of the magnetic field in poloidal and toroidal components and their spherical harmonics expansions. We find that the toroidal part of the magnetic field needs to vanish at the surface of the isolator. For the spectral spherical harmonics coefficients of the poloidal part we derive a Cauchy boundary condition, which includes the Gauss coefficients of a possible intrinsic field. Our non-conducting boundary condition can thus additionally include intrinsic dynamo fields as well as induction fields within electrically conductive subsurface layers such as subsurface oceans. We implement the new boundary condition in the MHD simulation code ZEUS-MP using spherical geometry. We apply these new magnetic boundary conditions to a model for Ganymede's plasma environment. With this model we can describe the in-situ observations by the Galileo spacecraft and Hubble Space Telescope observations of Ganmyede's aurora very well.
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.
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.
Continuous matrix product states with periodic boundary conditions and an application to atomtronics
NASA Astrophysics Data System (ADS)
Draxler, Damian; Haegeman, Jutho; Verstraete, Frank; Rizzi, Matteo
2017-01-01
We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system—an interacting Bose gas rotating in a ring shaped trap in the presence of a localized barrier potential.
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
Effect of kinetic boundary condition on the thermal transpiration coefficient
NASA Astrophysics Data System (ADS)
Sugimoto, Hiroshi; Amakawa, Kenjiro
2014-12-01
The effect of kinetic boundary condition on the free molecular thermal transpiration coefficient γ is analyzed numerically. The Maxwell model boundary condition is applied in its original form in the sense that its accommodation coefficient depends on the speed of incident molecules. The results show that the value of γ depends much on the velocity dependency of the accommodation coefficient. The experimental result, γ < 0.5, can be reproduced if the grazing molecules reflect diffusely. This makes a sharp contrast with the previous works that γ =0.5 for the velocity independent accommodation coefficient.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Rana, Anirudh Singh; Struchtrup, Henning
2016-02-15
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
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.
Poroelastic modeling of seismic boundary conditions across afracture
Schoenberg, M.A.; Nakagawa, S.
2006-06-29
A fracture within a porous background is modeled as a thin porous layer with increased compliance and finite permeability. For small layer thickness, a set of boundary conditions can be derived that relate particle velocity and stress across a fracture, induced by incident poroelastic waves. These boundary conditions are given via phenomenological parameters that can be used to examine and characterize the seismic response of a fracture. One of these parameters, here it is called membrane permeability, is shown through several examples to control the scattering amplitude of the slow P waves for very low-permeability fractures, which in turn controls the intrinsic attenuation of the waves.
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.
Effective boundary condition at a rough surface starting from a slip condition
NASA Astrophysics Data System (ADS)
Dalibard, Anne-Laure; Gérard-Varet, David
We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ɛ. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ɛ=0 is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in Basson and Gérard-Varet (2008) [6] and Gerard-Varet and Masmoudi (2010) [13], in which the special case of a Dirichlet condition at the rough boundary was examined.
Boundary condition optimal control problem in lava flow modelling
NASA Astrophysics Data System (ADS)
Ismail-Zadeh, Alik; Korotkii, Alexander; Tsepelev, Igor; Kovtunov, Dmitry; Melnik, Oleg
2016-04-01
We study a problem of steady-state fluid flow with known thermal conditions (e.g., measured temperature and the heat flux at the surface of lava flow) at one segment of the model boundary and unknown conditions at its another segment. This problem belongs to a class of boundary condition optimal control problems and can be solved by data assimilation from one boundary to another using direct and adjoint models. We derive analytically the adjoint model and test the cost function and its gradient, which minimize the misfit between the known thermal condition and its model counterpart. Using optimization algorithms, we iterate between the direct and adjoint problems and determine the missing boundary condition as well as thermal and dynamic characteristics of the fluid flow. The efficiency of optimization algorithms - Polak-Ribiere conjugate gradient and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms - have been tested with the aim to get a rapid convergence to the solution of this inverse ill-posed problem. Numerical results show that temperature and velocity can be determined with a high accuracy in the case of smooth input data. A noise imposed on the input data results in a less accurate solution, but still acceptable below some noise level.
The Ablowitz-Ladik system with linearizable boundary conditions
NASA Astrophysics Data System (ADS)
Biondini, Gino; Bui, Anh
2015-09-01
The boundary value problem (BVP) for the Ablowitz-Ladik (AL) system on the natural numbers with linearizable boundary conditions is studied. In particular: (i) a discrete analogue is derived of the Bäcklund transformation that was used to solved similar BVPs for the nonlinear Schrödinger equation; (ii) an explicit proof is given that the Bäcklund-transformed solution of AL remains within the class of solutions that can be studied by the inverse scattering transform; (iii) an explicit linearizing transformation for the Bäcklund transformation is provided; (iv) explicit relations are obtained among the norming constants associated with symmetric eigenvalues; (v) conditions for the existence of self-symmetric eigenvalues are obtained. The results are illustrated by several exact soliton solutions, which describe the soliton reflection at the boundary with or without the presence of self-symmetric eigenvalues. This article is dedicated to Mark Ablowitz on the occasion of his seventieth birthday.
Boundary conditions for the Boltzmann equation for rough walls
NASA Astrophysics Data System (ADS)
Brull, Stéphane; Charrier, Pierre
2014-12-01
In some applications, rarefied gases have to considered in a domain whose boundary presents some nanoscale roughness. That is why, we have considered (Brull,2014) a new derivation of boundary conditions for the Boltzmann equation, where the wall present some nanoscale roughness. In this paper, the interaction between the gas and the wall is represented by a kinetic equation defined in a surface layer at the scale of the nanometer close to the wall. The boundary conditions are obtained from a formal asymptotic expansion and are describded by a scattering kernel satisfying classical properties (non-negativeness, normalization, reciprocity). Finally, we present some numerical simulations of scattering diagrams showing the importance of the consideration of roughness for small scales in the model.
Yang - Mills - Higgs equations with nonhomogeneous boundary conditions
NASA Astrophysics Data System (ADS)
Tafel, Jacek
1997-01-01
The Yang - Mills - Higgs equations in a spatially bounded subset of the Minkowski space are studied under the assumption of a temporal gauge. It is shown that the Cauchy problem for these equations is uniquely solvable (locally in time) if nonhomogeneous boundary conditions of the metallic type are imposed.
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.
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.
Unconstrained periodic boundary conditions for solid state elasticity
NASA Astrophysics Data System (ADS)
Linna, R. P.; Åström, J. A.; Timonen, J.
2004-03-01
We introduce a method to implement dynamics on an elastic lattice without imposing constraints via boundary or loading conditions. Using this method we are able to examine fracture processes in two-dimensional systems previously inaccessible for reliable computer simulations. We show the validity of the method by benchmarking and report a few preliminary results.
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.
On boundary conditions in the Lattice-Boltzmann method
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Sarmah, Deep
2004-11-01
A critical issue in computational fluid dynamics is the treatment of boundary conditions adopted in particle-simulation methods based on discrete Lattice-Boltzmann (LB) kinetic descriptions. In fact, although progress has been in the past made regarding the mathematical treatment of boundary conditions in LB approaches [see for example 1,2 and references therein], the problem cannot be considered fully solved from the physical standpoint for several different reasons. In particular, the action of surface forces or local volume forces ( localized interactions), may be significant not only in the case of free boundaries, but also for fixed or moving boundaries characterized by prescribed velocity. Purpose of this work is to propose a novel LB approach which embodies not only the possible effect of localized interactions but also assures the correct fulfillment of fluid equations on fixed or moving boundaries. References 1 - R.Mei, W.Shyy, L.Luo, J.Comput.Phys.161(2), 680 (2000). 2 - X.Zhang, J.W.Crawford, A.G.Bengough, Y.M.Young, Ad. Wat. Res. 25, 601 (2002).
Sheath Physics and Boundary Conditions for Edge Plasmas
Cohen, R H; Ryutov, D D
2003-09-03
The boundary conditions of mass, momentum, energy, and charge appropriate for fluid formulations of edge plasmas are surveyed. We re-visit the classic problem of 1-dimensional flow, and note that the ''Bohm sheath criterion'' is requirement of connectivity of the interior plasma with the external world, not the result of termination of the plasma by a wall. We show that the nature of the interior plasma solution is intrinsically different for ion sources that inject above and below the electron sound speed. We survey the appropriate conditions to apply, and resultant fluxes, for a magnetic field obliquely incident on a wall, including the presence of drifts and radial transport. We discuss the consequences of toroidal asymmetries in wall properties, as well as experimental tests of such effects. Finally, we discuss boundary-condition modifications in the case of rapidly varying plasma conditions.
Effect of different wall boundary conditions on the numerical simulation of bubbling fluidized beds
NASA Astrophysics Data System (ADS)
Haghgoo, Mohammad Reza; Bergstrom, Donald J.; Spiteri, Raymond J.
2015-11-01
There are distinct wall boundary conditions proposed in the literature for the particulate phase in the context of a continuum description of gas-particle flows. It is not yet clear how these different wall boundary conditions affect the simulated flow behavior, nor is it clear which are the most realistic. To investigate this issue, an Eulerian-Eulerian two-fluid model was used to investigate the effect of different particle-phase wall boundary conditions on the numerical prediction of bubbling/slugging gas-particle fluidized beds. Because the bed dynamics are strongly influenced by the motion of the bubbles, the impact of wall boundary conditions on the bubble statistics was examined specifically. In addition, the averaged field variables, such as the particle velocity, were compared to published experimental measurements. The comparison shows good agreement between the numerical results, generated by the Mfix code, and their experimental counterparts. It is found that the particle wall boundary condition does play a significant role in predicting the flow behavior. However, it appears that the influence of the wall boundary conditions is more significant for the instantaneous flow variables and bubble statistics than for the averaged quantities.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-15
Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.
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.
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.
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.
Zhao, Shan; Wei, G. W.
2010-01-01
SUMMARY High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered. PMID:20485574
Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.
van Maanen, Leendert; Couto, Joaquina; Lebreton, Mael
2016-01-01
The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.
Bond chaos in spin glasses revealed through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.
2016-06-01
Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of chaos in spin glasses is of much importance. The use of thermal boundary conditions is an effective approach to study chaotic phenomena. Here we generalize population annealing Monte Carlo, combined with thermal boundary conditions, to study bond chaos due to small perturbations in the spin-spin couplings of the three-dimensional Edwards-Anderson Ising spin glass. We show that bond and temperature-induced chaos share the same scaling exponents and that bond chaos is stronger than temperature chaos.
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.
Benchmarking sheath subgrid boundary conditions for macroscopic-scale simulations
NASA Astrophysics Data System (ADS)
Jenkins, T. G.; Smithe, D. N.
2015-02-01
The formation of sheaths near metallic or dielectric-coated wall materials in contact with a plasma is ubiquitous, often giving rise to physical phenomena (sputtering, secondary electron emission, etc) which influence plasma properties and dynamics both near and far from the material interface. In this paper, we use first-principles PIC simulations of such interfaces to formulate a subgrid sheath boundary condition which encapsulates fundamental aspects of the sheath behavior at the interface. Such a boundary condition, based on the capacitive behavior of the sheath, is shown to be useful in fluid simulations wherein sheath scale lengths are substantially smaller than scale lengths for other relevant physical processes (e.g. radiofrequency wavelengths), in that it enables kinetic processes associated with the presence of the sheath to be numerically modeled without explicit resolution of spatial and temporal sheath scales such as electron Debye length or plasma frequency.
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.
Boundary conditions for simulating large SAW devices using ANSYS.
Peng, Dasong; Yu, Fengqi; Hu, Jian; Li, Peng
2010-08-01
In this report, we propose improved substrate left and right boundary conditions for simulating SAW devices using ANSYS. Compared with the previous methods, the proposed method can greatly reduce computation time. Furthermore, the longer the distance from the first reflector to the last one, the more computation time can be reduced. To verify the proposed method, a design example is presented with device center frequency 971.14 MHz.
Hydrodynamic boundary condition of water on hydrophobic surfaces.
Schaeffel, David; Yordanov, Stoyan; Schmelzeisen, Marcus; Yamamoto, Tetsuya; Kappl, Michael; Schmitz, Roman; Dünweg, Burkhard; Butt, Hans-Jürgen; Koynov, Kaloian
2013-05-01
By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ = 108°) or perfluorosilane (Θ = 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.
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.
Energy Based Multiscale Modeling with Non-Periodic Boundary Conditions
2013-05-13
was implemented numerically utilizing Python scripting to invoke the nested FE solution within the commercial FE software ABAQUS. To reduce initial...between Python and the ABAQUS solver. The left-hand side of Figure 8 highlights the localization process which involves passing of the macroscopic...deformation gradient from the UMAT to the custom Python script which then modifies the boundary conditions to a unit-cell, or RVE, ABAQUS input file
Arterial wall tethering as a distant boundary condition
NASA Astrophysics Data System (ADS)
Hodis, S.; Zamir, M.
2009-11-01
A standing difficulty in the problem of blood vessel tethering has been that only one of the two required boundary conditions can be fully specified, namely, that at the inner (endothelial) wall surface. The other, at the outer layer of the vessel wall, is not known except in the limiting case where the wall is fully tethered such that its outer layer is prevented from any displacement. In all other cases, where the wall is either free or partially tethered, a direct boundary condition is not available. We present a method of determining this missing boundary condition by considering the limiting case of a semi-infinite wall. The result makes it possible to define the degree of tethering imposed by surrounding tissue more accurately in terms of the displacement of the outer layer of the vessel wall, rather than in terms of equivalent added mass which has been done in the past. This new approach makes it possible for the first time to describe the effect of partial tethering in its full range, from zero to full tethering. The results indicate that high tethering leads to high stresses and low displacements within the vessel wall, while low tethering leads to low stresses and high displacements. Since both extremes would be damaging to wall tissue, particularly elastin, this suggest that moderate tethering would be optimum in the physiological setting.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
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.
Role of Boundary Conditions in Monte Carlo Simulation of MEMS Devices
NASA Technical Reports Server (NTRS)
Nance, Robert P.; Hash, David B.; Hassan, H. A.
1997-01-01
A study is made of the issues surrounding prediction of microchannel flows using the direct simulation Monte Carlo method. This investigation includes the introduction and use of new inflow and outflow boundary conditions suitable for subsonic flows. A series of test simulations for a moderate-size microchannel indicates that a high degree of grid under-resolution in the streamwise direction may be tolerated without loss of accuracy. In addition, the results demonstrate the importance of physically correct boundary conditions, as well as possibilities for reducing the time associated with the transient phase of a simulation. These results imply that simulations of longer ducts may be more feasible than previously envisioned.
Nonstationary Stokes System in Cylindrical Domains Under Boundary Slip Conditions
NASA Astrophysics Data System (ADS)
Zaja¸czkowski, Wojciech M.
2017-03-01
Existence and uniqueness of solutions to the nonstationary Stokes system in a cylindrical domain {Ωsubset{R}^3} and under boundary slip conditions are proved in anisotropic Sobolev spaces. Assuming that the external force belong to {L_r(Ω×(0,T))} and initial velocity to {W_r^{2-2/r}(Ω)} there exists a solution such that velocity belongs to {W_r^{2,1}(Ω×(0,T))} and gradient of pressure to {L_r(Ω×(0,T))}, {rin(1,∞)}, {T > 0}. Thanks to the slip boundary conditions and a partition of unity the Stokes system is transformed to the Poisson equation for pressure and the heat equation for velocity. The existence of solutions to these equations is proved by applying local considerations. In this case we have to consider neighborhoods near the edges which by local mapping can be transformed to dihedral angle {π/2}. Hence solvability of the problem bases on construction local Green functions (near an interior point, near a point of a smooth part of the boundary, near a point of the edge) and their appropriate estimates. The technique presented in this paper can also work in other functional spaces: Sobolev-Slobodetskii, Besov, Nikolskii, Hölder and so on.
