Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.

2016-07-13

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

NASA Technical Reports Server (NTRS)

Jones, Jim E.

1996-01-01

A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

Controlling sign problems in spin models using tensor renormalization

NASA Astrophysics Data System (ADS)

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan

2014-01-01

We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Generalized source Finite Volume Method for radiative transfer equation in participating media

NASA Astrophysics Data System (ADS)

Zhang, Biao; Xu, Chuan-Long; Wang, Shi-Min

2017-03-01

Temperature monitoring is very important in a combustion system. In recent years, non-intrusive temperature reconstruction has been explored intensively on the basis of calculating arbitrary directional radiative intensities. In this paper, a new method named Generalized Source Finite Volume Method (GSFVM) was proposed. It was based on radiative transfer equation and Finite Volume Method (FVM). This method can be used to calculate arbitrary directional radiative intensities and is proven to be accurate and efficient. To verify the performance of this method, six test cases of 1D, 2D, and 3D radiative transfer problems were investigated. The numerical results show that the efficiency of this method is close to the radial basis function interpolation method, but the accuracy and stability is higher than that of the interpolation method. The accuracy of the GSFVM is similar to that of the Backward Monte Carlo (BMC) algorithm, while the time required by the GSFVM is much shorter than that of the BMC algorithm. Therefore, the GSFVM can be used in temperature reconstruction and improvement on the accuracy of the FVM.

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Movies of Finite Deformation within Western North American Plate Boundary Zone

NASA Astrophysics Data System (ADS)

Holt, W. E.; Birkes, B.; Richard, G. A.

2004-12-01

Animations of finite strain within deforming continental zones can be an important tool for both education and research. We present finite strain models for western North America. We have found that these moving images, which portray plate motions, landform uplift, and subsidence, are highly useful for enabling students to conceptualize the dramatic changes that can occur within plate boundary zones over geologic time. These models use instantaneous rates of strain inferred from both space geodetic observations and Quaternary fault slip rates. Geodetic velocities and Quaternary strain rates are interpolated to define a continuous, instantaneous velocity field for western North America. This velocity field is then used to track topography points and fault locations through time (both backward and forward in time), using small time steps, to produce a 6 million year image. The strain rate solution is updated at each time step, accounting for changes in boundary conditions of plate motion, and changes in fault orientation. Assuming zero volume change, Airy isostasy, and a ratio of erosion rate to tectonic uplift rate, the topography is also calculated as a function of time. The animations provide interesting moving images of the transform boundary, highlighting ongoing extension and subsidence, convergence and uplift, and large translations taking place within the strike-slip regime. Moving images of the strain components, uplift volume through time, and inferred erosion volume through time, have also been produced. These animations are an excellent demonstration for education purposes and also hold potential as an important tool for research enabling the quantification of finite rotations of fault blocks, potential erosion volume, uplift volume, and the influence of climate on these parameters. The models, however, point to numerous shortcomings of taking constraints from instantaneous calculations to provide insight into time evolution and reconstruction models. More rigorous calculations are needed to account for changes in dynamics (body forces) through time and resultant changes in fault behavior and crustal rheology.

Free Wake Analysis of Helicopter Rotor Blades in Hover Using a Finite Volume Technique

DTIC Science & Technology

1988-10-01

inboard, and root) which were replaced by a far wake model after four revolutions. Murman and Stremel 1121 calculated j two-dimensional unsteady wake...distributed to a fixed mesh, on which the velocities were calculated by a finite difference solution of Laplace’s equation. Stremel [131 applied this two...Analysis of a Hovering Rotor," Vertica, Vol. 6, No. 2, 1982. 12. Murman, E.M., and Stremel , P.M., "A Vortex Wake Capturing Method Po- tential Flow

Finite-volume and partial quenching effects in the magnetic polarizability of the neutron

NASA Astrophysics Data System (ADS)

Hall, J. M. M.; Leinweber, D. B.; Young, R. D.

2014-03-01

There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modeling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behavior of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, βn=1.93(11)stat(11)sys×10-4 fm3, which is in agreement with current experimental results.

Computing Reliabilities Of Ceramic Components Subject To Fracture

NASA Technical Reports Server (NTRS)

Nemeth, N. N.; Gyekenyesi, J. P.; Manderscheid, J. M.

1992-01-01

CARES calculates fast-fracture reliability or failure probability of macroscopically isotropic ceramic components. Program uses results from commercial structural-analysis program (MSC/NASTRAN or ANSYS) to evaluate reliability of component in presence of inherent surface- and/or volume-type flaws. Computes measure of reliability by use of finite-element mathematical model applicable to multiple materials in sense model made function of statistical characterizations of many ceramic materials. Reliability analysis uses element stress, temperature, area, and volume outputs, obtained from two-dimensional shell and three-dimensional solid isoparametric or axisymmetric finite elements. Written in FORTRAN 77.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Nicholson, S.; Moore, J.

1986-01-01

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

The influence of injection volume and capsular bag contraction on the refractive power of polymer refilled lenses - a finite element modelling simulation study.

PubMed

Martin, Heiner; Guthoff, Rudolf; Schmitz, Klaus-Peter

2011-09-01

Polymer injection into the capsular bag after phakoemulsification is an interesting and promising approach to lens surgery. Safe clinical application of this technique will require an appropriate estimate of the effect of implantation variables on the lens power. This article details the results of finite element investigations into the effects of the injected polymer volume and capsular bag contraction on the resultant lens power and accommodation amplitude. An axisymmetric finite element model was created from literature sources. Polymer injection and the capsular contraction were simulated, and their effect on the lens power was calculated. The simulations show that overfilling during polymer injection leads to a refractive power increase of the lens. Capsular bag contraction also results in a power increase. The calculated accommodative amplitude of the lens is minimally affected by capsular bag contraction but decreases significantly with increased capsular bag stiffness as a result of fibrosis. © 2010 The Authors. Journal compilation © 2010 Acta Ophthalmol.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Nontrivial thermodynamics in 't Hooft's large-N limit

NASA Astrophysics Data System (ADS)

Cubero, Axel Cortés

2015-05-01

We study the finite volume/temperature correlation functions of the (1 +1 )-dimensional SU (N ) principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large N , and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Nonperturbative evaluation for anomalous dimension in 2-dimensional O (3 ) sigma model

NASA Astrophysics Data System (ADS)

Calle Jimenez, Sergio; Oka, Makoto; Sasaki, Kiyoshi

2018-06-01

We nonperturbatively calculate the wave-function renormalization in the two-dimensional O (3 ) sigma model. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite-volume scheme through an analysis of the step-scaling function. Results are compared with a perturbative evaluation, and reasonable behavior is observed.

Singularity embedding method in potential flow calculations

NASA Technical Reports Server (NTRS)

Jou, W. H.; Huynh, H.

