Symmetries and Boundary Conditions with a Twist

NASA Astrophysics Data System (ADS)

Zawadzki, Krissia; D'Amico, Irene; Oliveira, Luiz N.

2017-10-01

Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2-7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.

Boundary Conditions for Jet Flow Computations

NASA Technical Reports Server (NTRS)

Hayder, M. E.; Turkel, E.

1994-01-01

Ongoing activities are focused on capturing the sound source in a supersonic jet through careful large eddy simulation (LES). One issue that is addressed is the effect of the boundary conditions, both inflow and outflow, on the predicted flow fluctuations, which represent the sound source. In this study, we examine the accuracy of several boundary conditions to determine their suitability for computations of time-dependent flows. Various boundary conditions are used to compute the flow field of a laminar axisymmetric jet excited at the inflow by a disturbance given by the corresponding eigenfunction of the linearized stability equations. We solve the full time dependent Navier-Stokes equations by a high order numerical scheme. For very small excitations, the computed growth of the modes closely corresponds to that predicted by the linear theory. We then vary the excitation level to see the effect of the boundary conditions in the nonlinear flow regime.

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.

Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 variousmore » 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.« less

Optimal boundary conditions for ORCA-2 model

NASA Astrophysics Data System (ADS)

Kazantsev, Eugene

2013-08-01

A 4D-Var data assimilation technique is applied to ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of boundary conditions on the solution is analyzed both within and beyond the assimilation window. It is shown that the optimal bottom and surface boundary conditions allow us to better represent the jet streams, such as Gulf Stream and Kuroshio. Analyzing the reasons of the jets reinforcement, we notice that data assimilation has a major impact on parametrization of the bottom boundary conditions for u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.

Permeability models affecting nonlinear stability in the asymptotic suction boundary layer: the Forchheimer versus the Darcy model

NASA Astrophysics Data System (ADS)

Wedin, Håkan; Cherubini, Stefania

2016-12-01

The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability {\\hat{K}}2 and of the wall suction {\\hat{V}}0, whereas the Darcian wall permeability {\\hat{K}}1 is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of {\\hat{K}}1 both models produce almost identical TW solutions. However, when both increasing the suction {\\hat{V}}0 to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for a≳ 0.70, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number {{Fo}}\\max ≳ 0.5 is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, {{Re}}g, for which the Navier-Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that {{Re}}g is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of

Numerical implementation of isolated horizon boundary conditions

NASA Astrophysics Data System (ADS)

Jaramillo, José Luis; Ansorg, Marcus; Limousin, François

2007-01-01

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasiequilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the conformal thin sandwich equations. As main results, we first establish the consistency of including in the set of boundary conditions a constant surface gravity prescription, interpretable as a lapse boundary condition, and second we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the conformal transverse traceless equations with quasiequilibrium horizon conditions extend to the conformal thin sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.

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.

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.

Numerical implementation of isolated horizon boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jaramillo, Jose Luis; Ansorg, Marcus; Limousin, Francois

2007-01-15

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasiequilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the conformal thin sandwich equations. As main results, we first establish the consistency of including in the set of boundary conditions a constant surface gravity prescription, interpretable as a lapse boundary condition, and second we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the conformalmore » transverse traceless equations with quasiequilibrium horizon conditions extend to the conformal thin sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.« less

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 Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

Integral Method of Boundary Characteristics: Neumann Condition

NASA Astrophysics Data System (ADS)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

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.

Influence of overconsolidated condition on permeability evolution in silica sand

NASA Astrophysics Data System (ADS)

Kimura, S.; Kaneko, H.; Ito, T.; Nishimura, O.; Minagawa, H.

2013-12-01

Permeability of sediments is important factors for production of natural gas from natural gas hydrate bearing layers. Methane-hydrate is regarded as one of the potential resources of natural gas. As results of coring and logging, the existence of a large amount of methane-hydrate is estimated in the Nankai Trough, offshore central Japan, where many folds and faults have been observed. In the present study, we investigate the permeability of silica sand specimen forming the artificial fault zone after large displacement shear in the ring-shear test under two different normal consolidated and overconsolidated conditions. The significant influence of overconsolidation ratio (OCR) on permeability evolution is not found. The permeability reduction is influenced a great deal by the magnitude of normal stress during large displacement shearing. The grain size distribution and structure observation in the shear zone of specimen after shearing at each normal stress level are analyzed by laser scattering type particle analyzer and scanning electron microscope, respectively. It is indicated that the grain size and porosity reduction due to the particle crushing are the factor of the permeability reduction. This study is financially supported by METI and Research Consortium for Methane Hydrate Resources in Japan (the MH21 Research Consortium).

Effect of preparation conditions on properties and permeability of chitosan-sodium hexametaphosphate capsules.

PubMed

Angelova, N; Hunkeler, D

2001-01-01

Capsules were obtained by interpolymer complexation between chitosan (polycation) and sodium hexametaphosphate (SMP, oligoanion). The effect of the preparation conditions on the capsule characteristics was evaluated. Specifically, the influence of variables such as pH, ionic strength, reagent concentration, and additives on the capsule permeability properties was investigated using dextran as a model permeant. The capsule membrane permeability was found to increase by decreasing the chitosan/SMP ratio as well as adding mannitol to the oligoanion recipient bath. Increasing the ionic strength or the pH of the initial chitosan solution was also found to enhance the membrane permeability, moving the membrane exclusion limit to higher values. Generally, the capsules prepared tinder all tested conditions had a relatively low permeability which rarely exceeded a molecular cut-off of 40 kD based on dextran standards. Furthermore, the diffusion rate showed a strong temporal dependence, indicating that the capsules prepared under various conditions exhibit different apparent pore size densities on the surface. The results indicated that, in order to obtain the desired capsule mass-transfer properties, the preparation conditions should be carefully considered and adjusted. Adding a polyol as well as low salt amount (less than 0.15%) is preferable as a means of modulating the diffusion characteristics, without disturbing the capsule mechanical stability.

Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

NASA Technical Reports Server (NTRS)

Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun

1997-01-01

Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

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.

Air permeability and trapped-air content in two soils

USGS Publications Warehouse

Stonestrom, David A.; Rubin, Jacob

1989-01-01

To improve understanding of hysteretic air permeability relations, a need exists for data on the water content dependence of air permeability, matric pressure, and air trapping (especially for wetting-drying cycles). To obtain these data, a special instrument was designed. The instrument is a combination of a gas permeameter (for air permeability determination), a suction plate apparatus (for retentivity curve determination), and an air pycnometer (for trapped-air-volume determination). This design allowed values of air permeability, matric pressure, and air trapping to be codetermined, i.e., determined at the same values of water content using the same sample and the same inflow-outflow boundaries. Such data were obtained for two nonswelling soils. The validity of the air permeability determinations was repeatedly confirmed by rigorous tests of Darcy's law. During initial drying from complete water saturation, supplementary measurements were made to assess the magnitude of gas slip. The extended Darcy equation accurately described the measured flux gradient relations for each condition of absolute gas pressure tested. Air permeability functions exhibited zero-permeability regions at high water contents as well as an abruptly appearing hysteresis at low water contents. Measurements in the zero-permeability regions revealed that the total amount of air in general exceeded the amount of trapped air. This indicates that the medium' s air space is partitioned into three measurable domains: through-flowing air, locally accessible air (i.e., air accessible from only one flow boundary), and trapped air. During repeated wetting and drying, the disappearance and reappearance of air permeability coincided closely with the reappearance and disappearance, respectively, of trapped air. The observed relation between critical features of the air permeability functions and those of the air-trapping functions suggest that water-based blockages play a significant role in the

Effect of Boundary Conditions on Numerically Simulated Tornado-like Vortices.

NASA Astrophysics Data System (ADS)

Smith, David R.

1987-02-01

The boundary conditions for Rotunno's numerical model which simulates tornado-like vortices are examined. In particular, the lateral boundary condition for tangential velocity and the upper boundary condition for radial and tangential velocities are considered to determine if they have any significant impact on vortex development.The choice of the lateral boundary condition did not appear to have any real effect on the development of the vortex over the range of swirl ratios studied (0.87-2.61).The upper boundary conditions attempt to simulate both the presence and absence of the flow-straightening baffle. The boundary condition corresponding to the baffle in place produced a distinct boundary layer in the u and v field and very strong upflow and downflow within the vortex core. When this condition is removed, there is both radial and tangential motion throughout the domain and a reduction of the vertical velocity. At small swirl ratio (S = 0.87) this boundary condition has a profound impact on the narrow vortex, producing changes in the pressure field that intensifies the vortex. At higher swirl ratio the vortex is apparently broad enough to better adjust to the changes of the upper boundary condition and, thus, experiences little change in the development of the vortex.

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.

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.

Oxygen Permeability and Grain-Boundary Diffusion Applied to Alumina Scales

NASA Technical Reports Server (NTRS)

Smialek, James L.; Jacobson, Nathan S.; Gleeson, Brian; Hovis, David B.; Heuer, Arthur H.

2013-01-01

High-temperature oxygen permeability measurements had determined grain-boundary diffusivities (deltaD(sub gb)) in bulk polycrystalline alumina (Wada, Matsudaira, and Kitaoka). They predict that oxygen deltaD(sub gb,O) varies with oxygen pressure as P(O2)(sup -1/6) at low pressure whereas aluminum deltaD(sub gb),Al varies with P(O2)(sup +3/16) at high pressure. These relations were used to evaluate alumina scale growth in terms of diffusivity and grain size. A modified Wagner treatment for dominant inward oxygen growth produces the concise solution: ?(sub i) = k(sub p,i)×G(sub i) = 12 deltaD(sub gb,O,int), where ?(sub i) is a constant and k(sub p,i) and G(sub i) refer to instantaneous values of the scale parabolic growth constant and grain size, respectively. A commercial FeCrAl(Zr) alloy was oxidized at 1100 to 1400 degC to determine k(sub p,i), interfacial grain size, ?, and thus deltaD(sub gb,O,int). The deltaD(sub gb,O,int) values predicted from oxidation at (375 kJ/mole) were about 20 times less than those obtained above (at 298 kJ/mole), but closer than extrapolations from high-temperature bulk measurements. The experimental oxidation results agree with similar FeCrAl(X) studies, especially where both k(sub p,i) and G(sub i) were characterized. This complete approach accounts for temperature-sensitive oxidation effects of grain enlargement, equilibrium interface pressure variation, and grain-boundary diffusivity.

Boundary Conditions for Scalar (Co)Variances over Heterogeneous Surfaces

NASA Astrophysics Data System (ADS)

Machulskaya, Ekaterina; Mironov, Dmitrii

2018-05-01

The problem of boundary conditions for the variances and covariances of scalar quantities (e.g., temperature and humidity) at the underlying surface is considered. If the surface is treated as horizontally homogeneous, Monin-Obukhov similarity suggests the Neumann boundary conditions that set the surface fluxes of scalar variances and covariances to zero. Over heterogeneous surfaces, these boundary conditions are not a viable choice since the spatial variability of various surface and soil characteristics, such as the ground fluxes of heat and moisture and the surface radiation balance, is not accounted for. Boundary conditions are developed that are consistent with the tile approach used to compute scalar (and momentum) fluxes over heterogeneous surfaces. To this end, the third-order transport terms (fluxes of variances) are examined analytically using a triple decomposition of fluctuating velocity and scalars into the grid-box mean, the fluctuation of tile-mean quantity about the grid-box mean, and the sub-tile fluctuation. The effect of the proposed boundary conditions on mixing in an archetypical stably-stratified boundary layer is illustrated with a single-column numerical experiment. The proposed boundary conditions should be applied in atmospheric models that utilize turbulence parametrization schemes with transport equations for scalar variances and covariances including the third-order turbulent transport (diffusion) terms.

Oil recovery by imbibition in low-permeability chalk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cuiec, L.; Bourbiaux, B.; Kalaydjian, F.

1994-09-01

This paper describes experimental studies of spontaneous imbibition of oil by water in a low-permeability outcrop chalk. At constant and high interfacial tension (IFT), the importance of capillary forces and the existence of a predominantly countercurrent mechanism were established. Additional experiments were performed to investigate the influence of length and of various boundary conditions. In another investigation the authors modified the IFT at the sample boundary by using pairs of conjugate phases of the n-hexane/ethanol/brine ternary system. Final recovery increased when IFT was lowered. They give a numerical interpretation for this last result.

Implementation of Slater Boundary Condition into OVERFLOW

NASA Astrophysics Data System (ADS)

Duncan, Sean

Bleed is one of the primary methods of controlling the flow within a mixed compression inlet. In this work the Slater boundary condition, first applied in WindUS, is implemented in OVERFLOW. Further, a simulation using discrete holes is run in order to show the differences between use of the boundary condition and use of the bleed hole geometry. Recent tests at Wright Patterson Air Force Base seek to provide a baseline for study of mixed compression inlets. The inlet used by the Air Force Research Laboratory is simulated in the modified OVERFLOW. The results from the experiment are compared to the CFD to qualitatively assess the accuracy of the simulations. The boundary condition is shown to be robust and viable in studying bleed.

Boundary condition for Ginzburg-Landau theory of superconducting layers

NASA Astrophysics Data System (ADS)

Koláček, Jan; Lipavský, Pavel; Morawetz, Klaus; Brandt, Ernst Helmut

2009-05-01

Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy. We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations.

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

Slip Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc

2017-11-01

The slip boundary conditions for the compressible Navier-Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman-Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar-Gross-Krook model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.

On the Boussinesq-Burgers equations driven by dynamic boundary conditions

NASA Astrophysics Data System (ADS)

Zhu, Neng; Liu, Zhengrong; Zhao, Kun

2018-02-01

We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.

Step Permeability on the Pt(111) Surface

NASA Astrophysics Data System (ADS)

Altman, Michael

2005-03-01

Surface morphology will be affected, or even dictated, by kinetic limitations that may be present during growth. Asymmetric step attachment is recognized to be an important and possibly common cause of morphological growth instabilities. However, the impact of this kinetic limitation on growth morphology may be hindered by other factors such as the rate limiting step and step permeability. This strongly motivates experimental measurements of these quantities in real systems. Using low energy electron microscopy, we have measured step flow velocities in growth on the Pt(111) surface. The dependence of step velocity upon adjacent terrace width clearly shows evidence of asymmetric step attachment and step permeability. Step velocity is modeled by solving the diffusion equation simultaneously on several adjacent terraces subject to boundary conditions at intervening steps that include asymmetric step attachment and step permeability. This analysis allows a quantitative evaluation of step permeability and the kinetic length, which characterizes the rate limiting step continuously between diffusion and attachment-detachment limited regimes. This work provides information that is greatly needed to set physical bounds on the parameters that are used in theoretical treatments of growth. The observation that steps are permeable even on a simple metal surface should also stimulate more experimental measurements and theoretical treatments of this effect.

Improved Boundary Conditions for Cell-centered Difference Schemes

NASA Technical Reports Server (NTRS)

VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.

Stability of hyperbolic-parabolic mixed type equations with partial boundary condition

NASA Astrophysics Data System (ADS)

Zhan, Huashui; Feng, Zhaosheng

2018-06-01

In this paper, we are concerned with the hyperbolic-parabolic mixed type equations with the non-homogeneous boundary condition. If it is degenerate on the boundary, the part of the boundary whose boundary value should be imposed, is determined by the entropy condition from the convection term. If there is no convection term in the equation, we show that the stability of solutions can be proved without any boundary condition. If the equation is completely degenerate, we show that the stability of solutions can be established just based on the partial boundary condition.

Boundary conditions and unitarity in AdS/CFT

NASA Astrophysics Data System (ADS)

Andrade, Tomas

This thesis investigates various issues regarding unitarity in the context of Anti-de Sitter/Conformal Field theory (AdS/CFT) dualities. When the boundary duals are conformal, unitarity implies that there are lower bounds on the dimension of primary operators. Now, the AdS/CFT dictionary relates insertions of boundary operators to different choices of boundary conditions on the gravity side. Therefore, we expect the possible choices of boundary conditions in AdS to be restricted accordingly. Our first main goal will be to identify what are the pathologies that occur in the gravitational side of the duality when the boundary operators violate the pertinent unitarity bounds. In all the studied cases, we find that such bulk theories are ill-defined as expected, although unitarity is not nec- essarily violated. As our first example we consider a Klein-Gordon field in AdS, and extend the analysis to bosonic fields of spin 1 and 2 later on, with analogous results. Interestingly, it turns our that the bulk settings are pathological even in the absence of strict conformal invariance. Secondly, we argue that introducing a geometrical cut-off in spacetime along with the appropriate modifications of the boundary conditions yields the resulting (IR) theories well-defined. By study- ing in detail a Klein-Gordon field with boundary conditions that correspond to double-trace deformations, we are able to explicitly verify this claim. Finally, we discuss future research directions which include generalizations of AdS/CFT-like dualities and potential applications for condensed matter theory.

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.

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.

Tidal Boundary Conditions in SEAWAT

USGS Publications Warehouse

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.

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.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

NASA Astrophysics Data System (ADS)

Silva, Goncalo; Talon, Laurent; Ginzburg, Irina

2017-04-01

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes-Brinkman-Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes-Brinkman-Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM

Transport synthetic acceleration with opposing reflecting boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 iteratingmore » 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.« less

Evaluation of general non-reflecting boundary conditions for industrial CFD applications

NASA Astrophysics Data System (ADS)

Basara, Branislav; Frolov, Sergei; Lidskii, Boris; Posvyanskii, Vladimir

2007-11-01

The importance of having proper boundary conditions for the calculation domain is a known issue in Computational Fluid Dynamics (CFD). In many situations, it is very difficult to define a correct boundary condition. The flow may enter and leave the computational domain at the same time and at the same boundary. In such circumstances, it is important that numerical implementation of boundary conditions enforces certain physical constraints leading to correct results which then ensures a better convergence rate. The aim of this paper is to evaluate recently proposed non-reflecting boundary conditions (Frolov et al., 2001, Advances in Chemical Propulsion) on industrial CFD applications. Derivation of the local non-reflecting boundary conditions at the open boundary is based on finding the solution of linearized Euler equations vanishing at infinity for both incompressible and compressible formulations. This is implemented into the in-house CFD package AVL FIRE and some numerical details will be presented as well. The key applications in this paper are from automotive industry, e.g. an external car aerodynamics, an intake port, etc. The results will show benefits of using effective non-reflecting boundary conditions.

Thermal Simulations, Open Boundary Conditions and Switches

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Florio, Adrien; Kaczmarek, Olaf; Mazur, Lukas

2018-03-01

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

Characterizing flow in oil reservoir rock using SPH: absolute permeability

NASA Astrophysics Data System (ADS)

Holmes, David W.; Williams, John R.; Tilke, Peter; Leonardi, Christopher R.

2016-04-01

In this paper, a three-dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale fluid flow in porous rock is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including flows related to permeable rock for both groundwater and petroleum reservoir research. While previous approaches to such problems using SPH have involved the use of idealized pore geometries (cylinder/sphere packs etc), in this paper we detail the characterization of flow in models with geometries taken from 3D X-ray microtomographic imaging of actual porous rock; specifically 25.12 % porosity dolomite. This particular rock type has been well characterized experimentally and described in the literature, thus providing a practical `real world' means of verification of SPH that will be key to its acceptance by industry as a viable alternative to traditional reservoir modeling tools. The true advantages of SPH are realized when adding the complexity of multiple fluid phases, however, the accuracy of SPH for single phase flow is, as yet, under developed in the literature and will be the primary focus of this paper. Flow in reservoir rock will typically occur in the range of low Reynolds numbers, making the enforcement of no-slip boundary conditions an important factor in simulation. To this end, we detail the development of a new, robust, and numerically efficient method for implementing no-slip boundary conditions in SPH that can handle the degree of complexity of boundary surfaces, characteristic of an actual permeable rock sample. A study of the effect of particle density is carried out and simulation results for absolute permeability are presented and compared to those from experimentation showing good agreement and validating the method for such applications.

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.

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.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Crystallization in a model glass: Influence of the boundary conditions

NASA Astrophysics Data System (ADS)

Jund, P.; Jullien, R.

1998-06-01

Using molecular dynamics calculations and the Voronoï tessellation, we study the evolution of the local structure of a soft-sphere glass vs. temperature starting from the liquid phase at different quenching rates. This study is done for different sizes and for two different boundary conditions, namely the usual cubic periodic boundary conditions and the isotropic hyperspherical boundary conditions for which the particles evolve on the surface of a hypersphere in four dimensions. Our results show that for small system sizes, crystallization can indeed be induced by the cubic boundary conditions. On the other hand, we show that finite-size effects are more pronounced on the hypersphere and that crystallization is artificially inhibited even for large system sizes.

Impacts of Lateral Boundary Conditions on US Ozone ...

EPA Pesticide Factsheets

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 impacts of different boundary conditions on ozone can be significant throughout the year. The National Exposure Research Laboratory (NERL) Computational Exposure Division (CED) develops and evaluates data, decision-support tools, and models to be applied to media-specific or receptor-specific problem areas. CED uses modeling-based approaches to characterize exposures, evaluate fate and transport, and support environmental diagnostics/forensics with input from multiple data sources. It also develops media- and receptor-specific models, process models, and decision support tools for use both within and outside of EPA.

Large Eddy Simulation in a Channel with Exit Boundary Conditions

NASA Technical Reports Server (NTRS)

Cziesla, T.; Braun, H.; Biswas, G.; Mitra, N. K.

1996-01-01

The influence of the exit boundary conditions (vanishing first derivative of the velocity components and constant pressure) on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbance which is mostly damped by the grid stretching. The difference between the fully developed turbulent channel flow obtained with LES with periodicity condition and the inlet and exit and the LES with fully developed flow at the inlet and the exit boundary condition is less than 10% for equidistant grids and less than 5% for the case grid stretching. The chosen boundary condition is of interest because it may be used in complex flows with backflow at exit.

Phase separation in the six-vertex model with a variety of boundary conditions

NASA Astrophysics Data System (ADS)

Lyberg, I.; Korepin, V.; Ribeiro, G. A. P.; Viti, J.

2018-05-01

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm for domain wall boundary conditions, proposed in the work of Allison and Reshetikhin [Ann. Inst. Fourier 55(6), 1847-1869 (2005)], we examine some modifications of these boundary conditions. To be precise, we discuss partial domain wall boundary conditions, reflecting ends, and half turn boundary conditions (domain wall boundary conditions with half turn symmetry). Dedicated to the memory of Ludwig Faddeev

Structural acoustic control of plates with variable boundary conditions: design methodology.

PubMed

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.

Permeable disks at low Reynolds numbers

NASA Astrophysics Data System (ADS)

Viola, Ignazio Maria; Cummins, Cathal; Mastropaolo, Enrico; Nakayama, Naomi

2017-11-01

The wake of a permeable disk can be rather exceptional: a toroidal vortex can form and remains stably at a fixed distance from the disk. The streamwise length of the vortex depends on the Reynolds and Darcy numbers. We investigate this fascinating flow for Reynolds numbers from 10 to 130 and Darcy numbers (Da) from 10-9 to 1. Direct numerical simulations are performed on a 2D grid with axisymmetric boundary conditions. Three flow regimes are observed: for low Da (effectively impervious), the wake is characterized by the presence of a toroidal vortex whose length is approximately equal to that of an impervious disk. For 10-6 < Da <10-3 , the increase in Da causes the vortex to shorten, and eventually vanishes at a critical Darcy number. It is demonstrated that increasing the permeability can lead to large variations in the length of the recirculating wake but with minimal effect on the drag coefficient. For higher Da (highly permeable), there is no recirculation, and an analytical expression for the drag force on the disk is derived, showing good agreement with the numerical results. This work was supported by the Leverhulme Trust [RPG-2015-255].

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.

Multiple solutions in MHD flow and heat transfer of Sisko fluid containing nanoparticles migration with a convective boundary condition: Critical points

NASA Astrophysics Data System (ADS)

Dhanai, Ruchika; Rana, Puneet; Kumar, Lokendra

2016-05-01

The motivation behind the present analysis is to focus on magneto-hydrodynamic flow and heat transfer characteristics of non-Newtonian fluid (Sisko fluid) past a permeable nonlinear shrinking sheet utilizing nanoparticles involving convective boundary condition. The non-homogenous nanofluid transport model considering the effect of Brownian motion, thermophoresis, suction/injection and no nanoparticle flux at the sheet with convective boundary condition has been solved numerically by the RKF45 method with shooting technique. Critical points for various pertinent parameters are evaluated in this study. The dual solutions (both first and second solutions) are captured in certain range of material constant (nc< n < ∞) , mass transfer parameter (sc < s < ∞) and shrinking parameter (χc < χ < 0) . For both the branches (upper and lower branch), the rate of heat transfer is an increasing function of the power-law index, Prandtl number and Biot number, whereas it is a decreasing function of the material constant and thermophoresis parameter.

Diffusive growth of a single droplet with three different boundary conditions

NASA Astrophysics Data System (ADS)

Tavassoli, Z.; Rodgers, G. J.

2000-02-01

We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as $[t/\\ln(t)]^{1/3}$ is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky \\cite{krapquasi} where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times.

Localized rotating convection with no-slip boundary conditions

NASA Astrophysics Data System (ADS)

Beaume, Cédric; Kao, Hsien-Ching; Knobloch, Edgar; Bergeon, Alain

2013-12-01

Localized patches of stationary convection embedded in a background conduction state are called convectons. Multiple states of this type have recently been found in two-dimensional Boussinesq convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom, and rotating about the vertical. The convectons differ in their lengths and in the strength of the self-generated shear within which they are embedded, and exhibit slanted snaking. We use homotopic continuation of the boundary conditions to show that similar structures exist in the presence of no-slip boundary conditions at the top and bottom of the layer and show that such structures exhibit standard snaking. The homotopic continuation allows us to study the transformation from slanted snaking characteristic of systems with a conserved quantity, here the zonal momentum, to standard snaking characteristic of systems with no conserved quantity.

Sharp Permeability Transitions due to Shallow Diagenesis of Subduction Zone Sediments

NASA Astrophysics Data System (ADS)

James, S.; Screaton, E.

2013-12-01

The permeability of hemipelagic sediments is an important factor in fluid flow in subduction zones and can be affected by porosity changes and cementation-dissolution processes acting during diagenesis. Anomalously high porosities have been observed in cores from the Shikoku Basin sediments approaching the Nankai Trough subduction zone. These high porosities have been attributed to the presence of minor amounts of amorphous silica cement that strengthen the sediment and inhibit consolidation. The porosity rapidly drops from 66-68% to 54-56% at a diagenetic boundary where the amorphous silica cement dissolves. Although the anomalous porosity profiles at Nankai have received attention, the magnitude of the corresponding permeability change has not been addressed. In this study, permeability profiles were constructed using permeability-porosity relationships from previous studies, to estimate the magnitude and rate of permeability changes with depth. The predicted permeability profiles for the Nankai Trough sediment cores indicate that permeability drops by almost one order of magnitude across the diagenetic boundary. This abrupt drop in permeability has the potential to facilitate significant changes in pore fluid pressures and thus to influence the deformation of the sediment onto the accretionary prism. At the Costa Rica subduction zone, results vary with location. Site U1414 offshore the Osa Peninsula shows porosities stable at 69% above 145 mbsf and then decrease to 54% over a 40 m interval. A porosity drop of that magnitude is predicted to correlate to an order of magnitude permeability decrease. In contrast, porosity profiles from Site 1039 offshore the Nicoya Peninsula and Site U1381 offshore the Osa Peninsula show anomalously high porosities but no sharp drop. It is likely that sediments do not cross the diagenetic boundary due to the extremely low (<10°C/km) thermal gradient at Site 1039 and the thin (<100 m) sediment cover at Site U1381. At these locations

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silva, Goncalo, E-mail: goncalo.nuno.silva@gmail.com; Talon, Laurent, E-mail: talon@fast.u-psud.fr; Ginzburg, Irina, E-mail: irina.ginzburg@irstea.fr

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies themore » effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance

Discrete transparent boundary conditions for the mixed KDV-BBM equation

NASA Astrophysics Data System (ADS)

Besse, Christophe; Noble, Pascal; Sanchez, David

2017-09-01

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) and Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data.