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.
Transport across nanogaps using self-consistent boundary conditions
NASA Astrophysics Data System (ADS)
Biswas, D.; Kumar, R.
2012-06-01
Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework. The determination of self-consistent boundary conditions across the gap forms the central theme in order to allow for realistic interface potentials (such as metal-vacuum) which are smooth at the boundary and do not abruptly assume a constant value at the interface. It is shown that a semiclassical expansion of the transmitted wavefunction leads to approximate but self consistent boundary conditions without assuming any specific form of the potential beyond the gap. Neglecting the exchange and correlation potentials, the quantum Child-Langmuir law is investigated. It is shown that at zero injection energy, the quantum limiting current density (Jc) is found to obey the local scaling law Jc ~ Vgα/D5-2α with the gap separation D and voltage Vg. The exponent α > 1.1 with α → 3/2 in the classical regime of small de Broglie wavelengths.
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.
Negative bending mode curvature via Robin boundary conditions
NASA Astrophysics Data System (ADS)
Adams, Samuel D. M.; Craster, Richard V.; Guenneau, Sébastien
2009-06-01
We examine the band spectrum, and associated Floquet-Bloch eigensolutions, arising in straight walled acoustic waveguides that have periodic structure along the guide. Homogeneous impedance (Robin) conditions are imposed along the guide walls and we find that in certain circumstances, negative curvature of the lowest (bending) mode can be achieved. This is unexpected, and has not been observed in a variety of physical situations examined by other authors. Further unexpected properties include the existence of the bending mode only on a subset of the Brillouin zone, as well as permitting otherwise unobtainable velocities of energy transmission. We conclude with a discussion of how such boundary conditions might be physically reproduced using effective conditions and homogenization theory, although the methodology to achieve these effective conditions is an open problem. To cite this article: S.D.M. Adams et al., C. R. Physique 10 (2009).
Boundary conditions towards realistic simulation of jet engine noise
NASA Astrophysics Data System (ADS)
Dhamankar, Nitin S.
Strict noise regulations at major airports and increasing environmental concerns have made prediction and attenuation of jet noise an active research topic. Large eddy simulation coupled with computational aeroacoustics has the potential to be a significant research tool for this problem. With the emergence of petascale computer clusters, it is now computationally feasible to include the nozzle geometry in jet noise simulations. In high Reynolds number experiments on jet noise, the turbulent boundary layer on the inner surface of the nozzle separates into a turbulent free shear layer. Inclusion of a nozzle with turbulent inlet conditions is necessary to simulate this phenomenon realistically. This will allow a reasonable comparison of numerically computed noise levels with the experimental results. Two viscous wall boundary conditions are implemented for modeling the nozzle walls. A characteristic-based approach is compared with a computationally cheaper, extrapolation-based formulation. In viscous flow over a circular cylinder under two different regimes, excellent agreement is observed between the results of the two approaches. The results agree reasonably well with reference experimental and numerical results. Both the boundary conditions are thus found to be appropriate, the extrapolation-based formulation having an edge with its low cost. This is followed with the crucial step of generation of a turbulent boundary layer inside the nozzle. A digital filter-based turbulent inflow condition, extended in a new way to non-uniform curvilinear grids is implemented to achieve this. A zero pressure gradient flat plate turbulent boundary layer is simulated at a high Reynolds number to show that the method is capable of producing sustained turbulence. The length of the adjustment region necessary for synthetic inlet turbulence to recover from modeling errors is estimated. A low Reynolds number jet simulation including a round nozzle geometry is performed and the method
Convolution quadrature for the wave equation with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Sauter, S. A.; Schanz, M.
2017-04-01
We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem. For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients. Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation.
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.
Boundary Condition Effects on Taylor States in SSX
NASA Astrophysics Data System (ADS)
Han, Jeremy; Shrock, Jaron; Kaur, Manjit; Brown, Michael; Schaffner, David
2016-10-01
Three different boundary conditions are applied to the SSX 0.15 m diameter plasma wind tunnel and the resultant Taylor states are characterized. The glass walls of the wind tunnel act as an insulating boundary condition. For the second condition, a flux conserver is wrapped around the tunnel to trap magnetic field lines inside the SSX. For the last condition, the flux conserver is segmented to add theta pinch coils, which will accelerate the plasma. We used resistive stainless steel and copper mesh for the flux conservers, which have soak times of 3 μs and 250 μs , respectively. The goal is to increase the speed, temperature, and density of the plasma plume by adding magnetic energy into the system using the coils and compressing the plasma into small volumes by stagnation. The time of flight is measured by using a linear array of magnetic pick-up loops, which track the plasma plume's location as a function of time. The density is measured by precision quadrature He-Ne laser interferometry, and the temperature is measured by ion Doppler spectroscopy. Speed and density without the coils are 30km /s and 1015cm-3 . We will reach a speed of 100km /s and density of 1016cm-3 by adding the coil. Work supported by DOE OFES and ARPA-E ALPHA program.
A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators
NASA Technical Reports Server (NTRS)
Hagstrom, T.; Hariharan, S. I.
1998-01-01
In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.
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
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
Livshits, Gideon I.
2014-02-15
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
Hawking radiation, covariant boundary conditions, and vacuum states
Banerjee, Rabin; Kulkarni, Shailesh
2009-04-15
The basic characteristics of the covariant chiral current
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.
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.
Periodic boundary conditions for dislocation dynamics simulations in three dimensions
Bulatov, V V; Rhee, M; Cai, W
2000-11-20
This article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.
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.
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.
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.
Effects of mass addition on blunt-body boundary-layer transition and heat transfer
NASA Technical Reports Server (NTRS)
Kaattari, G. E.
1978-01-01
The model bodies tested at Mach number 7.32 were hemispheres, blunt cones, and spherical segments. The mass addition consisted of air ejected through porous forward surfaces of the models. The experimental data consisted of heat transfer measurements from which boundary layer transitions were deduced. The data verified various applicable boundary layer codes in the laminar and transitional flow regimes. Empirical heating rate data correlations were developed for the laminar and turbulent flow regimes.
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
Johnson, Anthony N; Hromadka, T V
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
Johnson, Anthony N.; Hromadka, T.V.
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function. PMID:26151000
Effective slip boundary conditions for sinusoidally corrugated surfaces
NASA Astrophysics Data System (ADS)
Guo, Lin; Chen, Shiyi; Robbins, Mark O.
2016-11-01
Molecular dynamics simulations are used to investigate the effective slip boundary condition for a simple fluid flowing over surfaces with one-dimensional sinusoidal roughness in the Wenzel state. The effective slip length is calculated as a function of the corrugation amplitude for flows along two principal orientations: transverse and longitudinal to the corrugation. Different atomic configurations, bent and stepped, are examined for strong and weak wall-fluid interactions and high and low wall densities. Molecular dynamics results for sparse bent surfaces quantitatively agree with continuum hydrodynamic predictions with a constant local slip length. Increasing the roughness amplitude reduces the effective slip length and the reduction is larger for transverse flow than longitudinal flow. Atomic effects become important for dense surfaces, because the local slip length varies with the local curvature and atomic spacing along the wall. These effects can be captured by applying a spatially varying boundary condition to the Navier-Stokes equations. Results for stepped surfaces are qualitatively different than continuum predictions, with the effect of corrugation rising linearly with corrugation amplitude rather than quadratically. There is an increased drag for transverse flow that is proportional to the density of step edges and lowers the slip length. Edges tend to increase the slip length for longitudinal flow because of order induced along the edges.
Mixed singular-regular boundary conditions in multislab radiation transport
NASA Astrophysics Data System (ADS)
de Abreu, Marcos Pimenta
2004-06-01
This article reports a computational method for approximately solving radiation transport problems with anisotropic scattering defined on multislab domains irradiated from one side with a beam of monoenergetic neutral particles. We assume here that the incident beam may have a monodirectional component and a continuously distributed component in angle. We begin by defining the target problem representing the class of radiation transport problems that we are focused on. We then Chandrasekhar decompose the target problem into an uncollided transport problem with left singular boundary conditions and a diffusive transport problem with regular boundary conditions. We perform an analysis of these problems to derive the exact solution of the uncollided transport problem and a discrete ordinates solution in open form to the diffusive transport problem. These solutions are the basis for the definition of a computational method for approximately solving the target problem. We illustrate the numerical accuracy of our method with three basic problems in radiative transfer and neutron transport, and we conclude this article with a discussion and directions for future work.
Complex Wall Boundary Conditions for Modeling Combustion in Catalytic Channels
NASA Astrophysics Data System (ADS)
Zhu, Huayang; Jackson, Gregory
2000-11-01
Monolith catalytic reactors for exothermic oxidation are being used in automobile exhaust clean-up and ultra-low emissions combustion systems. The reactors present a unique coupling between mass, heat, and momentum transport in a channel flow configuration. The use of porous catalytic coatings along the channel wall presents a complex boundary condition when modeled with the two-dimensional channel flow. This current work presents a 2-D transient model for predicting the performance of catalytic combustion systems for methane oxidation on Pd catalysts. The model solves the 2-D compressible transport equations for momentum, species, and energy, which are solved with a porous washcoat model for the wall boundary conditions. A time-splitting algorithm is used to separate the stiff chemical reactions from the convective/diffusive equations for the channel flow. A detailed surface chemistry mechanism is incorporated for the catalytic wall model and is used to predict transient ignition and steady-state conversion of CH4-air flows in the catalytic reactor.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Fernández, P.; García-Mazarío, M.; Lancha, A. M.; Lapeña, J.
2004-08-01
The aim of this paper is to describe the microstructural investigations, the mechanical properties (hardness, tensile and charpy) and the grain boundary microchemistry studied by Auger electron spectroscopy (AES), of the Eurofer'97 steel aged in the range of temperatures from 400 to 600 °C up to 10 000 h. After these thermal aging treatments the steel showed a high microstructural stability, and similar values of hardness, ultimate tensile strength and 0.2% proof stress regardless of the material condition. A slight DBTT increase was observed in the material aged at 600 °C for 5000 and 10 000 h. The Auger results showed chromium enrichment at grain boundaries in all material conditions. In addition, phosphorus was detected at the grain boundaries after the aging treatments at 500 °C.
A Comparison of Transparent Boundary Conditions for the Fresnel Equation
NASA Astrophysics Data System (ADS)
Yevick, David; Friese, Tilmann; Schmidt, Frank
2001-04-01
We consider two numerical transparent boundary conditions that have been previously introduced in the literature. The first condition (BPP) was proposed by Baskakov and Popov (1991, Wave Motion14, 121-128) and Papadakis et al. (1992, J. Acoust. Soc. Am.92, 2030-2038) while the second (SDY) is that of Schmidt and Deuflhard (1995, Comput. Math. Appl.29, 53-76) and Schmidt and Yevick (1997, J. Comput. Phys.134, 96-107). The latter procedure is explicitly tailored to the form of the underlying numerical propagation scheme and is therefore unconditionally stable and highly precise. Here we present a new derivation of the SDY approach. As a result of this analysis, we obtain a simple modification of the BPP method that guarantees accuracy and stability for long propagation step lengths.
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.
NASA Astrophysics Data System (ADS)
Duling, Stefan; Saur, Joachim; Wicht, Johannes
2014-06-01
The interaction of planetary bodies with their surrounding magnetized plasma can often be described with the magnetohydrodynamic (MHD) equations, which are commonly solved by numerical models. For these models it is necessary to define physically correct boundary conditions for the plasma mass and energy density, the plasma velocity, and the magnetic field. Many planetary bodies have surfaces whose electrical conductivity is negligibly small and thus no electric current penetrates their surfaces. Magnetic boundary conditions, which consider that the associated radial electric current at the planetary surface is zero, are difficult to implement because they include the curl of the magnetic field. Here we derive new boundary conditions by a decomposition of the magnetic field in poloidal and toroidal parts. We find that the toroidal part of the magnetic field needs to vanish at the surface of the insulator. For the spherical harmonics coefficients of the poloidal part, we derive a Cauchy boundary condition, which also matches a possible intrinsic field by including its Gauss coefficients. Thus, we can additionally include planetary dynamo fields as well as time-variable induction fields within electrically conductive subsurface layers. We implement the nonconducting boundary condition in the MHD simulation code ZEUS-MP using spherical geometry and provide a numerical implementation in Fortran 90 as supporting information on the JGR website. We apply it to a model for Ganymede's plasma environment. Our model also includes a consistent set of boundary conditions for the other MHD variables density, velocity, and energy. With this model we can describe Galileo spacecraft observations in and around Ganymede's minimagnetosphere very well.
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
Homogenized boundary conditions and resonance effects in Faraday cages.
Hewett, D P; Hewitt, I J
2016-05-01
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.
Homogenized boundary conditions and resonance effects in Faraday cages
NASA Astrophysics Data System (ADS)
Hewett, D. P.; Hewitt, I. J.
2016-05-01
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.
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.
Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations
NASA Technical Reports Server (NTRS)
Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel
2012-01-01
Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?
Haber, S; Filipovic, N; Kojic, M; Tsuda, A
2006-10-01
The dissipative particle dynamics (DPD) method was used to simulate the flow in a system comprised of a fluid occupying the space between two cylinders rotating with equal angular velocities. The fluid, initially at rest, ultimately reaches a steady, linear velocity distribution (a rigid-body rotation). Since the induced flow field is solely associated with the no-slip boundary condition at the walls, we employed this system as a benchmark to examine the effect of bounce-back reflections, specular reflections, and Pivkin-Karniadakis no-slip boundary conditions, upon the steady-state velocity, density, and temperature distributions. An additional advantage of the foregoing system is that the fluid occupies inherently a finite bounded domain so that the results are affected by the prescribed no-slip boundary conditions only. Past benchmark systems such as Couette flow between two infinite parallel plates or Poiseuille flow in an infinitely long cylinder must employ artificial periodic boundary conditions at arbitrary upstream and downstream locations, a possible source of spurious effects. In addition, the effect of the foregoing boundary conditions on the time evolution of the simulated velocity profile was compared with that of the known, time-dependent analytical solution. It was shown that bounce-back reflection yields the best results for the velocity distributions with small fluctuations in density and temperature at the inner fluid domain and larger deviations near the walls. For the unsteady solutions a good fit is obtained if the DPD friction coefficient is proportional to the kinematic viscosity. Based on dimensional analysis and the numerical results a universal correlation is suggested between the friction coefficient and the kinematic viscosity.
Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data
Couto, Joaquina; Lebreton, Mael
2016-01-01
The notion of “mixtures” has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied–for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes. PMID:27893868
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 ADMINISTRATION, DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH LICENSE General § 415.11 Additional license...
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...
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...
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...
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...
Atom-partitioned multipole expansions for electrostatic potential boundary conditions
NASA Astrophysics Data System (ADS)
Lee, M.; Leiter, K.; Eisner, C.; Knap, J.
2017-01-01
Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.
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.
Modeling solar wind with boundary conditions from interplanetary scintillations
Manoharan, P.; Kim, T.; Pogorelov, N. V.; ...