1982-01-01

The so-called H-type mesh is used in a finite-element (or finite-volume) calculation of the potential flow past an airfoil. Due to coordinate singularity at the leading edge, a special singular trial function is used for the elements neighboring the leading edge. The results using the special singular elements are compared to those using the regular elements. It is found that the unreasonable pressure distribution obtained by the latter is removed by the embedding of the singular element. Suggestions to extend the present method to transonic cases are given.

Effects of damping on mode shapes, volume 1

NASA Technical Reports Server (NTRS)

Gates, R. M.

1977-01-01

Displacement, velocity, and acceleration admittances were calculated for a realistic NASTRAN structural model of space shuttle for three conditions: liftoff, maximum dynamic pressure and end of solid rocket booster burn. The realistic model of the orbiter, external tank, and solid rocket motors included the representation of structural joint transmissibilities by finite stiffness and damping elements. Methods developed to incorporate structural joints and their damping characteristics into a finite element model of the space shuttle, to determine the point damping parameters required to produce realistic damping in the primary modes, and to calculate the effect of distributed damping on structural resonances through the calculation of admittances.

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

Endres, Michael G.; Shindler, Andrea; Tiburzi, Brian C.

The commonly adopted approach for including electromagnetic interactions in lattice QCD simulations relies on using finite volume as the infrared regularization for QED. The long-range nature of the electromagnetic interaction, however, implies that physical quantities are susceptible to power-law finite volume corrections, which must be removed by performing costly simulations at multiple lattice volumes, followed by an extrapolation to the infinite volume limit. In this work, we introduce a photon mass as an alternative means for gaining control over infrared effects associated with electromagnetic interactions. We present findings for hadron mass shifts due to electromagnetic interactions (i.e., for the proton,more » neutron, charged and neutral kaon) and corresponding mass splittings, and compare the results with those obtained from conventional QCD+QED calculations. Results are reported for numerical studies of three flavor electroquenched QCD using ensembles corresponding to 800 MeV pions, ensuring that the only appreciable volume corrections arise from QED effects. The calculations are performed with three lattice volumes with spatial extents ranging from 3.4 - 6.7 fm. As a result, we find that for equal computing time (not including the generation of the lattice configurations), the electromagnetic mass shifts can be extracted from computations on a single (our smallest) lattice volume with comparable or better precision than the conventional approach.« less

Massive photons: An infrared regularization scheme for lattice QCD + QED

DOE PAGES

Endres, Michael G.; Shindler, Andrea; Tiburzi, Brian C.; ...

2016-08-10

The commonly adopted approach for including electromagnetic interactions in lattice QCD simulations relies on using finite volume as the infrared regularization for QED. The long-range nature of the electromagnetic interaction, however, implies that physical quantities are susceptible to power-law finite volume corrections, which must be removed by performing costly simulations at multiple lattice volumes, followed by an extrapolation to the infinite volume limit. In this work, we introduce a photon mass as an alternative means for gaining control over infrared effects associated with electromagnetic interactions. We present findings for hadron mass shifts due to electromagnetic interactions (i.e., for the proton,more » neutron, charged and neutral kaon) and corresponding mass splittings, and compare the results with those obtained from conventional QCD+QED calculations. Results are reported for numerical studies of three flavor electroquenched QCD using ensembles corresponding to 800 MeV pions, ensuring that the only appreciable volume corrections arise from QED effects. The calculations are performed with three lattice volumes with spatial extents ranging from 3.4 - 6.7 fm. As a result, we find that for equal computing time (not including the generation of the lattice configurations), the electromagnetic mass shifts can be extracted from computations on a single (our smallest) lattice volume with comparable or better precision than the conventional approach.« less

Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis.

PubMed

Wen, Xin-Xin; Xu, Chao; Zong, Chun-Lin; Feng, Ya-Fei; Ma, Xiang-Yu; Wang, Fa-Qi; Yan, Ya-Bo; Lei, Wei

2016-07-01

Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E. Copyright © 2016 Elsevier Ltd. All rights reserved.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Moore, J.; Nicholson, S.; Moore, J. G.

1985-01-01

Research at NASA Lewis Research Center gave the opportunity to incorporate new control volumes in the Denton 3-D finite-volume time marching code. For duct flows, the new control volumes require no transverse smoothing and this allows calculations with large transverse gradients in properties without significant numerical total pressure losses. Possibilities for improving the Denton code to obtain better distributions of properties through shocks were demonstrated. Much better total pressure distributions through shocks are obtained when the interpolated effective pressure, needed to stabilize the solution procedure, is used to calculate the total pressure. This simple change largely eliminates the undershoot in total pressure down-stream of a shock. Overshoots and undershoots in total pressure can then be further reduced by a factor of 10 by adopting the effective density method, rather than the effective pressure method. Use of a Mach number dependent interpolation scheme for pressure then removes the overshoot in static pressure downstream of a shock. The stability of interpolation schemes used for the calculation of effective density is analyzed and a Mach number dependent scheme is developed, combining the advantages of the correct perfect gas equation for subsonic flow with the stability of 2-point and 3-point interpolation schemes for supersonic flow.

Are artificial opals non-close-packed fcc structures?

NASA Astrophysics Data System (ADS)

García-Santamaría, F.; Braun, P. V.

2007-06-01

The authors report a simple experimental method to accurately measure the volume fraction of artificial opals. The results are modeled using several methods, and they find that some of the most common yield very inaccurate results. Both finite size and substrate effects play an important role in calculations of the volume fraction. The experimental results show that the interstitial pore volume is 4%-15% larger than expected for close-packed structures. Consequently, calculations performed in previous work relating the amount of material synthesized in the opal interstices with the optical properties may need revision, especially in the case of high refractive index materials.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Explicit finite-volume time-marching calculations of total temperature distributions in turbulent flow

NASA Technical Reports Server (NTRS)

Nicholson, Stephen; Moore, Joan G.; Moore, John

1987-01-01

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. This paper investigates the introduction of a new formulation of the energy equation which gives improved transient behavior as the calculation converges. The effect of variable Prandtl number on the temperature distribution through the boundary layer is also investigated. A turbulent boundary layer in an adverse pressure gradient (M = 0.55) is used to demonstrate the improved transient temperature distribution obtained when the new formulation of the energy equation is used. A flat plate turbulent boundary layer with a supersonic free-stream Mach number of 2.8 is used to investigate the effect of Prandtl number on the distribution of properties through the boundary layer. The computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Explicit finite-volume time-marching calculations of total temperature distributions in turbulent flow

NASA Technical Reports Server (NTRS)

Nicholson, Stephen; Moore, Joan G.; Moore, John

1986-01-01

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. This paper investigates the introduction of a new formulation of the energy equation which gives improved transient behavior as the calculation converges. The effect of variable Prandtl number on the temperature distribution through the boundary layer is also investigated. A turbulent boundary layer in an adverse pressure gradient (M = 0.55) is used to demonstrate the improved transient temperature distribution obtained when the new formulation of the energy equation is used. A flat plate turbulent boundary layer with a supersonic free-stream Mach number of 2.8 is used to investigate the effect of Prandtl number on the distribution of properties through the boundary layer. The computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Massive Photons: An Infrared Regularization Scheme for Lattice QCD+QED.