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.

Additional boundary conditions and surface exciton dispersion relations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rimbey, P.R.

1977-01-15

The surface-exciton dispersion curves in ZnO are derived from the surface impedances developed by Fuchs and Kliewer (FK) and Rimbey and Mahan (RM) including retardation. There exists a distinctive splitting between the two dispersions, the FK additional boundary conditions having longitudinal character, the RM additional boundary conditions being transverse. Surface-mode attenuation due to spatial dispersion is more pronouced in the RM formalism, although inclusion of a phenomenological damping parameter does not alter either dispersion curve. (AIP)

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.

A new method of imposing boundary conditions for hyperbolic equations

NASA Technical Reports Server (NTRS)

Funaro, D.; ative.

1987-01-01

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.

Work and personal life boundary management: boundary strength, work/personal life balance, and the segmentation-integration continuum.

PubMed

Bulger, Carrie A; Matthews, Russell A; Hoffman, Mark E

2007-10-01

While researchers are increasingly interested in understanding the boundaries surrounding the work and personal life domains, few have tested the propositions set forth by theory. Boundary theory proposes that individuals manage the boundaries between work and personal life through processes of segmenting and/or integrating the domains. The authors investigated boundary management profiles of 332 workers in an investigation of the segmentation-integration continuum. Cluster analysis indicated consistent clusters of boundary management practices related to varying segmentation and integration of the work and personal life domains. But, the authors suggest that the segmentation-integration continuum may be more complicated. Results also indicated relationships between boundary management practices and work-personal life interference and work-personal life enhancement. Less flexible and more permeable boundaries were related to more interference, while more flexible and more permeable boundaries were related to more enhancement.

Automated Boundary Conditions for Wind Tunnel Simulations

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2018-01-01

Computational fluid dynamic (CFD) simulations of models tested in wind tunnels require a high level of fidelity and accuracy particularly for the purposes of CFD validation efforts. Considerable effort is required to ensure the proper characterization of both the physical geometry of the wind tunnel and recreating the correct flow conditions inside the wind tunnel. The typical trial-and-error effort used for determining the boundary condition values for a particular tunnel configuration are time and computer resource intensive. This paper describes a method for calculating and updating the back pressure boundary condition in wind tunnel simulations by using a proportional-integral-derivative controller. The controller methodology and equations are discussed, and simulations using the controller to set a tunnel Mach number in the NASA Langley 14- by 22-Foot Subsonic Tunnel are demonstrated.

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.

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.

Estimation of the REV Size and Equivalent Permeability Coefficient of Fractured Rock Masses with an Emphasis on Comparing the Radial and Unidirectional Flow Configurations

NASA Astrophysics Data System (ADS)

Wang, Zhechao; Li, Wei; Bi, Liping; Qiao, Liping; Liu, Richeng; Liu, Jie

2018-05-01

A method to estimate the representative elementary volume (REV) size for the permeability and equivalent permeability coefficient of rock mass with a radial flow configuration was developed. The estimations of the REV size and equivalent permeability for the rock mass around an underground oil storage facility using a radial flow configuration were compared with those using a unidirectional flow configuration. The REV sizes estimated using the unidirectional flow configuration are much higher than those estimated using the radial flow configuration. The equivalent permeability coefficient estimated using the radial flow configuration is unique, while those estimated using the unidirectional flow configuration depend on the boundary conditions and flow directions. The influences of the fracture trace length, spacing and gap on the REV size and equivalent permeability coefficient were investigated. The REV size for the permeability of fractured rock mass increases with increasing the mean trace length and fracture spacing. The influence of the fracture gap length on the REV size is insignificant. The equivalent permeability coefficient decreases with the fracture spacing, while the influences of the fracture trace length and gap length are not determinate. The applicability of the proposed method to the prediction of groundwater inflow into rock caverns was verified using the measured groundwater inflow into the facility. The permeability coefficient estimated using the radial flow configuration is more similar to the representative equivalent permeability coefficient than those estimated with different boundary conditions using the unidirectional flow configuration.

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.

Formulation and Implementation of Inflow/Outflow Boundary Conditions to Simulate Propulsive Effects

NASA Technical Reports Server (NTRS)

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian

2018-01-01

Boundary conditions appropriate for simulating flow entering or exiting the computational domain to mimic propulsion effects have been implemented in an adaptive Cartesian simulation package. A robust iterative algorithm to control mass flow rate through an outflow boundary surface is presented, along with a formulation to explicitly specify mass flow rate through an inflow boundary surface. The boundary conditions have been applied within a mesh adaptation framework based on the method of adjoint-weighted residuals. This allows for proper adaptive mesh refinement when modeling propulsion systems. The new boundary conditions are demonstrated on several notional propulsion systems operating in flow regimes ranging from low subsonic to hypersonic. The examples show that the prescribed boundary state is more properly imposed as the mesh is refined. The mass-flowrate steering algorithm is shown to be an efficient approach in each example. To demonstrate the boundary conditions on a realistic complex aircraft geometry, two of the new boundary conditions are also applied to a modern low-boom supersonic demonstrator design with multiple flow inlets and outlets.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Simulations of QCD and QED with C* boundary conditions

NASA Astrophysics Data System (ADS)

Hansen, Martin; Lucini, Biagio; Patella, Agostino; Tantalo, Nazario

2018-03-01

We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The primary features of the simulation code are presented and we discuss some details regarding the implementation of C* boundary conditions and the simulated lattice action. Preprint: CP3-Origins-2017-046 DNRF90, CERN-TH-2017-214

Theoretical Evaluation of the Transient Response of Constant Head and Constant Flow-Rate Permeability Tests

USGS Publications Warehouse

Zhang, M.; Takahashi, M.; Morin, R.H.; Esaki, T.

1998-01-01

A theoretical analysis is presented that compares the response characteristics of the constant head and the constant flowrate (flow pump) laboratory techniques for quantifying the hydraulic properties of geologic materials having permeabilities less than 10-10 m/s. Rigorous analytical solutions that describe the transient distributions of hydraulic gradient within a specimen are developed, and equations are derived for each method. Expressions simulating the inflow and outflow rates across the specimen boundaries during a constant-head permeability test are also presented. These solutions illustrate the advantages and disadvantages of each method, including insights into measurement accuracy and the validity of using Darcy's law under certain conditions. The resulting observations offer practical considerations in the selection of an appropriate laboratory test method for the reliable measurement of permeability in low-permeability geologic materials.

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

A device adaptive inflow boundary condition for Wigner equations of quantum transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Haiyan; Lu, Tiao; Cai, Wei, E-mail: wcai@uncc.edu

2014-02-01

In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device atmore » zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.« less

On the symmetry of the boundary conditions of the volume potential

NASA Astrophysics Data System (ADS)

Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan

2017-09-01

It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.

Derivation and application of a class of generalized boundary conditions

NASA Technical Reports Server (NTRS)

Senior, Thomas B. A.; Volakis, John L.

1989-01-01

Boundary conditions involving higher order derivatives are presented for simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to nonplanar surfaces. As an illustration, the simulation of metal-backed uniform and three-layer dielectric coatings is given. It is shown that fourth order conditions are capable of providing an accurate simulation for uniform coating at least a quarter of a wavelength in thickness.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

Oblique radiation lateral open boundary conditions for a regional climate atmospheric model

NASA Astrophysics Data System (ADS)

Cabos Narvaez, William; De Frutos Redondo, Jose Antonio; Perez Sanz, Juan Ignacio; Sein, Dmitry

2013-04-01

The prescription of lateral boundary conditions in regional atmospheric models represent a very important issue for limited area models. The ill-posed nature of the open boundary conditions makes it necessary to devise schemes in order to filter spurious wave reflections at boundaries, being desirable to have one boundary condition per variable. On the other side, due to the essentially hyperbolic nature of the equations solved in state of the art atmospheric models, external data is required only for inward boundary fluxes. These circumstances make radiation lateral boundary conditions a good choice for the filtering of spurious wave reflections. Here we apply the adaptive oblique radiation modification proposed by Mikoyada and Roseti to each of the prognostic variables of the REMO regional atmospheric model and compare it to the more common normal radiation condition used in REMO. In the proposed scheme, special attention is paid to the estimation of the radiation phase speed, essential to detecting the direction of boundary fluxes. One of the differences with the classical scheme is that in case of outward propagation, the adaptive nudging imposed in the boundaries allows to minimize under and over specifications problems, adequately incorporating the external information.

A New Parallel Boundary Condition for Turbulence Simulations in Stellarators

NASA Astrophysics Data System (ADS)

Martin, Mike F.; Landreman, Matt; Dorland, William; Xanthopoulos, Pavlos

2017-10-01

For gyrokinetic simulations of core turbulence, the ``twist-and-shift'' parallel boundary condition (Beer et al., PoP, 1995), which involves a shift in radial wavenumber proportional to the global shear and a quantization of the simulation domain's aspect ratio, is the standard choice. But as this condition was derived under the assumption of axisymmetry, ``twist-and-shift'' as it stands is formally incorrect for turbulence simulations in stellarators. Moreover, for low-shear stellarators like W7X and HSX, the use of a global shear in the traditional boundary condition places an inflexible constraint on the aspect ratio of the domain, requiring more grid points to fully resolve its extent. Here, we present a parallel boundary condition for ``stellarator-symmetric'' simulations that relies on the local shear along a field line. This boundary condition is similar to ``twist-and-shift'', but has an added flexibility in choosing the parallel length of the domain based on local shear consideration in order to optimize certain parameters such as the aspect ratio of the simulation domain.

General slip regime permeability model for gas flow through porous media

NASA Astrophysics Data System (ADS)

Zhou, Bo; Jiang, Peixue; Xu, Ruina; Ouyang, Xiaolong

2016-07-01

A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, "Effective correlation of apparent gas permeability in tight porous media," Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.

Effect of thermal radiation on laminar boundary layer flow over a permeable flat plate with Newtonian heating

NASA Astrophysics Data System (ADS)

Khairul Anuar Mohamed, Muhammad; Zuki Salleh, Mohd; Noar, Nor Aida Zuraimi Md; Ishak, Anuar

2017-09-01

The laminar boundary layer flow over a permeable flat plat with the presence of thermal radiation and Newtonian heating is numerically studied. The non linear partial differential equations that governed the model are transformed to ordinary differential equations before being solved numerically by Runge-Kutta-Fehlberg (RKF) method using Maple software. The influenced and characteristic of pertinent parameters which are the Prandtl number, the suction/blowing parameter, the thermal radiation parameter and the conjugate parameter are analyzed and discussed. It is found that the presence of thermal radiation and blowing parameter has increased the value of wall temperature. Meanwhile, the trend is contrary with the suction effect.

Experimental verification of free-space singular boundary conditions in an invisibility cloak

NASA Astrophysics Data System (ADS)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

2016-04-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

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.

A new approach to implement absorbing boundary condition in biomolecular electrostatics.

PubMed

Goni, Md Osman

2013-01-01

This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.

A boundary condition for layer to level ocean model interaction

NASA Astrophysics Data System (ADS)

Mask, A.; O'Brien, J.; Preller, R.

2003-04-01

A radiation boundary condition based on vertical normal modes is introduced to allow a physical transition between nested/coupled ocean models that are of differing vertical structure and/or differing physics. In this particular study, a fine resolution regional/coastal sigma-coordinate Naval Coastal Ocean Model (NCOM) has been successfully nested to a coarse resolution (in the horizontal and vertical) basin scale NCOM and a coarse resolution basin scale Navy Layered Ocean Model (NLOM). Both of these models were developed at the Naval Research Laboratory (NRL) at Stennis Space Center, Mississippi, USA. This new method, which decomposes the vertical structure of the models into barotropic and baroclinic modes, gives improved results in the coastal domain over Orlanski radiation boundary conditions for the test cases. The principle reason for the improvement is that each mode has the radiation boundary condition applied individually; therefore, the packet of information passing through the boundary is allowed to have multiple phase speeds instead of a single-phase speed. Allowing multiple phase speeds reduces boundary reflections, thus improving results.

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

NASA Astrophysics Data System (ADS)

Sarna, Neeraj; Torrilhon, Manuel

2018-01-01

We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

Maxwell boundary condition and velocity dependent accommodation coefficient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Struchtrup, Henning, E-mail: struchtr@uvic.ca

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.

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

Evaluation of Far-Field Boundary Conditions for the Gust Response Problem

NASA Technical Reports Server (NTRS)

Scott, James R.; Kreider, Kevin L.; Heminger, John A.

2002-01-01

This paper presents a detailed situ dy of four far-field boundary conditions used in solving the single airfoil gust response problem. The boundary conditions, examined are the partial Sommerfeld radiation condition with only radial derivatives, the full Sommerfeld radiation condition with both radial and tangential derivatives, the Bayliss-Turkel condition of order one, and the Hagstrom-Hariharan condition of order one. The main objectives of the study were to determine which far-field boundary condition was most accurate, which condition was least sensitive to changes in grid. and which condition was best overall in terms of both accuracy and efficiency. Through a systematic study of the flat plate gust response problem, it was determined that the Hagstrom-Hariharan condition was most accurate, the Bayliss-Turkel condition was least sensitive to changes in grid, and Bayliss-Turkel was best in terms of both accuracy and efficiency.

Low Permeability Oil and Gas Plays

EIA Publications

The map shows boundaries, structure (elevation of the top contours), and isopachs (thickness contours) for major low permeability oil and gas plays in the lower 48 States. Additionally, related oil and gas infrastructure layers are included

Impacts of Lateral Boundary Conditions on U.S. Ozone Modeling Analyses

EPA Science Inventory

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...

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.

Permeability of the San Andreas Fault Zone at Depth

NASA Astrophysics Data System (ADS)

Rathbun, A. P.; Song, I.; Saffer, D.

2010-12-01

to 90 MPa axial stress. In these tests, axial stress is increased via a constant rate of displacement, and the excess pore pressure build up at the base of the sample is measured. Stress, pore pressure and strain are monitored to calculate coefficient of consolidation and volumetric compressibility in addition to permeability. In triaxial experiments, permeability is measured from by flow through tests under constant head boundary conditions. Permeability of the CDZ rapidly decreases to ~10-19 m2 by 20 MPa axial stress in our CRS tests. Over axial stresses from 20-85 MPa, permeability decreases log-linearly with effective stress from 8x10-20 m2 to 1x10-20 m2. Flow-through tests in the triaxial system under isostatic conditions yield permeabilities of 2.2x10-19 m2 and 1x10-20 m2 at 5 and 10 MPa, respectively. Our results are consistent with published geochemical data from SAFOD mud gas samples and inferred pore pressures during drilling [Zoback et al., 2010], which together suggest that the fault is a barrier to regional fluid flow. Our results indicate that the permeability of the fault core is sufficiently low to result in effectively undrained behavior during slip, thus allowing dynamic processes including thermal pressurization and dilatancy hardening to affect slip behavior.

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

PubMed Central

Lei, Huan; Fedosov, Dmitry A.; Karniadakis, George Em

2011-01-01

We propose a simple method to impose both no-slip boundary conditions at fluid-wall interfaces and at outflow boundaries in fully developed regions for Dissipative Particle Dynamics (DPD) fluid systems. The procedure to enforce the no-slip condition is based on a velocity-dependent shear force, which is a generalized force to represent the presence of the solid-wall particles and to maintain locally thermodynamic consistency. We show that this method can be implemented in both steady and time-dependent fluid systems and compare the DPD results with the continuum limit (Navier-Stokes) results. We also develop a force-adaptive method to impose the outflow boundary conditions for fully developed flow with unspecified outflow velocity profile or pressure value. We study flows over the backward-facing step and in idealized arterial bifurcations using a combination of the two new boundary methods with different flow rates. Finally, we explore the applicability of the outflow method in time-dependent flow systems. The outflow boundary method works well for systems with Womersley number of O(1), i.e., when the pressure and flowrate at the outflow are approximately in-phase. PMID:21499548

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.

General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

NASA Astrophysics Data System (ADS)

De Vincenzo, Salvatore; Sánchez, Carlet

2018-05-01

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.

Theoretical aspect of suitable spatial boundary condition specified for adjoint model on limited area

NASA Astrophysics Data System (ADS)

Wang, Yuan; Wu, Rongsheng

2001-12-01

Theoretical argumentation for so-called suitable spatial condition is conducted by the aid of homotopy framework to demonstrate that the proposed boundary condition does guarantee that the over-specification boundary condition resulting from an adjoint model on a limited-area is no longer an issue, and yet preserve its well-poseness and optimal character in the boundary setting. The ill-poseness of over-specified spatial boundary condition is in a sense, inevitable from an adjoint model since data assimilation processes have to adapt prescribed observations that used to be over-specified at the spatial boundaries of the modeling domain. In the view of pragmatic implement, the theoretical framework of our proposed condition for spatial boundaries indeed can be reduced to the hybrid formulation of nudging filter, radiation condition taking account of ambient forcing, together with Dirichlet kind of compatible boundary condition to the observations prescribed in data assimilation procedure. All of these treatments, no doubt, are very familiar to mesoscale modelers.

Evolution of fracture permeability of ultramafic rocks undergoing serpentinization at hydrothermal conditions: An experimental study

NASA Astrophysics Data System (ADS)

Farough, A.; Moore, D. E.; Lockner, D. A.; Lowell, R. P.

2016-01-01

We performed flow-through laboratory experiments on five cylindrically cored samples of ultramafic rocks, in which we generated a well-mated through-going tensile fracture, to investigate evolution of fracture permeability during serpentinization. The samples were tested in a triaxial loading machine at a confining pressure of 50 MPa, pore pressure of 20 MPa, and temperature of 260°C, simulating a depth of 2 km under hydrostatic conditions. A pore pressure difference of up to 2 MPa was imposed across the ends of the sample. Fracture permeability decreased by 1-2 orders of magnitude during the 200-330 h experiments. Electron microprobe and SEM data indicated the formation of needle-shaped crystals of serpentine composition along the walls of the fracture, and chemical analyses of sampled pore fluids were consistent with dissolution of ferro-magnesian minerals. By comparing the difference between fracture permeability and matrix permeability measured on intact samples of the same rock types, we concluded that the contribution of the low matrix permeability to flow is negligible and essentially all of the flow is focused in the tensile fracture. The experimental results suggest that the fracture network in long-lived hydrothermal circulation systems can be sealed rapidly as a result of mineral precipitation, and generation of new permeability resulting from a combination of tectonic and crystallization-induced stresses is required to maintain fluid circulation.

Evolution of fracture permeability of ultramafic rocks undergoing serpentinization at hydrothermal conditions: An experimental study

USGS Publications Warehouse

Farough, Aida; Moore, Diane E.; Lockner, David A.; Lowell, R.P.

2016-01-01

We performed flow-through laboratory experiments on five cylindrically cored samples of ultramafic rocks, in which we generated a well-mated through-going tensile fracture, to investigate evolution of fracture permeability during serpentinization. The samples were tested in a triaxial loading machine at a confining pressure of 50 MPa, pore pressure of 20 MPa, and temperature of 260°C, simulating a depth of 2 km under hydrostatic conditions. A pore pressure difference of up to 2 MPa was imposed across the ends of the sample. Fracture permeability decreased by 1–2 orders of magnitude during the 200–330 h experiments. Electron microprobe and SEM data indicated the formation of needle-shaped crystals of serpentine composition along the walls of the fracture, and chemical analyses of sampled pore fluids were consistent with dissolution of ferro-magnesian minerals. By comparing the difference between fracture permeability and matrix permeability measured on intact samples of the same rock types, we concluded that the contribution of the low matrix permeability to flow is negligible and essentially all of the flow is focused in the tensile fracture. The experimental results suggest that the fracture network in long-lived hydrothermal circulation systems can be sealed rapidly as a result of mineral precipitation, and generation of new permeability resulting from a combination of tectonic and crystallization-induced stresses is required to maintain fluid circulation.

An effective absorbing layer for the boundary condition in acoustic seismic wave simulation

NASA Astrophysics Data System (ADS)

Yao, Gang; da Silva, Nuno V.; Wu, Di

2018-04-01

Efficient numerical simulation of seismic wavefields generally involves truncating the Earth model in order to keep computing time and memory requirements down. Absorbing boundary conditions, therefore, are applied to remove the boundary reflections caused by this truncation, thereby allowing for accurate modeling of wavefields. In this paper, we derive an effective absorbing boundary condition for both acoustic and elastic wave simulation, through the simplification of the damping term of the split perfectly matched layer (SPML) boundary condition. This new boundary condition is accurate, cost-effective, and easily implemented, especially for high-performance computing. Stability analysis shows that this boundary condition is effectively as stable as normal (non-absorbing) wave equations for explicit time-stepping finite differences. We found that for full-waveform inversion (FWI), the strengths of the effective absorbing layer—a reduction of the computational and memory cost coupled with a simplistic implementation—significantly outweighs the limitation of incomplete absorption of outgoing waves relative to the SPML. More importantly, we demonstrate that this limitation can easily be overcome through the use of two strategies in FWI, namely variable cell size and model extension thereby fully compensating for the imperfectness of the proposed absorbing boundary condition.

On two-point boundary correlations in the six-vertex model with domain wall boundary conditions

NASA Astrophysics Data System (ADS)

Colomo, F.; Pronko, A. G.

2005-05-01

The six-vertex model with domain wall boundary conditions on an N × N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point boundary correlators of the model on N × N and (N - 1) × (N - 1) lattices. In alternating sign matrix (ASM) language this result implies that the doubly refined x-enumerations of ASMs are just appropriate combinations of the singly refined ones.

The PPP model of alternant cyclic polyenes with modified boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

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.

Single particle nonlocality, geometric phases and time-dependent boundary conditions

NASA Astrophysics Data System (ADS)

Matzkin, A.

2018-03-01

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

Evaluation of several non-reflecting computational boundary conditions for duct acoustics

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Zorumski, William E.; Hodge, Steve L.

1994-01-01

Several non-reflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each non-reflecting boundary conditions. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other non-reflecting conditions.

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.

Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

NASA Astrophysics Data System (ADS)

Hejranfar, Kazem; Parseh, Kaveh

2017-09-01

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

QCT/FEA predictions of femoral stiffness are strongly affected by boundary condition modeling

PubMed Central

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

Superradiance in the BTZ black hole with Robin boundary conditions

NASA Astrophysics Data System (ADS)

Dappiaggi, Claudio; Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.

2018-03-01

We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.

Modeling of Permeability Structure Using Pore Pressure and Borehole Strain Monitoring

NASA Astrophysics Data System (ADS)

Kano, Y.; Ito, H.

2011-12-01

Hydraulic or transport property, especially permeability, of the rock affect the behavior of the fault during earthquake rupture and also interseismic period. The methods to determine permeability underground are hydraulic test utilizing borehole and packer or core measurement in laboratory. Another way to know the permeability around a borehole is to examine responses of pore pressure to natural loading such as barometric pressure change at surface or earth tides. Using response to natural deformation is conventional method for water resource research. The scale of measurement is different among in-situ hydraulic test, response method, and core measurement. It is not clear that the relationship between permeability values form each method for an inhomogeneous medium such as a fault zone. Supposing the measurement of the response to natural loading, we made a model calculation of permeability structure around a fault zone. The model is 2 dimensional and constructed with vertical high-permeability layer in uniform low-permeability zone. We assume the upper and lower boundaries are drained and no-flow condition. We calculated the flow and deformation of the model for step and cyclic loading by numerically solving a two-dimensional diffusion equation. The model calculation shows that the width of the high-permeability zone and contrast of the permeability between high- and low- permeability zones control the contribution of the low-permeability zone. We made a calculation with combinations of permeability and fault width to evaluate the sensitivity of the parameters to in-situ measurement of permeability. We applied the model calculation to the field results of in-situ packer test, and natural response of water level and strain monitoring carried out in the Kamioka mine. The model calculation shows that knowledge of permeability in host rock is also important to obtain permeability of fault zone itself. The model calculations help to design long-term pore pressure

A far-field non-reflecting boundary condition for two-dimensional wake flows

NASA Technical Reports Server (NTRS)

Danowitz, Jeffrey S.; Abarbanel, Saul A.; Turkel, Eli

1995-01-01

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

DREAM-3D and the importance of model inputs and boundary conditions

NASA Astrophysics Data System (ADS)

Friedel, Reiner; Tu, Weichao; Cunningham, Gregory; Jorgensen, Anders; Chen, Yue

2015-04-01

Recent work on radiation belt 3D diffusion codes such as the Los Alamos "DREAM-3D" code have demonstrated the ability of such codes to reproduce realistic magnetospheric storm events in the relativistic electron dynamics - as long as sufficient "event-oriented" boundary conditions and code inputs such as wave powers, low energy boundary conditions, background plasma densities, and last closed drift shell (outer boundary) are available. In this talk we will argue that the main limiting factor in our modeling ability is no longer our inability to represent key physical processes that govern the dynamics of the radiation belts (radial, pitch angle and energy diffusion) but rather our limitations in specifying accurate boundary conditions and code inputs. We use here DREAM-3D runs to show the sensitivity of the modeled outcomes to these boundary conditions and inputs, and also discuss alternate "proxy" approaches to obtain the required inputs from other (ground-based) sources.

Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries

NASA Astrophysics Data System (ADS)

Morales Escalante, José A.; Gamba, Irene M.

2018-06-01

We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann-Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k →). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.

Absorbing Boundary Conditions For Optical Pulses In Dispersive, Nonlinear Materials

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that provides absorbing boundary conditions for optical pulses in dispersive, nonlinear materials. A new numerical absorber at the boundaries has been developed that is responsive to the spectral content of the pulse. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of "light bullet" like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. Comparisons will be shown of calculations that use the standard boundary conditions and the new ones.

Boundary conditions in Chebyshev and Legendre methods

NASA Technical Reports Server (NTRS)

Canuto, C.

1984-01-01

Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

A New Model for Gas Transfer and Storage in a Permeable Volcanic Edifice

NASA Astrophysics Data System (ADS)

Collinson, A. D.; Neuberg, J.

2011-12-01

There is a marked contrast between the behaviour of a volcano in an open system compared to one which is closed. It is therefore essential to understand degassing, to appreciate how much gas is lost and where. Previous studies by a variety of scientists have led to the accumulation of data via field evidence from both active and fossil volcanoes (Stasiuk et al., 1996), laboratory experiments (Moore et al., 1994) and conceptual modelling, in which Darcy's law has become increasingly applicable (Eichelberger et al., 1986; Edmonds et al., 2003). Of particular interest for this study, is the effect different permeabilities have on the degree and pattern of the gas flux. A new method has been devised to investigate gas transport and storage in a permeable volcanic edifice. The continuity equation and Darcy's law are amalgamated to derive a partial differential equation which is solved using a finite element method to obtain the gas pressure. The associated pressure gradient is then used within Darcy's law to calculate the gas flux. The properties of the gas are described by the ideal gas law. The strength of this method is that it allows the modelling of two and three dimensional structures both in stationary equilibrium and as a time dependent progression. A geometry is created and the pressure and permeabilites incorporated into the model as boundary and domain conditions respectively. The aim of the model is to investigate how variable permeability and pressure gradients influence the gas flux, for example highly permeable cracks in the dome, or impermeable layers within the volcanic structure. We also use this gas model to complement the model of Neuberg et al. (2006) in which brittle failure of the conduit-wall boundary is used as a trigger mechanism of low-frequency earthquakes. The associated behaviour of the gas in response to the brittle failure is simulated in our model by increasing the permeability through a narrow zone at the boundary between the conduit

Galilean-invariant algorithm coupling immersed moving boundary conditions and Lees-Edwards boundary conditions

NASA Astrophysics Data System (ADS)

Zhou, Guofeng; Wang, Limin; Wang, Xiaowei; Ge, Wei

2011-12-01

Many investigators have coupled the Lees-Edwards boundary conditions (LEBCs) and suspension methods in the framework of the lattice Boltzmann method to study the pure bulk properties of particle-fluid suspensions. However, these suspension methods are all link-based and are more or less exposed to the disadvantages of violating Galilean invariance. In this paper, we have coupled LEBCs with a node-based suspension method, which is demonstrated to be Galilean invariant in benchmark simulations. We use the coupled algorithm to predict the viscosity of a particle-fluid suspension at very low Reynolds number, and the simulation results are in good agreement with the semiempirical Krieger-Dougherty formula.