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
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.
Simulating flight boundary conditions for orbiter payload modal survey
NASA Technical Reports Server (NTRS)
Chung, Y. T.; Sernaker, M. L.; Peebles, J. H.
1993-01-01
An approach to simulate the characteristics of the payload/orbiter interfaces for the payload modal survey was developed. The flexure designed for this approach is required to provide adequate stiffness separation in the free and constrained interface degrees of freedom to closely resemble the flight boundary condition. Payloads will behave linearly and demonstrate similar modal effective mass distribution and load path as the flight if the flexure fixture is used for the payload modal survey. The potential non-linearities caused by the trunnion slippage during the conventional fixed base modal survey may be eliminated. Consequently, the effort to correlate the test and analysis models can be significantly reduced. An example is given to illustrate the selection and the sensitivity of the flexure stiffness. The advantages of using flexure fixtures for the modal survey and for the analytical model verification are also demonstrated.
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.
Thermal Momentum Distribution from Path Integrals with Shifted Boundary Conditions
NASA Astrophysics Data System (ADS)
Giusti, Leonardo; Meyer, Harvey B.
2011-04-01
For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.
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.
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
Equilibrium boundary conditions, dynamic vacuum energy, and the big bang
Klinkhamer, F. R.
2008-10-15
The near-zero value of the cosmological constant {lambda} in an equilibrium context may be due to the existence of a self-tuning relativistic vacuum variable q. Here, a cosmological nonequilibrium context is considered with a corresponding time-dependent cosmological parameter {lambda}(t) or vacuum energy density {rho}{sub V}(t). A specific model of a closed Friedmann-Robertson-Walker universe is presented, which is determined by equilibrium boundary conditions at one instant of time (t=t{sub eq}) and a particular form of vacuum-energy dynamics (d{rho}{sub V}/dt{proportional_to}{rho}{sub M}). This homogeneous and isotropic model has a standard big bang phase at early times (t<
Gas cushion model and hydrodynamic boundary conditions for superhydrophobic textures
NASA Astrophysics Data System (ADS)
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.
Sensitivity and uncertainty analysis of the recharge boundary condition
NASA Astrophysics Data System (ADS)
Jyrkama, M. I.; Sykes, J. F.
2006-01-01
The reliability analysis method is integrated with MODFLOW to study the impact of recharge on the groundwater flow system at a study area in New Jersey. The performance function is formulated in terms of head or flow rate at a pumping well, while the recharge sensitivity vector is computed efficiently by implementing the adjoint method in MODFLOW. The developed methodology not only quantifies the reliability of head at the well in terms of uncertainties in the recharge boundary condition, but it also delineates areas of recharge that have the highest impact on the head and flow rate at the well. The results clearly identify the most important land use areas that should be protected in order to maintain the head and hence production at the pumping well. These areas extend far beyond the steady state well capture zone used for land use planning and management within traditional wellhead protection programs.
Introduction of periodic boundary conditions into UNRES force field.
Sieradzan, Adam K
2015-05-05
In this article, implementation of periodic boundary conditions (PBC) into physics-based coarse-grained UNited RESidue (UNRES) force field is presented, which replaces droplet-like restraints previously used. Droplet-like restraints are necessary to keep multichain systems together and prevent them from dissolving to infinitely low concentration. As an alternative for droplet-like restrains cuboid PBCs with imaging of the molecules were introduced. Owing to this modification, artificial forces which arose from restraints keeping a droplet together were eliminated what leads to more realistic trajectories. Due to computational reasons cutoff and smoothing functions were introduced on the long range interactions. The UNRES force field with PBC was tested by performing microcanonical simulations. Moreover, to asses the behavior of the thermostat in PBCs Langevin and Berendsen thermostats were studied. The influence of PBCs on association pattern was compared with droplet-like restraints on the ββα hetero tetramer 1 protein system.
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
Behavior of the Reversed Field Pinch with Nonideal Boundary Conditions.
NASA Astrophysics Data System (ADS)
Ho, Yung-Lung
The linear and nonlinear magnetohydrodynamic stability of current-driven modes is studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. These results then help to guide the nonlinear study, and also help to interpret the quasilinear aspect of the nonlinear results. The nonlinear behaviors are studied with a three -dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v times b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. If the loop voltage is held constant, the current decreases and the plasma evolves toward a nonreversed tokamak-like state. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v times b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and
Behavior of the reversed field pinch with nonideal boundary conditions
NASA Astrophysics Data System (ADS)
Ho, Yung-Lung
1988-11-01
The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed.
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.
NASA Astrophysics Data System (ADS)
Tang, Liang; Cong, Shengyi; Ling, Xianzhang; Ju, Nengpan
2017-01-01
Boundary conditions can significantly affect a slope's behavior under strong earthquakes. To evaluate the importance of boundary conditions for finite element (FE) simulations of a shake-table experiment on the slope response, a validated three-dimensional (3D) nonlinear FE model is presented, and the numerical and experimental results are compared. For that purpose, the robust graphical user-interface "SlopeSAR", based on the open-source computational platform OpenSees, is employed, which simplifies the effort-intensive pre- and post-processing phases. The mesh resolution effect is also addressed. A parametric study is performed to evaluate the influence of boundary conditions on the FE model involving the boundary extent and three types of boundary conditions at the end faces. Generally, variations in the boundary extent produce inconsistent slope deformations. For the two end faces, fixing the y-direction displacement is not appropriate to simulate the shake-table experiment, in which the end walls are rigid and rough. In addition, the influence of the length of the 3D slope's top face and the width of the slope play an important role in the difference between two types of boundary conditions at the end faces (fixing the y-direction displacement and fixing the ( y, z) direction displacement). Overall, this study highlights that the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions.
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.
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.
2015-01-05
discretization of the steady- state Navier-Stokes equations at the inflow boundaries, numerically algebraic equations are imposed as boundary conditions...conditions for the counterflow configuration is presented. Upon discretization of the steady- state Navier-Stokes equations at the inflow boundaries...boundary conditions for the counterflow configu- ration is presented. Upon discretization of the steady- state Navier-Stokes equations at the inflow
NASA Astrophysics Data System (ADS)
Pinto, Carlos
2016-03-01
We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.
NASA Astrophysics Data System (ADS)
Seo, Jongmin; Bose, Sanjeeb; Garcia-Mayoral, Ricardo; Mani, Ali
2012-11-01
Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions. Supported by the Office of Naval Research and the Kwanjeong Educational Scholarship Foundation.
An Implementation of Hydrostatic Boundary Conditions for Variable Density Lattice Boltzmann Methods
NASA Astrophysics Data System (ADS)
Bardsley, K. J.; Thorne, D. T.; Lee, J. S.; Sukop, M. C.
2006-12-01
Lattice Boltzmann Methods (LBMs) have been under development for the last two decades and have become another capable numerical method for simulating fluid flow. Recent advances in lattice Boltzmann applications involve simulation of density-dependent fluid flow in closed (Dixit and Babu, 2006; D'Orazio et al., 2004) or periodic (Guo and Zhao, 2005) domains. However, standard pressure boundary conditions (BCs) are incompatible with concentration-dependent density flow simulations that use a body force for gravity. An implementation of hydrostatic BCs for use under these conditions is proposed here. The basis of this new implementation is an additional term in the pressure BC. It is derived to account for the incorporation of gravity as a body force and the effect of varying concentration in the fluid. The hydrostatic BC expands the potential of density-dependent LBM to simulate domains with boundaries other than the closed or periodic boundaries that have appeared in previous literature on LBM simulations. With this new implementation, LBM will be able to simulate complex concentration-dependent density flows, such as salt water intrusion in the classic Henry and Henry-Hilleke problems. This is demonstrated using various examples, beginning with a closed box system, and ending with a system containing two solid walls, one velocity boundary and one pressure boundary, as in the Henry problem. References Dixit, H. N., V. Babu, (2006), Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transfer, 49, 727-739. D'Orazio, A., M. Corcione, G.P. Celata, (2004), Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions, Int. J. Thermal Sci., 43, 575-586. Gou, Z., T.S. Zhao, (2005), Lattice Boltzmann simulation of natural convection with temperature-dependant viscosity in a porous cavity, Numerical Heat Transfer, Part B
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
NASA Technical Reports Server (NTRS)
Funaro, D.; Gottlieb, D.
1988-01-01
A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.
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.
NASA Astrophysics Data System (ADS)
Gatsonis, Nikolaos A.; Chamberlin, Ryan E.; Averkin, Sergey N.
2013-01-01
The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical
Space-fractional advection-diffusion and reflective boundary condition.
Krepysheva, Natalia; Di Pietro, Liliana; Néel, Marie-Christine
2006-02-01
Anomalous diffusive transport arises in a large diversity of disordered media. Stochastic formulations in terms of continuous time random walks (CTRWs) with transition probability densities showing space- and/or time-diverging moments were developed to account for anomalous behaviors. A broad class of CTRWs was shown to correspond, on the macroscopic scale, to advection-diffusion equations involving derivatives of noninteger order. In particular, CTRWs with Lévy distribution of jumps and finite mean waiting time lead to a space-fractional equation that accounts for superdiffusion and involves a nonlocal integral-differential operator. Within this framework, we analyze the evolution of particles performing symmetric Lévy flights with respect to a fluid moving at uniform speed . The particles are restricted to a semi-infinite domain limited by a reflective barrier. We show that the introduction of the boundary condition induces a modification in the kernel of the nonlocal operator. Thus, the macroscopic space-fractional advection-diffusion equation obtained is different from that in an infinite medium.
Heating the Solar Corona: Observations for Model Boundary Conditions
NASA Astrophysics Data System (ADS)
Nestlerode, C. M.; Poland, A. I.
2005-12-01
A prominent question in solar physics concerns the sources of coronal heating. This problem can be addressed through observations of closed magnetic loops which have high enough density to provide adequate temporal, spatial, and spectral resolution. Measurements of temperature, density, and velocity throughout the loop can be used for boundary conditions and compared with quantities for model calculations. In this paper, we present Solar Ultraviolet Measurements from Emitted Radiation (SUMER) data from the Solar and Heliospheric Observatory's (SOHO's) JOP 161 program. The SUMER instrument has high spatial and spectral resolution over several different spectral lines and therefore the data cover a large temperature range. The analyzed lines include Mg VIII, Mg IX, N III, N IV, Ne VIII, O IV, O V, S IV, S V, and S X with temperatures ranging from 60,000 K (S IV) to 0.9 MK (Mg IX). The velocity profiles are created using Gaussian fitting with wavelength calibration determined using average quiet Sun velocities from known Doppler velocity shifts. The velocity profiles show important changes in solar foot point plasma speed both spatially and temporally. This analysis builds on previous analysis of solar spectral lines observed with the SOHO Coronal Diagnostic Spectrometer (CDS); the advantage of the SUMER instrument is better resolution, both spectrally and spatially. This work was funded by NASA, Living with a Star Program.
Brain-skull boundary conditions in a computational deformation model
NASA Astrophysics Data System (ADS)
Ji, Songbai; Liu, Fenghong; Roberts, David; Hartov, Alex; Paulsen, Keith
2007-03-01
Brain shift poses a significant challenge to accurate image-guided neurosurgery. To this end, finite element (FE) brain models have been developed to estimate brain motion during these procedures. The significance of the brain-skull boundary conditions (BCs) for accurate predictions in these models has been explored in dynamic impact and inertial rotation injury computational simulations where the results have shown that the brain mechanical response is sensitive to the type of BCs applied. We extend the study of brain-skull BCs to quasi-static brain motion simulations which prevail in neurosurgery. Specifically, a frictionless brain-skull BC using a contact penalty method master-slave paradigm is incorporated into our existing deformation forward model (forced displacement method). The initial brain-skull gap (CSF thickness) is assumed to be 2mm for demonstration purposes. The brain surface nodes are assigned as either fixed (at bottom along the gravity direction), free (at brainstem), with prescribed displacement (at craniotomy) or as slave nodes potentially in contact with the skull (all the remaining). Each slave node is assigned a penalty parameter (β=5) such that when the node penetrates the rigid body skull inner-surface (master surface), a contact force is introduced proportionally to the penetration. Effectively, brain surface nodes are allowed to move towards or away from the cranium wall, but are ultimately restricted from penetrating the skull. We show that this scheme improves the model's ability to represent the brain-skull interface.
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
NASA Astrophysics Data System (ADS)
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
NASA Astrophysics Data System (ADS)
Pao, C. V.; Ruan, W. H.
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
Biondini, Gino; Kovačič, Gregor
2014-03-15
The inverse scattering transform for the focusing nonlinear Schrödinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the scattering eigenfunctions, the introduction of the appropriate Riemann surface and uniformization variable, the symmetries, discrete spectrum, asymptotics, trace formulae and the so-called theta condition, and the formulation of the inverse problem in terms of a Riemann-Hilbert problem. In addition, the general behavior of the soliton solutions is discussed, as well as the reductions to all special cases previously discussed in the literature.
Zero-derivative boundary condition for pulsed distributed systems. [column chromatography example
NASA Technical Reports Server (NTRS)
Lashmet, P. K.; Woodrow, P. T.
1975-01-01
To permit use of experimentally determined Peclet numbers in numerical simulations of pulsed distributed flow systems such as chromatograph columns, substitution of the zero-derivative boundary condition for the infinite boundary condition used in treating data is examined. Moment analysis shows that application of the zero-derivative condition external to the column will yield equivalent numerical results for the two boundary conditions. Criteria for locating this position are provided as a function of the Peclet number.
A Discrete Analysis of Non-reflecting Boundary Conditions for Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Hu, Fang Q.; Atkins, Harold L.
2003-01-01
We present a discrete analysis of non-reflecting boundary conditions for the discontinuous Galerkin method. The boundary conditions considered in this paper include the recently proposed Perfectly Matched Layer absorbing boundary condition for the linearized Euler equation and two non-reflecting boundary conditions based on the characteristic decomposition of the flux on the boundary. The analyses for the three boundary conditions are carried out in a unifled way. In each case, eigensolutions of the discrete system are obtained and applied to compute the numerical reflection coefficients of a specified out-going wave. The dependencies of the reflections at the boundary on the out-going wave angle and frequency as well as the mesh sizes arc? studied. Comparisons with direct numerical simulation results are also presented.
NASA Astrophysics Data System (ADS)
Chu, Yuchuan; Cao, Yong; He, Xiaoming; Luo, Min
2011-11-01
Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.
NASA Astrophysics Data System (ADS)
van den Berg, J. I.; Boerstoel, J. W.
An overview of the development, analysis, and numerical validation of a solid-wall boundary condition for cell-centered Euler-flow calculations is presented. This solid-wall boundary condition is provided by the theory of characteristics, and is based on a central-difference scheme. The boundary condition was developed to investigate the effect of various boundary-condition algorithms on the accuracy of calculation results for three-dimensional Euler flows around delta wings. A mathematical analysis of the boundary condition was performed. The numerical validation consists of a comparison of calculation results with various boundary conditions. Also discretization and convergence errors were investigated. As a test case, the NLR 7301 profile under supercritical, shock-free flow conditions of M = 0.721, alpha = -0.194 deg, were chosen.
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.