PubMed

Endres, Michael G; Shindler, Andrea; Tiburzi, Brian C; Walker-Loud, André

2016-08-12

Standard methods for including electromagnetic interactions in lattice quantum chromodynamics calculations result in power-law finite-volume corrections to physical quantities. Removing these by extrapolation requires costly computations at multiple volumes. We introduce a photon mass to alternatively regulate the infrared, and rely on effective field theory to remove its unphysical effects. Electromagnetic modifications to the hadron spectrum are reliably estimated with a precision and cost comparable to conventional approaches that utilize multiple larger volumes. A significant overall cost advantage emerges when accounting for ensemble generation. The proposed method may benefit lattice calculations involving multiple charged hadrons, as well as quantum many-body computations with long-range Coulomb interactions.

A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

USGS Publications Warehouse

Barall, Michael

2009-01-01

We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

Quantum Monte Carlo calculations of van der Waals interactions between aromatic benzene rings

NASA Astrophysics Data System (ADS)

Azadi, Sam; Kühne, T. D.

2018-05-01

The magnitude of finite-size effects and Coulomb interactions in quantum Monte Carlo simulations of van der Waals interactions between weakly bonded benzene molecules are investigated. To that extent, two trial wave functions of the Slater-Jastrow and Backflow-Slater-Jastrow types are employed to calculate the energy-volume equation of state. We assess the impact of the backflow coordinate transformation on the nonlocal correlation energy. We found that the effect of finite-size errors in quantum Monte Carlo calculations on energy differences is particularly large and may even be more important than the employed trial wave function. In addition to the cohesive energy, the singlet excitonic energy gap and the energy gap renormalization of crystalline benzene at different densities are computed.

Effects of damping on mode shapes, volume 2

NASA Technical Reports Server (NTRS)

Gates, R. M.; Merchant, D. H.; Arnquist, J. L.

1977-01-01

Displacement, velocity, and acceleration admittances were calculated for a realistic NASTRAN structural model of space shuttle for three conditions: liftoff, maximum dynamic pressure and end of solid rocket booster burn. The realistic model of the orbiter, external tank, and solid rocket motors included the representation of structural joint transmissibilities by finite stiffness and damping elements. Data values for the finite damping elements were assigned to duplicate overall low-frequency modal damping values taken from tests of similar vehicles. For comparison with the calculated admittances, position and rate gains were computed for a conventional shuttle model for the liftoff condition. Dynamic characteristics and admittances for the space shuttle model are presented.

Predictive Flow Control to Minimize Convective Time Delays

DTIC Science & Technology

2013-08-19

simulation. The CFO solver used is Cobalt, an unstructured finite-volume code developed for the solution of the compress- ible Navier-Stokes...cell-centered fin ite volume approach applicable to arbitrary cell topologies (e.g, hexahedra, prisms, tetrahedra). The spatial operator uses a Riemann ... solver , least squares gradient calculations using QR factorizati on to provide second order accuracy in space. A point implicit method using

Comparison of cell centered and cell vertex scheme in the calculation of high speed compressible flows

NASA Astrophysics Data System (ADS)

Rahman, Syazila; Yusoff, Mohd. Zamri; Hasini, Hasril

2012-06-01

This paper describes the comparison between the cell centered scheme and cell vertex scheme in the calculation of high speed compressible flow properties. The calculation is carried out using Computational Fluid Dynamic (CFD) in which the mass, momentum and energy equations are solved simultaneously over the flow domain. The geometry under investigation consists of a Binnie and Green convergent-divergent nozzle and structured mesh scheme is implemented throughout the flow domain. The finite volume CFD solver employs second-order accurate central differencing scheme for spatial discretization. In addition, the second-order accurate cell-vertex finite volume spatial discretization is also introduced in this case for comparison. The multi-stage Runge-Kutta time integration is implemented for solving a set of non-linear governing equations with variables stored at the vertices. Artificial dissipations used second and fourth order terms with pressure switch to detect changes in pressure gradient. This is important to control the solution stability and capture shock discontinuity. The result is compared with experimental measurement and good agreement is obtained for both cases.

SToRM: A Model for Unsteady Surface Hydraulics Over Complex Terrain

USGS Publications Warehouse

Simoes, Francisco J.

2014-01-01

A two-dimensional (depth-averaged) finite volume Godunov-type shallow water model developed for flow over complex topography is presented. The model is based on an unstructured cellcentered finite volume formulation and a nonlinear strong stability preserving Runge-Kutta time stepping scheme. The numerical discretization is founded on the classical and well established shallow water equations in hyperbolic conservative form, but the convective fluxes are calculated using auto-switching Riemann and diffusive numerical fluxes. The model’s implementation within a graphical user interface is discussed. Field application of the model is illustrated by utilizing it to estimate peak flow discharges in a flooding event of historic significance in Colorado, U.S.A., in 2013.

Development of a patient-specific model for calculation of pulmonary function

NASA Astrophysics Data System (ADS)

Zhong, Hualiang; Ding, Mingyue; Movsas, Benjamin; Chetty, Indrin J.

2011-06-01

The purpose of this paper is to develop a patient-specific finite element model (FEM) to calculate the pulmonary function of lung cancer patients for evaluation of radiation treatment. The lung model was created with an in-house developed FEM software with region-specific parameters derived from a four-dimensional CT (4DCT) image. The model was used first to calculate changes in air volume and elastic stress in the lung, and then to calculate regional compliance defined as the change in air volume corrected by its associated stress. The results have shown that the resultant compliance images can reveal the regional elastic property of lung tissue, and could be useful for radiation treatment planning and assessment.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Electromagnetic plasma simulation in realistic geometries

NASA Astrophysics Data System (ADS)

Brandon, S.; Ambrosiano, J. J.; Nielsen, D.