On the Huygens absorbing boundary conditions for electromagnetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berenger, Jean-Pierre

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 ABCmore » 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.« less

Permeability of soils in Mississippi

USGS Publications Warehouse

O'Hara, Charles G.

1994-01-01

The permeability of soils in Mississippi was determined and mapped using a geographic information system (GIS). Soil permeabilities in Mississippi were determined to range in value from nearly 0.0 to values exceeding 5.0 inches per hour. The U.S. Soil Conservation Service's State Soil Geographic Data Base (STATSGO) was used as the primary source of data for the determination of area-weighted soil permeability. STATSGO provides soil layer properties that are spatially referenced to mapped areas. These mapped areas are referred to as polygons in the GIS. The polygons arc boundaries of soils mapped as a group and are given unique Map Unit Identifiers (MUIDs). The data describing the physical characteristics of the soils within each polygon are stored in a tabular data base format and are referred to as attributes. The U.S. Soil Conservation Service developed STATSGO to be primarily used as a guide for regional resource planning, management, and monitoring. STATSGO was designed so that soil information could be extracted from properties tables at the layer level, combined by component, and statistically expanded to cover the entire map unit. The results of this study provide a mapped value for permeability which is representative of the vertical permeability of soils in that area. The resultant permeability map provides a representative vertical soil permeability for a given area sufficient for county, multi- county, and area planning, and will be used as the soil permeability data component in the evaluation of the susceptibility of major aquifers to contami- nation in Mississippi.

Time-dependent density functional theory with twist-averaged boundary conditions

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

2016-05-01

Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

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.

CFD determination of flow perturbation boundary conditions for seal rotordynamic modeling

NASA Astrophysics Data System (ADS)

Venkatesan, Ganesh

2002-09-01

A new approach has been developed and utilized to determine the flow field perturbations (i.e. disturbance due to rotor eccentricity and/or motion) upstream of and within a non-contacting seal. The results are proposed for use with bulk-flow perturbation and CFD-perturbation seal rotordynamic models, as well as in fully 3-D CFD models, to specify approximate boundary conditions for the first-order variables at the computational domain inlet. The perturbation quantities were evaluated by subtracting the numerical flow field solutions corresponding to the concentric rotor position from that for an eccentric rotor position. The disturbance pressure quantities predicted from the numerical solutions were validated by comparing with previous pressure measurements. A parametric study was performed to understand the influence of upstream chamber height, seal clearance, shaft speed, whirl speed, zeroth-order streamwise and swirl velocities, and downstream pressure on the distribution of the first-order quantities in the upstream chamber, seal inlet and seal exit regions. Radially bulk-averaged first-order quantities were evaluated in the upstream chamber, as well as at the seal inlet and exit. The results were finally presented in the form of generalized dimensionless boundary condition correlations so that they can be applied to seal rotordynamic models over a wide range of operating conditions and geometries. To examine the effect of the proposed, approximate first-order boundary conditions on the solutions of the fully 3-D CFD rotordynamic models, the first-order boundary condition correlations for the upstream chamber were used to adjust the circumferential distribution of domain inlet values. The benefit of the boundary condition expressions was assessed for two previously measured test cases, one for a gas seal and the other for a liquid seal. For the gas seal case, a significant improvement in the prediction of the cross-coupled stiffness, when including the proposed

Physical modeling in geomorphology: are boundary conditions necessary?

NASA Astrophysics Data System (ADS)

Cantelli, A.

2012-12-01

Referring to the physical experimental design in geomorphology, boundary conditions are key elements that determine the quality of the results and therefore the study development. For years engineers have modeled structures, such as dams and bridges, with high precision and excellent results. Until the last decade, a great part of the physical experimental work in geomorphology has been developed with an engineer-like approach, requiring an accurate scaling analysis to determine inflow parameters and initial geometrical conditions. However, during the last decade, the way we have been approaching physical experiments has significantly changed. In particular, boundary conditions and initial conditions are considered unknown factors that need to be discovered during the experiment. This new philosophy leads to a more demanding data acquisition process but relaxes the obligation to a priori know the appropriate input and initial conditions and provides the flexibility to discover those data. Here I am going to present some practical examples of this experimental approach in deepwater geomorphology; some questions about scaling of turbidity currents and a new large experimental facility built at the Universidade Federal do Rio Grande do Sul, Brasil.

Friction-term response to boundary-condition type in flow models

USGS Publications Warehouse

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.

A Novel Method for Modeling Neumann and Robin Boundary Conditions in Smoothed Particle Hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.more » 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.« less

Control of the permeability of fractures in geothermal rocks

NASA Astrophysics Data System (ADS)

Faoro, Igor

This thesis comprises three journal articles that will be submitted for publication (Journal of Geophysical Research-Solid Earth). Their respective titles are: "Undrained through Drained Evolution of Permeability in Dual Permeability Media" by Igor Faoro, Derek Elsworth and Chris Marone, "Evolution of Stiffness and Permeability in Fractures Subject to Thermally-and Mechanically-Activated Dissolution" by Igor Faoro, Derek Elsworth Chris Marone; "Linking permeability and mechanical damage for basalt from Mt. Etna volcano (Italy)" by Igor Faoro, Sergio Vinciguerra, Chris Marone and Derek Elsworth. Undrained through Drained Evolution of Permeability in Dual Permeability Media: temporary permeability changes of fractured aquifers subject to earthquakes have been observed and recorded worldwide, but their comprehension still remains a complex issue. In this study we report on flow-through fracture experiments on cracked westerly cores that reproduce, at laboratory scale, those (steps like) permeability changes that have been recorded when earthquakes occur. In particular our experiments show that under specific test boundary conditions, rapid increments of pore pressure induce transient variations of flow rate of the fracture whose peak magnitudes decrease as the variations of the effective stresses increase. We identify that the observed hydraulic behavior of the fracture is due to two principal mechanisms of origin; respectively mechanical (shortening of core) and poro-elastic (radial diffusion of the pore fluid into the matrix of the sample) whose interaction cause respectively an instantaneous opening and then a progressive closure of the fracture. Evolution of Stiffness and Permeability in Fractures Subject to Thermally-and Mechanically-Activated Dissolution: we report the results of radial flow-through experiments conducted on heated samples of Westerly granite. These experiments are performed to examine the influence of thermally and mechanically activated

Boundary conditions for the Middle Miocene Climate Transition (MMCT v1.0)

NASA Astrophysics Data System (ADS)

Frigola, Amanda; Prange, Matthias; Schulz, Michael

2018-04-01

The Middle Miocene Climate Transition was characterized by major Antarctic ice sheet expansion and global cooling during the interval ˜ 15-13 Ma. Here we present two sets of boundary conditions for global general circulation models characterizing the periods before (Middle Miocene Climatic Optimum; MMCO) and after (Middle Miocene Glaciation; MMG) the transition. These boundary conditions include Middle Miocene global topography, bathymetry, and vegetation. Additionally, Antarctic ice volume and geometry, sea level, and atmospheric CO2 concentration estimates for the MMCO and the MMG are reviewed. The MMCO and MMG boundary conditions have been successfully applied to the Community Climate System Model version 3 (CCSM3) to provide evidence of their suitability for global climate modeling. The boundary-condition files are available for use as input in a wide variety of global climate models and constitute a valuable tool for modeling studies with a focus on the Middle Miocene.

Boundary Conditions of Radiative Cooling in Gravitationally Unstable Protoplanetary Disks

NASA Astrophysics Data System (ADS)

Cai, K.; Durisen, R. H.; Mejía, A. C.

2004-05-01

In order to create 3D hydrodynamic disk simulations which reproduce the observable properties of young stellar disks and which realistically probe the possibility of planet formation by gravitational instabilities, it is crucial to include a proper treatment of the radiative energy transport within the disk. Our recent simulations (Mejía 2004, Ph.D. dissertation) suggest that the boundary conditions between optically thin and thick regions are important in treating radiative cooling in protoplanetary disks. Although the initial cooling times are shorter than one rotation period, these disks adjust their structures over a few rotations to much longer cooling times, at which Gammie's (2001) criterion predicts they are stable against fragmentation into dense clumps. In fact, the disks do not fragment in Mejía's calculations. Boss (2001, 2002), on the other hand, using different boundary conditions, finds rapid cooling and fragmentation in his own disk simulations with radiative cooling. He attributes the rapid cooling to convection, which does not occur in Mejía's calculations. This apparent disagreement is critical because disk fragmentation has been proposed as a gas giant planet formation mechanism. To test the importance of boundary conditions, we are running simulations which compare a Boss-like treatment of boundary conditions with Mejía's for the case of a disk heated from above by a hot envelope. Preliminary results will be presented.

New boundary conditions for fluid interaction with hydrophobic surface

NASA Astrophysics Data System (ADS)

Pochylý, František; Fialová, Simona; Havlásek, Michal

2018-06-01

Solution of both laminar and turbulent flow with consideration of hydrophobic surface is based on the original Navier assumption that the shear stress on the hydrophobic surface is directly proportional to the slipping velocity. In the previous work a laminar flow analysis with different boundary conditions was performed. The shear stress value on the tube walls directly depends on the pressure gradient. In the solution of the turbulent flow by the k-ɛ model, the occurrence of the fluctuation components of velocity on the hydrophobic surface is considered. The fluctuation components of the velocity affect the size of the adhesive forces. We assume that the boundary condition for ɛ depending on the velocity gradients will not need to be changed. When the liquid slips over the surface, non-zero fluctuation velocity components occur in the turbulent flow. These determine the non-zero value of the turbulent kinetic energy K. In addition, the fluctuation velocity components also influence the value of the adhesive forces, so it is necessary to include these in the formulation of new boundary conditions for turbulent flow on the hydrophobic surface.

Scale effect of slip boundary condition at solid–liquid interface

PubMed Central

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

In vitro porcine blood-brain barrier model for permeability studies: pCEL-X software pKa(FLUX) method for aqueous boundary layer correction and detailed data analysis.

PubMed

Yusof, Siti R; Avdeef, Alex; Abbott, N Joan

2014-12-18

In vitro blood-brain barrier (BBB) models from primary brain endothelial cells can closely resemble the in vivo BBB, offering valuable models to assay BBB functions and to screen potential central nervous system drugs. We have recently developed an in vitro BBB model using primary porcine brain endothelial cells. The model shows expression of tight junction proteins and high transendothelial electrical resistance, evidence for a restrictive paracellular pathway. Validation studies using small drug-like compounds demonstrated functional uptake and efflux transporters, showing the suitability of the model to assay drug permeability. However, one limitation of in vitro model permeability measurement is the presence of the aqueous boundary layer (ABL) resulting from inefficient stirring during the permeability assay. The ABL can be a rate-limiting step in permeation, particularly for lipophilic compounds, causing underestimation of the permeability. If the ABL effect is ignored, the permeability measured in vitro will not reflect the permeability in vivo. To address the issue, we explored the combination of in vitro permeability measurement using our porcine model with the pKa(FLUX) method in pCEL-X software to correct for the ABL effect and allow a detailed analysis of in vitro (transendothelial) permeability data, Papp. Published Papp using porcine models generated by our group and other groups are also analyzed. From the Papp, intrinsic transcellular permeability (P0) is derived by simultaneous refinement using a weighted nonlinear regression, taking into account permeability through the ABL, paracellular permeability and filter restrictions on permeation. The in vitro P0 derived for 22 compounds (35 measurements) showed good correlation with P0 derived from in situ brain perfusion data (r(2)=0.61). The analysis also gave evidence for carrier-mediated uptake of naloxone, propranolol and vinblastine. The combination of the in vitro porcine model and the software

Impact of lateral boundary conditions on regional analyses

NASA Astrophysics Data System (ADS)

Chikhar, Kamel; Gauthier, Pierre

2017-04-01

Regional and global climate models are usually validated by comparison to derived observations or reanalyses. Using a model in data assimilation results in a direct comparison to observations to produce its own analyses that may reveal systematic errors. In this study, regional analyses over North America are produced based on the fifth-generation Canadian Regional Climate Model (CRCM5) combined with the variational data assimilation system of the Meteorological Service of Canada (MSC). CRCM5 is driven at its boundaries by global analyses from ERA-interim or produced with the global configuration of the CRCM5. Assimilation cycles for the months of January and July 2011 revealed systematic errors in winter through large values in the mean analysis increments. This bias is attributed to the coupling of the lateral boundary conditions of the regional model with the driving data particularly over the northern boundary where a rapidly changing large scale circulation created significant cross-boundary flows. Increasing the time frequency of the lateral driving and applying a large-scale spectral nudging improved significantly the circulation through the lateral boundaries which translated in a much better agreement with observations.

Dual boundary conditions in 3d SCFT's

NASA Astrophysics Data System (ADS)

Dimofte, Tudor; Gaiotto, Davide; Paquette, Natalie M.

2018-05-01

We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d N=2 gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation of supersymmetric indices. Examples include basic abelian dualities, level-rank dualities, and Aharony dualities.

Artificial Boundary Conditions for Finite Element Model Update and Damage Detection

DTIC Science & Technology

2017-03-01

BOUNDARY CONDITIONS FOR FINITE ELEMENT MODEL UPDATE AND DAMAGE DETECTION by Emmanouil Damanakis March 2017 Thesis Advisor: Joshua H. Gordis...REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE ARTIFICIAL BOUNDARY CONDITIONS FOR FINITE ELEMENT MODEL UPDATE AND DAMAGE DETECTION...release. Distribution is unlimited. 12b. DISTRIBUTION CODE 13. ABSTRACT (maximum 200 words) In structural engineering, a finite element model is often

Reanalysis of in situ permeability measurements in the Barbados décollement

USGS Publications Warehouse

Bekins, B.A.; Matmon, D.; Screaton, E.J.; Brown, K.M.

2011-01-01

A cased and sealed borehole in the Northern Barbados accretionary complex was the site of the first attempts to measure permeability in situ along a plate boundary décollement. Three separate efforts at Hole 949C yielded permeability estimates for the décollement spanning four orders of magnitude. An analysis of problems encountered during installation of the casing and seals provides insights into how the borehole conditions may have led to the wide range of results. During the installation, sediments from the surrounding formation repeatedly intruded into the borehole and casing. Stress analysis shows that the weak sediments were deforming plastically and the radial and tangential stresses around the borehole were significantly lower than lithostatic. This perturbed stress state may explain why the test pressure records showed indications of hydrofracture at pressures below lithostatic, and permeabilities rose rapidly as the estimated effective stress dropped below 0.8 MPa. Even after the borehole was sealed, the plastic deformation of the formation and relatively large gap of the wire wrapped screen allowed sediment to flow into the casing. Force equilibrium calculations predict sediment would have filled the borehole to 10 cm above the top of the screen by the time slug tests were conducted 1.5 years after the borehole was sealed. Reanalysis of the slug test results with these conditions yields several orders of magnitude higher permeability estimates than the original analysis which assumed an open casing. Overall the results based on only the tests with no sign of hydrofracture yield a permeability range of 10−14–10−15 m2 and a rate of increase in permeability with decreasing effective stress consistent with laboratory tests on samples from the décollement zone.

Effects of Uncertainties in Electric Field Boundary Conditions for Ring Current Simulations

NASA Astrophysics Data System (ADS)

Chen, Margaret W.; O'Brien, T. Paul; Lemon, Colby L.; Guild, Timothy B.

2018-01-01

Physics-based simulation results can vary widely depending on the applied boundary conditions. As a first step toward assessing the effect of boundary conditions on ring current simulations, we analyze the uncertainty of cross-polar cap potentials (CPCP) on electric field boundary conditions applied to the Rice Convection Model-Equilibrium (RCM-E). The empirical Weimer model of CPCP is chosen as the reference model and Defense Meteorological Satellite Program CPCP measurements as the reference data. Using temporal correlations from a statistical analysis of the "errors" between the reference model and data, we construct a Monte Carlo CPCP discrete time series model that can be generalized to other model boundary conditions. RCM-E simulations using electric field boundary conditions from the reference model and from 20 randomly generated Monte Carlo discrete time series of CPCP are performed for two large storms. During the 10 August 2000 storm main phase, the proton density at 10 RE at midnight was observed to be low (< 1.4 cm-3) and the observed disturbance Dst index is bounded by the simulated Dst values. In contrast, the simulated Dst values during the recovery phases of the 10 August 2000 and 31 August 2005 storms tend to underestimate systematically the observed late Dst recovery. This suggests a need to improve the accuracy of particle loss calculations in the RCM-E model. Application of this technique can aid modelers to make efficient choices on either investing more effort on improving specification of boundary conditions or on improving descriptions of physical processes.

Solvability of a fourth-order boundary value problem with periodic boundary conditions II

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

Permeability changes induced by microfissure closure and opening in tectonized materials. Effect on slope pore pressure regime.

NASA Astrophysics Data System (ADS)

De la Fuente, Maria; Vaunat, Jean; Pedone, Giuseppe; Cotecchia, Federica; Sollecito, Francesca; Casini, Francesca

2015-04-01

Tectonized clays are complex materials characterized by several levels of structures that may evolve during load and wetting/drying processes. Some microstructural patterns, as microfissures, have a particular influence on the value of permeability which is one of the main factors controlling pore pressure regime in slopes. In this work, the pore pressure regime measured in a real slope of tectonized clay in Southern Italy is analyzed by a numerical model that considers changes in permeability induced by microfissure closure and opening during the wetting and drying processes resulting from climatic actions. Permeability model accounts for the changes in Pore Size Distribution observed by Microscopy Intrusion Porosimetry. MIP tests are performed on representative samples of ground in initial conditions ("in situ" conditions) and final conditions (deformed sample after applying a wetting path that aims to reproduce the saturation of the soil under heavy rains). The resulting measurements allow for the characterization at microstructural level of the soil, identifying the distribution of dominant families pores in the sample and its evolution under external actions. Moreover, comparison of pore size density functions allows defining a microstructural parameter that depends on void ratio and degree of saturation and controls the variation of permeability. Model has been implemented in a thermo-hydro-mechanical code provided with a special boundary condition for climatic actions. Tool is used to analyze pore pressure measurements obtained in the tectonized clay slope. Results are analyzed at the light of the effect that permeability changes during wetting and drying have on the pore pressure regime.

Time-Shifted Boundary Conditions Used for Navier-Stokes Aeroelastic Solver

NASA Technical Reports Server (NTRS)

Srivastava, Rakesh

1999-01-01

Under the Advanced Subsonic Technology (AST) Program, an aeroelastic analysis code (TURBO-AE) based on Navier-Stokes equations is currently under development at NASA Lewis Research Center s Machine Dynamics Branch. For a blade row, aeroelastic instability can occur in any of the possible interblade phase angles (IBPA s). Analyzing small IBPA s is very computationally expensive because a large number of blade passages must be simulated. To reduce the computational cost of these analyses, we used time shifted, or phase-lagged, boundary conditions in the TURBO-AE code. These conditions can be used to reduce the computational domain to a single blade passage by requiring the boundary conditions across the passage to be lagged depending on the IBPA being analyzed. The time-shifted boundary conditions currently implemented are based on the direct-store method. This method requires large amounts of data to be stored over a period of the oscillation cycle. On CRAY computers this is not a major problem because solid-state devices can be used for fast input and output to read and write the data onto a disk instead of storing it in core memory.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Weiliang, E-mail: wwl@whu.edu.cn; Qu, Wenzhong, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com; Xiao, Li, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com

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 frommore » 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

Intermediate boundary conditions for LOD, ADI and approximate factorization methods

NASA Technical Reports Server (NTRS)

Leveque, R. J.

1985-01-01

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology

NASA Astrophysics Data System (ADS)

Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, L.; Barucq, H.; Chabassier, J.; Duruflé, M.

2017-12-01

The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ( 5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the "infinite atmosphere" solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.

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.

Planck scale boundary conditions and the Higgs mass

NASA Astrophysics Data System (ADS)

Holthausen, Martin; Lim, Kher Sham; Lindner, Manfred

2012-02-01

If the LHC does only find a Higgs boson in the low mass region and no other new physics, then one should reconsider scenarios where the Standard Model with three right-handed neutrinos is valid up to Planck scale. We assume in this spirit that the Standard Model couplings are remnants of quantum gravity which implies certain generic boundary conditions for the Higgs quartic coupling at Planck scale. This leads to Higgs mass predictions at the electroweak scale via renormalization group equations. We find that several physically well motivated conditions yield a range of Higgs masses from 127 - 142 GeV. We also argue that a random quartic Higgs coupling at the Planck scale favours M H > 150 GeV, which is clearly excluded. We discuss also the prospects for differentiating different boundary conditions imposed for λ( M pl) at the LHC. A striking example is M H = 127 ± 5 GeV corresponding to λ( M pl) = 0, which would imply that the quartic Higgs coupling at the electroweak scale is entirely radiatively generated.

Flow boundary conditions for chain-end adsorbing polymer blends.

PubMed

Zhou, Xin; Andrienko, Denis; Delle Site, Luigi; Kremer, Kurt

2005-09-08

Using the phenol-terminated polycarbonate blend as an example, we demonstrate that the hydrodynamic boundary conditions for a flow of an adsorbing polymer melt are extremely sensitive to the structure of the epitaxial layer. Under shear, the adsorbed parts (chain ends) of the polymer melt move along the equipotential lines of the surface potential whereas the adsorbed additives serve as the surface defects. In response to the increase of the number of the adsorbed additives the surface layer becomes thinner and solidifies. This results in a gradual transition from the slip to the no-slip boundary condition for the melt flow, with a nonmonotonic dependence of the slip length on the surface concentration of the adsorbed ends.

Velocity boundary conditions for vorticity formulations of the incompressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kempka, S.N.; Strickland, J.H.; Glass, M.W.

1995-04-01

formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. Anmore » analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.« less

Positivity and Almost Positivity of Biharmonic Green's Functions under Dirichlet Boundary Conditions

NASA Astrophysics Data System (ADS)

Grunau, Hans-Christoph; Robert, Frédéric

2010-03-01

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem, neither a maximum principle nor a comparison principle or—equivalently—a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for bounded smooth domains {Ω subsetmathbb{R}^n} , the negative part of the corresponding Green’s function is “small” when compared with its singular positive part, provided {n≥q 3} . Moreover, the biharmonic Green’s function in balls {Bsubsetmathbb{R}^n} under Dirichlet (that is, clamped) boundary conditions is known explicitly and is positive. It has been known for some time that positivity is preserved under small regular perturbations of the domain, if n = 2. In the present paper, such a stability result is proved for {n≥q 3}.

Using Global Plate Velocity Boundary Conditions for Embedded Regional Geodynamic Models

NASA Astrophysics Data System (ADS)

Taramon Gomez, Jorge; Morgan, Jason; Perez-Gussinye, Marta

2015-04-01

The treatment of far-field boundary conditions is one of the most poorly resolved issues for regional modeling of geodynamic processes. In viscous flow, the choice of far-field boundary conditions often strongly shapes the large-scale structure of a geosimulation. The mantle velocity field along the sidewalls and base of a modeling region is typically much more poorly known than the geometry of past global motions of the surface plates as constrained by global plate motion reconstructions. For regional rifting models it has become routine to apply highly simplified 'plate spreading' or 'uniform rifting' boundary conditions to a 3-D model that limits its ability to simulate the geodynamic evolution of a specific rifted margin. One way researchers are exploring the sensitivity of regional models to uncertain boundary conditions is to use a nested modeling approach in which a global model is used to determine a large-scale flow pattern that is imposed as a constraint along the boundaries of the region to be modeled. Here we explore the utility of a different approach that takes advantage of the ability of finite element models to use unstructured meshes than can embed much higher resolution sub-regions within a spherical global mesh. In our initial project to validate this approach, we create a global spherical mesh in which a higher resolution sub-region is created around the nascent South Atlantic Rifting Margin. Global Plate motion BCs and plate boundaries are applied for the time of the onset of rifting, continuing through several 10s of Ma of rifting. Thermal, compositional, and melt-related buoyancy forces are only non-zero within the high-resolution subregion, elsewhere, motions are constrained by surface plate-motion constraints. The total number of unknowns needed to solve an embedded regional model with this approach is less than 1/3 larger than that needed for a structured-mesh solution on a Cartesian or spherical cap sub-regional mesh. Here we illustrate

Investigating TIME-GCM Atmospheric Tides for Different Lower Boundary Conditions

NASA Astrophysics Data System (ADS)

Haeusler, K.; Hagan, M. E.; Lu, G.; Forbes, J. M.; Zhang, X.; Doornbos, E.

2013-12-01

It has been recently established that atmospheric tides generated in the lower atmosphere significantly influence the geospace environment. In order to extend our knowledge of the various coupling mechanisms between the different atmospheric layers, we rely on model simulations. Currently there exist two versions of the Global Scale Wave Model (GSWM), i.e. GSWM02 and GSWM09, which are used as a lower boundary (ca. 30 km) condition for the Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (TIME-GCM) and account for the upward propagating atmospheric tides that are generated in the troposphere and lower stratosphere. In this paper we explore the various TIME-GCM upper atmospheric tidal responses for different lower boundary conditions and compare the model diagnostics with tidal results from satellite missions such as TIMED, CHAMP, and GOCE. We also quantify the differences between results associated with GSWM02 and GSWM09 forcing and results of TIMEGCM simulations using Modern-Era Retrospective Analysis for Research and Application (MERRA) data as a lower boundary condition.

NASA Ames three-dimensional potential flow analyses system (POTFAN) boundary condition code (BCDN), version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Medan, R. T.

1977-01-01

This segment of the POTFAN system is used to generate right hand sides (boundary conditions) of the system of equations associated with the flow field under consideration. These specified flow boundary conditions are encountered in the oblique derivative boundary value problem (boundary value problem of the third kind) and contain the Neumann boundary condition as a special case. Arbitrary angle of attack and/or sideslip and/or rotation rates may be specified, as well as an arbitrary, nonuniform external flow field and the influence of prescribed singularity distributions.

Transducer placement for robustness to variations in boundary conditions for active structural acoustic control

NASA Astrophysics Data System (ADS)

Sprofera, Joseph D.; Clark, Robert L.; Cabell, Randolph H.; Gibbs, Gary P.

2005-05-01

Turbulent boundary layer (TBL) noise is considered a primary contribution to the interior noise present in commercial airliners. There are numerous investigations of interior noise control devoted to aircraft panels; however, practical realization is a potential challenge since physical boundary conditions are uncertain at best. In most prior studies, pinned or clamped boundary conditions were assumed; however, realistic panels likely display a range of boundary conditions between these two limits. Uncertainty in boundary conditions is a challenge for control system designers, both in terms of the compensator implemented and the location of transducers required to achieve the desired control. The impact of model uncertainties, specifically uncertain boundaries, on the selection of transducer locations for structural acoustic control is considered herein. The final goal of this work is the design of an aircraft panel structure that can reduce TBL noise transmission through the use of a completely adaptive, single-input, single-output control system. The feasibility of this goal is demonstrated through the creation of a detailed analytical solution, followed by the implementation of a test model in a transmission loss apparatus. Successfully realizing a control system robust to variations in boundary conditions can lead to the design and implementation of practical adaptive structures that could be used to control the transmission of sound to the interior of aircraft. Results from this research effort indicate it is possible to optimize the design of actuator and sensor location and aperture, minimizing the impact of boundary conditions on the desired structural acoustic control.

Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2018-05-01

In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

Minimization of vibration in elastic beams with time-variant boundary conditions

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Xie, Mingjun

1992-01-01

This paper presents an innovative method for minimizing the vibration of structures with time-variant boundary conditions (supports). The elastic body is modeled in two ways: (1) the first model is a letter seven type beam with a movable mass not to exceed the lower tip; (2) the second model has an arm that is a hollow beam with an inside mass with adjustable position. The complete solutions to both problems are carried out where the body is undergoing large rotation. The quasi-static procedure is used for the time-variant boundary conditions. The method developed employs partial differential equations governing the motion of the beam, including the effects of rigid-body motion, time-variant boundary conditions, and calculus of variations. The analytical solution is developed using Laplace and Fourier transforms. Examples of elastic robotic arms are given to illustrate the effectiveness of the methods developed.