Many-body-localization transition: sensitivity to twisted boundary conditions
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2017-03-01
For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle ϕ can be used to analyze the many-body-localization transition. The sensitivity of the energy levels {{E}n}(φ ) is measured by the level curvature {{K}n}=En\\prime \\prime(0) , or more precisely by the Thouless dimensionless curvature {{k}n}={{K}n}/{{ Δ }n} , where {{ Δ }n} is the level spacing that decays exponentially with the size L of the system. For instance {{ Δ }n}\\propto {{2}-L} in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight {{D}n}=L{{K}n} studied recently by Filippone et al (arxiv:1606.07291v1) involves a different rescaling. The sensitivity of the eigenstates |{{\\psi}n}(φ )> is characterized by the susceptibility {χn}=-Fn\\prime \\prime(0) of the fidelity {{F}n}= |<{{\\psi}n}(0)|{{\\psi}n}(φ )>| . Both observables are distributed with probability distributions displaying power-law tails {{P}β}(k)≃ {{A}β}|k{{|}-(2+β )} and Q(χ )≃ {{B}β}{χ-\\frac{3+β{2}}} , where β is the level repulsion index taking the values {β\\text{GOE}}=1 in the ergodic phase and {β\\text{loc}}=0 in the localized phase. The amplitudes {{A}β} and {{B}β} of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the many-body-localization transition by Serbyn et al (2015 Phys. Rev. X 5 041047).
Error transport equation boundary conditions for the Euler and Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Phillips, Tyrone S.; Derlaga, Joseph M.; Roy, Christopher J.; Borggaard, Jeff
2017-02-01
Discretization error is usually the largest and most difficult numerical error source to estimate for computational fluid dynamics, and boundary conditions often contribute a significant source of error. Boundary conditions are described with a governing equation to prescribe particular behavior at the boundary of a computational domain. Boundary condition implementations are considered sufficient when discretized with the same order of accuracy as the primary governing equations; however, careless implementations of boundary conditions can result in significantly larger numerical error. Investigations into different numerical implementations of Dirichlet and Neumann boundary conditions for Burgers' equation show a significant impact on the accuracy of Richardson extrapolation and error transport equation discretization error estimates. The development of boundary conditions for Burgers' equation shows significant improvements in discretization error estimates in general and a significant improvement in truncation error estimation. The latter of which is key to accurate residual-based discretization error estimation. This research investigates scheme consistent and scheme inconsistent implementations of inflow and outflow boundary conditions up to fourth order accurate and a formulation for a slip wall boundary condition for truncation error estimation are developed for the Navier-Stokes and Euler equations. The scheme consistent implementation resulted in much smoother truncation error near the boundaries and more accurate discretization error estimates.
Constructing non-reflecting boundary conditions using summation-by-parts in time
NASA Astrophysics Data System (ADS)
Frenander, Hannes; Nordström, Jan
2017-02-01
In this paper we provide a new approach for constructing non-reflecting boundary conditions. The boundary conditions are based on summation-by-parts operators and derived without Laplace transformation in time. We prove that the new non-reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.
NASA Astrophysics Data System (ADS)
Kastening, Boris
2002-11-01
A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.
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.
Boundary Conditions for Scalar Conservation Laws from a Kinetic Point of View
NASA Astrophysics Data System (ADS)
Nouri, A.; Omrane, A.; Vila, J. P.
1999-03-01
Boundary conditions for multidimensional scalar conservation laws are obtained in the context of hydrodynamic limits from a kinetic point of view. The initial boundary value kinetic problem is well posed since inward and outward characteristics of the domain can be distinguished. The convergence of the first momentum of the distribution function to an entropy solution of the conservation law is established. Boundary conditions are obtained. The equivalence with the Bardos, Leroux, and Nedelec conditions is studied.
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.
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).
An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition
Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J; Champagne, N J; Rockway, J D
2007-02-28
An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
Almost exact boundary condition for one-dimensional Schrödinger equations.
Pang, Gang; Bian, Lei; Tang, Shaoqiang
2012-12-01
An explicit local boundary condition is proposed for finite-domain simulations of the linear Schrödinger equation on an unbounded domain. Based on an exact boundary condition in terms of the Bessel functions, it takes a simple form with 16 neighboring grid points, and it involves no empirical parameter. While the computing load is rather low, the proposed boundary condition is effective in reflection suppression, comparable to the exact convolution treatments. An extension to nonlinear Schrödinger equations is also proposed. Numerical comparisons clearly demonstrate the effectiveness of this ALmost EXact (ALEX) boundary condition for both the linear and the cubic nonlinear Schrödinger equations.
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.
Boundary conditions for conformally coupled scalar in AdS4
NASA Astrophysics Data System (ADS)
Oh, Jae-Hyuk
2015-06-01
We consider conformally coupled scalar with ɸ4 coupling in AdS4 and study its various boundary conditions on AdS boundary. We have obtained perturbative solutions of equation of motion of the conformally coupled scalar with power expansion order by order in ɸ4 coupling λ up to λ2 order. In its dual CFT, we get 2, 4 and 6 point functions by using this solution with Dirichlet and Neumann boundary conditions via AdS/CFT dictionary. We also consider marginal deformation on AdS boundary and get its on-shell and boundary effective actions.
A Novel Method for Modeling Neumann and Robin Boundary Conditions in Smoothed Particle Hydrodynamics
Ryan, Emily M.; Tartakovsky, Alexandre M.; Amon, Cristina
2010-08-26
In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries. The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.
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.
Liu, Xin; Huang, Xun; Zhang, Xin
2014-11-01
This work develops the so-called compensated impedance boundary conditions that enable stable time domain simulations of sound propagation in a lined duct with uniform mean flow, which has important practical interest for noise emission by aero-engines. The proposed method is developed analytically from an unusual perspective of control that shows impedance boundary conditions act as closed-loop feedbacks to an overall duct acoustic system. It turns out that those numerical instabilities of time domain simulations are caused by deficient phase margins of the corresponding control-oriented model. A particular instability of very low frequencies in the presence of steady uniform background mean flow, in addition to the well known high frequency numerical instabilities at the grid size, can be identified using this analysis approach. Stable time domain impedance boundary conditions can be formulated by including appropriate phaselead compensators to achieve desired phase margins. The compensated impedance boundary conditions can be simply designed with no empirical parameter, straightforwardly integrated with ordinary linear acoustic models, and efficiently calculated with no need of resolving sheared boundary layers. The proposed boundary conditions are validated by comparing against asymptotic solutions of spinning modal sound propagation in a duct with a hard-soft interface and reasonable agreement is achieved.
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.
Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
NASA Astrophysics Data System (ADS)
Mei, Zhongtao; Bolech, C. J.
2017-03-01
Using the algebraic Bethe Ansatz, we derive a matrix product representation of the exact Bethe-Ansatz states of the six-vertex Heisenberg chain (either X X X or X X Z and spin-1/2 ) with open boundary conditions. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices that act on a tensor product of auxiliary spaces. As compared to the matrix product states of the same Heisenberg chain but with periodic boundary conditions, the dimension of the exact auxiliary matrices is enlarged as if the conserved number of spin-flips considered would have been doubled. This result is generic for any non-nested integrable model, as is clear from our derivation, and we further show this by providing an additional example of the same matrix product state construction for a well-known model of a gas of interacting bosons. Counterintuitively, the matrices do not depend on the spatial coordinate despite the open boundaries, and thus they suggest generic ways of exploiting (emergent) translational invariance both for finite size and in the thermodynamic limit.
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.
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.
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.
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.
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.
Shim, Jae Wan; Gatignol, Renée
2010-04-01
We show that the heat exchange between fluid particles and boundary walls can be achieved by controlling the velocity change rate following the particles' collision with a wall in discrete kinetic theory, such as the lattice-gas cellular automata and the lattice Boltzmann method. We derive a relation between the velocity change rate and temperature so that we can control the velocity change rate according to a given temperature boundary condition. This relation enables us to deal with the thermal boundary whose temperature varies along a wall in contrast to the previous works of the lattice-gas cellular automata. In addition, we present simulation results to compare our method to the existing and give an example in a microchannel with a high temperature gradient boundary condition by the lattice-gas cellular automata.
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.
Conditions affecting boundary response to messages out of awareness.
Fisher, S
1976-05-01
Multiple studies evaluated the role of the following parameters in mediating the effects of auditory subliminal inputs upon the body boundary: being made aware that exposure to subliminal stimuli is occurring, nature of the priming preliminary to the input, length of exposure, competing sensory input, use of specialized content messages, tolerance for unrealistic experience, and masculinity-feminity. A test-retest design was typically employed that involved measuring the baseline Barrier score with the Holtzman bolts and then ascertaining the Barrier change when responding to a second series of Holtzman blots at the same time that subliminal input was occurring. Complex results emerged that defined in considerably new detail what facilitates and blocks the boundary-disrupting effects of subliminal messages in men and to a lesser degree in women.
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).
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.
Impacts of Lateral Boundary Conditions on U.S. Ozone Modeling Analyses
Chemical boundary conditions are a key input to regional-scale photochemical models. In this study, we perform annual simulations over North America with chemical boundary conditions prepared from two global models (GEOS-CHEM and Hemispheric CMAQ). Results indicate that the impac...
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.
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.
Existence Result for the Kinetic Neutron Transport Problem with a General Albedo Boundary Condition
NASA Astrophysics Data System (ADS)
Sanchez, Richard; Bourhrara, Lahbib
2011-09-01
We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied.
Trickle-down boundary conditions in aeolian dune-field pattern formation
NASA Astrophysics Data System (ADS)
Ewing, R. C.; Kocurek, G.
2015-12-01
One the one hand, wind-blown dune-field patterns emerge within the overarching boundary conditions of climate, tectonics and eustasy implying the presence of these signals in the aeolian geomorphic and stratigraphic record. On the other hand, dune-field patterns are a poster-child of self-organization, in which autogenic processes give rise to patterned landscapes despite remarkable differences in the geologic setting (i.e., Earth, Mars and Titan). How important are climate, tectonics and eustasy in aeolian dune field pattern formation? Here we develop the hypothesis that, in terms of pattern development, dune fields evolve largely independent of the direct influence of 'system-scale' boundary conditions, such as climate, tectonics and eustasy. Rather, these boundary conditions set the stage for smaller-scale, faster-evolving 'event-scale' boundary conditions. This 'trickle-down' effect, in which system-scale boundary conditions indirectly influence the event scale boundary conditions provides the uniqueness and richness of dune-field patterned landscapes. The trickle-down effect means that the architecture of the stratigraphic record of dune-field pattern formation archives boundary conditions, which are spatially and temporally removed from the overarching geologic setting. In contrast, the presence of an aeolian stratigraphic record itself, reflects changes in system-scale boundary conditions that drive accumulation and preservation of aeolian strata.
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.
NASA Astrophysics Data System (ADS)
Gvelesiani, Simon; Lippoth, Friedrich; Walker, Christoph
2015-12-01
We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic Hölder spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.
NASA Astrophysics Data System (ADS)
Choi, Jung-Eun
1993-01-01
In Part One of this two-part thesis, laminar and turbulent solutions are presented for the Stokes-wave/flat-plate boundary-layer and wake for small - large wave steepness, including exact and approximate treatments of the viscous free-surface boundary conditions. The macro-scale flow exhibits the wave-induced pressure-gradient effects described in a precursory work. For laminar flow, the micro-scale flow indicates that the free-surface boundary conditions have a profound influence over the boundary layer and near and intermediate wake: the wave elevation and slopes correlate with the depthwise velocity; the streamwise and transverse velocities and vorticity display large variations, including islands of maximum/minimum values, whereas the depthwise velocity and pressure indicate small variations; significant free-surface vorticity flux and complex vorticity transport are displayed; wave-induced effects normalized by wave steepness are larger for small steepness with the exception of wave-induced separation; order-of-magnitude estimates are confirmed; and appreciable errors are introduced through approximations to the free-surface boundary conditions. For turbulent flow, the results are similar, but preliminary due to the present uncertainty in appropriate treatment of the free-surface boundary conditions and meniscus boundary layer. In Part Two, Navier-Stokes, boundary-layer, and perturbation expansion solutions are presented for the model problem of a flat-plate boundary layer and wake with temporal, spatial, and traveling horizontal-wave external flows, which are characterized by Stokes-layer overshoots, phase angles, and streaming and nonlinearities. The temporal wave displays close agreement with previous studies and is useful for validation and placing the current work in technical perspective. The spatial wave indicates significantly increased magnitudes and complex nature (e.g., wake bias), which is attributed to nonlinearities associated with large
Finite-size corrections in the Ising model with special boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh.
2010-11-01
The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz (BK) is analyzed. We derive exact finite-size corrections for the free energy F of the critical ferromagnetic Ising model on the M×N square lattice with Brascamp-Kunz boundary conditions [H.J. Brascamp, H. Kunz, J. Math. Phys. 15 (1974) 66]. We show that finite-size corrections strongly depend not only on the boundary conditions but also on the shape and pattern of the lattice. In the limit N→∞ we obtain the expansion of the free energy and the inverse correlation lengths for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions.
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.
Neumann-Type Boundary Conditions for Hamilton-Jacobi Equations in Smooth Domains
Day, Martin V.
2006-05-15
Neumann or oblique derivative boundary conditions for viscosity solutions of Hamilton-Jacobi equations are considered. As developed by P.L. Lions, such boundary conditions are naturally associated with optimal control problems for which the state equations employ 'Skorokhod' or reflection dynamics to ensure that the state remains in a prescribed set, assumed here to have a smooth boundary. We develop connections between the standard formulation of viscosity boundary conditions and an alternative formulation using a naturally occurring discontinuous Hamiltonian which incorporates the reflection dynamics directly. (This avoids the dependence of such equivalence on existence and uniqueness results, which may not be available in some applications.) At points of differentiability, equivalent conditions for the boundary conditions are given in terms of the Hamiltonian and the geometry of the state trajectories using optimal controls.
A convective-like energy-stable open boundary condition for simulations of incompressible flows
NASA Astrophysics Data System (ADS)
Dong, S.
2015-12-01
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.
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.
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.
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.
New approximate boundary conditions for large eddy simulations of wall-bounded flows
NASA Technical Reports Server (NTRS)
Piomelli, Ugo; Ferziger, Joel; Moin, Parviz; Kim, John
1989-01-01
Two new approximate boundary conditions have been applied to the large eddy simulation of channel flow with and without transpiration. These new boundary conditions give more accurate results than those previously in use, and allow significant reduction of the required CPU time over simulations in which no-slip conditions are applied. Mean velocity profiles and turbulence intensities compare well both with experimental data and with the results of resolved simulations. The influence of the approximate boundary conditions remains confined near the point of application and does not affect the turbulence statistics in the core of the flow.
Code of Federal Regulations, 2011 CFR
2011-01-01
... management plan, and addition of multiple-site components. (a) Changes in the boundary of a Reserve and major changes to the final management plan, including state laws or regulations promulgated specifically for the... management plan change. Changes in the boundary of a Reserve involving the acquisition of properties...
Code of Federal Regulations, 2010 CFR
2010-01-01
... management plan, and addition of multiple-site components. (a) Changes in the boundary of a Reserve and major changes to the final management plan, including state laws or regulations promulgated specifically for the... management plan change. Changes in the boundary of a Reserve involving the acquisition of properties...
NASA Astrophysics Data System (ADS)
King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.
2015-03-01
We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.