1991-08-01

Particle-in-Cell (PIC) calculations have become an indispensable tool to model the nonlinear collective behavior of charged particle species in electromagnetic fields. Traditional finite difference codes, such as CONDOR (2-D) and ARGUS (3-D), are used extensively to design experiments and develop new concepts. A wide variety of physical processes can be modeled simply and efficiently by these codes. However, experiments have become more complex. Geometrical shapes and length scales are becoming increasingly more difficult to model. Spatial resolution requirements for the electromagnetic calculation force large grids and small time steps. Many hours of CRAY YMP time may be required to complete 2-D calculation -- many more for 3-D calculations. In principle, the number of mesh points and particles need only to be increased until all relevant physical processes are resolved. In practice, the size of a calculation is limited by the computer budget. As a result, experimental design is being limited by the ability to calculate, not by the experimenters ingenuity or understanding of the physical processes involved. Several approaches to meet these computational demands are being pursued. Traditional PIC codes continue to be the major design tools. These codes are being actively maintained, optimized, and extended to handle large and more complex problems. Two new formulations are being explored to relax the geometrical constraints of the finite difference codes. A modified finite volume test code, TALUS, uses a data structure compatible with that of standard finite difference meshes. This allows a basic conformal boundary/variable grid capability to be retrofitted to CONDOR. We are also pursuing an unstructured grid finite element code, MadMax. The unstructured mesh approach provides maximum flexibility in the geometrical model while also allowing local mesh refinement.

Algorithm development for Maxwell's equations for computational electromagnetism

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.

1990-01-01

A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

Calculation and measurement of the influence of flow parameters on rotordynamic coefficients in labyrinth seals

NASA Technical Reports Server (NTRS)

Kwanka, K.; Ortinger, W.; Steckel, J.

1994-01-01

First experimental investigations performed on a new test rig are presented. For a staggered labyrinth seal with fourteen cavities the stiffness coefficient and the leakage flow are measured. The experimental results are compared to calculated results which are obtained by a one-volume bulk-flow theory. A perturbation analysis is made for seven terms. It is found out that the friction factors have great impact on the dynamic coefficients. They are obtained by turbulent flow computation by a finite-volume model with the Reynolds equations used as basic equations.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2015-11-01

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

The effectiveness of a new algorithm on a three-dimensional finite element model construction of bone trabeculae in implant biomechanics.

PubMed

Sato, Y; Teixeira, E R; Tsuga, K; Shindoi, N

1999-08-01

More validity of finite element analysis (FEA) in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To evaluate the effectiveness of a new algorithm established for more valid FEA model construction without downsizing, three-dimensional FEA bone trabeculae models with different element sizes (300, 150 and 75 micron) were constructed. Four algorithms of stepwise (1 to 4 ranks) assignment of Young's modulus accorded with bone volume in the individual cubic element was used and then stress distribution against vertical loading was analysed. The model with 300 micron element size, with 4 ranks of Young's moduli accorded with bone volume in each element presented similar stress distribution to the model with the 75 micron element size. These results show that the new algorithm was effective, and the use of the 300 micron element for bone trabeculae representation was proposed, without critical changes in stress values and for possible savings on computer memory and calculation time in the laboratory.

Ash3d: A finite-volume, conservative numerical model for ash transport and tephra deposition

USGS Publications Warehouse

Schwaiger, Hans F.; Denlinger, Roger P.; Mastin, Larry G.

2012-01-01

We develop a transient, 3-D Eulerian model (Ash3d) to predict airborne volcanic ash concentration and tephra deposition during volcanic eruptions. This model simulates downwind advection, turbulent diffusion, and settling of ash injected into the atmosphere by a volcanic eruption column. Ash advection is calculated using time-varying pre-existing wind data and a robust, high-order, finite-volume method. Our routine is mass-conservative and uses the coordinate system of the wind data, either a Cartesian system local to the volcano or a global spherical system for the Earth. Volcanic ash is specified with an arbitrary number of grain sizes, which affects the fall velocity, distribution and duration of transport. Above the source volcano, the vertical mass distribution with elevation is calculated using a Suzuki distribution for a given plume height, eruptive volume, and eruption duration. Multiple eruptions separated in time may be included in a single simulation. We test the model using analytical solutions for transport. Comparisons of the predicted and observed ash distributions for the 18 August 1992 eruption of Mt. Spurr in Alaska demonstrate to the efficacy and efficiency of the routine.

Variational principle model for the nuclear caloric curve

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

Das Gupta, S.

2005-12-15

Following the lead of a recent work, I perform a variational principle model calculation for the nuclear caloric curve. A Skyrme-type interaction with and without momentum dependence is used. The calculation is done for a large nucleus, i.e., in the nuclear matter limit. Thus I address the issue of volume fragmentation only. Nonetheless, the results are similar to the previous, largely phenomenological calculation for a finite nucleus. I find that the onset of fragmentation can be sudden as a function of temperature or excitation energy.

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

NASA Astrophysics Data System (ADS)

Blum, Thomas; Christ, Norman; Hayakawa, Masashi; Izubuchi, Taku; Jin, Luchang; Jung, Chulwoo; Lehner, Christoph

2017-08-01

In our previous work, Blum et al. [Phys. Rev. Lett. 118, 022005 (2017), 10.1103/PhysRevLett.118.022005], the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g -2 ) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1 /L2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

DOE PAGES

Blum, Thomas; Christ, Norman; Hayakawa, Masashi; ...

2017-08-22

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L 2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy.more » We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.« less

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

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

Blum, Thomas; Christ, Norman; Hayakawa, Masashi

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L 2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy.more » We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.« less

Analytical Studies of Three-Dimensional Combustion Processes

DTIC Science & Technology

1989-05-01

Include Area Code) 22c OFFICE SYMBOL Raghunath S. Boray 513-255-9991 WRDC/POPT DD Form 1473, JUN 86 Previous editions are obsolete. SECURITY...enthalpy, and momentum are calculated for each finite volume by summing the contributions from all groups of droplets. Thus, ( Sm )i,J N ((PpM-p)in

The application of rational approximation in the calculation of a temperature field with a non-linear surface heat-transfer coefficient during quenching for 42CrMo steel cylinder

NASA Astrophysics Data System (ADS)

Cheng, Heming; Huang, Xieqing; Fan, Jiang; Wang, Honggang

1999-10-01

The calculation of a temperature field has a great influence upon the analysis of thermal stresses and stains during quenching. In this paper, a 42CrMo steel cylinder was used an example for investigation. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as functions of temperature and the volume fraction of phase constituents. The rational approximation was applied to the finite element method. The temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated using this technique, which can effectively avoid oscillationin the numerical solution for a small time step. The experimental results of the temperature field calculation coincide with the numerical solutions.

Noise Reduction Design of the Volute for a Centrifugal Compressor

NASA Astrophysics Data System (ADS)

Song, Zhen; Wen, Huabing; Hong, Liangxing; Jin, Yudong

2017-08-01

In order to effectively control the aerodynamic noise of a compressor, this paper takes into consideration a marine exhaust turbocharger compressor as a research object. According to the different design concept of volute section, tongue and exit cone, six different volute models were established. The finite volume method is used to calculate the flow field, whiles the finite element method is used for the acoustic calculation. Comparison and analysis of different structure designs from three aspects: noise level, isentropic efficiency and Static pressure recovery coefficient. The results showed that under the concept of volute section model 1 yielded the best result, under the concept of tongue analysis model 3 yielded the best result and finally under exit cone analysis model 6 yielded the best results.