CFD Modeling of a CFB Riser Using Improved Inlet Boundary Conditions

NASA Astrophysics Data System (ADS)

Peng, B. T.; Zhang, C.; Zhu, J. X.; Qi, X. B.

2010-03-01

A computational fluid dynamics (CFD) model based on Eulerian-Eulerian approach coupled with granular kinetics theory was adopted to investigate the hydrodynamics and flow structures in a circulating fluidized bed (CFB) riser column. A new approach to specify the inlet boundary conditions was proposed in this study to simulate gas-solids flow in CFB risers more accurately. Simulation results were compared with the experimental data, and good agreement between the numerical results and experimental data was observed under different operating conditions, which indicates the effectiveness and accuracy of the CFD model with the proposed inlet boundary conditions. The results also illustrate a clear core annulus structure in the CFB riser under all operating conditions both experimentally and numerically.

A comparison of time domain boundary conditions for acoustic waves in wave guides

NASA Technical Reports Server (NTRS)

Banks, H. T.; Propst, G.; Silcox, R. J.

1991-01-01

Researchers consider several types of boundary conditions in the context of time domain models for acoustic waves. Experiments with four different duct terminations (hard wall, free radiation, foam, and wedge) were carried out in a wave duct from which reflection coefficients over a wide frequency range were measured. These reflection coefficients were used to estimate parameters in the time domain boundary conditions. A comparison of the relative merits of the models in describing the data is presented. Boundary conditions which yield a good fit of the model to the experimental data were found for all duct terminations except the wedge.

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.

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.

Influence of electrical boundary conditions on molecular dynamics simulations of ionic liquid electrosprays.

PubMed

Borner, Arnaud; Wang, Pengxiang; Levin, Deborah A

2014-12-01

Molecular dynamics (MD) simulations are coupled to solutions of Poisson's equation to study the effects of the electrical boundary conditions on the emission modes of an electrospray thruster fed with an ionic liquid. A comparison of a new tip boundary condition with an analytical model based on a semihyperboloidal shape offers good agreement, although the analytical model overestimates the maximum value of the tangential electric field since it does not take into account the space charge that reduces the field at the liquid surface. It is found that a constant electric field model gives similar agreement to the more rigorous and computationally expensive tip boundary condition at lower flow rates. However, at higher mass flow rates the constant electric field produces extruded particles with higher Coulomb energy per ion, consistent with droplet formation. Furthermore, the MD simulations show that ion emission sites differ based on the boundary condition and snapshots offer an explanation as to why some boundary condition models will predict emission in a purely ionic mode, whereas others suggest a mixed ion-droplet regime. Finally, specific impulses and thrusts are compared for the different models and are found to vary up to 30% due to differences in the average charge to mass ratio.

Influence of electrical boundary conditions on molecular dynamics simulations of ionic liquid electrosprays

NASA Astrophysics Data System (ADS)

Borner, Arnaud; Wang, Pengxiang; Levin, Deborah A.

2014-12-01

Molecular dynamics (MD) simulations are coupled to solutions of Poisson's equation to study the effects of the electrical boundary conditions on the emission modes of an electrospray thruster fed with an ionic liquid. A comparison of a new tip boundary condition with an analytical model based on a semihyperboloidal shape offers good agreement, although the analytical model overestimates the maximum value of the tangential electric field since it does not take into account the space charge that reduces the field at the liquid surface. It is found that a constant electric field model gives similar agreement to the more rigorous and computationally expensive tip boundary condition at lower flow rates. However, at higher mass flow rates the constant electric field produces extruded particles with higher Coulomb energy per ion, consistent with droplet formation. Furthermore, the MD simulations show that ion emission sites differ based on the boundary condition and snapshots offer an explanation as to why some boundary condition models will predict emission in a purely ionic mode, whereas others suggest a mixed ion-droplet regime. Finally, specific impulses and thrusts are compared for the different models and are found to vary up to 30% due to differences in the average charge to mass ratio.

Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.

PubMed

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.

Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data

PubMed Central

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

Influence of the lower boundary in lysimeter observations

NASA Astrophysics Data System (ADS)

Weller, Ulrich; Richter, Katja; Gubis, Jozef; Vogel, Hans-Jörg

2014-05-01

Lysimeters are a valuable tool to study the water household in soils under close to natural conditions. One major drawback is that they are cut off at the lower boundary. This influences strongly the percolation of water. As long as water is leaching down in the soil, it is stagnating at the lower boundary until saturated conditions are reached and the water can percolate through the gravel filter, and under unsaturated conditions there is no flow at all at the lower boundary. In natural soils the water potential at the same depth differs considerably from the regime in a lysimeter. If the depth of the soil or the soil forming substrate is deep enough, the lower boundary is at the potential that allows the percolation of the long term mean of percolation. In other situations, a water table may influence the matric potential in the natural soil, or a less permeable layer may impede free drainage. In all these situations the matric potential at the depth of the lower boundary of the lysimeter will differ substantially in the natural soil. The latest generation of lysimeter therefore has a controlled lower boundary. The matric potential can be actively adjusted to a desired value over a broad range. Most applications connect the suction in the lysimeter to a reference value obtained in the field at the same depth in order to mimic the correct distribution of the soil water. In this presentation we demonstrate the long term influence of the different lower boundary regimes on percolation and evaporation of water based on soil physical models, and we show first field data on the practical implementations with several months of observations.

Perm-Fit: a new program to estimate permeability at high P-T conditions

NASA Astrophysics Data System (ADS)

Moulas, Evangelos; Madonna, Claudio

2016-04-01

Several geological processes are controlled by porous fluid flow. The circulation of porous fluids influences many physical phenomena and in turn it depends on the rock permeability. The permeability of rocks is a physical property that needs to be measured since it depends on many factors such as secondary porosity (fractures etc). We present a numerical approach to estimate permeability using the transient step method (Brace et al., 1968). When a non-reacting, compressible fluid is considered in a relative incompressible solid matrix, the only unknown parameter in the equations of porous flow is permeability. Porosity is assumed to be known and the physical properties of the fluid (compressibility, density, viscosity) are taken from the NIST database. Forward numerical calculations for different values of permeability are used and the results are compared to experimental measurements. The extracted permeability value is the one that minimizes the misfit between experimental and numerical results. The uncertainty on the value of permeability is estimated using a Monte Carlo method. REFERENCES Brace, W.F., Walsh J.B., & Frangos, W.T. 1968: Permeability of Granite under High Pressure, Journal of Geophysical Research, 73, 6, 2225-2236

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Discontinuities in effective permeability due to fracture percolation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hyman, Jeffrey De'Haven; Karra, Satish; Carey, James William

Motivated by a triaxial coreflood experiment with a sample of Utica shale where an abrupt jump in permeability was observed, possibly due to the creation of a percolating fracture network through the sample, we perform numerical simulations based on the experiment to characterize how the effective permeability of otherwise low-permeability porous media depends on fracture formation, connectivity, and the contrast between the fracture and matrix permeabilities. While a change in effective permeability due to fracture formation is expected, the dependence of its magnitude upon the contrast between the matrix permeability and fracture permeability and the fracture network structure is poorlymore » characterized. We use two different high-fidelity fracture network models to characterize how effective permeability changes as percolation occurs. The first is a dynamic two-dimensional fracture propagation model designed to mimic the laboratory settings of the experiment. The second is a static three-dimensional discrete fracture network (DFN) model, whose fracture and network statistics are based on the fractured sample of Utica shale. Once the network connects the inflow and outflow boundaries, the effective permeability increases non-linearly with network density. In most networks considered, a jump in the effective permeability was observed when the embedded fracture network percolated. We characterize how the magnitude of the jump, should it occur, depends on the contrast between the fracture and matrix permeabilities. For small contrasts between the matrix and fracture permeabilities the change is insignificant. However, for larger contrasts, there is a substantial jump whose magnitude depends non-linearly on the difference between matrix and fracture permeabilities. A power-law relationship between the size of the jump and the difference between the matrix and fracture permeabilities is observed. In conclusion, the presented results underscore the importance of

Discontinuities in effective permeability due to fracture percolation

DOE PAGES

Hyman, Jeffrey De'Haven; Karra, Satish; Carey, James William; ...

2018-01-31

Motivated by a triaxial coreflood experiment with a sample of Utica shale where an abrupt jump in permeability was observed, possibly due to the creation of a percolating fracture network through the sample, we perform numerical simulations based on the experiment to characterize how the effective permeability of otherwise low-permeability porous media depends on fracture formation, connectivity, and the contrast between the fracture and matrix permeabilities. While a change in effective permeability due to fracture formation is expected, the dependence of its magnitude upon the contrast between the matrix permeability and fracture permeability and the fracture network structure is poorlymore » characterized. We use two different high-fidelity fracture network models to characterize how effective permeability changes as percolation occurs. The first is a dynamic two-dimensional fracture propagation model designed to mimic the laboratory settings of the experiment. The second is a static three-dimensional discrete fracture network (DFN) model, whose fracture and network statistics are based on the fractured sample of Utica shale. Once the network connects the inflow and outflow boundaries, the effective permeability increases non-linearly with network density. In most networks considered, a jump in the effective permeability was observed when the embedded fracture network percolated. We characterize how the magnitude of the jump, should it occur, depends on the contrast between the fracture and matrix permeabilities. For small contrasts between the matrix and fracture permeabilities the change is insignificant. However, for larger contrasts, there is a substantial jump whose magnitude depends non-linearly on the difference between matrix and fracture permeabilities. A power-law relationship between the size of the jump and the difference between the matrix and fracture permeabilities is observed. In conclusion, the presented results underscore the importance of

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

NASA Astrophysics Data System (ADS)

Hill, Peter; Shanahan, Brendan; Dudson, Ben

2017-04-01

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n-axisymmetric configurations for a simple diffusion model in a "straight stellarator" magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

NASA Astrophysics Data System (ADS)

Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

2017-11-01

We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

Generalized second-order slip boundary condition for nonequilibrium gas flows

NASA Astrophysics Data System (ADS)

Guo, Zhaoli; Qin, Jishun; Zheng, Chuguang

2014-01-01

It is a challenging task to model nonequilibrium gas flows within a continuum-fluid framework. Recently some extended hydrodynamic models in the Navier-Stokes formulation have been developed for such flows. A key problem in the application of such models is that suitable boundary conditions must be specified. In the present work, a generalized second-order slip boundary condition is developed in which an effective mean-free path considering the wall effect is used. By combining this slip scheme with certain extended Navier-Stokes constitutive relation models, we obtained a method for nonequilibrium gas flows with solid boundaries. The method is applied to several rarefied gas flows involving planar or curved walls, including the Kramers' problem, the planar Poiseuille flow, the cylindrical Couette flow, and the low speed flow over a sphere. The results show that the proposed method is able to give satisfied predictions, indicating the good potential of the method for nonequilibrium flows.

Heat kernel for the elliptic system of linear elasticity with boundary conditions

NASA Astrophysics Data System (ADS)

Taylor, Justin; Kim, Seick; Brown, Russell

2014-10-01

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1997-01-01

We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow problem numerically, we discretize the governing equations (Navier-Stokes) on a finite-difference grid. The grid obviously cannot stretch from the body up to infinity, because the number of the discrete variables in that case would not be finite. Therefore, prior to the discretization we truncate the original unbounded flow domain by introducing some artificial computational boundary at a finite distance of the body. Typically, the artificial boundary is introduced in a natural way as the external boundary of the domain covered by the grid. The flow problem formulated only on the finite computational domain rather than on the original infinite domain is clearly subdefinite unless some artificial boundary conditions (ABC's) are specified at the external computational boundary. Similarly, the discretized flow problem is subdefinite (i.e., lacks equations with respect to unknowns) unless a special closing procedure is implemented at this artificial boundary. The closing procedure in the discrete case is called the ABC's as well. In this paper, we present an innovative approach to constructing highly accurate ABC's for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) by Ryaben'kii. The resulting ABC's appear spatially nonlocal but particularly easy to implement along with the existing solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic (including incompressible limit) and transonic flow regimes. As demonstrated by the computational experiments

Derivation and application of a class of generalized impedance boundary conditions, part 2

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Senior, T. B. A.; Jin, J.-M.

1989-01-01

Boundary conditions involving higher order derivatives are presented by simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to non-planar surfaces. As an illustration, the simulation of metal-backed uniform and three-layer dielectric coatings is given. It is shown that fourth order conditions are capable of providing an accurate simulation for the uniform coating at least a quarter of a wavelength in thickness. Provided, though, some compromise in accuracy is acceptable, it is also shown that a third order condition may be sufficient for practical purposes when simulating uniform coatings.

The transition from brittle faulting to cataclastic flow: Permeability evolution

NASA Astrophysics Data System (ADS)

Zhu, Wenlu; Wong, Teng-Fong

1997-02-01

Triaxial compression experiments were conducted to investigate influences of stress and failure mode on axial permeability of five sandstones with porosities ranging from 15% to 35%. In the cataclastic flow regime, permeability and porosity changes closely track one another. A drastic decrease in permeability was triggered by the onset of shear-enhanced compaction caused by grain crushing and pore collapse. The compactive yield stress C* maps out a boundary in stress space separating two different types of permeability evolution. Before C* is attained, permeability and porosity both decrease with increasing effective mean stress, but they are independent of deviatoric stresses. However, with loading beyond C*, both permeability and porosity changes are strongly dependent on the deviatoric and effective mean stresses. In the brittle faulting regime, permeability and porosity changes are more complex. Before the onset of shear-induced dilation C', both permeability and porosity decrease with increasing effective mean stress. Beyond C', permeability may actually decrease in a dilating rock prior to brittle failure. After the peak stress has been attained, the development of a relatively impermeable shear band causes an accelerated decrease of permeability. Permeability evolution in porous sandstones is compared with that in low-porosity crystalline rocks. A conceptual model for the coupling of deformation and fluid transport is proposed in the form of a deformation-permeability map.

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…

Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elizalde, E.; Odintsov, S. D.; Institucio Catalana de Recerca i Estudis Avanccats

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 Robinmore » 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.« less

Assignment of boundary conditions in embedded ground water flow models

USGS Publications Warehouse

Leake, S.A.

1998-01-01

Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger-scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger.scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.

Perfluoropolyalkylether Oil Degradation: Inference of FeF3 Formation on Steel Surfaces under Boundary Conditions

DTIC Science & Technology

1985-08-01

REPORT SD-TR-85-37 O,-) Lfl Perfluoropolyalkylether Oil Degradation: Inference of FeF 3 Formation on Steel Surfaces I under Boundary Conditions DAVID...S. TYPE OF REPORT & PERIOD COVERED PERFLUOROPOLYALKYLETHER OIL DEGRADATION: INFERENCE OF FeF3 FORMATION ON STEELSURFACES UNDER BOUNDARY CONDITIONS 0...number) Boundary conditions Oil Degradation Perfluoropolyalkylether FeF3 Wear test Lubrication .... 440C 20. ABSTRACT (Contlnue o 0 ,systes sI . I

Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-02-01

In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

Artificial Boundary Conditions for Computation of Oscillating External Flows

NASA Technical Reports Server (NTRS)

Tsynkov, S. V.

1996-01-01

In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABC's for oscillating flows is based on an essential assumption: the Navier-Stokes equations can be linearized in the far field against the free-stream back- ground. To actually compute the ABC's, we represent the far-field solution as a Fourier series in time and then apply the Difference Potentials Method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABC's for time-periodic external flows. Based on our experience in implementing analogous ABC's for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.

Effect of temperature on the permeability of gas adsorbed coal under triaxial stress conditions

NASA Astrophysics Data System (ADS)

Li, Xiangchen; Yan, Xiaopeng; Kang, Yili

2018-04-01

The combined effects of gas sorption, stress and temperature play a significant role in the changing behavior of gas permeability in coal seams. The effect of temperature on nitrogen and methane permeability of naturally fractured coal is investigated. Coal permeability, P-wave velocity and axial strain were simultaneously measured under two effective stresses and six different temperatures. The results showed that the behavior of nitrogen and methane permeability presented nonmonotonic changes with increasing temperature. The variation in the P-wave velocity and axial strain showed a good correspondence with coal permeability. A higher effective stress limited the bigger deformation and caused the small change in permeability. Methane adsorption and desorption significantly influence the mechanical properties of coal and play an important role in the variations in coal permeability. The result of coal permeability during a complete stress-strain process showed that the variation in permeability is determined by the evolution of the internal structure. The increase in the temperature of the gas saturated coal causes the complex interaction between matrix swelling, matrix shrinkage and micro-fracture generation, which leads to the complex changes in coal structure and permeability. These results are helpful to understand the gas transport mechanism for exploiting coal methane by heat injection.

Grain-Size Dynamics Beneath Mid-Ocean Ridges: Implications for Permeability and Melt Extraction

NASA Astrophysics Data System (ADS)

Turner, A. J.; Katz, R. F.; Behn, M. D.

2014-12-01

The permeability structure of the sub-ridge mantle plays an important role in how melt is focused and extracted at mid-ocean ridges. Permeability is controlled by porosity and the grain size of the solid mantle matrix, which is in turn controlled by the deformation conditions. To date, models of grain size evolution and mantle deformation have not been coupled to determine the influence of spatial variations in grain-size on the permeability structure at mid-ocean ridges. Rather, current models typically assume a constant grain size for the whole domain [1]. Here, we use 2-D numerical models to evaluate the influence of grain-size variability on the permeability structure beneath a mid-ocean ridge and use these results to speculate on the consequences for melt focusing and extraction. We construct a two-dimensional, single phase model for the steady-state grain size beneath a mid-ocean ridge. The model employs a composite rheology of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a brittle stress limiter. Grain size is calculated using the "wattmeter" model of Austin and Evans [2]. We investigate the sensitivity of the model to global variations in grain growth exponent, potential temperature, spreading-rate, and grain boundary sliding parameters [3,4]. Our model predicts that permeability varies by two orders of magnitude due to the spatial variability of grain size within the expected melt region of a mid-ocean ridge. The predicted permeability structure suggests grain size may promote focusing of melt towards the ridge axis. Furthermore, the calculated grain size structure should focus melt from a greater depth than models that exclude grain-size variability. Future work will involve evaluating this hypothesis by implementing grain-size dynamics within a two-phase mid-ocean ridge model. The developments of such a model will be discussed. References: [1] R. F. Katz, Journal of Petrology, volume 49, issue 12, page 2099

Three-dimensional piezoelectric boundary elements

NASA Astrophysics Data System (ADS)

Hill, Lisa Renee

boundary element method is demonstrated with two problems: a two-dimensional circular void and a three-dimensional spherical cavity, both inside infinite solids. Application of the program to a finite body with a centered, spherical void illustrates the complex nature of the mechanical and electrical coupling. Mode I fracture is also examined, combining the linear boundary element solution with the modified crack closure integral to determine strain energy release rates. Experimental research has shown that the strain, rather than the total, energy release rate is a better predictor of crack growth in piezoelectric materials. Solutions for a two-dimensional slit-like crack and for three-dimensional penny and elliptical cracks are presented. These solutions are developed using the insulated crack face electrical boundary condition. Although this boundary condition is used by most researchers, recent discussion indicates that it may not be an accurate model for the slender crack geometry. The boundary element method is used with the penny crack problem to investigate the effect of different electrical boundary conditions on the strain energy release rate. Use of a conductive crack face boundary condition, rather than an insulated one, acts to increase the strain energy release rate for the penny crack. These conductive strain energies are closer to the values determined using a permeable electrical boundary condition than to the original conductive boundary condition ones. It is shown that conclusions about structural integrity are strongly dependent on the choice of boundary conditions.

Grain-size dynamics beneath mid-ocean ridges: Implications for permeability and melt extraction.

PubMed

Turner, Andrew J; Katz, Richard F; Behn, Mark D

2015-03-01

Grain size is an important control on mantle viscosity and permeability, but is difficult or impossible to measure in situ. We construct a two-dimensional, single phase model for the steady state mean grain size beneath a mid-ocean ridge. The mantle rheology is modeled as a composite of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a plastic stress limiter. The mean grain size is calculated by the paleowattmeter relationship of Austin and Evans (2007). We investigate the sensitivity of our model to global variations in grain growth exponent, potential temperature, spreading-rate, and mantle hydration. We interpret the mean grain-size field in terms of its permeability to melt transport. The permeability structure due to mean grain size may be approximated as a high permeability region beneath a low permeability region. The transition between high and low permeability regions occurs across a boundary that is steeply inclined toward the ridge axis. We hypothesize that such a permeability structure generated from the variability of the mean grain size may focus melt toward the ridge axis, analogous to Sparks and Parmentier (1991)-type focusing. This focusing may, in turn, constrain the region where significant melt fractions are observed by seismic or magnetotelluric surveys. This interpretation of melt focusing via the grain-size permeability structure is consistent with MT observation of the asthenosphere beneath the East Pacific Rise. The grain-size field beneath MORs can vary over orders of magnitude The grain-size field affects the rheology and permeability of the asthenosphere The grain-size field may focus melt toward the ridge axis.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

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.

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.

Off-wall boundary conditions for turbulent flows obtained from buffer-layer minimal flow units

NASA Astrophysics Data System (ADS)

Garcia-Mayoral, Ricardo; Pierce, Brian; Wallace, James

2012-11-01

There is strong evidence that the transport processes in the buffer region of wall-bounded turbulence are common across various flow configurations, even in the embryonic turbulence in transition (Park et al., Phys. Fl. 24). We use this premise to develop off-wall boundary conditions for turbulent simulations. Boundary conditions are constructed from DNS databases using periodic minimal flow units and reduced order modeling. The DNS data was taken from a channel at Reτ = 400 and a zero-pressure gradient transitional boundary layer (Sayadi et al., submitted to J . FluidMech .) . Both types of boundary conditions were first tested on a DNS of the core of the channel flow with the aim of extending their application to LES and to spatially evolving flows. 2012 CTR Summer Program.

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.

Inhomogeneous Radiation Boundary Conditions Simulating Incoming Acoustic Waves for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Fang, Jun; Kurbatskii, Konstantin A.

1996-01-01

A set of nonhomogeneous radiation and outflow conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as nondispersive ans nondissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is necessary The proposed nonhomogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes.

Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hintermueller, M., E-mail: hint@math.hu-berlin.de; Kao, C.-Y., E-mail: Ckao@claremontmckenna.edu; Laurain, A., E-mail: laurain@math.hu-berlin.de

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 thresholdmore » 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.« less

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

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

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

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

Transient pressure-pulse decay permeability measurements in the Barnett shale

NASA Astrophysics Data System (ADS)

Bhandari, A. R.; Reece, J.; Cronin, M. B.; Flemings, P. B.; Polito, P. J.

2012-12-01

We conducted transient pressure-pulse decay permeability measurements on core plugs of the Barnett shale using a hydrostatic pressure cell. Core plugs, 3.8 cm in diameter and less than 2.5 cm in length, were prepared from a core obtained at a depth of approximately 2330 m from the Mitchel Energy 2 T. P. Sims well in the Mississippian Barnett Formation (Loucks and Ruppel, 2007). We performed permeability measurements of the core plugs using argon at varying confining pressures in two different directions (perpendicular and parallel to bedding planes). We calculate gas permeability from changes in pressure with time using the analytical solution of the pressure diffusion equation with appropriate boundary conditions for our test setup (Dicker and Smits, 1988). Based on our limited results, we interpret 2 × 10-18 m2 for vertical permeability and 156 × 10-18 m2 for horizontal permeability. We demonstrate an extreme stress dependence of the horizontal flow permeability where permeability decreases from 156 × 10-18 m2 to 2.5 × 10-18 m2 as the confining stress is increased from 3.5 to 35 MPa. These permeability measurements are at the high side of other pulsed permeability measurements in the Barnett shale (Bustin et al. 2008; Vermylen, 2011). Permeabilities calculated from mercury injection capillary pressure curves, using theoretically derived permeability-capillary pressure models based on parallel tubes assumption, are orders of magnitude less than our transient pressure-pulse decay permeability measurements (for example, 3.7×10-21 m2 (this study), 10-21 -10-20 m2 (Sigal, 2007), 10-20 -10-17 m2 (Prince et al., 2010)). We interpret that the high measured permeabilities are due to microfractures in the sample. At this point, we do not know if the microfractures are due to sampling disturbance (stress-relief induced) or represent an in-situ fracture network. Our study illustrates the importance of characterization of microfractures at the core scale to understand

Fluid flow in a porous medium with transverse permeability discontinuity

NASA Astrophysics Data System (ADS)

Pavlovskaya, Galina E.; Meersmann, Thomas; Jin, Chunyu; Rigby, Sean P.

2018-04-01

Magnetic resonance imaging (MRI) velocimetry methods are used to study fully developed axially symmetric fluid flow in a model porous medium of cylindrical symmetry with a transverse permeability discontinuity. Spatial mapping of fluid flow results in radial velocity profiles. High spatial resolution of these profiles allows estimating the slip in velocities at the boundary with a permeability discontinuity zone in a sample. The profiles are compared to theoretical velocity fields for a fully developed axially symmetric flow in a cylinder derived from the Beavers-Joseph [G. S. Beavers and D. D. Joseph, J. Fluid Mech. 30, 197 (1967), 10.1017/S0022112067001375] and Brinkman [H. C. Brinkman, Appl. Sci. Res. A 1, 27 (1947), 10.1007/BF02120313] models. Velocity fields are also computed using pore-scale lattice Boltzmann modeling (LBM) where the assumption about the boundary could be omitted. Both approaches give good agreement between theory and experiment, though LBM velocity fields follow the experiment more closely. This work shows great promise for MRI velocimetry methods in addressing the boundary behavior of fluids in opaque heterogeneous porous media.

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nordström, Jan, E-mail: jan.nordstrom@liu.se; Wahlsten, Markus, E-mail: markus.wahlsten@liu.se

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 themore » Euler equations.« less

On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains

NASA Astrophysics Data System (ADS)

Cantrell, Robert Stephen; Cosner, Chris

We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions.

Boundary conditions, dimensionality, topology and size dependence of the superconducting transition temperature

NASA Astrophysics Data System (ADS)

Fink, Herman J.; Haley, Stephen B.; Giuraniuc, Claudiu V.; Kozhevnikov, Vladimir F.; Indekeu, Joseph O.

2005-11-01

For various sample geometries (slabs, cylinders, spheres, hypercubes), de Gennes' boundary condition parameter b is used to study its effect upon the transition temperature Tc of a superconductor. For b > 0 the order parameter at the surface is decreased, and as a consequence Tc is reduced, while for b < 0 the order parameter at the surface is increased, thereby enhancing Tc of a specimen in zero magnetic field. Exact solutions, derived by Fink and Haley (Int. J. mod. Phys. B, 17, 2171 (2003)), of the order parameter of a slab of finite thickness as a function of temperature are presented, both for reduced and enhanced transition (nucleation) temperatures. At the nucleation temperature the order parameter approaches zero. This concise review closes with a link established between de Gennes' microscopic boundary condition and the Ginzburg-Landau phenomenological approach, and a discussion of some relevant experiments. For example, applying the boundary condition with b < 0 to tin whiskers elucidates the increase of Tc with strain.

MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

PubMed Central

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

A new technique for observationally derived boundary conditions for space weather

NASA Astrophysics Data System (ADS)

Pagano, Paolo; Mackay, Duncan Hendry; Yeates, Anthony Robinson

2018-04-01

Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods: To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results.The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4 R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4 R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions: In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.

Evolution of passive movement in advective environments: General boundary condition

NASA Astrophysics Data System (ADS)

Zhou, Peng; Zhao, Xiao-Qiang

2018-03-01

In a previous work [16], Lou et al. studied a Lotka-Volterra competition-diffusion-advection system, where two species are supposed to differ only in their advection rates and the environment is assumed to be spatially homogeneous and closed (no-flux boundary condition), and showed that weaker advective movements are more beneficial for species to win the competition. In this paper, we aim to extend this result to a more general situation, where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard Dirichlet, Neumann and Robin type conditions as special cases. Our main approaches are to exclude the existence of co-existence (positive) steady state and to provide a clear picture on the stability of semi-trivial steady states, where we introduced new ideas and techniques to overcome the emerging difficulties. Based on these two aspects and the theory of abstract competitive systems, we achieve a complete understanding on the global dynamics.