Reconstruction of an unknown cavity with Robin boundary condition inside a heat conductor
NASA Astrophysics Data System (ADS)
Nakamura, Gen; Wang, Haibing
2015-12-01
Active thermography is a non-destructive testing technique to detect the internal structure of a heat conductor, which is widely applied in industrial engineering. In this paper, we consider the problem of identifying an unknown cavity with Robin boundary condition inside a heat conductor from boundary measurements. To set up the inverse problem mathematically, we first state the corresponding forward problem and show its well-posedness in an anisotropic Sobolev space by the integral equation method. Then, taking the Neumann-to-Dirichlet map as mathematically idealized measurement data for the active thermography, we present a linear sampling method for reconstructing the unknown Robin-type cavity and give its mathematical justification by using the layer potential argument. In addition, we analyze the indicator function used in this method and show its pointwise asymptotic behavior by investigating the reflected solution of the fundamental solution. Based on our asymptotic analysis, we can establish a pointwise reconstruction scheme for the boundary of the cavity, and can also know the distance to the unknown cavity as we probe it from its inside. The numerical results are presented to show the performance of the reconstruction scheme and the asymptotic behavior.
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.
Boundary conditions for Maxwell fields in Kerr-AdS spacetimes
NASA Astrophysics Data System (ADS)
Wang, Mengjie
2016-05-01
Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Verschaeve, Joris C. G.
2009-09-01
An analytical and numerical analysis of the no-slip boundary condition at walls at rest for the lattice Boltzmann Bhatnagar-Gross-Krook method is performed. The main result of this analysis is an alternative formulation for the no-slip boundary condition at walls at rest. Numerical experiments assess the accuracy and stability of this formulation for Poiseuille and Womersley flows, flow over a backward facing step, and unsteady flow around a square cylinder. This no-slip boundary condition is compared analytically and numerically to the boundary conditions of Inamuro [Phys. Fluids 7, 2928 (1995)] and Zou and He [Phys. Fluids 9, 1591 (1997)] and it is found that all three make use of the same mechanism for the off-diagonal element of the stress tensor. Mass conservation, however, is only assured by the present one. In addition, our analysis points out which mechanism lies behind the instabilities also observed by Lätt [Phys. Rev. E 77, 056703 (2008)] for this kind of boundary conditions. We present a way to remove these instabilities, allowing one to reach relaxation frequencies considerably closer to 2.
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.
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.
Second-Order Far Field Computational Boundary Conditions for Inviscid Duct Flow Problems
1990-03-01
COMPUTATIONAL BOUNDARY CONDITIONS INTERNAL FLOW COMPUTATIONS EULER METHODS 19. ABSTRACT (Continue on reverse if necessary and identify by block number...SOLUTIONS OF THE LINEARIZED, SECOND-ORDER EULER EQUATIONS. THE EULER EQUATIONS ARE LINEARIZED ABOUT A CONSTANT PRESSURE, RECTILINEAR FLOW C)NDITION...THE BOUNDARY PROCEDURE CAN BE USED WITH ANY NUMERICAL EULER SOLUTION METHOD AND ALLOWS COMPUTATIONAL BOUNDARIES TO BE LOCATED EXTREMELY CLOSE TO THE
Surface boundary conditions for the numerical solution of the Euler equations
NASA Technical Reports Server (NTRS)
Dadone, A.; Grossman, B.
1993-01-01
We consider the implementation of boundary conditions at solid walls in inviscid Euler solutions by upwind, finite-volume methods. We review some current methods for the implementation of surface boundary conditions and examine their behavior for the problem of an oblique shock reflecting off a planar surface. We show the importance of characteristic boundary conditions for this problem and introduce a method of applying the classical flux-difference splitting of Roe as a characteristic boundary condition. Consideration of the equivalent problem of the intersection of two (equal and opposite) oblique shocks was very illuminating on the role of surface boundary conditions for an inviscid flow and led to the introduction of two new boundary-condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique. Examples of the effects of the various surface boundary conditions considered are presented for the supersonic blunt body problem and the subcritical compressible flow over a circular cylinder. Dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown, with regard to numerical entropy generation, total pressure loss, drag and grid convergence.
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…
Nunez, Dario; Sarbach, Olivier
2010-02-15
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We specify nine boundary conditions for this system with the following properties: (i) they impose the momentum constraint at the boundary, which is shown to preserve all the constraints throughout evolution; (ii) they approximately control the incoming gravitational degrees of freedom by specifying the Weyl scalar {Psi}{sub 0} at the boundary; (iii) they control the gauge freedom by requiring a Neumann boundary condition for the lapse, by setting the normal component of the shift to zero, and by imposing a Sommerfeld-like condition on the tangential components of the shift; and (iv) they are shown to yield a well-posed problem in the limit of weak gravity. Possible numerical applications of our results are also discussed briefly.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.
1991-01-01
Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.
The PPP model of alternant cyclic polyenes with modified boundary conditions
Bendazzoli, G.L.; Evangelisti, S.
1995-08-15
The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of alternant cyclic polyenes (CH){sub N} (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Moebius) orbitals are used to perform energy extrapolations for N {yields} {infinity}. 38 refs., 2 figs., 5 tabs.
Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions
ERIC Educational Resources Information Center
Aliev, Nihan; Jahanshahi, Mohammad
2002-01-01
Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…
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
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).
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.
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.
Investigating the non-classical boundary conditions relevant to strain gradient theories
NASA Astrophysics Data System (ADS)
Jafari, Akbar; Ezzati, Meysam
2017-02-01
In the present study, two classes of non-classical constitutive equations consisting of the first and the second order strain gradients theories (FSG and SSG) were applied in order to develop the governing equations of static and free vibrational behavior of beam structures. The governing equations in orders of six and eight were constructed for FSG and SSG theories, respectively. Therefore, higher order or in other words non-classical boundary conditions (HOBCs or NCBCs) came into play in addition to the classical ones (CBCs). Some explanations were presented about the concept of the non-classical boundary conditions. Analytical and finite element (FE) approaches were employed to solve the governing equations. The analytical solutions were utilized in validation and convergence study of FE results. Comparisons were made with the relevant data reported in the open literature; however, to the best of the authors' knowledge, few references have been published on SSG theory and HOBCs. In the numerical studies, the effects of applying different combinations of CBCs and HOBCs to the static and free vibration behaviors of the beam were investigated. Moreover, the impacts of non-classical elastic constants and the beam size on its behavior were also studied.
Additional Results of Glaze Icing Scaling in SLD Conditions
NASA Technical Reports Server (NTRS)
Tsao, Jen-Ching
2016-01-01
This presentation reports results from recent icing scaling tests in NASA Glenn Icing Research Tunnel (IRT) to evaluate how well the scaling method recommended for Appendix C conditions might apply to SLD conditions.
Towards an effective non-reflective boundary condition for computational aeroacoustics
NASA Astrophysics Data System (ADS)
Gill, James; Fattah, Ryu; Zhang, Xin
2017-03-01
A generic, non-reflective zonal transverse characteristic boundary condition is described for computational aeroacoustics, which shows superior performance to existing non-reflective boundary conditions for two-dimensional linearized Euler simulations. The new condition is based on a characteristic non-reflective method, and also contains optimised use of transverse characteristic terms and a zonal forcing region. The performance of the new method and several existing non-reflective acoustic boundary conditions is quantitatively compared using a plane wave test case. The performance of buffer zone, perfectly matched layer, far-field, and characteristic non-reflective methods is compared, following an optimisation of the tuneable parameters in each method to give best performance. The study uses a high-order linearised Euler equation solver to assess non-reflective boundary conditions with a variety of cases. The performance is compared for downstream travelling acoustic waves with varying frequency and incident angle, and at various Mach numbers. The current study includes a more comprehensive evaluation than previous studies which used constant values of tuneable parameters or qualitative assessment methods. The new zonal transverse characteristic boundary condition is shown to give improved performance in comparison to the other tested outflow boundary conditions for two-dimensional linearized Euler simulations, and is also shown to give good performance when used as an inflow condition.
Geomagnetic Secular Variation Prediction with Thermal Heterogeneous Boundary Conditions
NASA Technical Reports Server (NTRS)
Kuang, Weijia; Tangborn, Andrew; Jiang, Weiyuan
2011-01-01
It has long been conjectured that thermal heterogeneity at the core-mantle boundary (CMB) affects the geodynamo substantially. The observed two pairs of steady and strong magnetic flux lobes near the Polar Regions and the low secular variation in the Pacific over the past 400 years (and perhaps longer) are likely the consequences of this CMB thermal heterogeneity. There are several studies on the impact of the thermal heterogeneity with numerical geodynamo simulations. However, direct correlation between the numerical results and the observations is found very difficult, except qualitative comparisons of certain features in the radial component of the magnetic field at the CMB. This makes it difficult to assess accurately the impact of thermal heterogeneity on the geodynamo and the geomagnetic secular variation. We revisit this problem with our MoSST_DAS system in which geomagnetic data are assimilated with our geodynamo model to predict geomagnetic secular variations. In this study, we implement a heterogeneous heat flux across the CMB that is chosen based on the seismic tomography of the lowermost mantle. The amplitude of the heat flux (relative to the mean heat flux across the CMB) varies in the simulation. With these assimilation studies, we will examine the influences of the heterogeneity on the forecast accuracies, e.g. the accuracies as functions of the heterogeneity amplitude. With these, we could be able to assess the model errors to the true core state, and thus the thermal heterogeneity in geodynamo modeling.
Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation
NASA Astrophysics Data System (ADS)
Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.
2001-12-01
We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating 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 “nonreflecting 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 nondeteriorating 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-dimensional 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 unmodified scheme. In this 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 ABC algorithm.
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.
NASA Astrophysics Data System (ADS)
Aziz, Abdul
2010-03-01
In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non-similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this fundamental problem for the case of a constant heat flux boundary condition has remained unexplored in the literature. It was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.
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.
High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions
NASA Astrophysics Data System (ADS)
Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake
2017-03-01
We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.
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.
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.
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…
NASA Astrophysics Data System (ADS)
Vitillaro, Enzo
2017-03-01
The aim of this paper is to study the problem u_{tt}-Δ u+P(x,u_t)=f(x,u) quad & in (0,∞)×Ω, u=0 & on (0,∞)× Γ_0, u_{tt}+partial_ν u-Δ_Γ u+Q(x,u_t)=g(x,u)quad & on (0,∞)× Γ_1, u(0,x)=u_0(x),quad u_t(0,x)=u_1(x) & in overline Ω, where {Ω} is a open bounded subset of R^N with C 1 boundary ({N ≥ 2}), {Γ = partialΩ}, {(Γ0,Γ1)} is a measurable partition of {Γ}, {Δ_{Γ}} denotes the Laplace-Beltrami operator on {Γ}, {ν} is the outward normal to {Ω}, and the terms P and Q represent nonlinear damping terms, while f and g are nonlinear subcritical perturbations. In the paper a local Hadamard well-posedness result for initial data in the natural energy space associated to the problem is given. Moreover, when {Ω} is C 2 and {overline{Γ0} \\cap overline{Γ1} = emptyset}, the regularity of solutions is studied. Next a blow-up theorem is given when P and Q are linear and f and g are superlinear sources. Finally a dynamical system is generated when the source parts of f and g are at most linear at infinity, or they are dominated by the damping terms.
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.
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.
Simulating thermal boundary conditions of spin-lattice models with weighted averages
NASA Astrophysics Data System (ADS)
Wang, Wenlong
2016-07-01
Thermal boundary conditions have played an increasingly important role in revealing the nature of short-range spin glasses and is likely to be relevant also for other disordered systems. Diffusion method initializing each replica with a random boundary condition at the infinite temperature using population annealing has been used in recent large-scale simulations. However, the efficiency of this method can be greatly suppressed because of temperature chaos. For example, most samples have some boundary conditions that are completely eliminated from the population in the process of annealing at low temperatures. In this work, I study a weighted average method to solve this problem by simulating each boundary conditions separately and collect data using weighted averages. The efficiency of the two methods is studied using both population annealing and parallel tempering, showing that the weighted average method is more efficient and accurate.
Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph; Valentino, Alessandro
2013-07-01
We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively.
On Korn's first inequality for tangential or normal boundary conditions with explicit constants
NASA Astrophysics Data System (ADS)
Bauer, Sebastian; Pauly, Dirk
2016-12-01
We will prove that for piecewise smooth and concave domains Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant square root of 2.
An analysis of boundary condition effects on the thermomechanical modeling of the FSW process
NASA Astrophysics Data System (ADS)
Guedoiri, A.; Moufki, A.; Favier, V.; Zahrouni, H.
2011-01-01
The aim of the present work is to study the influence of thermal boundary conditions on the simulation of friction stir welding process "FSW". Generally, dimensions of the workpieces to be welded are very large and a very small zone surrounding the welding tool is modeled for the thermomechanical study of the process. This area, named box, should be small enough to reduce the computation time and large enough to minimize effects of boundary conditions. It is well known that during welding, the mixing zone is closed arround the tool; it is easily identified by analyzing the velocity field which is complex in contact interface with the tool and which tends rapidly to the tool traverse speed far from the tool. In the thermal analysis, the boundary conditions are not obvious since they depend on the welding parameters, on the workpiece dimensions and on its vicinity. We propose in this study a numerical strategy for determining the thermal boundary conditions on the box.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A 1-D implementation for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique.
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.
2015-05-18
Towards direct simulations of counterflow flames with consistent numerical differential-algebraic boundary conditions The views, opinions and/or...Research Triangle Park, NC 27709-2211 counterflow laminar flame model REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR...simulations of counterflow flames with consistent numerical differential-algebraic boundary conditions Report Title A new approach for the
Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes
2012-07-01
and Grossman advocate a curvature corrected symmetry condition for an inviscid wall [3]. Balakrishnan and Fernandez advocate a variety of other methods...boundary source terms is straightforward, generally requiring much less algebraic manipulation than interior source terms. A number of test cases...Meeting, Reno, NV, January 1986. [3] A. Dadone and B. Grossman . Surface boundary conditions for the numerical solution of the euler equations. AIAA
Sobolev type equations of time-fractional order with periodical boundary conditions
NASA Astrophysics Data System (ADS)
Plekhanova, Marina
2016-08-01
The existence of a unique local solution for a class of time-fractional Sobolev type partial differential equations endowed by the Cauchy initial conditions and periodical with respect to every spatial variable boundary conditions on a parallelepiped is proved. General results are applied to study of the unique solvability for the initial boundary value problem to Benjamin-Bona-Mahony-Burgers and Allair partial differential equations.
On pressure and velocity boundary conditions for the lattice Boltzmann BGK model
Zou, Q. |; He, X.
1997-06-01
Pressure (density) and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model [J. Stat. Phys. {bold 81}, 35 (1995)] the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure (density) difference. The half-way wall bounceback boundary condition is also used with the pressure (density) inlet/outlet conditions proposed in this paper and in Phys. Fluids {bold 8}, 2527 (1996) to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. {copyright} {ital 1997 American Institute of Physics.}
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 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 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.
ALmost EXact boundary conditions for transient Schrödinger–Poisson system
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016-05-15
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.
Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions
2007-09-01
ER, barp, shape, error, a_cp, modep , ap, % modelabelp, FOMABClabelp, FOMPLUSlabelp % abc_con, abc_conT % ABC, base % plus_con, plus_conT...error = round(rel_freqERROR(ER:ER+15)*100)/100; a_cp = 1; for modep = 1:3 %3 sets of modes per boundry condition ap = [a_cp...int2str(a_cp:a_cp+4); FOMABC = int2str(FOM_ABC5per(intervelp+ modep )); FOMABClabelp = sprintf(’System FOM = %s’, FOMABC
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.