Calculations of Flowfield About Indented Nosetips,

DTIC Science & Technology

1982-08-23

agreement is good. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOE(ft,. Date E -t. , - NSWC TR 82-286 FOREWORD A finite difference computer program has been...Specific heat at constant pressure and volume respectively e Total energy per unit volume E ,F,H,R,S,T Functions of U AHT, HT Error in total enthalpy and...total enthalpy respectively ijGrid index in E and n directions respectively SI Identity matrix J,K Maximum grid point in E and n directions respectively

Nucleon axial charge in (2+1)-flavor dynamical-lattice QCD with domain-wall fermions.

PubMed

Yamazaki, T; Aoki, Y; Blum, T; Lin, H W; Lin, M F; Ohta, S; Sasaki, S; Tweedie, R J; Zanotti, J M

2008-05-02

We present results for the nucleon axial charge g{A} at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16;{3} x 32 and 24;{3} x 64 lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_{pi} is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m{pi}=330 MeV. We also find a scaling with the single variable m{pi}L which can also be seen in previous two-flavor domain wall and Wilson fermion calculations. Using this scaling to eliminate the finite-volume effect, we obtain g{A}=1.20(6)(4) at the physical pion mass, m_{pi}=135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when V>or=(2.4 fm);{3}. We argue this is a dynamical quark effect.

Applications of algebraic topology to compatible spatial discretizations.

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

Bochev, Pavel Blagoveston; Hyman, James M.

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstructionmore » operator and when they are equivalent.« less

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2010-01-01

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Accurate solutions for transonic viscous flow over finite wings

NASA Technical Reports Server (NTRS)

Vatsa, V. N.

1986-01-01

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

PubMed

Renteria Marquez, I A; Bolborici, V

2017-05-01

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.

Spatial Convergence of Three Dimensional Turbulent Flows

NASA Technical Reports Server (NTRS)

Park, Michael A.; Anderson, W. Kyle

2016-01-01

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with a physical pion mass

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

Blum, Thomas; Christ, Norman; Hayakawa, Masashi

We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at a physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the 48 3 × 96 ensemble generated with a physical pion mass and a 5.5 fm spatial extent by the RBC and UKQCD Collaborations using the chiral, domain wall fermion formulation. We find a HLbL μ = 5.35(1.35) × 10 –10, where the error is statistical only. The finite-volume and finite lattice-spacing errorsmore » could be quite large and are the subject of ongoing research. Finally, the omitted disconnected graphs, while expected to give a correction of order 10%, also need to be computed.« less

Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with a physical pion mass

DOE PAGES

Blum, Thomas; Christ, Norman; Hayakawa, Masashi; ...

2017-01-11

We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at a physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the 48 3 × 96 ensemble generated with a physical pion mass and a 5.5 fm spatial extent by the RBC and UKQCD Collaborations using the chiral, domain wall fermion formulation. We find a HLbL μ = 5.35(1.35) × 10 –10, where the error is statistical only. The finite-volume and finite lattice-spacing errorsmore » could be quite large and are the subject of ongoing research. Finally, the omitted disconnected graphs, while expected to give a correction of order 10%, also need to be computed.« less

Effects of finite volume on the K L – K S mass difference

DOE PAGES

Christ, N.  H.; Feng, X.; Martinelli, G.; ...

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

Coupling of a 3D Finite Element Model of Cardiac Ventricular Mechanics to Lumped Systems Models of the Systemic and Pulmonic Circulation

PubMed Central

Kerckhoffs, Roy C. P.; Neal, Maxwell L.; Gu, Quan; Bassingthwaighte, James B.; Omens, Jeff H.; McCulloch, Andrew D.

2010-01-01

In this study we present a novel, robust method to couple finite element (FE) models of cardiac mechanics to systems models of the circulation (CIRC), independent of cardiac phase. For each time step through a cardiac cycle, left and right ventricular pressures were calculated using ventricular compliances from the FE and CIRC models. These pressures served as boundary conditions in the FE and CIRC models. In succeeding steps, pressures were updated to minimize cavity volume error (FE minus CIRC volume) using Newton iterations. Coupling was achieved when a predefined criterion for the volume error was satisfied. Initial conditions for the multi-scale model were obtained by replacing the FE model with a varying elastance model, which takes into account direct ventricular interactions. Applying the coupling, a novel multi-scale model of the canine cardiovascular system was developed. Global hemodynamics and regional mechanics were calculated for multiple beats in two separate simulations with a left ventricular ischemic region and pulmonary artery constriction, respectively. After the interventions, global hemodynamics changed due to direct and indirect ventricular interactions, in agreement with previously published experimental results. The coupling method allows for simulations of multiple cardiac cycles for normal and pathophysiology, encompassing levels from cell to system. PMID:17111210

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

NASA Astrophysics Data System (ADS)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

Evaluation of HIFU-induced lesion region using temperature threshold and equivalent thermal dose methods

NASA Astrophysics Data System (ADS)

Chang, Shihui; Xue, Fanfan; Zhou, Wenzheng; Zhang, Ji; Jian, Xiqi

2017-03-01

Usually, numerical simulation is used to predict the acoustic filed and temperature distribution of high intensity focused ultrasound (HIFU). In this paper, the simulated lesion volumes obtained by temperature threshold (TRT) 60 °C and equivalent thermal dose (ETD) 240 min were compared with the experimental results which were obtained by animal tissue experiment in vitro. In the simulation, the calculated model was established according to the vitro tissue experiment, and the Finite Difference Time Domain (FDTD) method was used to calculate the acoustic field and temperature distribution in bovine liver by the Westervelt formula and Pennes bio-heat transfer equation, and the non-linear characteristics of the ultrasound was considered. In the experiment, the fresh bovine liver was exposed for 8s, 10s, 12s under different power conditions (150W, 170W, 190W, 210W), and the exposure was repeated 6 times under the same dose. After the exposures, the liver was sliced and photographed every 0.2mm, and the area of the lesion region in every photo was calculated. Then, every value of the areas was multiplied by 0.2mm, and summed to get the approximation volume of the lesion region. The comparison result shows that the lesion volume of the region calculated by TRT 60 °C in simulation was much closer to the lesion volume obtained in experiment, and the volume of the region above 60 °C was larger than the experimental results, but the volume deviation was not exceed 10%. The volume of the lesion region calculated by ETD 240 min was larger than that calculated by TRT 60 °C in simulation, and the volume deviations were ranged from 4.9% to 23.7%.