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

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.

(2,2) and (0,4) supersymmetric boundary conditions in 3d N =4 theories and type IIB branes

NASA Astrophysics Data System (ADS)

Chung, Hee-Joong; Okazaki, Tadashi

2017-10-01

The half-BPS boundary conditions preserving N =(2 ,2 ) and N =(0 ,4 ) supersymmetry in 3d N =4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Nahm-like equations arise in the vector multiplet BPS boundary condition preserving N =(0 ,4 ) supersymmetry, and Robin-type boundary conditions appear for the hypermultiplet coupled to the vector multiplet when N =(2 ,2 ) supersymmetry is preserved. The half-BPS boundary conditions are realized in the brane configurations of type IIB string theory.

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

NASA Astrophysics Data System (ADS)

Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

2016-07-01

The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the ;free; operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.

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.

Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines

NASA Astrophysics Data System (ADS)

Qian, Wei; Werner, Wendelin

2018-06-01

We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary-touching zero-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.

Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density groundwater benchmark problem

USGS Publications Warehouse

Konikow, Leonard 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.

Definition of boundary and initial conditions in the analysis of saturated ground-water flow systems - An introduction

USGS Publications Warehouse

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.

Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan

2017-07-01

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.

Involving the Navier-Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method.

PubMed

Verschaeve, Joris C G

2011-06-13

By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

Caprock integrity susceptibility to permeable fracture creation

DOE PAGES

Frash, Luke; Carey, James William; Ickes, Timothy Lee; ...

2017-07-14

Caprock leakage is of crucial concern for environmentally and economically sustainable development of carbon dioxide sequestration and utilization operations. One potential leakage pathway is through fractures or faults that penetrate the caprock. In this study, we investigate the permeability induced by fracturing initially intact Marcellus shale outcrop specimens at stressed conditions using a triaxial direct-shear method. Measurements of induced permeability, fracture geometry, displacement, and applied stresses were all obtained at stressed conditions to investigate the coupled processes of fracturing and fluid flow as may occur in the subsurface. Fracture geometry was directly observed at stressed conditions using X-ray radiography video.more » Numerical simulation was performed to evaluate the stress distribution developed in the experiments. Our experiments show that permeability induced by fracturing is strongly dependent on the stresses at which the fractures are created, the magnitude of shearing displacement, and the duration of flow. The strongest permeability contrast was observed when comparing specimens fractured at low stress to others fractured at higher stress. Measureable fracture permeability decreased by up to 7 orders of magnitude over a corresponding triaxial confining stress range of 3.5 MPa to 30 MPa. These results show that increasing stress, depth, and time are all significant permeability inhibitors that may limit potential leakage through fractured caprock.« less

Caprock integrity susceptibility to permeable fracture creation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frash, Luke; Carey, James William; Ickes, Timothy Lee

Caprock leakage is of crucial concern for environmentally and economically sustainable development of carbon dioxide sequestration and utilization operations. One potential leakage pathway is through fractures or faults that penetrate the caprock. In this study, we investigate the permeability induced by fracturing initially intact Marcellus shale outcrop specimens at stressed conditions using a triaxial direct-shear method. Measurements of induced permeability, fracture geometry, displacement, and applied stresses were all obtained at stressed conditions to investigate the coupled processes of fracturing and fluid flow as may occur in the subsurface. Fracture geometry was directly observed at stressed conditions using X-ray radiography video.more » Numerical simulation was performed to evaluate the stress distribution developed in the experiments. Our experiments show that permeability induced by fracturing is strongly dependent on the stresses at which the fractures are created, the magnitude of shearing displacement, and the duration of flow. The strongest permeability contrast was observed when comparing specimens fractured at low stress to others fractured at higher stress. Measureable fracture permeability decreased by up to 7 orders of magnitude over a corresponding triaxial confining stress range of 3.5 MPa to 30 MPa. These results show that increasing stress, depth, and time are all significant permeability inhibitors that may limit potential leakage through fractured caprock.« less

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.

A 3D Model for Gas Transfer, Storage and Resulting Displacement in a Permeable Volcanic Edifice

NASA Astrophysics Data System (ADS)

Collinson, Amy; Neuberg, Jurgen

2014-05-01

The total volume of gas in a magma, dissolved and subsequently exsolved, greatly influences the degree of explosiveness of a volcanic system. There is a marked contrast between the behaviour of a volcano in an open system compared to one which is closed. Whilst gas release is evident from surface gas emission measurements, gas storage is also thought to play an important role, as evidenced by large gas emissions after some large dome collapse events, suggesting gas may be stored in large volumes at shallow depths within the dome and edifice. Consequently, it is essential to understand degassing, to appreciate how much gas may be stored and where, and under what conditions it may be transferred or emitted to the atmosphere. We use previous experimental data on permeabilities to create 3D numerical models to investigate gas transport and storage in a permeable volcanic edifice. We combine the continuity equation, Darcy's law and the ideal gas law to derive a partial differential equation which is solved using a finite element method to obtain the gas pressure. The associated pressure gradient is then used within Darcy's law to calculate the gas velocity. In addition, we use the momentum equation to investigate how the presence of gas and variations in permeability influence the rate and degree of deformation in the volcanic edifice. Hence this provides two important surface constraints: gas emissions and surface displacement. Geometries are created to simulate the topography of actual volcanoes and the pressure and permeabilities incorporated into the model as boundary and domain conditions, respectively. This method is applied to investigate a variety of volcanological phenomena affecting gas, for example regions of high permeability due to fractures, or low permeability due to sealing.

Acoustic impedance of micro perforated membranes: Velocity continuity condition at the perforation boundary.

PubMed

Li, Chenxi; Cazzolato, Ben; Zander, Anthony

2016-01-01

The classic analytical model for the sound absorption of micro perforated materials is well developed and is based on a boundary condition where the velocity of the material is assumed to be zero, which is accurate when the material vibration is negligible. This paper develops an analytical model for finite-sized circular micro perforated membranes (MPMs) by applying a boundary condition such that the velocity of air particles on the hole wall boundary is equal to the membrane vibration velocity (a zero-slip condition). The acoustic impedance of the perforation, which varies with its position, is investigated. A prediction method for the overall impedance of the holes and the combined impedance of the MPM is also provided. The experimental results for four different MPM configurations are used to validate the model and good agreement between the experimental and predicted results is achieved.

Experimental Validation of Model Updating and Damage Detection via Eigenvalue Sensitivity Methods with Artificial Boundary Conditions

DTIC Science & Technology

2017-09-01

VALIDATION OF MODEL UPDATING AND DAMAGE DETECTION VIA EIGENVALUE SENSITIVITY METHODS WITH ARTIFICIAL BOUNDARY CONDITIONS by Matthew D. Bouwense...VALIDATION OF MODEL UPDATING AND DAMAGE DETECTION VIA EIGENVALUE SENSITIVITY METHODS WITH ARTIFICIAL BOUNDARY CONDITIONS 5. FUNDING NUMBERS 6. AUTHOR...unlimited. EXPERIMENTAL VALIDATION OF MODEL UPDATING AND DAMAGE DETECTION VIA EIGENVALUE SENSITIVITY METHODS WITH ARTIFICIAL BOUNDARY

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.

Evaporation from soils subjected to natural boundary conditions at the land-atmospheric interface

NASA Astrophysics Data System (ADS)

Smits, K.; Illngasekare, T.; Ngo, V.; Cihan, A.

2012-04-01

Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance in semiarid and arid regions. However, there is no agreement on the best methodology to determine evaporation under different boundary conditions at the land surface. This becomes critical in developing models that couples land to the atmosphere. Because it is difficult to measure evaporation from soil, with the exception of using lysimeters, numerous formulations have been proposed to establish a relationship between the rate of evaporation and soil moisture and/or soil temperature and thermal properties. Different formulations vary in how they partition available energy. A need exists to systematically compare existing methods to experimental data under highly controlled conditions not achievable in the field. The goal of this work is to perform controlled experiments under transient conditions of soil moisture, temperature and wind at the land/atmospheric interface to test different conceptual and mathematical formulations for the soil surface boundary conditions to develop appropriate numerical models to be used in simulations. In this study, to better understand the coupled water-vapor-heat flow processes in the shallow subsurface near the land surface, we modified a previously developed theory by Smits et al. [2011] that allows non-equilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. The model did not implement fitting parameters such as a vapor enhancement factor that is commonly introduced into the vapor diffusion coefficient as an arbitrary multiplication factor. In order to experimentally test the numerical formulations/code, we performed a two-dimensional physical model experiment under varying boundary conditions using test sand for which the hydraulic and thermal properties were well characterized. Precision data under well-controlled transient heat and

Influence of Boundary Conditions on Simulated U.S. Air Quality

EPA Science Inventory

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...

A mixed boundary representation to simulate the displacement of a biofluid by a biomaterial in porous media.

PubMed

Widmer, René P; Ferguson, Stephen J

2011-05-01

Characterization of the biomaterial flow through porous bone is crucial for the success of the bone augmentation process in vertebroplasty. The biofluid, biomaterial, and local morphological bone characteristics determine the final shape of the filling, which is important both for the post-treatment mechanical loading and the risk of intraoperative extraosseous leakage. We have developed a computational model that describes the flow of biomaterials in porous bone structures by considering the material porosity, the region-dependent intrinsic permeability of the porous structure, the rheological properties of the biomaterial, and the boundary conditions of the filling process. To simulate the process of the substitution of a biofluid (bone marrow) by a biomaterial (bone cement), we developed a hybrid formulation to describe the evolution of the fluid boundary and properties and coupled it to a modified version of Darcy's law. The apparent rheological properties are derived from a fluid-fluid interface tracking algorithm and a mixed boundary representation. The region- specific intrinsic permeability of the bone is governed by an empirical relationship resulting from a fitting process of experimental data. In a first step, we verified the model by studying the displacement process in spherical domains, where the spreading pattern is known in advance. The mixed boundary model demonstrated, as expected, that the determinants of the spreading pattern are the local intrinsic permeability of the porous matrix and the ratio of the viscosity of the fluids that are contributing to the displacement process. The simulations also illustrate the sensitivity of the mixed boundary representation to anisotropic permeability, which is related to the directional dependent microstructural properties of the porous medium. Furthermore, we compared the nonlinear finite element model to different published experimental studies and found a moderate to good agreement (R(2)=0.9895 for a one

Imaging and computational considerations for image computed permeability: Operating envelope of Digital Rock Physics

NASA Astrophysics Data System (ADS)

Saxena, Nishank; Hows, Amie; Hofmann, Ronny; Alpak, Faruk O.; Freeman, Justin; Hunter, Sander; Appel, Matthias

2018-06-01

This study defines the optimal operating envelope of the Digital Rock technology from the perspective of imaging and numerical simulations of transport properties. Imaging larger volumes of rocks for Digital Rock Physics (DRP) analysis improves the chances of achieving a Representative Elementary Volume (REV) at which flow-based simulations (1) do not vary with change in rock volume, and (2) is insensitive to the choice of boundary conditions. However, this often comes at the expense of image resolution. This trade-off exists due to the finiteness of current state-of-the-art imaging detectors. Imaging and analyzing digital rocks that sample the REV and still sufficiently resolve pore throats is critical to ensure simulation quality and robustness of rock property trends for further analysis. We find that at least 10 voxels are needed to sufficiently resolve pore throats for single phase fluid flow simulations. If this condition is not met, additional analyses and corrections may allow for meaningful comparisons between simulation results and laboratory measurements of permeability, but some cases may fall outside the current technical feasibility of DRP. On the other hand, we find that the ratio of field of view and effective grain size provides a reliable measure of the REV for siliciclastic rocks. If this ratio is greater than 5, the coefficient of variation for single-phase permeability simulations drops below 15%. These imaging considerations are crucial when comparing digitally computed rock flow properties with those measured in the laboratory. We find that the current imaging methods are sufficient to achieve both REV (with respect to numerical boundary conditions) and required image resolution to perform digital core analysis for coarse to fine-grained sandstones.

Boundary conditions estimation on a road network using compressed sensing.

DOT National Transportation Integrated Search

2016-02-01

This report presents a new boundary condition estimation framework for transportation networks in which : the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a : Hamilton-Jacobi equation, we pose th...

Micromechanics, Fracture Mechanics and Gas Permeability of Composite Laminates for Cryogenic Storage Systems

NASA Technical Reports Server (NTRS)

Choi, Sukjoo; Sankar, Bhavani; Ebaugh, Newton C.

2005-01-01

A micromechanics method is developed to investigate microcrack propagation in a liquid hydrogen composite tank at cryogenic temperature. The unit cell is modeled using square and hexagonal shapes depends on fiber and matrix layout from microscopic images of composite laminates. Periodic boundary conditions are applied to the unit cell. The temperature dependent properties are taken into account in the analysis. The laminate properties estimated by the micromechanics method are compared with empirical solutions using constituent properties. The micro stresses in the fiber and matrix phases based on boundary conditions in laminate level are calculated to predict the formation of microcracks in the matrix. The method is applied to an actual liquid hydrogen storage system. The analysis predicts micro stresses in the matrix phase are large enough to cause microcracks in the composite. Stress singularity of a transverse crack normal to a ply-interface is investigated to predict the fracture behavior at cryogenic conditions using analytical and finite element analysis. When a transverse crack touches a ply-interface of a composite layer with same fiber orientation, the stress singularity is equal to 1/2. When the transverse crack propagates to a stiffer layer normal to the ply-direction, the singularity becomes less than 1/2 and vice versa. Finite element analysis is performed to predict the fracture toughness of a laminated beam subjected to fracture loads measured by four-point bending tests at room and cryogenic temperatures. As results, the fracture load at cryogenic temperature is significantly lower than that at room temperature. However, when thermal stresses are taken into consideration, for both cases of room and cryogenic temperatures, the difference of the fracture toughness becomes insignificant. The result indicates fracture toughness is a characteristic property, which is independent to temperature changes. The experimental analysis is performed to

Continuum theory of edge states of topological insulators: variational principle and boundary conditions.

PubMed

Medhi, Amal; Shenoy, Vijay B

2012-09-05

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

On flows of viscoelastic fluids under threshold-slip boundary conditions

NASA Astrophysics Data System (ADS)

Baranovskii, E. S.

2018-03-01

We investigate a boundary-value problem for the steady isothermal flow of an incompressible viscoelastic fluid of Oldroyd type in a 3D bounded domain with impermeable walls. We use the Fujita threshold-slip boundary condition. This condition states that the fluid can slip along a solid surface when the shear stresses reach a certain critical value; otherwise the slipping velocity is zero. Assuming that the flow domain is not rotationally symmetric, we prove an existence theorem for the corresponding slip problem in the framework of weak solutions. The proof uses methods for solving variational inequalities with pseudo-monotone operators and convex functionals, the method of introduction of auxiliary viscosity, as well as a passage-to-limit procedure based on energy estimates of approximate solutions, Korn’s inequality, and compactness arguments. Also, some properties and estimates of weak solutions are established.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Detergent Induction of HEK 293A Cell Membrane Permeability Measured under Quiescent and Superfusion Conditions Using Whole Cell Patch Clamp

PubMed Central

2015-01-01

Detergents have several biological applications but present cytotoxicity concerns, since they can solubilize cell membranes. Using the IonFlux 16, an ensemble whole cell planar patch clamp, we observed that anionic sodium dodecyl sulfate (SDS), cationic cetyltrimethylammonium bromide (CTAB), and cationic, fluorescent octadecyl rhodamine B (ORB) increased the membrane permeability of cells substantially within a second of exposure, under superfusion conditions. Increased permeability was irreversible for 15 min. At subsolubilizing detergent concentrations, patched cells showed increased membrane currents that reached a steady state and were intact when imaged using fluorescence microscopy. SDS solubilized cells at concentrations of 2 mM (2× CMC), while CTAB did not solubilize cells even at concentrations of 10 mM (1000× CMC). The relative activity for plasma membrane current induction was 1:20:14 for SDS, CTAB, and ORB, respectively. Under quiescent conditions, the relative ratio of lipid to detergent in cell membranes at the onset of membrane permeability was 1:7:5 for SDS, CTAB, and ORB, respectively. The partition constants (K) for SDS, CTAB, and ORB were 23000, 55000, and 39000 M–1, respectively. Combining the whole cell patch clamp data and XTT viability data, SDS ≤ 0.2 mM and CTAB and ORB ≤ 1 mM induced cell membrane permeability without causing acute toxicity. PMID:24548291

An Evaluation of a Phase-Lag Boundary Condition for Francis Hydroturbine Simulations Using a Pressure-Based Solver

NASA Astrophysics Data System (ADS)

Wouden, Alex; Cimbala, John; Lewis, Bryan

2014-11-01

While the periodic boundary condition is useful for handling rotational symmetry in many axisymmetric geometries, its application fails for analysis of rotor-stator interaction (RSI) in multi-stage turbomachinery flow. The inadequacy arises from the underlying geometry where the blade counts per row differ, since the blade counts are crafted to deter the destructive harmonic forces of synchronous blade passing. Therefore, to achieve the computational advantage of modeling a single blade passage per row while preserving the integrity of the RSI, a phase-lag boundary condition is adapted to OpenFOAM® software's incompressible pressure-based solver. The phase-lag construct is accomplished through restating the implicit periodic boundary condition as a constant boundary condition that is updated at each time step with phase-shifted data from the coupled cells adjacent to the boundary. Its effectiveness is demonstrated using a typical Francis hydroturbine modeled as single- and double-passages with phase-lag boundary conditions. The evaluation of the phase-lag condition is based on the correspondence of the overall computational performance and the calculated flow parameters of the phase-lag simulations with those of a baseline full-wheel simulation. Funded in part by DOE Award Number: DE-EE0002667.

Automatic Generation of Boundary Conditions Using Demons Nonrigid Image Registration for Use in 3-D Modality-Independent Elastography

PubMed Central

Ou, Jao J.; Ong, Rowena E.; Miga, Michael I.

2013-01-01

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method. PMID:21690002

Automatic generation of boundary conditions using demons nonrigid image registration for use in 3-D modality-independent elastography.

PubMed

Pheiffer, Thomas S; Ou, Jao J; Ong, Rowena E; Miga, Michael I

2011-09-01

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method.

Numerical simulation of supersonic flow using a new analytical bleed boundary condition

NASA Technical Reports Server (NTRS)

Harloff, G. J.; Smith, G. E.

1995-01-01

A new analytical bleed boundary condition is used to compute flowfields for a strong oblique shock wave/boundary layer interaction with a baseline and three bleed rates at a freestream Mach number of 2.47 with an 8 deg shock generator. The computational results are compared to experimental Pitot pressure profiles and wall static pressures through the interaction region. An algebraic turbulence model is employed for the bleed and baseline cases, and a one equation model is also used for the baseline case where the boundary layer is separated.

Influence of the outer boundary condition on models of AGB stars

NASA Astrophysics Data System (ADS)

Wagstaff, G.; Weiss, A.

2018-07-01

Current implementations of the stellar atmosphere typically derive boundary conditions for the interior model from either grey plane-parallel atmospheres or scaled solar atmospheres, neither of which can be considered to have appropriate underlying assumptions for the Thermally Pulsing Asymptotic Giant Branch (TP-AGB). This paper discusses the treatment and influence of the outer boundary condition within stellar evolution codes, and the resulting effects on the AGB evolution. The complex interaction of processes, such as the third dredge up and mass-loss, governing the TP-AGB can be affected by varying the treatment of this boundary condition. Presented here are the results from altering the geometry, opacities, and the implementation of a grid of MARCS/COMARCS model atmospheres in order to improve this treatment. Although there are changes in the TP-AGB evolution, observable quantities, such as the final core mass, are not significantly altered as a result of the change of atmospheric treatment. During the course of the investigation, a previously unseen phenomenon in the AGB models was observed and further investigated. This is believed to be physical, although arising from specific conditions which make its presence unlikely. If it were present in stars, this phenomenon would increase the carbon-star lifetime above 10 Myr and increase the final core mass by ˜0.1 M⊙ in the narrow initial-mass range where it was observed (˜2-2.3 M⊙).

Influence of the Outer Boundary Condition on models of AGB stars

NASA Astrophysics Data System (ADS)

Wagstaff, G.; Weiss, A.

2018-04-01

Current implementations of the stellar atmosphere typically derive boundary conditions for the interior model from either grey plane-parallel atmospheres or scaled solar atmospheres, neither of which can be considered to have appropriate underlying assumptions for the Thermally Pulsing Asymptotic Giant Branch (TP-AGB). This paper discusses the treatment and influence of the outer boundary condition within stellar evolution codes, and the resulting effects on the AGB evolution. The complex interaction of processes, such as the third dredge up and mass loss, governing the TP-AGB can be affected by varying the treatment of this boundary condition. Presented here are the results from altering the geometry, opacities and the implementation of a grid of MARCS/COMARCS model atmospheres in order to improve this treatment. Although there are changes in the TP-AGB evolution, observable quantities, such as the final core mass, are not significantly altered as a result of the change of atmospheric treatment. During the course of the investigation, a previously unseen phenomena in the AGB models was observed and further investigated. This is believed to be physical, although arising from specific conditions which make its presence unlikely. If it were present in stars, this phenomenon would increase the carbon-star lifetime above 10Myr and increase the final core mass by ˜0.1M⊙ in the narrow initial-mass range where it was observed (˜2 - 2.3M⊙).

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.

Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

NASA Astrophysics Data System (ADS)

Dappiaggi, Claudio; Ferreira, Hugo R. C.; Juárez-Aubry, Benito A.

2018-04-01

We study a real, massive Klein-Gordon field in the Poincaré fundamental domain of the (d +1 )-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a nonhomogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincaré fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.

Experimental verification of electrostatic boundary conditions in gate-patterned quantum devices

NASA Astrophysics Data System (ADS)

Hou, H.; Chung, Y.; Rughoobur, G.; Hsiao, T. K.; Nasir, A.; Flewitt, A. J.; Griffiths, J. P.; Farrer, I.; Ritchie, D. A.; Ford, C. J. B.

2018-06-01

In a model of a gate-patterned quantum device, it is important to choose the correct electrostatic boundary conditions (BCs) in order to match experiment. In this study, we model gated-patterned devices in doped and undoped GaAs heterostructures for a variety of BCs. The best match is obtained for an unconstrained surface between the gates, with a dielectric region above it and a frozen layer of surface charge, together with a very deep back boundary. Experimentally, we find a  ∼0.2 V offset in pinch-off characteristics of 1D channels in a doped heterostructure before and after etching off a ZnO overlayer, as predicted by the model. Also, we observe a clear quantised current driven by a surface acoustic wave through a lateral induced n-i-n junction in an undoped heterostructure. In the model, the ability to pump electrons in this type of device is highly sensitive to the back BC. Using the improved boundary conditions, it is straightforward to model quantum devices quite accurately using standard software.

Transverse Chemotactic Migration of Bacteria from High to Low Permeability Regions in a Dual Permeability Porous Microfluidic Device

NASA Astrophysics Data System (ADS)

Singh, R.; Olson, M. S.

2011-12-01

Low permeability regions sandwiched between high permeability regions such as clay lenses are difficult to treat using conventional treatment methods. Trace concentrations of contaminants such as non-aqueous phase liquids (NAPLs) remain trapped in these regions and over the time diffuse out into surrounding water thereby acting as a long term source of groundwater contamination. Bacterial chemotaxis (directed migration toward a contaminant source), may be helpful in enhancing bioremediation of such contaminated sites. This study is focused on simulating a two-dimensional dual-permeability groundwater contamination scenario using microfluidic devices and evaluating transverse chemotactic migration of bacteria from high to low permeability regions. A novel bi-layer polydimethylsiloxane (PDMS) microfluidic device was fabricated using photolithography and soft lithography techniques to simulate contamination of a dual- permeability region due to leakage from an underground storage tank into a low permeability region. This device consists of a porous channel through which a bacterial suspension (Escherchia Coli HCB33) is flown and another channel for injecting contaminant/chemo-attractant (DL-aspertic acid) into the porous channel. The pore arrangement in the porous channel contains a 2-D low permeability region surrounded by high permeability regions on both sides. Experiments were performed under chemotactic and non-chemotactic (replacing attractant with buffer solution in the non porous channel) conditions. Images were captured in transverse pore throats at cross-sections 4.9, 9.8, and 19.6 mm downstream from the attractant injection point and bacteria were enumerated in the middle of each pore throat. Bacterial chemotaxis was quantified in terms of the change in relative bacterial counts in each pore throat at cross-sections 9.8 and 19.6 mm with respect to counts at the cross-section at 4.9 mm. Under non-chemotactic conditions, relative bacterial count was observed

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Dual permeability flow behavior for modeling horizontal well production in fractured-vuggy carbonate reservoirs

NASA Astrophysics Data System (ADS)

Guo, Jian-Chun; Nie, Ren-Shi; Jia, Yong-Lu

2012-09-01

SummaryFractured-vuggy carbonate reservoirs are composed of by matrix, fracture, and vug systems. This paper is the first investigation into the dual permeability flow issue for horizontal well production in a fractured-vuggy carbonate reservoir. Considering dispersed vugs in carbonate reservoirs and treating media directly connected with horizontal wellbore as the matrix and fracture systems, a test analysis model of a horizontal well was created, and triple porosity and dual permeability flow behavior were modeled. Standard log-log type curves were drawn up by numerical simulation and flow behavior characteristics were thoroughly analyzed. Numerical simulations showed that type curves are dominated by external boundary conditions as well as the permeability ratio of the fracture system to the sum of fracture and matrix systems. The parameter κ is only relevant to the dual permeability model, and if κ is one, then the dual permeability model is equivalent to the single permeability model. There are seven main flow regimes with constant rate of horizontal well production and five flow regimes with constant wellbore pressure of horizontal well production; different flow regimes have different flow behavior characteristics. Early radial flow and linear flow regimes are typical characteristics of horizontal well production; duration of early radial flow regime is usually short because formation thickness is generally less than 100 m. Derivative curves are W-shaped, which is a reflection of inter-porosity flows between matrix, fracture, and vug systems. A distorted W-shape, which could be produced in certain situations, such as one involving an erroneously low time of inter-porosity flows, would handicap the recognition of a linear flow regime. A real case application was successfully implemented, and some useful reservoir parameters (e.g., permeability and inter-porosity flow factor) were obtained from well testing interpretation.

Family boundary characteristics, work-family conflict and life satisfaction: A moderated mediation model.

PubMed

Qiu, Lin; Fan, Jinyan

2015-10-01

Although work-family border and boundary theory suggest individuals' boundary characteristics influence their work-family relationship, it is largely unknown how boundary flexibility and permeability mutually influence work-family conflict and subsequent employee outcomes. Moreover, the existing work-family conflict research has been mainly conducted in the United States and other Western countries. To address these gaps in the work-family literature, the present study examines a moderated mediation model regarding how family boundary characteristics may influence individuals' work-family conflict and life satisfaction with a sample of 278 Chinese full-time employees. Results showed that employees' family flexibility negatively related to their perceived work interference with family (WIF) and family interference with work (FIW), and both these two relationships were augmented by individuals' family permeability. In addition, WIF mediated the relationship between family flexibility and life satisfaction; the indirect effect of family flexibility on life satisfaction via WIF was stronger for individuals with higher family permeability. The theoretical and managerial implications of these findings are discussed. © 2014 International Union of Psychological Science.

Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions.

PubMed

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.

Gas storage, transport and pressure changes in an evolving permeable volcanic edifice

NASA Astrophysics Data System (ADS)

Collinson, A. S. D.; Neuberg, J. W.