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.
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.
Instanton-dyon ensembles with quarks with modified boundary conditions
NASA Astrophysics Data System (ADS)
Larsen, Rasmus; Shuryak, Edward
2016-11-01
We modify the quark periodicity condition on the thermal circle by the introduction of some phases—known also as "flavor holonomies"— different quark flavors. These phases provide a valuable tool, to be used for better understanding of deconfinement and chiral restoration phase transitions: by changing them, one can dramatically modify both phase transitions. In the language of instanton constituents—instanton-dyons or monopoles—changing the quark periodicity condition has a very direct explanation: the interplay of flavor and color holonomies can switch topological zero modes between various dyon types. The model we will study in detail, the so-called ZN c-symmetric QCD model with equal number of colors and flavors Nc=Nf=2 and special arrangement of flavor and color holonomies, ensures the "most democratic" setting, in which each quark flavor and each dyon type are in one-to-one correspondence. The usual QCD has the opposite "most exclusive" arrangement: all quarks are antiperiodic and, thus, all zero modes fall on only one—twisted or L —dyon type. As we show by ensemble simulation, deconfinement and chiral restoration phase transitions in these two models are dramatically different. In the usual QCD, both are smooth crossovers: but in the case of the Z2-symmetric model, deconfinement becomes a strong first-order transition, while chiral symmetry remains broken for all dyon densities studied. These results are in good correspondence with those from recent lattice simulations.
Impact of Boundary Conditions on Pumping in a Fully Bounded Aquifer
NASA Astrophysics Data System (ADS)
Lu, C.; Xin, P.; Li, L.; Luo, J.
2014-12-01
The flow field may be affected by aquifer boundaries, when pumping in a small-scale aquifer or a long term pumping activity is required especially under a large pumping rate. Using potential theory, the image-well method and superposition principle, analytical solutions are derived for pumping in a fully bounded rectangular aquifer with five different boundary condition scenarios: (1) one constant-head boundary (in horizontal direction in plan view) and three impermeable boundaries, (2) two parallel constant-head boundaries (in horizontal direction) and two parallel impermeable boundaries (in vertical direction), (3) two pairs of orthogonal impermeable and constant-head boundaries, (4) three constant-head boundaries and one impermeable boundary, and (5) four constant-head boundaries. For each scenario, closed-form expressions are derived in three different types: (1) summation of the series in horizontal and vertical directions; (2) summation of the series in horizontal direction and exact potential in vertical direction, and (3) summation of the series in vertical direction and exact potential in horizontal direction. It is found that all the three types of closed-form expressions can produce an accurate potential for scenarios (3)-(5). For scenarios (1) and (2), by contrast, the third type closed-form expression can yield an accurate solution, while the second type close-form expression always generates an unacceptable solution. Therefore, the third type closed-form is recommended to solve the potential of a flow field created by a pumping well subjected to multiple impermeable and/or constant-head boundary conditions, due to its accuracy as well as computational efficiency.
Small-charge underwater explosion bubble experiments under various boundary conditions
NASA Astrophysics Data System (ADS)
Cui, P.; Zhang, A. M.; Wang, S. P.
2016-11-01
Small-charge underwater explosion experiments were performed to investigate bubbles subjected to gravity and various boundary conditions, including single boundary (free surface and rigid wall boundary), combined boundaries of free surface and solid wall, solid wall boundaries with a circular opening, and resilient wall boundaries. With high speed camera and pressure sensors, the behavior of explosion bubbles was studied and features of associated pressure pulses were analyzed. Detailed image analysis on the final stages of bubble collapse was carried out and revealed a possible explanation for the weakening of pressure waves at bubble rebound as the bubble approaches a wall boundary. Certain features also indicate that the magnitude of the pressure peaks induced by bubble rebound is related to the shape of the bubble shape during collapse. Pressure pulses arising from the two types of bubble behavior, specifically the collision of an annular jet and the impact of a jet with the wall boundary, were measured. Other curious types of bubble behavior were found, including jetting induced by suction when a bubble collapses covering a circular opening on a solid wall, and bubble splitting in interaction with a resilient wall boundary.
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.
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.
Nonreflecting boundary conditions for the complete unsteady transonic small-disturbance equation
NASA Astrophysics Data System (ADS)
Whitlow, W., Jr.; Seidel, D. A.
1985-02-01
Nonreflecting far-field boundary conditions that are consistent with the complete transonic small-disturbance (TSD) equations are derived. They are implemented in a new code for solving the complete TSD equation and are tested for a harmonically oscillating NACA 64A010 airfoil in transonic flow and for a flat-plate airfoil with a pulse in the angle of attack. Using the new boundary conditions on a relatively small grid, solutions for the airfoil that are obtained that agree with large-grid calculations, resulting in a 44 percent savings in computer time. Frequency responses for the flat plate show that most of the disturbances incident on the computational boundaries are absorbed by the boundary conditions.
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.
Velocity and magnetic field measurements of Taylor plumes in SSX under different boundary conditions
NASA Astrophysics Data System (ADS)
Kaur, Manjit; Brown, M. R.; Han, J.; Shrock, J. E.; Schaffner, D. A.
2016-10-01
The SSX device has been modified by the addition of a 1 m long glass extension for accommodating pulsed theta pinch coils. The Taylor plumes are launched from a magnetized plasma gun and flow to an expansion volume downstream. The time of flight (TOF) measurements of these plumes are carried out using a linear array of Ḃ probes (separated by 10cm). TOF of the plasma plumes from one probe location to the next is determined by direct comparison of the magnetic field structures as well as by carrying out a cross-correlation analysis. With the glass boundary, the typical velocity of the Taylor plumes is found to be 25km /s , accompanied by a fast plasma (>= 50km /s) at the leading edge. Magnetic field embedded in the Taylor plumes is measured in the expansion chamber using a three-dimensional array of Ḃ probes and is found to be 700G . Some flux conservation of the Taylor plumes is provided by using a resistive (soak time 3 μs) and a mesh (soak time 170 μs > discharge time) liner around the glass tube for improving the downstream Taylor state velocity as well as the magnetic field. The results from these different boundary conditions will be presented. Work supported by DOE OFES and ARPA-E ALPHA programs.
Critical dense polymers with Robin boundary conditions, half-integer Kac labels and Z4 fermions
NASA Astrophysics Data System (ADS)
Pearce, Paul A.; Rasmussen, Jørgen; Tipunin, Ilya Yu.
2014-12-01
For general Temperley-Lieb loop models, including the logarithmic minimal models LM (p ,p‧) with p ,p‧ coprime integers, we construct an infinite family of Robin boundary conditions on the strip as linear combinations of Neumann and Dirichlet boundary conditions. These boundary conditions are Yang-Baxter integrable and allow loop segments to terminate on the boundary. Algebraically, the Robin boundary conditions are described by the one-boundary Temperley-Lieb algebra. Solvable critical dense polymers is the first member LM (1 , 2) of the family of logarithmic minimal models and has loop fugacity β = 0 and central charge c = - 2. Specialising to LM (1 , 2) with our Robin boundary conditions, we solve the model exactly on strips of arbitrary finite size N and extract the finite-size conformal corrections using an Euler-Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double row transfer matrices. This inversion identity is established directly in the Temperley-Lieb algebra. We classify the eigenvalues of the double row transfer matrices using the physical combinatorics of the patterns of zeros in the complex spectral parameter plane and obtain finitised characters related to spaces of coinvariants of Z4 fermions. In the continuum scaling limit, the Robin boundary conditions are associated with irreducible Virasoro Verma modules with conformal weights Δ r , s -1/2 =1/32 (L2 - 4) where L = 2 s - 1 - 4 r, r ∈ Z, s ∈ N. These conformal weights populate a Kac table with half-integer Kac labels. Fusion of the corresponding modules with the generators of the Kac fusion algebra is examined and general fusion rules are proposed.
Open boundary conditions for internal gravity wave modelling using polarization relations
NASA Astrophysics Data System (ADS)
Marsaleix, Patrick; Ulses, Caroline; Pairaud, Ivane; Herrmann, Marine Julie; Floor, Jochem Willem; Estournel, Claude; Auclair, Francis
This paper proposes an original approach of the open boundary condition problem, within the framework of internal hydrostatic wave theory. These boundary conditions are based on the relations of polarization of internal waves. The method is presented progressively, beginning with a simple case (non-rotating regime, propagation direction normal to the open boundary), ending with a more general situation (rotating regime, multimodal & multi-dimensional propagations and variable background field). In the non-rotating case and as far as we assume that the direction of propagation is locally normal to the open boundary, the so-called PRM (polarization relation method) scheme can be seen as a three-dimensional version of the barotropic Flather boundary conditions. The discrete form of the scheme is detailed. Numerical stability issues proper to leap-frog time stepping are in particular discussed. It is shown that errors on phase speed prescribed in the boundary conditions can notably deteriorate radiation properties. The normal mode approach is introduced to identify coherent structures of propagation and their corresponding phase speed. A simple and robust multi-dimensional propagation scheme can easily be derived from polarization relations. The rotating case is more difficult but it is possible, to some extent, to get around the dependency of phase speed on wave frequency and to keep the non-rotating formulation of the PRM conditions almost unchanged. The PRM scheme being applied to field anomalies, the question of the background reference state is addressed. The latter can be used to introduce incoming waves across the open boundaries or, alternatively, to represent the low-frequency variability of the model itself. The consistency of the pressure and tracer boundary conditions is finally discussed.
Computing Green's function of elasticity in a half-plane with impedance boundary condition
NASA Astrophysics Data System (ADS)
Durán, Mario; Godoy, Eduardo; Nédélec, Jean-Claude
2006-12-01
This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Durán et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate Gˆ as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in R (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. To cite this article: M. Durán et al., C. R. Mecanique 334 (2006).
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.
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.
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.
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 inches and the scale model had a chord of 21 inches. Reference tests were run with airspeeds of 100 and 130.3 knots and with MVD's of 85 and 170 microns. Two scaling methods were considered. One was based on the modified Ruff method with scale velocity found by matching the Weber number W (sub eL). 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 non-dimensional water-film thickness expression and the film Weber number W (sub ef). All tests were conducted at 0 degrees angle of arrival. Results will be presented for stagnation freezing fractions of 0.2 and 0.3. For non-dimensional reference and scale ice shape comparison, a new post-scanning ice shape digitization procedure was developed for extracting 2-dimensional ice shape profiles at any selected span-wise location from the high fidelity 3-dimensional scanned ice shapes obtained in the IRT.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
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 incompability 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 inevita bly 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. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
Green's function of the heat equation with periodic and antiperiodic boundary conditions
NASA Astrophysics Data System (ADS)
Imanbaev, Nurlan; Erzhanov, Nurzhan
2016-12-01
In this work a non-local initial-boundary value problem for a non-homogeneous one-dimensional heat equation is con-sidered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A non-local periodic boundary condition with respect to 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 non-local initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
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.
NASA Astrophysics Data System (ADS)
FRIKHA, S.; GAUDIN, M.; COFFIGNAL, G.
2001-03-01
There is an increasing interest in experimental analysis of in-operation structures where a part of the boundary conditions is poorly known. This concerns particularly the case of coupled systems where some complex physical phenomena make the behaviour of both the system and its connectivity dependent on the functioning conditions. In this context, this paper presents a new frequency approach for parametric structural updating in the vibration and acoustic fields. This methodology is developed here in the case of piping systems. It follows the boundary conditions identification method previously developed by the authors. A boundary conditions error is presented and its efficiency to translate structural parameters error is shown. Thus, the proposed approach allows performing the identification of some unknown boundary conditions and, simultaneously, updating the model of the tested structure. The pertinence of a frequency choice criteria based on the smallest singular value of the solved system during the identification of the boundary conditions is shown. It specifically allows avoiding the bands of critical frequencies. The developed updating technique is tested with two actual cases: a laboratory test case and an industrial example.
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.
NASA Astrophysics Data System (ADS)
Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan
2017-02-01
We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.
Reflecting boundary conditions for classical molecular dynamics simulations of nonideal plasmas
NASA Astrophysics Data System (ADS)
Lavrinenko, Ya S.; Morozov, I. V.; Valuev, I. A.
2016-11-01
The influence of boundary conditions on results of the classical molecular dynamics simulations of nonideal electron-ion plasma is analyzed. A comprehensive study is performed for the convergence of per-particle potential energy and pressure with the number of particles using both the nearest image method (periodic boundaries) and harmonic reflective boundaries. As a result an error caused by finiteness of the simulation box is estimated. Moreover the electron oscillations given by the spectra of the current autocorrelation function are analyzed for both types of the boundary conditions. Nonideal plasmas with the nonideality parameter in range 0.26-2.6 is considered. To speed up the classical molecular dynamics simulations the graphics accelerators code is used.
Buckling of stiffened shells with random initial imperfections, thickness and boundary conditions
NASA Technical Reports Server (NTRS)
Elishakoff, I.; Arbocz, J.; Starnes, J. H., Jr.
1992-01-01
The paper proposes a method to predict the buckling load of stiffened, composite shells reliably, where besides the randomness of the initial geometric imperfections also a random variation of the wall thickness and the uncertainty of the precise edge conditions is included in the analysis. The introduction of the variability in the thickness from shell to shell, in an ensemble of nominally identical shells, produced by the same manufacturing procedure is motivated by the growing realization of the importance of thickness variations by composite shells. The probabilistic treatment of the boundary conditions is dictated by the fact that 'true', deterministically specified boundary conditions are unlikely to be realizable in practice.
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.
Far Field Numerical Boundary Conditions for Internal and Cascade Flow Computations
1988-11-01
for the treatment of the fa field boundary conditions, Verhoff and O’Neil (1984), to more ,,eneral formulations of the Euler equations and to cascade...4eometries. linearized solutions ,-f the Euler equations are developed for the perturbations from the tiniform free stream, for ducts and cascades...Fourier expansion in the direction al on tlie inlet or exit boundaries. Resul obtained from an Euler code are shown ftor duCts and cascadels , rompa rin
2012-12-01
then et∗ →0 as hl →0. This is essentially modifying the grid to include the point zb, and that modification could be different for each fixed x. But in...convergence rate, a rectangu- lar grid is used over the physical space. When the physical domain does not conform to the rectangular grid , appropriate...boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary. A related
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.
Spectrum of one BVP with discontinuities and spectral parameter in the boundary conditions
NASA Astrophysics Data System (ADS)
Aydemir, K.; Mukhtarov, O. Sh.; Olǧar, H.
2016-04-01
The aim this of paper is to investigate the spectral problem for the equation -(pu')'(x) + q(x)u(x) = λu(x), under eigen-dependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we esthabilish some properties of the eigenvalues and eigenfunction.
On the Boundary Conditions at an Oscillating Contact Line: A Physical/Numerical Experimental Program
NASA Technical Reports Server (NTRS)
Perlin, Marc; Schultz, William W.