Calculation of Derivative Thermodynamic Hydration and Aqueous Partial Molar Properties of Ions Based on Atomistic Simulations.

PubMed

Dahlgren, Björn; Reif, Maria M; Hünenberger, Philippe H; Hansen, Niels

2012-10-09

The raw ionic solvation free energies calculated on the basis of atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [Kastenholz, M. A.; Hünenberger, P. H. J. Chem. Phys.2006, 124, 224501 and Reif, M. M.; Hünenberger, P. H. J. Chem. Phys.2011, 134, 144104], the application of an appropriate correction scheme allows for a conversion of the methodology-dependent raw data into methodology-independent results. In this work, methodology-independent derivative thermodynamic hydration and aqueous partial molar properties are calculated for the Na(+) and Cl(-) ions at P° = 1 bar and T(-) = 298.15 K, based on the SPC water model and on ion-solvent Lennard-Jones interaction coefficients previously reoptimized against experimental hydration free energies. The hydration parameters considered are the hydration free energy and enthalpy. The aqueous partial molar parameters considered are the partial molar entropy, volume, heat capacity, volume-compressibility, and volume-expansivity. Two alternative calculation methods are employed to access these properties. Method I relies on the difference in average volume and energy between two aqueous systems involving the same number of water molecules, either in the absence or in the presence of the ion, along with variations of these differences corresponding to finite pressure or/and temperature changes. Method II relies on the calculation of the hydration free energy of the ion, along with variations of this free energy corresponding to finite pressure or/and temperature changes. Both methods are used considering two distinct variants in the application of the correction scheme. In variant A, the raw values from the simulations are corrected after the application of finite difference in pressure or/and temperature, based on correction terms specifically designed for derivative parameters at P° and T(-). In variant B, these raw values are corrected prior to differentiation, based on corresponding correction terms appropriate for the different simulation pressures P and temperatures T. The results corresponding to the different calculation schemes show that, except for the hydration free energy itself, accurate methodological independence and quantitative agreement with even the most reliable experimental parameters (ion-pair properties) are not yet reached. Nevertheless, approximate internal consistency and qualitative agreement with experimental results can be achieved, but only when an appropriate correction scheme is applied, along with a careful consideration of standard-state issues. In this sense, the main merit of the present study is to set a clear framework for these types of calculations and to point toward directions for future improvements, with the ultimate goal of reaching a consistent and quantitative description of single-ion hydration thermodynamics in molecular dynamics simulations.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

Hadron mass and decays constant predictions of the valence approximation to lattice QCD

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

Weingarten, D.

1993-05-01

A key goal of the lattice formulation of QCD is to reproduce the masses and decay constants of the low-lying baryons and mesons. Lattice QCD mass and decay constant predictions for the real world are supposed to be obtained from masses and decay constants calculated with finite lattice spacing and finite lattice volume by taking the limits of zero spacing and infinite volume. In addition, since the algorithms used for hadron mass and decay constant calculations become progressively slower for small quark masses, results are presently found with quark masses much larger than the expected values of the up andmore » down quark masses. Predictions for the properties of hadrons containing up and down quarks then require a further extrapolation to small quark masses. The author reports here mass and decay constant predictions combining all three extrapolations for Wilson quarks in the valence (quenched) approximation. This approximation may be viewed as replacing the momentum and frequency dependent color dielectric constant arising from quark-antiquark vacuum polarization with its zero-momentum, zero-frequency limit. These calculations used approximately one year of machine time on the GF11 parallel computer running at a sustained rate of between 5 and 7 Gflops.« less

High Performance Computing Technologies for Modeling the Dynamics and Dispersion of Ice Chunks in the Arctic Ocean

DTIC Science & Technology

2016-08-23

SECURITY CLASSIFICATION OF: Hybrid finite element / finite volume based CaMEL shallow water flow solvers have been successfully extended to study wave...effects on ice floes in a simplified 10 sq-km ocean domain. Our solver combines the merits of both the finite element and finite volume methods and...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 sea ice dynamics, shallow water, finite element , finite volume

A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

2001-01-01

Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

NASA Technical Reports Server (NTRS)

Chang, I-Chung

1990-01-01

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE PAGES

Svyatsky, Daniil; Lipnikov, Konstantin

2017-03-18

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

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

Svyatsky, Daniil; Lipnikov, Konstantin

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Investigation of supersonic chemically reacting and radiating channel flow

NASA Technical Reports Server (NTRS)

Mani, Mortaza; Tiwari, Surendra N.

1988-01-01

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD

NASA Astrophysics Data System (ADS)

Lujan, M.; Alexandru, A.; Freeman, W.; Lee, F. X.

2016-10-01

We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild, and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is αK0 phys=0.356 (74 )(46 )×10-4 fm3 . In contrast, for neutron, the electric polarizability depends strongly on the volume. After removing the finite volume corrections, our neutron polarizability results are in good agreement with chiral perturbation theory. For the connected part of the neutral pion polarizability, the negative trend persists, and it is not due to finite volume effects but likely sea quark charging effects.

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

NASA Astrophysics Data System (ADS)

Tůma, K.; Stupkiewicz, S.; Petryk, H.

2016-10-01

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.

Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory.

PubMed

Pogue, B W; Patterson, M S

1994-07-01

The goal of frequency-domain optical absorption spectroscopy is the non-invasive determination of the absorption coefficient of a specific tissue volume. Since this allows the concentration of endogenous and exogenous chromophores to be calculated, there is considerable potential for clinical application. The technique relies on the measurement of the phase and modulation of light, which is diffusely reflected or transmitted by the tissue when it is illuminated by an intensity-modulated source. A model of light propagation must then be used to deduce the absorption coefficient. For simplicity, it is usual to assume the tissue is either infinite in extent (for transmission measurements) or semi-infinite (for reflectance measurements). The goal of this paper is to examine the errors introduced by these assumptions when measurements are actually performed on finite volumes. Diffusion-theory calculations and experimental measurements were performed for slabs, cylinders and spheres with optical properties characteristic of soft tissues in the near infrared. The error in absorption coefficient is presented as a function of object size as a guideline to when the simple models may be used. For transmission measurements, the error is almost independent of the true absorption coefficient, which allows absolute changes in absorption to be measured accurately. The implications of these errors in absorption coefficient for two clinical problems--quantitation of an exogenous photosensitizer and measurement of haemoglobin oxygenation--are presented and discussed.

Electrostatic Estimation of Intercalant Jump-Diffusion Barriers Using Finite-Size Ion Models.