2012-10-01

The total volume of gas in a magma, dissolved and subsequently exsolved, greatly influences the degree of explosiveness of a volcanic system. There is a marked contrast between the behaviour of a volcano in an "open" system compared to one which is "closed". It is therefore essential to understand the entire degassing process: gas transport, storage and loss. A particular focus of this study is the effect different permeabilities and pressure gradients within a volcanic edifice have on the degree and pattern of the gas velocity. Gas loss is modelled numerically in two dimensions using a finite element approach, which allows the specification of boundary conditions with respect to pressure and different permeability domains within the volcanic edifice. By combining the time-dependent continuity equation and Darcy's law, a partial differential equation is derived and solved for the pressure. The associated pressure gradient is then used within Darcy's law to determine the corresponding gas velocity distribution. This method is used not only for stationary systems in equilibrium, but also as a time-dependent progression. It permits the modelling of different situations to study how various volcanic characteristics affect the gas loss. The model is used to investigate the change in pressure and gas in response to time-dependent scenarios. These are a dome collapse or sudden increase in permeability by magma rupture at the conduit margin, the formation of cracks within the lava dome and sealing by crystallisation. Our results show that a combination of high and low permeability regions is required for effective gas storage. High permeability allows the gas to enter the system, but impermeable areas act to confine the gas, thereby increasing its pressure and consequently, increasing the amount of gas which may be dissolved in the melt. Furthermore, our results show that permeability is an essential factor influencing the response time to system changes, which could be

Reactive multi-particle collision dynamics with reactive boundary conditions

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Rohlf, Katrin

2018-07-01

In the present study, an off-lattice particle-based method called the reactive multi-particle collision (RMPC) dynamics is extended to model reaction-diffusion systems with reactive boundary conditions in which the a priori diffusion coefficient of the particles needs to be maintained throughout the simulation. To this end, the authors have made use of the so-called bath particles whose purpose is only to ensure proper diffusion of the main particles in the system. In order to model partial adsorption by a reactive boundary in the RMPC, the probability of a particle being adsorbed, once it hits the boundary, is calculated by drawing an analogy between the RMPC and Brownian Dynamics. The main advantages of the RMPC compared to other molecular based methods are less computational cost as well as conservation of mass, energy and momentum in the collision and free streaming steps. The proposed approach is tested on three reaction-diffusion systems and very good agreement with the solutions to their corresponding partial differential equations is observed.

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus

2005-03-01

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at 1-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace-type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding 1-loop divergences and 1-loop effective action actually exists. The present paper shows that, on the Euclidean 4-ball, only the scalar part of perturbative modes for quantum gravity is affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is 'confined' to the remaining fourth sector. The integral representation of the resulting ζ-function asymptotics on the Euclidean 4-ball is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.

Effect of magnetization boundary condition on cavity magnon polariton of YIG thin film.

PubMed

Jiang, H H; Xiao, Y; Hu, C M; Guo, H; Xia, K

2018-06-22

Motivated by recent studies of cavity magnon polariton (CMP), we extended a previous theoretical work to generalize microwave transmission calculation with various magnetization boundary condition of YIG thin film embedded in cavity. It is found that numerical implementation given in this paper can be easily applied to other magnetization boundary condition and extended to magnetic multilayers. Numerical results show that ferromagnetic resonance mode of microwave transmission spectrum, which is absent in previous calculation, can be recovered by altering the pinning condition of surface spins. The demonstrated reliability of our theory opens attractive perspectives for studying CMP of thin film with complicated surface magnetization distribution and magnetic multilayers.

Effect of magnetization boundary condition on cavity magnon polariton of YIG thin film

NASA Astrophysics Data System (ADS)

Jiang, H. H.; Xiao, Y.; Hu, C. M.; Guo, H.; Xia, K.

2018-06-01

Motivated by recent studies of cavity magnon polariton (CMP), we extended a previous theoretical work to generalize microwave transmission calculation with various magnetization boundary condition of YIG thin film embedded in cavity. It is found that numerical implementation given in this paper can be easily applied to other magnetization boundary condition and extended to magnetic multilayers. Numerical results show that ferromagnetic resonance mode of microwave transmission spectrum, which is absent in previous calculation, can be recovered by altering the pinning condition of surface spins. The demonstrated reliability of our theory opens attractive perspectives for studying CMP of thin film with complicated surface magnetization distribution and magnetic multilayers.

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.

What is Wrong with the Boundary Conditions in Column Tracer Tests

NASA Astrophysics Data System (ADS)

Zhan, H.

2007-12-01

Solute transport in a column is probably one of the most fundamental problems investigated in contaminant hydrology and soil physics because it serves as a benchmark for testing transport theories, for measuring dispersivities, etc. Despite its importance, there are still dispute and inconsistency on how to deal with the boundary conditions involved in such problems. The boundary condition could impose great influence upon transport in a column, particularly when the length of the column is relatively short, or the so-called Peclet number is not large. There are three types of boundary conditions to choose for transport in a column. Among these three types of boundary conditions, only the third-type boundary satisfies the mass balance requirement rigorously. The first type boundary, despite its frequent use in previous studies, could lead to serious mass balance problems. The most serious problem is on how to deal with the outlet boundary. Some studies have used a zero concentration gradient at the outlet (the so-called Danckwerts' boundary condition). This is named the model A. Another idea is to treat the finite length column as a part of an infinitely long column and to calculate the concentration at the outlet based on a formula developed for an infinitely long column. This is named the model B. The model A satisfies the mass balance requirement but was found to fit with the experimental data poorly. The model B does not satisfy the mass balance requirement, but usually agree well with the experimental data. So, the dilemma is: which model to choose? At present, most investigators prefer to choose the model B because of its close agreement with the experimental data, despite of its violation of the mass balance requirement. But the question is: why the model A, which satisfies the mass balance requirement, does not fit with the experimental data? It turns out that the advection-dispersion equation (ADE) that uses the Fick's first law to describe the

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

The effect of inlet boundary conditions in image-based CFD modeling of aortic flow

NASA Astrophysics Data System (ADS)

Madhavan, Sudharsan; Kemmerling, Erica Cherry

2016-11-01

CFD of cardiovascular flow is a growing and useful field, but simulations are subject to a number of sources of uncertainty which must be quantified. Our work focuses on the uncertainty introduced by the selection of inlet boundary conditions in an image-based, patient-specific model of the aorta. Specifically, we examined the differences between plug flow, fully developed parabolic flow, linear shear flows, skewed parabolic flow profiles, and Womersley flow. Only the shape of the inlet velocity profile was varied-all other parameters were held constant between simulations, including the physiologically realistic inlet flow rate waveform and outlet flow resistance. We found that flow solutions with different inlet conditions did not exhibit significant differences beyond 1 . 75 inlet diameters from the aortic root. Time averaged wall shear stress (TAWSS) was also calculated. The linear shear velocity boundary condition solution exhibited the highest spatially averaged TAWSS, about 2 . 5 % higher than the fully developed parabolic velocity boundary condition, which had the lowest spatially averaged TAWSS.

Hydrodynamic boundary condition of water on hydrophobic surfaces.

PubMed

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.

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

PubMed Central

Bardhan, Jaydeep P.; Knepley, Matthew G.

2014-01-01

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.more » 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.« less

Permeability of model porous medium formed by random discs

NASA Astrophysics Data System (ADS)

Gubaidullin, A. A.; Gubkin, A. S.; Igoshin, D. E.; Ignatev, P. A.

2018-03-01

Two-dimension model of the porous medium with skeleton of randomly located overlapping discs is proposed. The geometry and computational grid are built in open package Salome. Flow of Newtonian liquid in longitudinal and transverse directions is calculated and its flow rate is defined. The numerical solution of the Navier-Stokes equations for a given pressure drop at the boundaries of the area is realized in the open package OpenFOAM. Calculated value of flow rate is used for defining of permeability coefficient on the base of Darcy law. For evaluating of representativeness of computational domain the permeability coefficients in longitudinal and transverse directions are compered.

Use of an Accurate DNS Particulate Flow Method to Supply and Validate Boundary Conditions for the MFIX Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhi-Gang Feng

2012-05-31

The simulation of particulate flows for industrial applications often requires the use of two-fluid models, where the solid particles are considered as a separate continuous phase. One of the underlining uncertainties in the use of the two-fluid models in multiphase computations comes from the boundary condition of the solid phase. Typically, the gas or liquid fluid boundary condition at a solid wall is the so called no-slip condition, which has been widely accepted to be valid for single-phase fluid dynamics provided that the Knudsen number is low. However, the boundary condition for the solid phase is not well understood. Themore » no-slip condition at a solid boundary is not a valid assumption for the solid phase. Instead, several researchers advocate a slip condition as a more appropriate boundary condition. However, the question on the selection of an exact slip length or a slip velocity coefficient is still unanswered. Experimental or numerical simulation data are needed in order to determinate the slip boundary condition that is applicable to a two-fluid model. The goal of this project is to improve the performance and accuracy of the boundary conditions used in two-fluid models such as the MFIX code, which is frequently used in multiphase flow simulations. The specific objectives of the project are to use first principles embedded in a validated Direct Numerical Simulation particulate flow numerical program, which uses the Immersed Boundary method (DNS-IB) and the Direct Forcing scheme in order to establish, modify and validate needed energy and momentum boundary conditions for the MFIX code. To achieve these objectives, we have developed a highly efficient DNS code and conducted numerical simulations to investigate the particle-wall and particle-particle interactions in particulate flows. Most of our research findings have been reported in major conferences and archived journals, which are listed in Section 7 of this report. In this report, we will

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.

Investigation on porosity and permeability change of Mount Simon sandstone (Knox County, IN, USA) under geological CO 2 sequestration conditions: a numerical simulation approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Liwei; Soong, Yee; Dilmore, Robert M.

In this paper, a numerical model was developed to simulate reactive transport with porosity and permeability change of Mount Simon sandstone (samples from Knox County, IN) after 180 days of exposure to CO 2-saturated brine under CO 2 sequestration conditions. The model predicted formation of a high-porosity zone adjacent to the surface of the sample in contact with bulk brine, and a lower porosity zone just beyond that high-porosity zone along the path from sample/bulk brine interface to sample core. The formation of the high porosity zone was attributed to dissolution of quartz and muscovite/illite, while the formation of themore » lower porosity zone adjacent to the aforementioned high porosity zone was attributed to precipitation of kaolinite and feldspar. The model predicted a 40% permeability increase for the Knox sandstone sample after 180 days of exposure to CO 2-saturated brine, which was consistent with laboratory-measured permeability results. Model-predicted solution chemistry results were also found to be consistent with laboratory-measured solution chemistry data. Finally, initial porosity, initial feldspar content and the exponent n value (determined by pore structure and tortuosity) used in permeability calculations were three important factors affecting permeability evolution of sandstone samples under CO 2 sequestration conditions.« less

Investigation on porosity and permeability change of Mount Simon sandstone (Knox County, IN, USA) under geological CO 2 sequestration conditions: a numerical simulation approach

DOE PAGES

Zhang, Liwei; Soong, Yee; Dilmore, Robert M.

2016-01-14

In this paper, a numerical model was developed to simulate reactive transport with porosity and permeability change of Mount Simon sandstone (samples from Knox County, IN) after 180 days of exposure to CO 2-saturated brine under CO 2 sequestration conditions. The model predicted formation of a high-porosity zone adjacent to the surface of the sample in contact with bulk brine, and a lower porosity zone just beyond that high-porosity zone along the path from sample/bulk brine interface to sample core. The formation of the high porosity zone was attributed to dissolution of quartz and muscovite/illite, while the formation of themore » lower porosity zone adjacent to the aforementioned high porosity zone was attributed to precipitation of kaolinite and feldspar. The model predicted a 40% permeability increase for the Knox sandstone sample after 180 days of exposure to CO 2-saturated brine, which was consistent with laboratory-measured permeability results. Model-predicted solution chemistry results were also found to be consistent with laboratory-measured solution chemistry data. Finally, initial porosity, initial feldspar content and the exponent n value (determined by pore structure and tortuosity) used in permeability calculations were three important factors affecting permeability evolution of sandstone samples under CO 2 sequestration conditions.« less

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

PubMed Central

Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

2015-01-01

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to

Stable boundary conditions and difference schemes for Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Dutt, P.

1985-01-01

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Cylindrical Couette flow of a rarefied gas: Effect of a boundary condition on the inverted velocity profile.

PubMed

Kosuge, Shingo

2015-07-01

The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated under the following two kinds of kinetic boundary conditions. One is the modified Maxwell-type boundary condition proposed by Dadzie and Méolans [J. Math. Phys. 45, 1804 (2004)] and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. An asymptotic analysis of the Boltzmann equation for small Knudsen numbers and a numerical analysis of the Bhatnagar-Gross-Krook model equation for a wide range of the Knudsen number are performed to clarify the effect of each accommodation coefficient as well as of the boundary condition itself on the behavior of the gas, especially on the flow-velocity profile. As a result, the velocity-slip and temperature-jump conditions corresponding to the above kinetic boundary conditions are derived, which are necessary for the fluid-dynamic description of the problem for small Knudsen numbers. The parameter range for the onset of the velocity inversion phenomenon, which is related mainly to the decrease in the tangential momentum accommodation, is also obtained.

The topological basis expression of four-qubit XXZ spin chain with twist boundary condition

NASA Astrophysics Data System (ADS)

Du, Guijiao; Xue, Kang; Zhou, Chengcheng; Sun, Chunfang; Wang, Gangcheng

2013-07-01

We investigate the XXZ model's characteristic with the twisted boundary condition and the topological basis expression. Owing to twist boundary condition, the ground state energy will changing back and forth between E_{13} and E_{15} by modulate the parameter φ . By using TLA generators, the XXZ model's Hamiltonian can be constructed. All the eigenstates can be expressed by topological basis, and the whole of eigenstates' entanglement are maximally entangle states (Q(|φ _i> )=1).

Changes in the lower boundary condition of water fluxes in the NOAH land surface scheme

NASA Astrophysics Data System (ADS)

Lohmann, D.; Peters-Lidard, C. D.

2002-05-01

One problem with current land surface schemes (LSS) used in weather prediction and climate models is their inabilty to reproduce streamflow in large river basins. This can be attributed to the weak representation of their upper (infiltration) and lower (baseflow) boundary conditions in their water balance / transport equations. Operational (traditional) hydrological models, which operate on the same spatial scale as a LSS, on the other hand, are able to reproduce streamflow time series. Their infiltration and baseflow equations are often empirically based and therefore have been neglected by the LSS community. It must be argued that we need to include a better representation of long time scales (as represented by groundwater and baseflow) into the current LSS to make valuable predictions of streamflow and water resources. This talk concentrates on the lower boundary condition of water fluxes within LSS. It reviews briefly previous attempts to incorporate groundwater and more realistic lower boundary conditions into LSS and summarizes the effect on the runoff (baseflow) production time scales as compared to currently used lower boundary conditions in LSS. The NOAH - LSM in the LDAS and DMIP setting is used to introduce a simplified groundwater model, based on the linearized Boussinesq equation, and the TOPMODEL. The NOAH - LSM will be coupled to a linear routing model to investigate the effects of the new lower boundary condition on the water balance (in particular, streamflow) in small to medium sized catchments in the LDAS / DMIP domain.

The boundary conditions for simulations of a shake-table experiment on the seismic response of 3D slope

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.

Understanding the impact of insulating and conducting endplate boundary conditions on turbulence in CSDX through nonlocal simulations

DOE PAGES

Vaezi, P.; Holland, C.; Thakur, S. C.; ...

2017-04-01

The Controlled Shear Decorrelation Experiment (CSDX) linear plasma device provides a unique platform for investigating the underlying physics of self-regulating drift-wave turbulence/zonal flow dynamics. A minimal model of 3D drift-reduced nonlocal cold ion fluid equations which evolves density, vorticity, and electron temperature fluctuations, with proper sheath boundary conditions, is used to simulate dynamics of the turbulence in CSDX and its response to changes in parallel boundary conditions. These simulations are then carried out using the BOUndary Turbulence (BOUT++) framework and use equilibrium electron density and temperature profiles taken from experimental measurements. The results show that density gradient-driven drift-waves are themore » dominant instability in CSDX. However, the choice of insulating or conducting endplate boundary conditions affects the linear growth rates and energy balance of the system due to the absence or addition of Kelvin-Helmholtz modes generated by the sheath-driven equilibrium E × B shear and sheath-driven temperature gradient instability. Moreover, nonlinear simulation results show that the boundary conditions impact the turbulence structure and zonal flow formation, resulting in less broadband (more quasi-coherent) turbulence and weaker zonal flow in conducting boundary condition case. These results are qualitatively consistent with earlier experimental observations.« less

Hawking radiation, covariant boundary conditions, and vacuum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Rabin; Kulkarni, Shailesh

2009-04-15

The basic characteristics of the covariant chiral current and the covariant chiral energy-momentum tensor are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

On the Effective Construction of Compactly Supported Wavelets Satisfying Homogenous Boundary Conditions on the Interval

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.

Ground state for a massive scalar field in the BTZ spacetime with Robin boundary conditions

NASA Astrophysics Data System (ADS)

Bussola, Francesco; Dappiaggi, Claudio; Ferreira, Hugo R. C.; Khavkine, Igor

2017-11-01

We consider a real, massive scalar field in Bañados-Teitelboim-Zanelli spacetime, a 2 +1 -dimensional black hole solution of Einstein's field equations with a negative cosmological constant. First, we analyze the space of classical solutions in a mode decomposition, and we characterize the collection of all admissible boundary conditions of Robin type which can be imposed at infinity. Second, we investigate whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that for a subclass of the boundary conditions it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases, we show that bound state mode solutions exist and, therefore, such construction is not possible.

Boundary condition identification for a grid model by experimental and numerical dynamic analysis

NASA Astrophysics Data System (ADS)

Mao, Qiang; Devitis, John; Mazzotti, Matteo; Bartoli, Ivan; Moon, Franklin; Sjoblom, Kurt; Aktan, Emin

2015-04-01

There is a growing need to characterize unknown foundations and assess substructures in existing bridges. It is becoming an important issue for the serviceability and safety of bridges as well as for the possibility of partial reuse of existing infrastructures. Within this broader contest, this paper investigates the possibility of identifying, locating and quantifying changes of boundary conditions, by leveraging a simply supported grid structure with a composite deck. Multi-reference impact tests are operated for the grid model and modification of one supporting bearing is done by replacing a steel cylindrical roller with a roller of compliant material. Impact based modal analysis provide global modal parameters such as damped natural frequencies, mode shapes and flexibility matrix that are used as indicators of boundary condition changes. An updating process combining a hybrid optimization algorithm and the finite element software suit ABAQUS is presented in this paper. The updated ABAQUS model of the grid that simulates the supporting bearing with springs is used to detect and quantify the change of the boundary conditions.

Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

NASA Astrophysics Data System (ADS)

Musharbash, Eleonora; Nobile, Fabio

2018-02-01

In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.

ACF7 regulates colonic permeability.

PubMed

Liang, Yong; Shi, Chenzhang; Yang, Jun; Chen, Hongqi; Xia, Yang; Zhang, Peng; Wang, Feng; Han, Huazhong; Qin, Huanlong

2013-04-01

Colonic paracellular permeability is regulated by various factors, including dynamics of the cytoskeleton. Recently, ACF7 has been found to play a critical role in cytoskeletal dynamics as an essential integrator. To elucidate the physiological importance of ACF7 and paracellular permeability, we conditionally knocked out ACF7 in the intestinal mucosa of mice. Histopathological findings indicated that ACF7 deficiency resulted in significant interstitial proliferation and columnar epithelial cell rearrangement. Decreased colonic paracellular permeability was detected using a Ussing chamber and the FITC-inulin method. In order to clarify the underlying mechanism, we further analyzed the expression levels of three important tight junction proteins. Downregulation of ZO-1, occludin and claudin-1 was identified. Immunofluorescence provided strong evidence that ZO-1, occludin and claudin-1 were weakly stained. We hypothesized that ACF7 regulates cytoskeleton dynamics to alter mucosal epithelial arrangement and colonic paracellular permeability.

Influence of Contact Angle Boundary Condition on CFD Simulation of T-Junction

NASA Astrophysics Data System (ADS)

Arias, S.; Montlaur, A.

2018-03-01

In this work, we study the influence of the contact angle boundary condition on 3D CFD simulations of the bubble generation process occurring in a capillary T-junction. Numerical simulations have been performed with the commercial Computational Fluid Dynamics solver ANSYS Fluent v15.0.7. Experimental results serve as a reference to validate numerical results for four independent parameters: the bubble generation frequency, volume, velocity and length. CFD simulations accurately reproduce experimental results both from qualitative and quantitative points of view. Numerical results are very sensitive to the gas-liquid-wall contact angle boundary conditions, confirming that this is a fundamental parameter to obtain accurate CFD results for simulations of this kind of problems.

On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

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.

Generalization of the Ehrenfest theorem to quantum systems with periodical boundary conditions

NASA Astrophysics Data System (ADS)

Sanin, Andrey L.; Bagmanov, Andrey T.

2005-04-01

A generalization of Ehrenfest's theorem is discussed. For this purpose the quantum systems with periodical boundary conditions are being revised. The relations for time derivations of mean coordinate and momentum are derived once again. In comparison with Ehrenfest's theorem and its conventional quantities, the additional local terms occur which are caused boundaries. Because of this, the obtained new relations can be named as generalized. An example for using these relations is given.

Permeability evolution of shale during spontaneous imbibition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, N.; Karpyn, Z. T.; Liu, S.

Shales have small pore and throat sizes ranging from nano to micron scales, low porosity and limited permeability. The poor permeability and complex pore connectivity of shales pose technical challenges to (a) understanding flow and transport mechanisms in such systems and, (b) in predicting permeability changes under dynamic saturation conditions. This paper presents quantitative experimental evidence of the migration of water through a generic shale core plug using micro CT imaging. In addition, in-situ measurements of gas permeability were performed during counter-current spontaneous imbibition of water in nano-darcy permeability Marcellus and Haynesville core plugs. It was seen that water blocksmore » severely reduced the effective permeability of the core plugs, leading to losses of up to 99.5% of the initial permeability in experiments lasting 30 days. There was also evidence of clay swelling which further hindered gas flow. When results from this study were compared with similar counter-current gas permeability experiments reported in the literature, the initial (base) permeability of the rock was found to be a key factor in determining the time evolution of effective gas permeability during spontaneous imbibition. With time, a recovery of effective permeability was seen in the higher permeability rocks, while becoming progressively detrimental and irreversible in tighter rocks. Finally, these results suggest that matrix permeability of ultra-tight rocks is susceptible to water damage following hydraulic fracturing stimulation and, while shut-in/soaking time helps clearing-up fractures from resident fluid, its effect on the adjacent matrix permeability could be detrimental.« less

Permeability evolution of shale during spontaneous imbibition

DOE PAGES

Chakraborty, N.; Karpyn, Z. T.; Liu, S.; ...

2017-01-05

Shales have small pore and throat sizes ranging from nano to micron scales, low porosity and limited permeability. The poor permeability and complex pore connectivity of shales pose technical challenges to (a) understanding flow and transport mechanisms in such systems and, (b) in predicting permeability changes under dynamic saturation conditions. This paper presents quantitative experimental evidence of the migration of water through a generic shale core plug using micro CT imaging. In addition, in-situ measurements of gas permeability were performed during counter-current spontaneous imbibition of water in nano-darcy permeability Marcellus and Haynesville core plugs. It was seen that water blocksmore » severely reduced the effective permeability of the core plugs, leading to losses of up to 99.5% of the initial permeability in experiments lasting 30 days. There was also evidence of clay swelling which further hindered gas flow. When results from this study were compared with similar counter-current gas permeability experiments reported in the literature, the initial (base) permeability of the rock was found to be a key factor in determining the time evolution of effective gas permeability during spontaneous imbibition. With time, a recovery of effective permeability was seen in the higher permeability rocks, while becoming progressively detrimental and irreversible in tighter rocks. Finally, these results suggest that matrix permeability of ultra-tight rocks is susceptible to water damage following hydraulic fracturing stimulation and, while shut-in/soaking time helps clearing-up fractures from resident fluid, its effect on the adjacent matrix permeability could be detrimental.« less

Fracture-permeability behavior of shale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carey, J. William; Lei, Zhou; Rougier, Esteban

The fracture-permeability behavior of Utica shale, an important play for shale gas and oil, was investigated using a triaxial coreflood device and X-ray tomography in combination with finite-discrete element modeling (FDEM). Fractures generated in both compression and in a direct-shear configuration allowed permeability to be measured across the faces of cylindrical core. Shale with bedding planes perpendicular to direct-shear loading developed complex fracture networks and peak permeability of 30 mD that fell to 5 mD under hydrostatic conditions. Shale with bedding planes parallel to shear loading developed simple fractures with peak permeability as high as 900 mD. In addition tomore » the large anisotropy in fracture permeability, the amount of deformation required to initiate fractures was greater for perpendicular layering (about 1% versus 0.4%), and in both cases activation of existing fractures are more likely sources of permeability in shale gas plays or damaged caprock in CO₂ sequestration because of the significant deformation required to form new fracture networks. FDEM numerical simulations were able to replicate the main features of the fracturing processes while showing the importance of fluid penetration into fractures as well as layering in determining fracture patterns.« less

Fracture-permeability behavior of shale

DOE PAGES

Carey, J. William; Lei, Zhou; Rougier, Esteban; ...

2015-05-08

The fracture-permeability behavior of Utica shale, an important play for shale gas and oil, was investigated using a triaxial coreflood device and X-ray tomography in combination with finite-discrete element modeling (FDEM). Fractures generated in both compression and in a direct-shear configuration allowed permeability to be measured across the faces of cylindrical core. Shale with bedding planes perpendicular to direct-shear loading developed complex fracture networks and peak permeability of 30 mD that fell to 5 mD under hydrostatic conditions. Shale with bedding planes parallel to shear loading developed simple fractures with peak permeability as high as 900 mD. In addition tomore » the large anisotropy in fracture permeability, the amount of deformation required to initiate fractures was greater for perpendicular layering (about 1% versus 0.4%), and in both cases activation of existing fractures are more likely sources of permeability in shale gas plays or damaged caprock in CO₂ sequestration because of the significant deformation required to form new fracture networks. FDEM numerical simulations were able to replicate the main features of the fracturing processes while showing the importance of fluid penetration into fractures as well as layering in determining fracture patterns.« less

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

An evaluation of models of bare soil evaporation formulated with different land surface boundary conditions and assumptions

NASA Astrophysics Data System (ADS)

Smits, Kathleen M.; Ngo, Viet V.; Cihan, Abdullah; Sakaki, Toshihiro; Illangasekare, Tissa H.

2012-12-01

Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance. However, there is no agreement on the best modeling methodology to determine evaporation under different atmospheric boundary conditions. Also, there is a lack of directly measured soil evaporation data for model validation to compare these methods to establish the validity of their mathematical formulations. Thus, a need exists to systematically compare evaporation estimates using existing methods to experimental observations. The goal of this work is to test different conceptual and mathematical formulations that are used to estimate evaporation from bare soils to critically investigate various formulations and surface boundary conditions. Such a comparison required the development of a numerical model that has the ability to incorporate these boundary conditions. For this model, we modified a previously developed theory that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. Precision data under well-controlled transient heat and wind boundary conditions were generated, and results from numerical simulations were compared with experimental data. Results demonstrate that the approaches based on different boundary conditions varied in their ability to capture different stages of evaporation. All approaches have benefits and limitations, and no one approach can be deemed most appropriate for every scenario. Comparisons of different formulations of the surface boundary condition validate the need for further research on heat and vapor transport processes in soil for better modeling accuracy.

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.