1996-01-01
We will pursue an improved physical understanding and mathematical model for the boundary condition at an oscillating contact line at high Reynolds number. We expect that the body force is locally unimportant for earth-based systems, and that the local behavior may dominate the mechanics of partially-filled reservoirs in the microgravity environment. One important space-based application for this contact-line study is for Faraday-waves. Oscillations in the direction of gravity (or acceleration) can dominate the fluid motion during take-off and reentry with large steady-state accelerations and in orbit, where fluctuations on the order of 10(exp -4)g occur about a zero mean. Our experience with Faraday waves has shown them to be 'cleaner' than those produced by vertical or horizontal oscillation of walls. They are easier to model analytically or computationally, and they do not have strong vortex formation at the bottom of the plate. Hence many, if not most, of the experiments will be performed in this manner. The importance of contact lines in the microgravity environment is well established. We will compare high resolution measurements of the velocity field (lO micro-m resolution) using particle-tracking and particle-image velocimetry as the fluid/fluid interface is approached from the lower fluid. The spatial gradients in the deviation provide additional means to determine an improved boundary condition and a measure of the slip region. Dissipation, the size of the eddy near the contact line, and hysteresis will be measured and compare to linear and nonlinear models of viscous and irrotational but dissipative models.
Boundary conditions for plasma fluid models at the magnetic presheath entrance
Loizu, J.; Ricci, P.; Halpern, F. D.; Jolliet, S.
2012-12-15
The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with T{sub i} Much-Less-Than T{sub e} and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v{sub ||i}, v{sub ||e}, n, {phi}, T{sub e}, and for the vorticity {omega}={nabla}{sub Up-Tack }{sup 2}{phi}. The effects of E Multiplication-Sign B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.
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.
Integral Method of Boundary Characteristics in Solving the Stefan Problem: Dirichlet Condition
NASA Astrophysics Data System (ADS)
Kot, V. A.
2016-09-01
The integral method of boundary characteristics is considered as applied to the solution of the Stefan problem with a Dirichlet condition. On the basis of the multiple integration of the heat-conduction equation, a sequence of identical equalities with boundary characteristics in the form of n-fold integrals of the surface temperature has been obtained. It is shown that, in the case where the temperature profile is defined by an exponential polynomial and the Stefan condition is not fulfilled at a moving interphase boundary, the accuracy of solving the Stefan problem with a Dirichlet condition by the integral method of boundary characteristics is higher by several orders of magnitude than the accuracy of solving this problem by other known approximate methods and that the solutions of the indicated problem with the use of the fourth-sixth degree polynomials on the basis of the integral method of boundary characteristics are exact in essence. This method surpasses the known numerical methods by many orders of magnitude in the accuracy of calculating the position of the interphase boundary and is approximately equal to them in the accuracy of calculating the temperature profile.
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.
Improving variational mass-consistent models of hydrodynamic flows via boundary conditions
NASA Astrophysics Data System (ADS)
Núñez, M. A.
2012-04-01
Variational mass-consistent models for the velocity field v have been used by mesoscale meteorological community to modeling the wind field from an observed field v 0 in a bounded region Ω with boundary Γ. Variational calculus reduces the problem to the solution of an elliptic equation for a Lagrange multiplier λ subject to Dirichlet Boundary Condition (DBC) on flow-through boundaries. In this work, it is shown that DBC decreases the regularity of λ and this in turn decreases the accuracy with which the velocity field satisfies the mass-balance. The boundary condition (BC) v · n = v T · ngiven by the true field v T on the whole boundary Γ, leads only to a Neumann boundary condition (NBC) for λ. Approximations of this BC are studied. Analytic and numerical results show that the velocity field U 0 obtained from v 0 by direct integration of the continuity equation, yields a NBC that improves significantly the fields obtained with DBC's.
NASA Astrophysics Data System (ADS)
Dubail, J.; Santachiara, R.; Emig, T.
2017-03-01
Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szegö formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface renormalization group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.
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.
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.
Scale effect of slip boundary condition at solid–liquid interface
NASA Astrophysics Data System (ADS)
Nagayama, Gyoko; Matsumoto, Takenori; Fukushima, Kohei; Tsuruta, Takaharu
2017-03-01
Rapid advances in microelectromechanical systems have stimulated the development of compact devices, which require effective cooling technologies (e.g., microchannel cooling). However, the inconsistencies between experimental and classical theoretical predictions for the liquid flow in microchannel remain unclarified. Given the larger surface/volume ratio of microchannel, the surface effects increase as channel scale decreases. Here we show the scale effect of the boundary condition at the solid–liquid interface on single-phase convective heat transfer characteristics in microchannels. We demonstrate that the deviation from classical theory with a reduction in hydraulic diameters is due to the breakdown of the continuum solid–liquid boundary condition. The forced convective heat transfer characteristics of single-phase laminar flow in a parallel-plate microchannel are investigated. Using the theoretical Poiseuille and Nusselt numbers derived under the slip boundary condition at the solid–liquid interface, we estimate the slip length and thermal slip length at the interface.
Scale effect of slip boundary condition at solid–liquid interface
Nagayama, Gyoko; Matsumoto, Takenori; Fukushima, Kohei; Tsuruta, Takaharu
2017-01-01
Rapid advances in microelectromechanical systems have stimulated the development of compact devices, which require effective cooling technologies (e.g., microchannel cooling). However, the inconsistencies between experimental and classical theoretical predictions for the liquid flow in microchannel remain unclarified. Given the larger surface/volume ratio of microchannel, the surface effects increase as channel scale decreases. Here we show the scale effect of the boundary condition at the solid–liquid interface on single-phase convective heat transfer characteristics in microchannels. We demonstrate that the deviation from classical theory with a reduction in hydraulic diameters is due to the breakdown of the continuum solid–liquid boundary condition. The forced convective heat transfer characteristics of single-phase laminar flow in a parallel-plate microchannel are investigated. Using the theoretical Poiseuille and Nusselt numbers derived under the slip boundary condition at the solid–liquid interface, we estimate the slip length and thermal slip length at the interface. PMID:28256536
Perfectly matched layer absorbing boundary condition for nonlinear two-fluid plasma equations
NASA Astrophysics Data System (ADS)
Sun, X. F.; Jiang, Z. H.; Hu, X. W.; Zhuang, G.; Jiang, J. F.; Guo, W. X.
2015-04-01
Numerical instability occurs when coupled Maxwell equations and nonlinear two-fluid plasma equations are solved using finite difference method through parallel algorithm. Thus, a perfectly matched layer (PML) boundary condition is set to avoid the instability caused by velocity and density gradients between vacuum and plasma. A splitting method is used to first decompose governing equations to time-dependent nonlinear and linear equations. Then, a proper complex variable is used for the spatial derivative terms of the time-dependent nonlinear equation. Finally, with several auxiliary function equations, the governing equations of the absorbing boundary condition are derived by rewriting the frequency domain PML in the original physical space and time coordinates. Numerical examples in one- and two-dimensional domains show that the PML boundary condition is valid and effective. PML stability depends on the absorbing coefficient and thickness of absorbing layers.
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.
Damping solitary wave under the second and third boundary condition of a viscous plasma
NASA Astrophysics Data System (ADS)
Li, G.; Ren, Y.-Q.
2017-02-01
In this paper, the solitary waves of a viscous plasma confined in a cylindrical pipe is investigated under two types of boundary condition. By using the reductive perturbation theory, a quasi-KdV equation is derived and a damping solitary wave is obtained. It is found that the damping rate increases with the viscosity coefficient of the plasma ν ' increasing and the radius of the cylindrical pipe R decreasing for second and third boundary condition. The magnitude of the damping rate is also dominated by boundary condition type. From the fact that the amplitude reduces rapidly when R approaches zero or ν ' approaches infinite, we confirm the existence of a damping solitary wave.
Scale effect of slip boundary condition at solid-liquid interface.
Nagayama, Gyoko; Matsumoto, Takenori; Fukushima, Kohei; Tsuruta, Takaharu
2017-03-03
Rapid advances in microelectromechanical systems have stimulated the development of compact devices, which require effective cooling technologies (e.g., microchannel cooling). However, the inconsistencies between experimental and classical theoretical predictions for the liquid flow in microchannel remain unclarified. Given the larger surface/volume ratio of microchannel, the surface effects increase as channel scale decreases. Here we show the scale effect of the boundary condition at the solid-liquid interface on single-phase convective heat transfer characteristics in microchannels. We demonstrate that the deviation from classical theory with a reduction in hydraulic diameters is due to the breakdown of the continuum solid-liquid boundary condition. The forced convective heat transfer characteristics of single-phase laminar flow in a parallel-plate microchannel are investigated. Using the theoretical Poiseuille and Nusselt numbers derived under the slip boundary condition at the solid-liquid interface, we estimate the slip length and thermal slip length at the interface.
Euler calculations with embedded Cartesian grids and small-perturbation boundary conditions
NASA Astrophysics Data System (ADS)
Liao, W.; Koh, E. P. C.; Tsai, H. M.; Liu, F.
2010-05-01
This study examines the use of stationary Cartesian mesh for steady and unsteady flow computations. The surface boundary conditions are imposed by reflected points. A cloud of nodes in the vicinity of the surface is used to get a weighted average of the flow properties via a gridless least-squares technique. If the displacement of the moving surface from the original position is typically small, a small-perturbation boundary condition method can be used. To ensure computational efficiency, multigrid solution is made via a framework of embedded grids for local grid refinement. Computations of airfoil wing and wing-body test cases show the practical usefulness of the embedded Cartesian grids with the small-perturbation boundary conditions approach.
NASA Astrophysics Data System (ADS)
Thoraval, C.; Richards, M. A.
1997-10-01
The authors address several of the most straightforward problems inherent in geoid modelling, namely the issues of viscosity structure resolution, uncertainties in appropriate boundary conditions, and differences among mantle heterogeneity models. A robust feature of all models is a lower-mantle viscosity at least a factor of 30 greater than that of the upper mantle, but there is little resolution with regard to finer details such as lithospheric or uppermost mantle ("low-viscosity zone") viscosity. Ironically, free-slip boundary conditions result in the best fits to the geoid in all cases, but all boundary conditions exhibit predictable trade-offs with the uppermost-mantle viscosity. Models with a single viscosity layer representing the lower mantle yield similar dynamic topography estimates of the order of 700-1000 m in amplitude, regardless of the finer details of upper-mantle viscosity structure, boundary conditions or input heterogeneity models. Comparing mantle heterogeneity models based on two independent seismological determinations (Harvard and Berkeley models) and on the history of subduction, the authors find that these models are virtually indistinguishable regarding inferences of mantle viscosity structure and amplitude of dynamic topography, and in terms of the effects of different boundary conditions. Uncertainties concerning which type of boundary condition is appropriate are much more important than which mantle heterogeneity model is chosen. Given other uncertainties in modelling the geoid, particularly the strong effects due to lateral viscosity variations for intermediate (<10,000 km) wavelengths, the authors conclude that the class of dynamic geoid models explored so far cannot reliably elucidate the details of upper-mantle viscosity structure.
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.
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.
Effect of altered boundary conditions on GCM studies of the climate of the last glacial maximum
Hyde, W.T.; Peltier, W.R.
1993-05-21
The authors address a problem discovered recently with global climate model results for the last glacial maximum. Bard, et. al. pointed out a mismatch in boundary conditions entered into the model. Ice sheet conditions were derived from CLIMAP based on a time 18000 radiocarbon years ago. It was assumed that radiocarbon and sidereal dates coincide. However it was recently shown that the sidereal data of the last glacial maximum is nearer 21kbp. The authors perform model calculations to attempt to evaluate the seriousness of this mismatch in terms of calculated results from the global climate model runs for the last glacial maximum. The authors find that one result of the timing mismatch is a sizable difference in northern hemisphere summer and Eurasian winter climates. These changes should have a major impact on circulation patterns in the GCM simulations. In addition new ice sheet model programs are available now which appear to improve on CLIMAP models. The authors urge that these GCM simulations be rerun.
42 CFR 88.17 - Addition of health conditions to the list of WTC-related health conditions.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 1 2013-10-01 2013-10-01 false Addition of health conditions to the list of WTC... HEALTH PROGRAM § 88.17 Addition of health conditions to the list of WTC-related health conditions. (a) Any interested party may petition the WTC Program Administrator to add a condition to the list of...
42 CFR 88.17 - Addition of health conditions to the list of WTC-related health conditions.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 42 Public Health 1 2014-10-01 2014-10-01 false Addition of health conditions to the list of WTC... HEALTH PROGRAM § 88.17 Addition of health conditions to the list of WTC-related health conditions. (a) Any interested party may petition the WTC Program Administrator to add a condition to the list of...
42 CFR 88.17 - Addition of health conditions to the list of WTC-related health conditions.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 42 Public Health 1 2012-10-01 2012-10-01 false Addition of health conditions to the list of WTC... HEALTH PROGRAM § 88.17 Addition of health conditions to the list of WTC-related health conditions. (a) Any interested party may petition the WTC Program Administrator to add a condition to the list of...
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.
NASA Astrophysics Data System (ADS)
Ansari, R.; Sahmani, S.; Rouhi, H.
2011-02-01
Eringen's nonlocality is incorporated into the shell theory to include the small-scale effects on the axial buckling of single-walled carbon nanotubes (SWCNTs) with arbitrary boundary conditions. To this end, the Rayleigh-Ritz solution technique is implemented in conjunction with the set of beam functions as modal displacement functions. Then, molecular dynamics simulations are employed to obtain the critical buckling loads of armchair and zigzag SWCNTs, the results of which are matched with those of nonlocal shell model to extract the appropriate values of nonlocal parameter. It is found that in contrast to the chirality, boundary conditions have a considerable influence on the proper values of nonlocal parameter.
Traffic flow of a roundabout crossing with an open boundary condition
NASA Astrophysics Data System (ADS)
Bai, Ke-Zhao; Tan, Hui-Li; Kong, Ling-Jiang; Liu, Mu-Ren
2010-04-01
This paper presents a cellular automaton traffic flow model with an open boundary condition to describe the traffic flow at a roundabout crossing with an inner roundabout lane and an outer roundabout lane. The simulation results show that the boundary condition, bottlenecks and the self-organization affect the traffic flow at the roundabout crossing. Because of the effect of bottlenecks, jams easily appear on the inner roundabout lane. To improve the capacity of the roundabout system, proper values of the enter probability α and the out probability β can be chosen.
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.
An Evaluation of Boundary Condition Specification for a Littoral Hydrodynamic Model
2011-09-01
from NCOM (blue) for 3 locations in the M2D model case. II. APPROACH Several comparisons of Delft3D model results were completed for a number...boundary conditions from OSU Tides (red) and time series boundary conditions from NCOM (blue) for 3 locations in the M2D model case. /; M2D and M3D...The M2D and M3D Delft3D applications cover approximately 33 square kilometers at a resolution of approximately 500 meters. The M2D model case is depth
NASA Astrophysics Data System (ADS)
Mácha, Václav; Tichý, Jakub
2014-10-01
We prove an L q theory result for generalized Stokes system in a {{C}^{2,1}} domain complemented with the perfect slip boundary conditions and under Φ-growth conditions. Since the interior regularity was obtained in Diening and Kaplický (Manu Math 141:336-361, 2013), a regularity up to the boundary is an aim of this paper. In order to get the main result, we use Calderón-Zygmund theory and the method developed in Caffarelli and Peral (Ann Math 130:189-213, 1989). We obtain higher integrability of the first gradient of a solution.
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.
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.
Verification Assessment of Flow Boundary Conditions for CFD Analysis of Supersonic Inlet Flows
NASA Technical Reports Server (NTRS)
Slater, John W.