PubMed

Zimmermann, Nils E R; Hannah, Daniel C; Rong, Ziqin; Liu, Miao; Ceder, Gerbrand; Haranczyk, Maciej; Persson, Kristin A

2018-02-01

We report on a scheme for estimating intercalant jump-diffusion barriers that are typically obtained from demanding density functional theory-nudged elastic band calculations. The key idea is to relax a chain of states in the field of the electrostatic potential that is averaged over a spherical volume using different finite-size ion models. For magnesium migrating in typical intercalation materials such as transition-metal oxides, we find that the optimal model is a relatively large shell. This data-driven result parallels typical assumptions made in models based on Onsager's reaction field theory to quantitatively estimate electrostatic solvent effects. Because of its efficiency, our potential of electrostatics-finite ion size (PfEFIS) barrier estimation scheme will enable rapid identification of materials with good ionic mobility.

SToRM: A Model for 2D environmental hydraulics

USGS Publications Warehouse

Simões, Francisco J. M.

2017-01-01

A two-dimensional (depth-averaged) finite volume Godunov-type shallow water model developed for flow over complex topography is presented. The model, SToRM, is based on an unstructured cell-centered finite volume formulation and on nonlinear strong stability preserving Runge-Kutta time stepping schemes. The numerical discretization is founded on the classical and well established shallow water equations in hyperbolic conservative form, but the convective fluxes are calculated using auto-switching Riemann and diffusive numerical fluxes. Computational efficiency is achieved through a parallel implementation based on the OpenMP standard and the Fortran programming language. SToRM’s implementation within a graphical user interface is discussed. Field application of SToRM is illustrated by utilizing it to estimate peak flow discharges in a flooding event of the St. Vrain Creek in Colorado, U.S.A., in 2013, which reached 850 m3/s (~30,000 f3 /s) at the location of this study.

Impact of Corrections to the Spallings Volume Calculation on Waste Isolation Pilot Plant Performance Assessment

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

Kicker, Dwayne Curtis; Herrick, Courtney G; Zeitler, Todd

2015-11-01

The numerical code DRSPALL (from direct release spallings) is written to calculate the volume of Waste Isolation Pilot Plant solid waste subject to material failure and transport to the surface (i.e., spallings) as a result of a hypothetical future inadvertent drilling intrusion into the repository. An error in the implementation of the DRSPALL finite difference equations was discovered and documented in a software problem report in accordance with the quality assurance procedure for software requirements. This paper describes the corrections to DRSPALL and documents the impact of the new spallings data from the modified DRSPALL on previous performance assessment calculations.more » Updated performance assessments result in more simulations with spallings, which generally translates to an increase in spallings releases to the accessible environment. Total normalized radionuclide releases using the modified DRSPALL data were determined by forming the summation of releases across each potential release pathway, namely borehole cuttings and cavings releases, spallings releases, direct brine releases, and transport releases. Because spallings releases are not a major contributor to the total releases, the updated performance assessment calculations of overall mean complementary cumulative distribution functions for total releases are virtually unchanged. Therefore, the corrections to the spallings volume calculation did not impact Waste Isolation Pilot Plant performance assessment calculation results.« less

IMRT head and neck treatment planning with a commercially available Monte Carlo based planning system

NASA Astrophysics Data System (ADS)

Boudreau, C.; Heath, E.; Seuntjens, J.; Ballivy, O.; Parker, W.

2005-03-01

The PEREGRINE Monte Carlo dose-calculation system (North American Scientific, Cranberry Township, PA) is the first commercially available Monte Carlo dose-calculation code intended specifically for intensity modulated radiotherapy (IMRT) treatment planning and quality assurance. In order to assess the impact of Monte Carlo based dose calculations for IMRT clinical cases, dose distributions for 11 head and neck patients were evaluated using both PEREGRINE and the CORVUS (North American Scientific, Cranberry Township, PA) finite size pencil beam (FSPB) algorithm with equivalent path-length (EPL) inhomogeneity correction. For the target volumes, PEREGRINE calculations predict, on average, a less than 2% difference in the calculated mean and maximum doses to the gross tumour volume (GTV) and clinical target volume (CTV). An average 16% ± 4% and 12% ± 2% reduction in the volume covered by the prescription isodose line was observed for the GTV and CTV, respectively. Overall, no significant differences were noted in the doses to the mandible and spinal cord. For the parotid glands, PEREGRINE predicted a 6% ± 1% increase in the volume of tissue receiving a dose greater than 25 Gy and an increase of 4% ± 1% in the mean dose. Similar results were noted for the brainstem where PEREGRINE predicted a 6% ± 2% increase in the mean dose. The observed differences between the PEREGRINE and CORVUS calculated dose distributions are attributed to secondary electron fluence perturbations, which are not modelled by the EPL correction, issues of organ outlining, particularly in the vicinity of air cavities, and differences in dose reporting (dose to water versus dose to tissue type).

Phase shifts in I = 2 ππ-scattering from two lattice approaches

NASA Astrophysics Data System (ADS)

Kurth, T.; Ishii, N.; Doi, T.; Aoki, S.; Hatsuda, T.

2013-12-01

We present a lattice QCD study of the phase shift of I = 2 ππ scattering on the basis of two different approaches: the standard finite volume approach by Lüscher and the recently introduced HAL QCD potential method. Quenched QCD simulations are performed on lattices with extents N s = 16 , 24 , 32 , 48 and N t = 128 as well as lattice spacing a ~ 0 .115 fm and a pion mass of m π ~ 940 MeV. The phase shift and the scattering length are calculated in these two methods. In the potential method, the error is dominated by the systematic uncertainty associated with the violation of rotational symmetry due to finite lattice spacing. In Lüscher's approach, such systematic uncertainty is difficult to be evaluated and thus is not included in this work. A systematic uncertainty attributed to the quenched approximation, however, is not evaluated in both methods. In case of the potential method, the phase shift can be calculated for arbitrary energies below the inelastic threshold. The energy dependence of the phase shift is also obtained from Lüscher's method using different volumes and/or nonrest-frame extension of it. The results are found to agree well with the potential method.

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

SAGUARO: a finite-element computer program for partially saturated porous flow problems

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

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

Optical properties of ordered vertical arrays of multi-walled carbon nanotubes from FDTD simulations.

PubMed

Bao, Hua; Ruan, Xiulin; Fisher, Timothy S

2010-03-15

A finite-difference time-domain (FDTD) method is used to model thermal radiative properties of vertical arrays of multi-walled carbon nanotubes (MWCNT). Individual CNTs are treated as solid circular cylinders with an effective dielectric tensor. Consistent with experiments, the results confirm that CNT arrays are highly absorptive. Compared with the commonly used Maxwell-Garnett theory, the FDTD calculations generally predict larger reflectance and absorbance, and smaller transmittance, which are attributed to the diffraction and scattering within the cylinder array structure. The effects of volume fraction, tube length, tube distance, and incident angle on radiative properties are investigated systematically. Low volume fraction and long tubes are more favorable to achieve low reflectance and high absorbance. For a fixed volume fraction and finite tube length, larger periodicity results in larger reflectance and absorbance. The angular dependence studies reveal an optimum incident angle at which the reflectance can be minimized. The results also suggest that an even darker material could be achieved by using CNTs with good alignment on the top surface.