Impacts of boundary condition changes on regional climate projections over West Africa

NASA Astrophysics Data System (ADS)

Kim, Jee Hee; Kim, Yeonjoo; Wang, Guiling

2017-06-01

Future projections using regional climate models (RCMs) are driven with boundary conditions (BCs) typically derived from global climate models. Understanding the impact of the various BCs on regional climate projections is critical for characterizing their robustness and uncertainties. In this study, the International Center for Theoretical Physics Regional Climate Model Version 4 (RegCM4) is used to investigate the impact of different aspects of boundary conditions, including lateral BCs and sea surface temperature (SST), on projected future changes of regional climate in West Africa, and BCs from the coupled European Community-Hamburg Atmospheric Model 5/Max Planck Institute Ocean Model are used as an example. Historical, future, and several sensitivity experiments are conducted with various combinations of BCs and CO2 concentration, and differences among the experiments are compared to identify the most important drivers for RCMs. When driven by changes in all factors, the RegCM4-produced future climate changes include significantly drier conditions in Sahel and wetter conditions along the Guinean coast. Changes in CO2 concentration within the RCM domain alone or changes in wind vectors at the domain boundaries alone have minor impact on projected future climate changes. Changes in the atmospheric humidity alone at the domain boundaries lead to a wetter Sahel due to the northward migration of rain belts during summer. This impact, although significant, is offset and dominated by changes of other BC factors (primarily temperature) that cause a drying signal. Future changes of atmospheric temperature at the domain boundaries combined with SST changes over oceans are sufficient to cause a future climate that closely resembles the projection that accounts for all factors combined. Therefore, climate variability and changes simulated by RCMs depend primarily on the variability and change of temperature aspects of the RCM BCs. Moreover, it is found that the response

Measurements in Transitional Boundary Layers Under High Free-Stream Turbulence and Strong Acceleration Conditions

NASA Technical Reports Server (NTRS)

Volino, Ralph J.; Simon, Terrence W.

1995-01-01

Measurements from transitional, heated boundary layers along a concave-curved test wall are presented and discussed. A boundary layer subject to low free-stream turbulence intensity (FSTI), which contains stationary streamwise (Gortler) vortices, is documented. The low FSTI measurements are followed by measurements in boundary layers subject to high (initially 8%) free-stream turbulence intensity and moderate to strong streamwise acceleration. Conditions were chosen to simulate those present on the downstream half of the pressure side of a gas turbine airfoil. Mean flow characteristics as well as turbulence statistics, including the turbulent shear stress, turbulent heat flux, and turbulent Prandtl number, are documented. A technique called "octant analysis" is introduced and applied to several cases from the literature as well as to data from the present study. Spectral analysis was applied to describe the effects of turbulence scales of different sizes during transition. To the authors'knowledge, this is the first detailed documentation of boundary layer transition under such high free-stream turbulence conditions.

Boundary conditions for simulating large SAW devices using ANSYS.

PubMed

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.

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

1993-01-01

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

New core-reflector boundary conditions for transient nodal reactor calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, E.K.; Kim, C.H.; Joo, H.K.

1995-09-01

New core-reflector boundary conditions designed for the exclusion of the reflector region in transient nodal reactor calculations are formulated. Spatially flat frequency approximations for the temporal neutron behavior and two types of transverse leakage approximations in the reflector region are introduced to solve the transverse-integrated time-dependent one-dimensional diffusion equation and then to obtain relationships between net current and flux at the core-reflector interfaces. To examine the effectiveness of new core-reflector boundary conditions in transient nodal reactor computations, nodal expansion method (NEM) computations with and without explicit representation of the reflector are performed for Laboratorium fuer Reaktorregelung und Anlagen (LRA) boilingmore » water reactor (BWR) and Nuclear Energy Agency Committee on Reactor Physics (NEACRP) pressurized water reactor (PWR) rod ejection kinetics benchmark problems. Good agreement between two NEM computations is demonstrated in all the important transient parameters of two benchmark problems. A significant amount of CPU time saving is also demonstrated with the boundary condition model with transverse leakage (BCMTL) approximations in the reflector region. In the three-dimensional LRA BWR, the BCMTL and the explicit reflector model computations differ by {approximately}4% in transient peak power density while the BCMTL results in >40% of CPU time saving by excluding both the axial and the radial reflector regions from explicit computational nodes. In the NEACRP PWR problem, which includes six different transient cases, the largest difference is 24.4% in the transient maximum power in the one-node-per-assembly B1 transient results. This difference in the transient maximum power of the B1 case is shown to reduce to 11.7% in the four-node-per-assembly computations. As for the computing time, BCMTL is shown to reduce the CPU time >20% in all six transient cases of the NEACRP PWR.« less

Graph Theory-Based Technique for Isolating Corrupted Boundary Conditions in Continental-Scale River Network Hydrodynamic Simulation

NASA Astrophysics Data System (ADS)

Yu, C. W.; Hodges, B. R.; Liu, F.

2017-12-01

Development of continental-scale river network models creates challenges where the massive amount of boundary condition data encounters the sensitivity of a dynamic nu- merical model. The topographic data sets used to define the river channel characteristics may include either corrupt data or complex configurations that cause instabilities in a numerical solution of the Saint-Venant equations. For local-scale river models (e.g. HEC- RAS), modelers typically rely on past experience to make ad hoc boundary condition adjustments that ensure a stable solution - the proof of the adjustment is merely the sta- bility of the solution. To date, there do not exist any formal methodologies or automated procedures for a priori detecting/fixing boundary conditions that cause instabilities in a dynamic model. Formal methodologies for data screening and adjustment are a critical need for simulations with a large number of river reaches that draw their boundary con- dition data from a wide variety of sources. At the continental scale, we simply cannot assume that we will have access to river-channel cross-section data that has been ade- quately analyzed and processed. Herein, we argue that problematic boundary condition data for unsteady dynamic modeling can be identified through numerical modeling with the steady-state Saint-Venant equations. The fragility of numerical stability increases with the complexity of branching in river network system and instabilities (even in an unsteady solution) are typically triggered by the nonlinear advection term in Saint-Venant equations. It follows that the behavior of the simpler steady-state equations (which retain the nonlin- ear term) can be used to screen the boundary condition data for problematic regions. In this research, we propose a graph-theory based method to isolate the location of corrupted boundary condition data in a continental-scale river network and demonstrate its utility with a network of O(10^4) elements. Acknowledgement

Measurements on stress dependent permeability

NASA Astrophysics Data System (ADS)

Risnes, R.; Faldaas, I.; Korsnes, R. I.; Norland, T.

2003-04-01

permeability are rather small, even if the tests are run beyond yield. The mid-section permeability seems to show a small increasing trend with increasing deviatoric stresses after yield. But the yield point does not seem to have any drastic effect on the permeability.(4) The overall permeability seems in general to show a decreasing trend under deviatoric stresses. The results indicate that permeability changes with pressure depletion under reservoir conditions may be much less than expected from hydrostatic tests or tests uncorrected for end-effects.

Toroidal current asymmetry and boundary conditions in disruptions

NASA Astrophysics Data System (ADS)

Strauss, Henry

2014-10-01

It was discovered on JET that disruptions were accompanied by toroidal asymmetry of the plasma current. The toroidal current asymmetry ΔIϕ is proportional to the vertical current moment ΔMIZ , with positive sign for an upward vertical displacement event (VDE) and negative sign for a downward VDE. It was claimed that this could only be explained by Hiro current. It is shown that instead it is essentially a kinematic effect produced by the VDE displacement of a 3D magnetic perturbation. This is verified by M3D simulations. The simulation results do not require penetration of plasma into the boundary, as in the Hiro current model. It is shown that the normal velocity perpendicular to the magnetic field vanishes at the wall, in the small Larmor radius limit of electromagnetic sheath boundary conditions. Plasma is absorbed into the wall only via the parallel velocity, which is small, penetrates only an infinitesimal distance into the wall, and does not affect forces exerted by the plasma on the wall. Supported by USDOE and ITER.

Application of mean wall shear stress boundary condition to complex turbulent flows using a wall-modeled large eddy simulation

NASA Astrophysics Data System (ADS)

Cho, Minjeong; Lee, Jungil; Choi, Haecheon

2012-11-01

The mean wall shear stress boundary condition was successfully applied to turbulent channel and boundary flows using large eddy simulation without resolving near-wall region (see Lee, Cho & Choi in this book of abstracts). In the present study, we apply this boundary condition to more complex flows where flow separation and redeveloping flow exist. As a test problem, we consider flow over a backward-facing step at Reh = 22860 based on the step height. Turbulent boundary layer flow at the inlet (Reθ = 1050) is obtained using inflow generation technique by Lund et al. (1998) but with wall shear stress boundary condition. First, we prescribe the mean wall shear stress distribution obtained from DNS (Kim, 2011, Ph.D. Thesis, Stanford U.) as the boundary condition of present simulation. Here we give no-slip boundary condition at flow-reversal region. The present results are in good agreements with the flow statistics by DNS. Currently, a dynamic approach of obtaining mean wall shear stress based on the log-law is being applied to the flow having flow separation and its results will be shown in the presentation. Supported by the WCU and NRF programs.

Numerical Simulations of Melting-Crystallisation Processes at the Boundaries Between Magma Oceans and Solid Mantle

NASA Astrophysics Data System (ADS)

Bolrão, D. P.; Rozel, A.; Morison, A.; Labrosse, S.; Tackley, P. J.

2017-12-01

The idea that the Earth had a global magma ocean, mostly created by impacts, core formation, radiogenic and tidal heating, is well accepted nowadays. When this ocean starts to crystallise, if the melt is denser than the solid, a basal magma ocean is created below the solid part. These two magma oceans influence the dynamics and evolution of solid mantle. Near the boundaries, the vertical flow in the solid part creates a topography. If this topography is destroyed by melting/crystallisation processes in a time scale much shorter than the time needed to adjust the topography by viscous relaxation, then matter can cross the boundary. In this case, the boundary is said to be permeable. On the other hand, if this time is longer, matter cannot cross and the boundary is said impermeable. This permeability is defined by a non-dimensional phase change number, φ, introduced by Deguen, 2013. This φ is the ratio of the two timescales mentioned, and defines a permeable boundary when φ « 1, and an impermeable one when φ » 1. To understand the impact of magma oceans on the dynamics of the solid mantle, we use the convection code StagYY, with a 2D spherical annulus geometry, to compute the convection of the solid part. Our results show different convection behaviours depending on the type of boundary chosen. For the permeable case, we investigate the thermo-compositional evolution of the solid domain, explicitly taking into account the compositional evolution of the magma oceans. Reference: Deguen, R. Thermal convection in a spherical shell with melting/freezing at either or both of its boundaries. Journal of Earth Science, Vol. 24, No. 5, p. 669-682, 2013. doi: 10.1007/s12583-013-0364-8

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions

PubMed

Niklasson; Datta; Dunn

2000-09-01

In this paper, effective boundary conditions for elastic wave propagation in plates with thin coatings are derived. These effective boundary conditions are used to obtain an approximate dispersion relation for guided waves in an isotropic plate with thin anisotropic coating layers. The accuracy of the effective boundary conditions is investigated numerically by comparison with exact solutions for two different material systems. The systems considered consist of a metallic core with thin superconducting coatings. It is shown that for wavelengths long compared to the coating thickness there is excellent agreement between the approximate and exact solutions for both systems. Furthermore, numerical results presented might be used to characterize coating properties by ultrasonic techniques.

Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Zhang, Kai

2018-06-01

In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise C α, C 1,α and C 2,α regularity. As byproducts, we also prove the A-B-P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Development of stress boundary conditions in smoothed particle hydrodynamics (SPH) for the modeling of solids deformation

NASA Astrophysics Data System (ADS)

Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.

2017-10-01

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.

Front propagation in a vortex lattice: dependence on boundary conditions and vortex depth.

PubMed

Beauvier, E; Bodea, S; Pocheau, A

2016-11-04

We experimentally address the propagation of reaction-diffusion fronts in vortex lattices by combining, in a Hele-Shaw cell and at low Reynolds number, forced electroconvective flows and an autocatalytic reaction in solution. We consider both vortex chains and vortex arrays, the former referring to mixed free/rigid boundary conditions for vortices and the latter to free boundary conditions. Varying the depth of the fluid layer, we observe no variation of the mean front velocities for vortex arrays and a noticeable variation for vortex chains. This questions the two-dimensional character of front propagation in low Reynolds number vortex lattices, as well as the mechanisms of this dependence.

Influence of Boundary Conditions on Regional Air Quality Simulations—Analysis of AQMEII Phase 3 Results

EPA Science Inventory

Chemical boundary conditions are a key input to regional-scale photochemical models. In this study, performed during the third phase of the Air Quality Model Evaluation International Initiative (AQMEII3), we perform annual simulations over North America with chemical boundary con...

Boundaries around Group Interaction: The Effect of Size and Status.

ERIC Educational Resources Information Center

Knowles, Eric S.

The stimulus value of group boundaries was investigated in a field experiment. It was hypothesized that the size of a group and the status of its members would reduce the permeability of a boundary around an interacting group. Two or 4 interacting people of high or low status interrupted the traffic flow in a university hallway. Results indicate…

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

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.

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.

Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm

NASA Astrophysics Data System (ADS)

Gvozdic, Branko D.; Djurdjevic, Dusan Z.

2017-01-01

Implementation of absorbing boundary condition (ABC) has a very important role in simulation performance and accuracy in finite difference time domain (FDTD) method. The perfectly matched layer (PML) is the most efficient type of ABC. The aim of this paper is to give detailed insight in and discussion of boundary conditions and hence to simplify the choice of PML used for termination of computational domain in FDTD method. In particular, we demonstrate that using the convolutional PML (CPML) has significant advantages in terms of implementation in FDTD method and reducing computer resources than using uniaxial PML (UPML). An extensive number of numerical experiments has been performed and results have shown that CPML is more efficient in electromagnetic waves absorption. Numerical code is prepared, several problems are analyzed and relative error is calculated and presented.

Factors Determining the Oxygen Permeability of Biological Membranes: Oxygen Transport Across Eye Lens Fiber-Cell Plasma Membranes.

PubMed

Subczynski, Witold Karol; Widomska, Justyna; Mainali, Laxman

2017-01-01

Electron paramagnetic resonance (EPR) spin-label oximetry allows the oxygen permeability coefficient to be evaluated across homogeneous lipid bilayer membranes and, in some cases, across coexisting membrane domains without their physical separation. The most pronounced effect on oxygen permeability is observed for cholesterol, which additionally induces the formation of membrane domains. In intact biological membranes, integral proteins induce the formation of boundary and trapped lipid domains with a low oxygen permeability. The effective oxygen permeability coefficient across the intact biological membrane is affected not only by the oxygen permeability coefficients evaluated for each lipid domain but also by the surface area occupied by these domains in the membrane. All these factors observed in fiber cell plasma membranes of clear human eye lenses are reviewed here.

Influence of thickness and permeability of endothelial surface layer on transmission of shear stress in capillaries

NASA Astrophysics Data System (ADS)

Zhang, SongPeng; Zhang, XiangJun; Tian, Yu; Meng, YongGang; Lipowsky, Herbert

2015-07-01

The molecular coating on the surface of microvascular endothelium has been identified as a barrier to transvascular exchange of solutes. With a thickness of hundreds of nanometers, this endothelial surface layer (ESL) has been treated as a porous domain within which fluid shear stresses are dissipated and transmitted to the solid matrix to initiate mechanotransduction events. The present study aims to examine the effects of the ESL thickness and permeability on the transmission of shear stress throughout the ESL. Our results indicate that fluid shear stresses rapidly decrease to insignificant levels within a thin transition layer near the outer boundary of the ESL with a thickness on the order of ten nanometers. The thickness of the transition zone between free fluid and the porous layer was found to be proportional to the square root of the Darcy permeability. As the permeability is reduced ten-fold, the interfacial fluid and solid matrix shear stress gradients increase exponentially two-fold. While the interfacial fluid shear stress is positively related to the ESL thickness, the transmitted matrix stress is reduced by about 50% as the ESL thickness is decreased from 500 to 100 nm, which may occur under pathological conditions. Thus, thickness and permeability of the ESL are two main factors that determine flow features and the apportionment of shear stresses between the fluid and solid phases of the ESL. These results may shed light on the mechanisms of force transmission through the ESL and the pathological events caused by alterations in thickness and permeability of the ESL.

CO2 breakthrough pressure and permeability for unsaturated low-permeability sandstone of the Ordos Basin

NASA Astrophysics Data System (ADS)

Zhao, Yan; Yu, Qingchun

2017-07-01

With rising threats from greenhouse gases, capture and injection of CO2 into suitable underground formations is being considered as a method to reduce anthropogenic emissions of CO2 to the atmosphere. As the injected CO2 will remain in storage for hundreds of years, the safety of CO2 geologic sequestration is a major concern. The low-permeability sandstone of the Ordos Basin in China is regarded as both caprock and reservoir rock, so understanding the breakthrough pressure and permeability of the rock is necessary. Because part of the pore volume experiences a non-wetting phase during the CO2 injection and migration process, the rock may be in an unsaturated condition. And if accidental leakage occurs, CO2 will migrate up into the unsaturated zone. In this study, breakthrough experiments were performed at various degrees of water saturation with five core samples of low-permeability sandstone obtained from the Ordos Basin. The experiments were conducted at 40 °C and pressures of >8 MPa to simulate the geological conditions for CO2 sequestration. The results indicate that the degree of water saturation and the pore structure are the main factors affecting the rock breakthrough pressure and permeability, since the influence of calcite dissolution and clay mineral swelling during the saturation process is excluded. Increasing the average pore radius or most probable pore radius leads to a reduction in the breakthrough pressure and an increase by several orders of magnitude in scCO2 effective permeability. In addition, the breakthrough pressure rises and the scCO2 effective permeability decreases when the water saturation increases. However, when the average pore radius is greater than 0.151 μm, the degree of water saturation will has a little effect on the breakthrough pressure. On this foundation, if the most probable pore radius of the core sample reaches 1.760 μm, the breakthrough pressure will not be impacted by the increasing water saturation. We establish

Nonlocal boundary conditions for corrugated acoustic metasurface with strong near-field interactions

NASA Astrophysics Data System (ADS)

Schwan, Logan; Umnova, Olga; Boutin, Claude; Groby, Jean-Philippe

2018-03-01

The propagation of long-wavelength sound in the presence of a metasurface made by arranging acoustic resonators periodically upon or slightly above an impervious substrate is studied. The method of two-scale asymptotic homogenization is used to derive effective boundary conditions, which account for both the surface corrugation and the low-frequency resonance. This method is applied to periodic arrays of resonators of any shape operating in the long-wavelength regime. The approach relies on the existence of a locally periodic boundary layer developed in the vicinity of the metasurface, where strong near-field interactions of the resonators with each other and with the substrate take place. These local effects give rise to an effective surface admittance supplemented by nonlocal contributions from the simple and double gradients of the pressure at the surface. These phenomena are illustrated for the periodic array of cylindrical Helmholtz resonators with an extended inner duct. Effects of the centre-to-centre spacing and orientation of the resonators' opening on the nonlocality and apparent resonance frequency are studied. The model could be used to design metasurfaces with specific effective boundary conditions required for particular applications.

Boundary conditions for the solution of compressible Navier-Stokes equations by an implicit factored method

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Smith, G. E.; Springer, G. S.; Rimon, Y.

1983-01-01

A method is presented for formulating the boundary conditions in implicit finite-difference form needed for obtaining solutions to the compressible Navier-Stokes equations by the Beam and Warming implicit factored method. The usefulness of the method was demonstrated (a) by establishing the boundary conditions applicable to the analysis of the flow inside an axisymmetric piston-cylinder configuration and (b) by calculating velocities and mass fractions inside the cylinder for different geometries and different operating conditions. Stability, selection of time step and grid sizes, and computer time requirements are discussed in reference to the piston-cylinder problem analyzed.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

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.

Homogenized boundary conditions and resonance effects in Faraday cages

PubMed Central

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

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.

Homogenized boundary conditions and resonance effects in Faraday cages.

PubMed

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.

Uniform stabilization of wave equation with localized internal damping and acoustic boundary condition with viscoelastic damping

NASA Astrophysics Data System (ADS)

Frota, Cícero Lopes; Vicente, André

2018-06-01

In this paper, we deal with the uniform stabilization to the mixed problem for a nonlinear wave equation and acoustic boundary conditions on a non-locally reacting boundary. The main purpose is to study the stability when the internal damping acts only over a subset ω of the domain Ω and the boundary damping is of the viscoelastic type.

Implementation and Testing of Advanced Surface Boundary Conditions Over Complex Terrain in A Semi-idealized Model

NASA Astrophysics Data System (ADS)

Li, Y.; Epifanio, C.

2017-12-01

In numerical prediction models, the interaction between the Earth's surface and the atmosphere is typically accounted for in terms of surface layer parameterizations, whose main job is to specify turbulent fluxes of heat, moisture and momentum across the lower boundary of the model domain. In the case of a domain with complex geometry, implementing the flux conditions (particularly the tensor stress condition) at the boundary can be somewhat subtle, and there has been a notable history of confusion in the CFD community over how to formulate and impose such conditions generally. In the atmospheric case, modelers have largely been able to avoid these complications, at least until recently, by assuming that the terrain resolved at typical model resolutions is fairly gentle, in the sense of having relatively shallow slopes. This in turn allows the flux conditions to be imposed as if the lower boundary were essentially flat. Unfortunately, while this flat-boundary assumption is acceptable for coarse resolutions, as grids become more refined and the geometry of the resolved terrain becomes more complex, the appproach is less justified. With this in mind, the goal of our present study is to explore the implementation and usage of the full, unapproximated version of the turbulent flux/stress conditions in atmospheric models, thus taking full account of the complex geometry of the resolved terrain. We propose to implement the conditions using a semi-idealized model developed by Epifanio (2007), in which the discretized boundary conditions are reduced to a large, sparse-matrix problem. The emphasis will be on fluxes of momentum, as the tensor nature of this flux makes the associated stress condition more difficult to impose, although the flux conditions for heat and moisture will be considered as well. With the resulotion of 90 meters, some of the results show that the typical differences between flat-boundary cases and full/stress cases are on the order of 10%, with extreme

A two-dimensional vibration analysis of piezoelectrically actuated microbeam with nonideal boundary conditions

NASA Astrophysics Data System (ADS)

Rezaei, M. P.; Zamanian, M.

2017-01-01

In this paper, the influences of nonideal boundary conditions (due to flexibility) on the primary resonant behavior of a piezoelectrically actuated microbeam have been studied, for the first time. The structure has been assumed to treat as an Euler-Bernoulli beam, considering the effects of geometric nonlinearity. In this work, the general nonideal supports have been modeled as a the combination of horizontal, vertical and rotational springs, simultaneously. Allocating particular values to the stiffness of these springs provides the mathematical models for the majority of boundary conditions. This consideration leads to use a two-dimensional analysis of the multiple scales method instead of previous works' method (one-dimensional analysis). If one neglects the nonideal effects, then this paper would be an effort to solve the two-dimensional equations of motion without a need of a combination of these equations using the shortening or stretching effect. Letting the nonideal effects equal to zero and comparing their results with the results of previous approaches have been demonstrated the accuracy of the two-dimensional solutions. The results have been identified the unique effects of constraining and stiffening of boundaries in horizontal, vertical and rotational directions. This means that it is inaccurate to suppose the nonideality of supports only in one or two of these directions like as previous works. The findings are of vital importance as a better prediction of the frequency response for the nonideal supports. Furthermore, the main findings of this effort can help to choose appropriate boundary conditions for desired systems.

Stokesian dynamics of pill-shaped Janus particles with stick and slip boundary conditions

NASA Astrophysics Data System (ADS)

Sun, Qiang; Klaseboer, Evert; Khoo, Boo Cheong; Chan, Derek Y. C.

2013-04-01

We study the forces and torques experienced by pill-shaped Janus particles of different aspect ratios where half of the surface obeys the no-slip boundary condition and the other half obeys the Navier slip condition of varying slip lengths. Using a recently developed boundary integral formulation whereby the traditional singular behavior of this approach is removed analytically, we quantify the strength of the forces and torques experienced by such particles in a uniform flow field in the Stokes regime. Depending on the aspect ratio and the slip length, the force transverse to the flow direction can change sign. This is a novel property unique to the Janus nature of the particles.

Boundary transfer matrices and boundary quantum KZ equations

NASA Astrophysics Data System (ADS)

Vlaar, Bart

2015-07-01

A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin's boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.

Structural and conformational determinants of macrocycle cell permeability.

PubMed

Over, Björn; Matsson, Pär; Tyrchan, Christian; Artursson, Per; Doak, Bradley C; Foley, Michael A; Hilgendorf, Constanze; Johnston, Stephen E; Lee, Maurice D; Lewis, Richard J; McCarren, Patrick; Muncipinto, Giovanni; Norinder, Ulf; Perry, Matthew W D; Duvall, Jeremy R; Kihlberg, Jan

2016-12-01

Macrocycles are of increasing interest as chemical probes and drugs for intractable targets like protein-protein interactions, but the determinants of their cell permeability and oral absorption are poorly understood. To enable rational design of cell-permeable macrocycles, we generated an extensive data set under consistent experimental conditions for more than 200 non-peptidic, de novo-designed macrocycles from the Broad Institute's diversity-oriented screening collection. This revealed how specific functional groups, substituents and molecular properties impact cell permeability. Analysis of energy-minimized structures for stereo- and regioisomeric sets provided fundamental insight into how dynamic, intramolecular interactions in the 3D conformations of macrocycles may be linked to physicochemical properties and permeability. Combined use of quantitative structure-permeability modeling and the procedure for conformational analysis now, for the first time, provides chemists with a rational approach to design cell-permeable non-peptidic macrocycles with potential for oral absorption.

Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations

DOE PAGES

Schuetrumpf, B.; Nazarewicz, W.

2015-10-21

Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at subsaturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100-m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite three-dimensional boxes assuming periodic boundary conditions. The resulting solutions are affected by spurious finite-size effects. To remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice quantum chromodynamics applications. In this work, we study the effectivenessmore » of TABC in the context of pasta phase simulations within nuclear density functional theory. We demonstrated that by applying TABC reliable results can be obtained from calculations performed in relatively small volumes. By studying various contributions to the total energy, we gain insights into pasta phases in mid-density range. Future applications will include the TABC extension of the adaptive multiresolution 3D Hartree-Fock solver and Hartree-Fock-Bogoliubov TABC applications to superfluid pasta phases and complex nucleonic topologies as in fission.« less

Measuring Permeability of Composite Cryotank Laminants

NASA Technical Reports Server (NTRS)

Oliver, Stanley T.; Selvidge, Shawn; Watwood, Michael C.

2004-01-01

This paper describes a test method developed to identify whether certain materials and material systems are suitable candidates for large pressurized reusable cryogenic tanks intended for use in current and future manned launch systems. It provides a quick way to screen numerous candidate materials for permeability under anticipated loading environments consistent with flight conditions, as well as addressing reusability issues. cryogenic tank, where the major design issue was hydrogen permeability. It was successfully used to evaluate samples subjected to biaxial loading while maintaining test temperatures near liquid hydrogen. After each sample was thermally preconditioned, a cyclic pressure load was applied to simulate the in-plane strain. First permeability was measured while a sample was under load. Then the sample was unloaded and allowed to return to ambient temperature. The test was repeated to simulate reusability, in order to evaluate its effects on material permeability.

Thermal stability of static coronal loops: Part 1: Effects of boundary conditions

NASA Technical Reports Server (NTRS)

Antiochos, S. K.; Shoub, E. C.; An, C. H.; Emslie, A. G.

1985-01-01

The linear stability of static coronal-loop models undergoing thermal perturbations was investigated. The effect of conditions at the loop base on the stability properties of the models was considered in detail. The question of appropriate boundary conditions at the loop base was considered and it was concluded that the most physical assumptions are that the temperature and density (or pressure) perturbations vanish there. However, if the base is taken to be sufficiently deep in the chromosphere, either several chromospheric scale heights or several coronal loop lengths in depth, then the effect of the boundary conditions on loop stability becomes negligible so that all physically acceptable conditions are equally appropriate. For example, one could as well assume that the velocity vanishes at the base. The growth rates and eigenmodes of static models in which gravity is neglected and in which the coronal heating is a relatively simple function, either constant per-unit mass or per-unit volume were calculated. It was found that all such models are unstable with a growth rate of the order of the coronal cooling time. The physical implications of these results for the solar corona and transition region are discussed.

Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

A new structure of permeable pavement for mitigating urban heat island.