2002-01-01
Boundary conditions for subsonic inflow, bleed, and subsonic outflow as implemented into the WIND CFD code are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets. Verification procedures include grid convergence studies and comparisons to analytical data. The objective is to examine errors, limitations, capabilities, and behavior of the boundary conditions. Computational studies were performed on configurations derived from a "parameterized" supersonic inlet. These include steady supersonic flows with normal and oblique shocks, steady subsonic flow in a diffuser, and unsteady flow with the propagation and reflection of an acoustic disturbance.
Bond and temperature chaos in spin glasses revealed through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Jonathan Machta Collaboration; Helmut G. Katzgraber Collaboration
Spin glasses are complex systems with rugged energy landscapes that exhibit chaotic behavior. Unfortunately, despite decades of study, there is still no clear understanding of the chaotic behavior found in these systems. The use of thermal boundary conditions has become a useful approach to study such phenomena. Here we discuss how to efficiently simulate bond and temperature chaos using thermal boundary conditions and population annealing Monte Carlo. We provide a simple scaling argument for bond and temperature chaos, and present numerical results of the scaling exponents. Similarities and differences of bond chaos and temperature chaos are also discussed. NSF DMR-120804.
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
The Sky is the Limit: Free Boundary Conditions in AdS3 Chern-Simons Theory
NASA Astrophysics Data System (ADS)
Apolo, Luis; Sundborg, Bo
We test the effects of new diffeomorphism invariant boundary terms in SL(2,R)×SL(2,R) Chern-Simons theory. The gravitational interpretation corresponds to free AdS3 boundary conditions, without restrictions on the boundary geometry. The boundary theory is the theory of a string in a target AdS3. Its Virasoro conditions can eliminate ghosts. Generalisations to SL(N,R)×SL(N,R) higher spin theories and many other questions are still unexplored.
Effects of Boundary Conditions and Flow on the Kink Instability in a Cylindrical Plasma Column
Furno, I; Intrator, T P; Lapenta, G; Dorf, L; Ryutov, D D
2007-02-06
An experimental investigation of the kink instability is presented in a linear plasma column where one end is line-tied to the plasma source, and the other end is not line-tied and therefore free to slide over the surface of the end-plate. This latter boundary condition is a result of plasma sheath resistance that insulates, at least partially, the plasma from the end-plate. The helical m = 1 kink mode is observed to grow when the plasma current exceeds a threshold and, close to the criticality, is characterized by an axial mode structure with maximum displacement at the free axial boundary. Azimuthal rotation of the mode is observed such that the helically kinked column always screws into the free axial boundary. The kink mode structure, rotation frequency and instability threshold are accurately reproduced by a recent kink theory [D. D. Ryutov, et al., Phys. Plasmas 13, 032105 (2006)], which includes axial plasma flow and one end of the plasma column that is free to move due to a perfect non-line-tying boundary condition which is experimentally verified. A brief review of the kink theory and its predictions for the boundary conditions relevant in the present experiments are presented.
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
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.
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.
A dual-pressure boundary condition for use in simulations of bifurcating conduits.
Gin, Ron; Straatman, Anthony G; Steinman, David A
2002-10-01
A dual-pressure boundary condition has been developed for computational modelling of bifurcating conduits. The condition involves the imposition of a constant pressure on one branch while adjusting iteratively the pressure on the other branch until the desired flow division is obtained. The dual-pressure condition eliminates the need for specifying fully-developed flow conditions, which thereby enables significant reduction of the outlet branch lengths. The dual-pressure condition is suitable for both steady and time-periodic simulations of laminar or turbulent flows.
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.
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.
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)
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.
On the Navier-Stokes system with the Coulomb friction law boundary condition
NASA Astrophysics Data System (ADS)
Bălilescu, Loredana; San Martín, Jorge; Takahashi, Takéo
2017-02-01
We propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier-Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two-dimensional problem and the existence of at least one solution in the three-dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method, and we present numerical simulations in two physical examples.
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
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
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
A laser Doppler system for the remote sensing of boundary layer winds in clear air conditions
NASA Technical Reports Server (NTRS)
Lawrence, T. R.; Krause, M. C.; Craven, C. E.; Morrison, L. K.; Thomson, J. A. L.; Cliff, W. C.; Huffaker, R. M.
1975-01-01
The system discussed uses a laser Doppler radar in combination with a velocity azimuth display mode of scanning to determine the three-dimensional wind field in the atmospheric boundary layer. An attractive feature of this CW monostatic system is that the ambient aerosol provides a 'sufficient' scattering target to permit operation under clear air conditions. Spatial resolution is achieved by focusing.
A prototype surface ozone concentration forecasting model system for the Eastern U.S. has been developed. The model system is consisting of a regional meteorological and a regional air quality model. It demonstrated a strong prediction dependence on its ozone boundary conditions....
2009-09-01
less forecast skill due to a coarser res- olution. Miguez- Macho and Paegle (2000) suggest that accurate initial and lateral boundary conditions for a...nondeveloping ver- sus developing systems. J. Atmos. Sci., 38, 1132–1151. Miguez- Macho , G., and J. Paegle, 2000: Sensitivity of a global forecast model
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)
Antipin, A. S.; Artem'eva, L. A.; Vasil'ev, F. P.
2017-01-01
An optimal control problem formulated as a system of linear ordinary differential equations with boundary conditions implicitly specified as a solution to a finite-dimensional minimization problem is considered. An extragradient method for solving this problem is proposed, and its convergence is studied.
Local inhomogeneities in a Robertson-Walker background. II - Flux conditions at boundary surfaces
NASA Astrophysics Data System (ADS)
Lake, K.
1980-12-01
Energy flux conditions imposed on spherical boundary surfaces are examined. The zero-flux restriction, which is the hallmark of the standard Swiss cheese type construction, is relaxed. A class of locally inhomogeneous exact solutions to the Einstein equations which admit an effectively Newtonian accretion model is discussed.
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.
Non-reflecting boundary conditions for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Abarbanel, S.; Bayliss, A.; Lustman, L.
1986-01-01
A small perturbation analysis, in the long wavelength regime, is used to obtain the downstream boundary condition for the pressure for the flow over a flat plate. The methodology is extendable to other geometries. Numerical results for high Reynolds number laminar flows show great improvement in convergence rate to steady state as well as the quality of the results.
Artificial Boundary Conditions for the Numerical Simulation of Unsteady Electromagnetic Waves
2003-01-01
Tsynkov, V. I. Turchaninov , Long-time numerical computation of wave-type solutions driven by moving sources, Appl. Numer. Math. 38 (2001) 187–222. [2...V. S. Ryaben’kii, S. V. Tsynkov, V. I. Turchaninov , Global discrete artificial boundary conditions for time-dependent wave propagation, J. Comput
Artificial Boundary Conditions for the Numerical Simulation of Unsteady Acoustic Waves
2003-01-01
Tsynkov, V. I. Turchaninov , Long-time numerical computation of wave-type solutions driven by moving sources, Appl. Numer. Math. 38 (2001) 187–222. [13...V. S. Ryaben’kii, S. V. Tsynkov, V. I. Turchaninov , Global discrete artificial boundary conditions for time-dependent wave propagation, J. Comput
Damage detection of fatigue cracks under nonlinear boundary condition using subharmonic resonance.
Zhang, Mengyang; Xiao, Li; Qu, Wenzhong; Lu, Ye
2017-05-01
In recent years, the nonlinear ultrasonic technique has been widely utilized for detecting fatigue crack, one of the most common forms of damage. However, one of limitations associated with this technique is that nonlinearities can be produced not only by damage but also by various intrinsic effects such as boundary conditions. The objective of this paper is to demonstrate the application of a nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as two elastic, frictionless half spaces that enter into contact during vibration and where the contact obeys the basic Hertz contact law. The nonlinear ordinary differential equation drawn from the developed model was solved with the method of multiple scales. The threshold of subharmonic generation was studied. Different threshold behaviors between the nonlinear boundary condition and the fatigue crack were found that can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments using 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 experimental results demonstrated that the subharmonic component of the sensing signal could be used to detect the fatigue crack and further to distinguish it from inherent nonlinear boundary conditions.
Prescribed mean curvature graphs with Neumann boundary conditions in some FLRW spacetimes
NASA Astrophysics Data System (ADS)
Mawhin, Jean; Torres, Pedro J.
2016-12-01
We identify a family of Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes such that the radially symmetric prescribed curvature problem with Neumann boundary condition is solvable on a ball of small radius. Such family contains some examples of interest in Cosmology.
Effective conditions for the neutron flux density at axial boundaries of the core
NASA Astrophysics Data System (ADS)
Aristarkhova, E. A.; Malofeev, V. M.
2016-12-01
Analytical expressions for elements of the triangular matrix of effective conditions at the boundary of the core with a multiregion reflector are derived in the few-group diffusion approximation. The developed technique is verified using the example of fuel assemblies of a light-water reactor with an intermediate neutron spectrum.
Construction of the Nuclear Effective Interaction from Energy Eigenstates and Boundary Conditions
NASA Astrophysics Data System (ADS)
McElvain, Kenneth; Haxton, Wick
2017-01-01
The original Harmonic Oscillator Based Effective Theory (HOBET) work by Haxton and Luu reduced H = T +VNN , with VNN a realistic potential, to Heff in a small basis defined by projection operator P while correctly including all scattering by H through an excluded space Q. Scattering by T is analytically included to all orders, leaving the ET expansion focused on the short range VNN. Results do not depend on the size P as the effect of scattering through Q is fully included, also distinguishing HOBET from other methods. In this talk we abandon VNN and determine the LECs of the ET expansion from energy levels and boundary conditions. In the infinite volume continuum case every energy is an eigenvalue of H with an associated scattering state. In the LQCD context boundary conditions are periodic. In either case the ET LECs can be determined from energy, boundary condition pairs. We show that the Cartesian HO ET LECs can be expressed in terms of the spherical ones, giving a spherical, infinite volume ET, bypassing the use of Luscher's method. The approach cleanly isolates operator mixing induced by the finite box, sequestering effects that vanish in the continuum limit in a Green's function constrained to match the boundary conditions. Supported by the DOE under contracts DE-SC00046548 and DE-AC02-98CH10886.
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.
Conditions for the appearance of boundary modes in topological phases of Heisenberg spin ladders
NASA Astrophysics Data System (ADS)
Robinson, Neil; Atland, Alexander; Egger, Reinhold; Gergs, Nkilas; Konik, Robert; Li, Wei; Schuricht, Dirk; Tsvelik, Alexei; Weichselbaum, Andreas
We consider the problem of delineating the necessary conditions for the appearance of boundary modes in extended SU (2) Heisenberg spin ladders. Specifically, we study Heisenberg ladders with rung exchange, J⊥, and ring exchange, JX, that admit a field theoretic description in terms of Majorana fermions in the continuum limit. In this description there are four Majorana fermions, arranged in a triplet and a singlet. This suggests there are four distinct phases, corresponding to the configurations of the signs of the triplet mt and singlet ms masses. We label these phases as: Haldane (mt > 0 ,ms < 0), rung singlet (mt < 0 ,ms > 0), VBS+ (mt ,ms > 0) and VBS- (mt ,ms < 0). Topologically, we find two of these phases support gapless boundary modes: the Haldane phase (the triplet forms a spin- 1 / 2 degree of freedom at the ends of the ladder) and the VBS+ phase, where all the Majorana fermions have gapless boundary modes. The absence of a gapless boundary mode in the rung singlet phase is surprising; we find that the singlet mode can become gapless if open boundary conditions are replaced with a continuous change in lattice parameters. We suggest a symmetry-allowed modification to the low-energy effective theory which may be responsible for this behavior.
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.
Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations.
2014-09-26
nonlinear system of mixed parabolic- hyperbolic type in two space dimensions and time, with four independent variables must be solved in an exterior...conditions. * III THE NAVIER-STOKES EQUATIONS AND CHARACTERISTIC VARIABLES : We now begin our discussion of the equations of gas dynamics. We will neglect...8217 Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations L°O * (. P.J. McKenna LA. DTIC * E.LECTE Final Report AFOSR Grant
The heat equation source determination for the case of non-smooth boundary and initial conditions
NASA Astrophysics Data System (ADS)
Solovi’ev, V. V.; Tkachenko, D. S.
2017-01-01
An inverse problem of reconstructing the source of a special kind for parabolic equations in a bounded region with smooth boundary is considered. Solutions are sought in the Holder classes. We prove an uniqueness criterion for the solution and sufficient conditions of Fredholm property of the task at hand. As a consequence of the sufficient conditions for existence and uniqueness of solution of the inhomogeneous inverse problems are found.
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.
Boundary conditions for convergent radial tracer tests and effect of well bore mixing volume
NASA Astrophysics Data System (ADS)
Zlotnik, Vitaly A.; David Logan, J.
Convergent radial flow tracer tests have a complex spatial nonaxial transport structure caused by the flow in the vicinity of the injection well and its finite mixing volume. The formulation of the boundary value problem, and especially the treatment of the boundary conditions at the injection well, is nontrivial. Hodgkinson and Lever [1983], Moench [1989, 1991], and Welty and Gelhar [1994] have developed different models and methods for the analysis of breakthrough curves in the extraction well. To extend interpretation techniques to breakthrough curves in the zone between injection and extraction wells, an analysis of conventional transport models is given, and improved boundary conditions are formulated for a convergent radial tracer test problem. The formulation of the boundary conditions is based upon a more detailed analysis of the kinematic flow structure and tracer mass balance in the neighborhood of the injection well. Two practical applications of revised boundary conditions for field data analysis are given. First, the note explains anomalous high well bore mixing volumes of injection wells found by Cady et al. [1993] and allows one to establish the role of mixing versus other processes (retardation, matrix diffusion, etc.). Second, it is shown that the improper use of Moench's [1989] model can produce bias in the characteristics of breakthrough curves in the extraction well under conditions that involve a significant mixing factor in the injection well. A numerical example indicates an error in peak concentrations on a breakthrough curve by as much as 70% and in peak arrival time by 10% for Peclet numbers Pe=102. The effect becomes slightly less significant for Pe=1.
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.
Thermodynamic potentials from shifted boundary conditions: the scalar-field theory case
NASA Astrophysics Data System (ADS)
Giusti, Leonardo; Meyer, Harvey B.
2011-11-01
In a thermal field theory, the cumulants of the momentum distribution can be extracted from the dependence of the Euclidean path integral on a shift in the fields built into the temporal boundary condition. When combined with the Ward identities associated with the invariance of the theory under the Poincaré group, thermodynamic potentials such as the entropy or the pressure can be directly inferred from the response of the system to the shift. Crucially the argument holds, up to harmless finite-size and discretization effects, even if translational and rotational invariance are broken to a discrete subgroup of finite shifts and rotations such as in a lattice box. The formulas are thus applicable at finite lattice spacing and volume provided the derivatives are replaced by their discrete counterpart, and no additive or multiplicative ultraviolet-divergent renormalizations are needed to take the continuum limit. In this paper we present a complete derivation of the relevant formulas in the scalar field theory, where several technical complications are avoided with respect to gauge theories. As a by-product we obtain a recursion relation among the cumulants of the momentum distribution, and formulæ for finite-volume corrections to several well-known thermodynamic identities.
Flow and heat transfer in Sisko fluid with convective boundary condition.
Malik, Rabia; Khan, Masood; Munir, Asif; Khan, Waqar Azeem
2014-01-01
In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a nonisothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index n, magnetic parameter M, stretching parameter s, generalized Prandtl number Pr and generalized Biot number γ are presented graphically. It is found that temperature profile increases with the increasing value of M and γ whereas it decreases for Pr. Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results.