PubMed

Liu, Yong; Li, Tian; Peng, Hangyu

2018-09-01

The urban heat island (UHI) effect has been a great threat to human habitation, and how to mitigate this problem has been a global concern over decades. This paper addresses the cooling effect of a novel permeable pavement called evaporation-enhancing permeable pavement, which has capillary columns in aggregate and a liner at the bottom. To explore the efficiency of mitigating the UHI, bench-scale permeable pavement units with capillary columns were developed and compared with conventional permeable pavement. Criteria of capillary capacities of the column, evaporation rates, and surface temperature of the pavements were monitored under simulated rainfall and Shanghai local weather conditions. Results show the capillary column was important in increasing evaporation by lifting water from the bottom to the surface, and the evaporation-enhancing permeable pavement was cooler than a conventional permeable pavement by as much as 9.4°C during the experimental period. Moreover, the cooling effect of the former pavement could persist more than seven days under the condition of no further rainfall. Statistical analysis result reveals that evaporation-enhancing permeable pavement can mitigate the UHI effect significantly more than a conventional permeable pavement. Copyright © 2018 Elsevier B.V. All rights reserved.

Imposing the free-slip condition with a continuous forcing immersed boundary method

NASA Astrophysics Data System (ADS)

Kempe, Tobias; Lennartz, Matthias; Schwarz, Stephan; Fröhlich, Jochen

2015-02-01

The numerical simulation of spherical and ellipsoidal bubbles in purified fluids requires the imposition of the free-slip boundary condition at the bubble surface. This paper describes a numerical method for the implementation of free-slip boundary conditions in the context of immersed boundary methods. In contrast to other numerical approaches for multiphase flows, the realization is not straightforward. The reason is that the immersed boundary method treats the liquid as well as the gas phase as a field of constant density and viscosity with a fictitious fluid inside the bubble. The motion of the disperse phase is computed explicitly by solving the momentum balance for each of its elements and is coupled to the continuous phase via additional source terms in the Navier-Stokes equations. The paper starts with illustrating that an ad hoc method is unsuccessful. On this basis, a new method is proposed employing appropriate direct forcing at the bubble surface. A central finding is that with common ratios between the step size of the grid and the bubble diameter, curvature terms need to be accounted for to obtain satisfactory results. The new method is first developed for spherical objects and then extended to generally curved interfaces. This is done by introducing a local coordinate system which approximates the surface in the vicinity of a Lagrangian marker with the help of the two principal curvatures of the surface at this point. The numerical scheme is then validated for spherical and ellipsoidal objects with or without prescribed constant angular velocity. It is shown that the proposed method achieves similar convergence behavior as the method for no-slip boundaries. The results are compared to analytical solutions for creeping flow around a sphere and to numerical reference data obtained on a body-fitted grid. The numerical tests confirm the excellent performance of the proposed method.

High-speed propeller noise predictions - Effects of boundary conditions used in blade loading calculations

NASA Technical Reports Server (NTRS)

Nallasamy, M.; Clark, B. J.; Groeneweg, J. F.

1987-01-01

The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.

High-speed propeller noise predictions: Effects of boundary conditions used in blade loading calculations

NASA Technical Reports Server (NTRS)

Nallasamy, M.; Clark, B. J.; Groeneweg, J. F.

1987-01-01

The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.

Experimental Investigation of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

NASA Technical Reports Server (NTRS)

Hultgren, Lennart S.; Volino, Ralph J.

2002-01-01

Modern low-pressure turbine airfoils are subject to increasingly stronger pressure gradients as designers impose higher loading in an effort to improve efficiency and to reduce part count. The adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation, particularly under cruise conditions. Separation bubbles, notably those which fail to reattach, can result in a significant degradation of engine efficiency. Accurate prediction of separation and reattachment is hence crucial to improved turbine design. This requires an improved understanding of the transition flow physics. Transition may begin before or after separation, depending on the Reynolds number and other flow conditions, has a strong influence on subsequent reattachment, and may even eliminate separation. Further complicating the problem are the high free-stream turbulence levels in a real engine environment, the strong pressure gradients along the airfoils, the curvature of the airfoils, and the unsteadiness associated with wake passing from upstream stages. Because of the complicated flow situation, transition in these devices can take many paths that can coexist, vary in importance, and possibly also interact, at different locations and instances in time. The present work was carried out in an attempt to systematically sort out some of these issues. Detailed velocity measurements were made along a flat plate subject to the same nominal dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil ('Pak-B'). The Reynolds number based on wetted plate length and nominal exit velocity, Re, was varied from 50;000 to 300; 000, covering cruise to takeoff conditions. Low, 0.2%, and high, 7%, inlet free-stream turbulence intensities were set using passive grids. These turbulence levels correspond to about 0.2% and 2.5% turbulence intensity in the test section when normalized with the exit velocity. The Reynolds number and free

An Alternative Frictional Boundary Condition for Computational Fluid Dynamics Simulation of Friction Stir Welding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Gaoqiang; Feng, Zhili; Zhu, Yucan

For better application of numerical simulation in optimization and design of friction stir welding (FSW), this paper presents a new frictional boundary condition at the tool/workpiece interface for computational fluid dynamics (CFD) modeling of FSW. The proposed boundary condition is based on an implementation of the Coulomb friction model. Using the new boundary condition, the CFD simulation yields non-uniform distribution of contact state over the tool/workpiece interface, as validated by the experimental weld macrostructure. It is found that interfacial sticking state is present over large area at the tool-workpiece interface, while significant interfacial sliding occurs at the shoulder periphery, themore » lower part of pin side, and the periphery of pin bottom. Due to the interfacial sticking, a rotating flow zone is found under the shoulder, in which fast circular motion occurs. The diameter of the rotating flow zone is smaller than the shoulder diameter, which is attributed to the presence of the interfacial sliding at the shoulder periphery. For the simulated welding condition, the heat generation due to friction and plastic deformation makes up 54.4 and 45.6% of the total heat generation rate, respectively. In conclusion, the simulated temperature field is validated by the good agreement to the experimental measurements.« less

An Alternative Frictional Boundary Condition for Computational Fluid Dynamics Simulation of Friction Stir Welding

DOE PAGES

Chen, Gaoqiang; Feng, Zhili; Zhu, Yucan; ...

2016-07-11

For better application of numerical simulation in optimization and design of friction stir welding (FSW), this paper presents a new frictional boundary condition at the tool/workpiece interface for computational fluid dynamics (CFD) modeling of FSW. The proposed boundary condition is based on an implementation of the Coulomb friction model. Using the new boundary condition, the CFD simulation yields non-uniform distribution of contact state over the tool/workpiece interface, as validated by the experimental weld macrostructure. It is found that interfacial sticking state is present over large area at the tool-workpiece interface, while significant interfacial sliding occurs at the shoulder periphery, themore » lower part of pin side, and the periphery of pin bottom. Due to the interfacial sticking, a rotating flow zone is found under the shoulder, in which fast circular motion occurs. The diameter of the rotating flow zone is smaller than the shoulder diameter, which is attributed to the presence of the interfacial sliding at the shoulder periphery. For the simulated welding condition, the heat generation due to friction and plastic deformation makes up 54.4 and 45.6% of the total heat generation rate, respectively. In conclusion, the simulated temperature field is validated by the good agreement to the experimental measurements.« less

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection.

PubMed

van der Poel, Erwin P; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, Detlef

2014-07-01

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10(8) and 10(11) the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra ≥ 10(10). Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

Evaluation of the permeability of agricultural films to various fumigants.

PubMed

Qian, Yaorong; Kamel, Alaa; Stafford, Charles; Nguyen, Thuy; Chism, William J; Dawson, Jeffrey; Smith, Charles W

2011-11-15

A variety of agricultural films are commercially available for managing emissions and enhancing pest control during soil fumigation. These films are manufactured using different materials and processes which can ultimately result in different permeability to fumigants. A systematic laboratory study of the permeability of the agricultural films to nine fumigants was conducted to evaluate the performance of commonly used film products, including polyethylene, metalized, and high-barrier films. The permeability, as expressed by mass transfer coefficient (cm/h), of 27 different films from 13 manufacturers ranged from below 1 × 10(-4) cm/h to above 10 cm/h at 25 °C under ambient relative humidity test conditions. The wide range in permeability of commercially available films demonstrates the need to use films which are appropriate for the fumigation application. The effects of environmental factors, such as temperature and humidity, on the film permeability were also investigated. It was found that high relative humidity could drastically increase the permeability of the high-barrier films. The permeability of some high-barrier films was increased by 2-3 orders of magnitude when the films were tested at high relative humidity. Increasing the temperature from 25 to 40 °C increased the permeability for some high-barrier films up to 10 times more than the permeability at 25 °C, although the effect was minimal for several of these films. Analysis of the distribution of the permeability of the films under ambient humidity conditions to nine fumigants indicated that the 27 films largely followed the material type, although the permeability varied considerably among the films of similar material.

Influence of fiber packing structure on permeability

NASA Technical Reports Server (NTRS)

Cai, Zhong; Berdichevsky, Alexander L.

1993-01-01

The study on the permeability of an aligned fiber bundle is the key building block in modeling the permeability of advanced woven and braided preforms. Available results on the permeability of fiber bundles in the literature show that a substantial difference exists between numerical and analytical calculations on idealized fiber packing structures, such as square and hexagonal packing, and experimental measurements on practical fiber bundles. The present study focuses on the variation of the permeability of a fiber bundle under practical process conditions. Fiber bundles are considered as containing openings and fiber clusters within the bundle. Numerical simulations on the influence of various openings on the permeability were conducted. Idealized packing structures are used, but with introduced openings distributed in different patterns. Both longitudinal and transverse flow are considered. The results show that openings within the fiber bundle have substantial effect on the permeability. In the longitudinal flow case, the openings become the dominant flow path. In the transverse flow case, the fiber clusters reduce the gap sizes among fibers. Therefore the permeability is greatly influenced by these openings and clusters, respectively. In addition to the porosity or fiber volume fraction, which is commonly used in the permeability expression, another fiber bundle status parameter, the ultimate fiber volume fraction, is introduced to capture the disturbance within a fiber bundle.

Crustal permeability

USGS Publications Warehouse

Gleeson, Tom; Ingebritsen, Steven E.

2016-01-01

Permeability is the primary control on fluid flow in the Earth’s crust and is key to a surprisingly wide range of geological processes, because it controls the advection of heat and solutes and the generation of anomalous pore pressures.  The practical importance of permeability – and the potential for large, dynamic changes in permeability – is highlighted by ongoing issues associated with hydraulic fracturing for hydrocarbon production (“fracking”), enhanced geothermal systems, and geologic carbon sequestration.  Although there are thousands of research papers on crustal permeability, this is the first book-length treatment.  This book bridges the historical dichotomy between the hydrogeologic perspective of permeability as a static material property and the perspective of other Earth scientists who have long recognized permeability as a dynamic parameter that changes in response to tectonism, fluid production, and geochemical reactions. 

Air Quality and Meteorological Boundary Conditions during the MCMA-2003 Field Campaign

NASA Astrophysics Data System (ADS)

Sosa, G.; Arriaga, J.; Vega, E.; Magaña, V.; Caetano, E.; de Foy, B.; Molina, L. T.; Molina, M. J.; Ramos, R.; Retama, A.; Zaragoza, J.; Martínez, A. P.; Márquez, C.; Cárdenas, B.; Lamb, B.; Velasco, E.; Allwine, E.; Pressley, S.; Westberg, H.; Reyes, R.

2004-12-01

A comprehensive field campaign to characterize photochemical smog in the Mexico City Metropolitan Area (MCMA) was conducted during April 2003. An important number of equipment was deployed all around the urban core and its surroundings to measure gas and particles composition from the various sources and receptor sites. In addition to air quality measurements, meteorology variables were also taken by regular weather meteorological stations, tethered balloons, radiosondes, sodars and lidars. One important issue with regard to the field campaign was the characterization of the boundary conditions in order to feed meteorological and air quality models. Four boundary sites were selected to measure continuously criteria pollutants, VOC and meteorological variables at surface level. Vertical meteorological profiles were measured at three other sites : radiosondes in Tacubaya site were launched every six hours daily; tethered balloons were launched at CENICA and FES-Cuautitlan sites according to the weather conditions, and one sodar was deployed at UNAM site in the south of the city. Additionally to these measurements, two fixed meteorological monitoring networks deployed along the city were available to complement these measurements. In general, we observed that transport of pollutants from the city to the boundary sites changes every day, according to the coupling between synoptic and local winds. This effect were less important at elevated sites such as Cerro de la Catedral and ININ, where synoptic wind were more dominant during the field campaign. Also, local sources nearby boundary sites hide the influence of pollution coming from the city some days, particularly at the La Reforma site.

Variable-viscosity thermal hemodynamic slip flow conveying nanoparticles through a permeable-walled composite stenosed artery

NASA Astrophysics Data System (ADS)

Akbar, Noreen Sher; Tripathi, Dharmendra; Bég, O. Anwar

2017-07-01

This paper presents a mathematical model for simulating viscous, incompressible, steady-state blood flow containing copper nanoparticles and coupled heat transfer through a composite stenosed artery with permeable walls. Wall slip hydrodynamic and also thermal buoyancy effects are included. The artery is simulated as an isotropic elastic tube, following Joshi et al. (2009), and a variable viscosity formulation is employed for the flowing blood. The equations governing the transport phenomena are non-dimensionalized and the resulting boundary value problem is solved analytically in the steady state subject to physically appropriate boundary conditions. Numerical computations are conducted to quantify the effects of relevant hemodynamic, thermophysical and nanoscale parameters emerging in the model on velocity and temperature profiles, wall shear stress, impedance resistance and also streamline distributions. The model may be applicable to drug fate transport modeling with nanoparticle agents and also to the optimized design of nanoscale medical devices for diagnosing stenotic diseases in circulatory systems.

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.

Effect of boundary conditions on measured water retention behavior within soils

NASA Astrophysics Data System (ADS)

Galindo-torres, S.; Scheuermann, A.; Pedroso, D.; Li, L.

2013-12-01

The Soil Water Characteristic Curve (SWCC) is a practical representation of the behavior of soil water by relating the suction (difference between the air and water pressures to the moisture content (water saturation). The SWCC is characterized by a hysteresis loop, which is thought to be unique in that any drainage-imbibition cycle lies within a main hysteresis loop limited by two different curves for drainage and imbibition. This 'uniqueness' is the main argument for considering the SWCC as a material-intrinsic feature that characterizes the pore structure and its interaction with fluids. Models have been developed with the SWCC as input data to describe the evolution of the water saturation and the suction within soils. One example of these models is the widely used Richard's equation [1]. In this work we present a series of numerical simulations to evaluate the 'unique' nature of the SWCC. The simulations involves the use of the Lattice Boltzmann Method (LBM) [2] within a regular soil, modelling the flow behavior of two immiscible fluids: wetting and non-wetting. The soil is packed within a cubic domain to resemble the experimental setups that are commonly used for measuring the SWCC[3]. The boundary conditions ensure that the non-wetting phase enters through one cubic face and the wetting phase enters trough the opposite phase, with no flow boundary conditions in the remaining 4 cubic faces. The SWCC known features are inspected including the presence of the common limit curves for different cycles involving varying limits for the suction. For this stage of simulations, the SWCC is indeed unique. Later, different boundary conditions are applied with the two fluids each injected from 3 opposing faces into the porous medium. The effect of this boundary condition change is a net flow direction, which is different from that in the previous case. A striking result is observed when both SWCC are compared and found to be noticeable different. Further analysis is

Permeability Changes of Coal Cores and Briquettes under Tri-Axial Stress Conditions

NASA Astrophysics Data System (ADS)

Wierzbicki, Mirosław; Konečný, Pavel; Kožušníková, Alena

2014-12-01

The paper is dealing with the permeability of coal in triaxial state of stress. The permeability of coal, besides coal's methane capacity, is the main parameter determining the quantity of methane inflow into underground excavations. The stress in a coal seam is one of the most important factors influencing coal permeability therefore the permeability measurements were performed in tri-axial state of stress. The hydrostatic three-axial state of stress was gradually increased from 5 MPa with steps of 5 MPa up to a maximum of 30 MPa. Nitrogen was applied as a gas medium in all experiments. The results of the permeability measurements of coal cores from the "Zofiówka" mine, Poland, and three mines from the Czech Republic are presented in this paper. As a "reference", permeability measurements were also taken for coal briquettes prepared from coal dust with defined porosity. It was confirmed that the decreasing porosity of coal briquettes affects the decreasing permeability. The advantage of experimentation on coal briquettes is its good repeatability. From the experimental results, an empirical relation between gas permeability and confining pressure has also been identified. The empirical relation for coal briquettes is in good correspondence with published results. However, for coal cores, the character of change differs. The influence of confining pressure has a different character and the decrease in permeability is stronger due to the increasing confining pressure Przepuszczalność węgla, oprócz pojemności sorpcyjnej względem metanu jest głównym parametrem określającym dopływ metanu do podziemnych wyrobiskach górniczych. W warunkach naturalnych wartość przepuszczalności jest ściśle związana ze stanem naprężenia w pokładzie węgla. W pracy przedstawiono wyniki pomiarów przepuszczalności wykonanych w trójosiowym stanie naprężenia. Hydrostatyczny trójosiowy stan naprężenia stopniowo zwiększano od 5 MPa do maksymalnie 30 MPa z krokiem

Conditions for Boundary Crossing: Social Practices of Newly Qualified Swedish Teachers

ERIC Educational Resources Information Center

Andersson, Ingrid; Andersson, Sven B.

2008-01-01

The purpose of this study is to gain knowledge about conditions for boundary crossing between academic and vocational practices and to identify dimensions of social practice within workplaces. The data consist of 28 questionnaires and 14 in-depth interviews with newly qualified secondary school teachers in their first year of teaching. We use the…

Ising antiferromagnet on a finite triangular lattice with free boundary conditions

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2015-11-01

The exact integer values for the density of states of the Ising model on an equilateral triangular lattice with free boundary conditions are evaluated up to L = 24 spins on a side for the first time by using the microcanonical transfer matrix. The total number of states is 2 N s = 2300 ≈ 2.037 × 1090 for L = 24, where N s = L( L+1)/2 is the number of spins. Classifying all 2300 spin states according to their energy values is an enormous work. From the density of states, the exact partition function zeros in the complex temperature plane of the triangular-lattice Ising model are evaluated. Using the density of states and the partition function zeros, we investigate the properties of the triangularlattice Ising antiferromagnet. The scaling behavior of the ground-state entropy and the form of the correlation length at T = 0 are studied for the triangular-lattice Ising antiferromagnet with free boundary conditions. Also, the scaling behavior of the Fisher edge singularity is investigated.

Simulating wave-turbulence on thin elastic plates with arbitrary boundary conditions

NASA Astrophysics Data System (ADS)

van Rees, Wim M.; Mahadevan, L.

2016-11-01

The statistical characteristics of interacting waves are described by the theory of wave turbulence, with the study of deep water gravity wave turbulence serving as a paradigmatic physical example. Here we consider the elastic analog of this problem in the context of flexural waves arising from vibrations of a thin elastic plate. Such flexural waves generate the unique sounds of so-called thunder machines used in orchestras - thin metal plates that make a thunder-like sound when forcefully shaken. Wave turbulence in elastic plates is typically investigated numerically using spectral simulations with periodic boundary conditions, which are not very realistic. We will present the results of numerical simulations of the dynamics of thin elastic plates in physical space, with arbitrary shapes, boundary conditions, anisotropy and inhomogeneity, and show first results on wave turbulence beyond the conventionally studied rectangular plates. Finally, motivated by a possible method to measure ice-sheet thicknesses in the open ocean, we will further discuss the behavior of a vibrating plate when floating on an inviscid fluid.

A Comparative Experimental Study of Fixed Temperature and Fixed Heat Flux Boundary Conditions in Turbulent Thermal Convection

NASA Astrophysics Data System (ADS)

Huang, Shi-Di; Wang, Fei; Xi, Heng-Dong; Xia, Ke-Qing

2014-11-01

We report an experimental study of the influences of thermal boundary condition in turbulent thermal convection. Two configurations were examined: one was fixed heat flux at the bottom boundary and fixed temperature at the top (HC cells); the other was fixed temperature at both boundaries (CC cells). It is found that the flow strength in the CC cells is on average 9% larger than that in the HC ones, which could be understood as change in plume emission ability under different boundary conditions. It is further found, rather surprisingly, that flow reversals of the large-scale circulation occur more frequently in the CC cell, despite a stronger large-scale flow and more uniform temperature distribution over the boundaries. These findings provide new insights into turbulent thermal convection and should stimulate further studies, especially experimental ones. This work is supported by the Hong Kong Research Grants Council under Grant No. CUHK 403712.

Modeling long period swell in Southern California: Practical boundary conditions from buoy observations and global wave model predictions

NASA Astrophysics Data System (ADS)

Crosby, S. C.; O'Reilly, W. C.; Guza, R. T.

2016-02-01

Accurate, unbiased, high-resolution (in space and time) nearshore wave predictions are needed to drive models of beach erosion, coastal flooding, and alongshore transport of sediment, biota and pollutants. On highly sheltered shorelines, wave predictions are sensitive to the directions of onshore propagating waves, and nearshore model prediction error is often dominated by uncertainty in offshore boundary conditions. Offshore islands and shoals, and coastline curvature, create complex sheltering patterns over the 250km span of southern California (SC) shoreline. Here, regional wave model skill in SC was compared for different offshore boundary conditions created using offshore buoy observations and global wave model hindcasts (National Oceanographic and Atmospheric Administration Wave Watch 3, WW3). Spectral ray-tracing methods were used to transform incident offshore swell (0.04-0.09Hz) energy at high directional resolution (1-deg). Model skill is assessed for predictions (wave height, direction, and alongshore radiation stress) at 16 nearshore buoy sites between 2000 and 2009. Model skill using buoy-derived boundary conditions is higher than with WW3-derived boundary conditions. Buoy-driven nearshore model results are similar with various assumptions about the true offshore directional distribution (maximum entropy, Bayesian direct, and 2nd derivative smoothness). Two methods combining offshore buoy observations with WW3 predictions in the offshore boundary condition did not improve nearshore skill above buoy-only methods. A case example at Oceanside harbor shows strong sensitivity of alongshore sediment transport predictions to different offshore boundary conditions. Despite this uncertainty in alongshore transport magnitude, alongshore gradients in transport (e.g. the location of model accretion and erosion zones) are determined by the local bathymetry, and are similar for all predictions.

A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, D; Fasenfest, B; Rieben, R

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 discretizedmore » Biot-Savart law.« less

The significance of task significance: Job performance effects, relational mechanisms, and boundary conditions.

PubMed

Grant, Adam M

2008-01-01

Does task significance increase job performance? Correlational designs and confounded manipulations have prevented researchers from assessing the causal impact of task significance on job performance. To address this gap, 3 field experiments examined the performance effects, relational mechanisms, and boundary conditions of task significance. In Experiment 1, fundraising callers who received a task significance intervention increased their levels of job performance relative to callers in 2 other conditions and to their own prior performance. In Experiment 2, task significance increased the job dedication and helping behavior of lifeguards, and these effects were mediated by increases in perceptions of social impact and social worth. In Experiment 3, conscientiousness and prosocial values moderated the effects of task significance on the performance of new fundraising callers. The results provide fresh insights into the effects, relational mechanisms, and boundary conditions of task significance, offering noteworthy implications for theory, research, and practice on job design, social information processing, and work motivation and performance. 2008 APA

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.

Shuttle orbiter boundary layer transition at flight and wind tunnel conditions

NASA Technical Reports Server (NTRS)

Goodrich, W. D.; Derry, S. M.; Bertin, J. J.

1983-01-01

Hypersonic boundary layer transition data obtained on the windward centerline of the Shuttle orbiter during entry for the first five flights are presented and analyzed. Because the orbiter surface is composed of a large number of thermal protection tiles, the transition data include the effects of distributed roughness arising from tile misalignment and gaps. These data are used as a benchmark for assessing and improving the accuracy of boundary layer transition predictions based on correlations of wind tunnel data taken on both aerodynamically rough and smooth orbiter surfaces. By comparing these two data bases, the relative importance of tunnel free stream noise and surface roughness on orbiter boundary layer transition correlation parameters can be assessed. This assessment indicates that accurate predications of transition times can be made for the orbiter at hypersonic flight conditions by using roughness dominated wind tunnel data. Specifically, times of transition onset and completion is accurately predicted using a correlation based on critical and effective values of a roughness Reynolds number previously derived from wind tunnel data.

Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions

NASA Astrophysics Data System (ADS)

Su, Zhu; Jin, Guoyong; Ye, Tiangui

2016-06-01

The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier series which consists of standard Fourier cosine series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt’s rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.

Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions

NASA Astrophysics Data System (ADS)

Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.

2018-04-01

It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a Bañados-Teitelboim-Zanelli (BTZ) black hole (BH) [1]. To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirrorlike cavity or in anti-de Sitter (AdS) space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/AdS space is an isolated system and include, as a particular case, the commonly considered Dirichlet boundary conditions (DBCs). Whereas the superradiant modes for some RBCs differ only mildly from the ones with DBCs, in both cases, we find that as we vary the RBCs the imaginary part of the frequency may attain arbitrarily large positive values. We interpret this growth as being sourced by a bulk instability of both confined geometries when certain RBCs are imposed to either the mirrorlike cavity or the AdS boundary, rather than by energy extraction from the BH, in analogy with the BTZ behavior.

A novel CFS-PML boundary condition for transient electromagnetic simulation using a fictitious wave domain method

NASA Astrophysics Data System (ADS)

Hu, Yanpu; Egbert, Gary; Ji, Yanju; Fang, Guangyou

2017-01-01

In this study, we apply fictitious wave domain (FWD) methods, based on the correspondence principle for the wave and diffusion fields, to finite difference (FD) modeling of transient electromagnetic (TEM) diffusion problems for geophysical applications. A novel complex frequency shifted perfectly matched layer (PML) boundary condition is adapted to the FWD to truncate the computational domain, with the maximum electromagnetic wave propagation velocity in the FWD used to set the absorbing parameters for the boundary layers. Using domains of varying spatial extent we demonstrate that these boundary conditions offer significant improvements over simpler PML approaches, which can result in spurious reflections and large errors in the FWD solutions, especially for low frequencies and late times. In our development, resistive air layers are directly included in the FWD, allowing simulation of TEM responses in the presence of topography, as is commonly encountered in geophysical applications. We compare responses obtained by our new FD-FWD approach and with the spectral Lanczos decomposition method on 3-D resistivity models of varying complexity. The comparisons demonstrate that our absorbing boundary condition in FWD for the TEM diffusion problems works well even in complex high-contrast conductivity models.

Permeability and strength structure around an ancient exhumed subduction-zone fault

NASA Astrophysics Data System (ADS)

Kato, A.; Sakaguchi, A.; Yoshida, S.; Kaneda, Y.

2003-12-01

Investigating the transporting properties of subduction zone faults is crucial for understanding shear strength and slip-stability, or instability, of subduction zone faults. Despite the influence of pore pressure on a wide range of subduction-zone fault processes, few previous studies have evaluated the permeability structure around the fault placed in a well-defined structural context. In this study, the aim is to gain the entire permeability and the shear strength structure around the ancient subduction zone fault. We have conducted a series of permeability measurements and shear failure experiments in seismogenic environments using intact rocks sampled at the outcrop of an exhumed fault zone in the Cretaceous Shimanto accretionary complex, in Shikoku, SW Japan, where a typical evidence for seismic fault rock of pseudotachylyte has been demonstrated [Ikesawa et al., 2003]. This fault zone is located at boundary between the sandstone-dominant coherent unit of the Nonokawa Formation and the Okitsu mélange. The porosity of each rock sample is less than 1 %, except for the shear zone. Cylindrical test specimens (length = 40 mm, diameter = 20 mm) were cored to an accuracy of within 0.02 mm. Most of values of permeability were evaluated at confining pressure Pc of 140 MPa and pore pressure Pp of 115 MPa simulating the depth of 5 km (suprahydrostatic pore pressure). It is found that the permeability at room temperature shows the heterogeneous structure across the fault zone. The permeability of sandstone-dominant coherent unit is the lowest (10-19 m2) across the fault zone. In contrast, high shear zone has the highest permeability (10-16 m2). Following the increase in temperature, permeability evolution has been investigated. The permeability at 250oC continuously decreases with hold time for all types of rock specimens, and the reduction rate of permeability against hold time seems to become small with hold time. It seems that the reduction rate does not

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.

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.