Pressure algorithm for elliptic flow calculations with the PDF method

NASA Technical Reports Server (NTRS)

Anand, M. S.; Pope, S. B.; Mongia, H. C.

1991-01-01

An algorithm to determine the mean pressure field for elliptic flow calculations with the probability density function (PDF) method is developed and applied. The PDF method is a most promising approach for the computation of turbulent reacting flows. Previous computations of elliptic flows with the method were in conjunction with conventional finite volume based calculations that provided the mean pressure field. The algorithm developed and described here permits the mean pressure field to be determined within the PDF calculations. The PDF method incorporating the pressure algorithm is applied to the flow past a backward-facing step. The results are in good agreement with data for the reattachment length, mean velocities, and turbulence quantities including triple correlations.

Timelike pion form factor in lattice QCD

NASA Astrophysics Data System (ADS)

Feng, Xu; Aoki, Sinya; Hashimoto, Shoji; Kaneko, Takashi

2015-03-01

We perform a nonperturbative lattice calculation of the complex phase and modulus of the pion form factor in the timelike momentum region using the finite-volume technique. We use two ensembles of 2 +1 -flavor overlap fermions at pion masses mπ=380 and 290 MeV. By calculating the I =1 correlators in the center-of-mass and three moving frames, we obtain the form factor at ten different values of the timelike momentum transfer around the vector resonance. We compare the results with the phenomenological model of Gounaris-Sakurai and its variant.

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.; Nemeth, Noel N.

1987-01-01

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Volume-weighted measure for eternal inflation

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

Winitzki, Sergei

2008-08-15

I propose a new volume-weighted probability measure for cosmological 'multiverse' scenarios involving eternal inflation. The 'reheating-volume (RV) cutoff' calculates the distribution of observable quantities on a portion of the reheating hypersurface that is conditioned to be finite. The RV measure is gauge-invariant, does not suffer from the 'youngness paradox', and is independent of initial conditions at the beginning of inflation. In slow-roll inflationary models with a scalar inflaton, the RV-regulated probability distributions can be obtained by solving nonlinear diffusion equations. I discuss possible applications of the new measure to 'landscape' scenarios with bubble nucleation. As an illustration, I compute themore » predictions of the RV measure in a simple toy landscape.« less

Two-dimensional HID light source radiative transfer using discrete ordinates method

NASA Astrophysics Data System (ADS)

Ghrib, Basma; Bouaoun, Mohamed; Elloumi, Hatem

2016-08-01

This paper shows the implementation of the Discrete Ordinates Method for handling radiation problems in High Intensity Discharge (HID) lamps. Therefore, we start with presenting this rigorous method for treatment of radiation transfer in a two-dimensional, axisymmetric HID lamp. Furthermore, the finite volume method is used for the spatial discretization of the Radiative Transfer Equation. The atom and electron densities were calculated using temperature profiles established by a 2D semi-implicit finite-element scheme for the solution of conservation equations relative to energy, momentum, and mass. Spectral intensities as a function of position and direction are first calculated, and then axial and radial radiative fluxes are evaluated as well as the net emission coefficient. The results are given for a HID mercury lamp on a line-by-line basis. A particular attention is paid on the 253.7 nm resonance and 546.1 nm green lines.

Numerical study of the transient flow in the driven tube and the nozzle section of a shock tunnel

NASA Technical Reports Server (NTRS)

Tokarcik-Polsky, Susan; Cambier, Jean-Luc

1993-01-01

The initial flow in a shock tunnel was examined numerically using computational fluid dynamics (CFD). A finite-volume total variation diminishing (TVD) scheme was used to calculate the transient flow in a shock tunnel. Both viscous and inviscid, chemically nonreacting flows were studied. The study consisted of two parts, the first dealt with the transient flow in the driven-tube/nozzle interface region (inviscid calculations). The effects of varying the geometry in this region was examined. The second part of the study examined the transient flow in the nozzle (viscous calculations). The results were compared to experimental data.

Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135

NASA Astrophysics Data System (ADS)

Toyokuni, G.; Takenaka, H.

2007-12-01

We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.

Three-body unitarity in the finite volume

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

Mai, M.; Döring, M.

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Three-body unitarity in the finite volume

DOE PAGES

Mai, M.; Döring, M.

2017-12-18

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Establishing the 3-D finite element solid model of femurs in partial by volume rendering.

PubMed

Zhang, Yinwang; Zhong, Wuxue; Zhu, Haibo; Chen, Yun; Xu, Lingjun; Zhu, Jianmin

2013-01-01

It remains rare to report three-dimensional (3-D) finite element solid model of femurs in partial by volume rendering method, though several methods of femoral 3-D finite element modeling are already available. We aim to analyze the advantages of the modeling method by establishing the 3-D finite element solid model of femurs in partial by volume rendering. A 3-D finite element model of the normal human femurs, made up of three anatomic structures: cortical bone, cancellous bone and pulp cavity, was constructed followed by pretreatment of the CT original image. Moreover, the finite-element analysis was carried on different material properties, three types of materials given for cortical bone, six assigned for cancellous bone, and single for pulp cavity. The established 3-D finite element of femurs contains three anatomical structures: cortical bone, cancellous bone, and pulp cavity. The compressive stress primarily concentrated in the medial surfaces of femur, especially in the calcar femorale. Compared with whole modeling by volume rendering method, the 3-D finite element solid model created in partial is more real and fit for finite element analysis. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.

Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

NASA Technical Reports Server (NTRS)

Svard, Magnus; Gong, Jing; Nordstrom, Jan

2006-01-01

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

Development of mapped stress-field boundary conditions based on a Hill-type muscle model.

PubMed

Cardiff, P; Karač, A; FitzPatrick, D; Flavin, R; Ivanković, A

2014-09-01

Forces generated in the muscles and tendons actuate the movement of the skeleton. Accurate estimation and application of these musculotendon forces in a continuum model is not a trivial matter. Frequently, musculotendon attachments are approximated as point forces; however, accurate estimation of local mechanics requires a more realistic application of musculotendon forces. This paper describes the development of mapped Hill-type muscle models as boundary conditions for a finite volume model of the hip joint, where the calculated muscle fibres map continuously between attachment sites. The applied muscle forces are calculated using active Hill-type models, where input electromyography signals are determined from gait analysis. Realistic muscle attachment sites are determined directly from tomography images. The mapped muscle boundary conditions, implemented in a finite volume structural OpenFOAM (ESI-OpenCFD, Bracknell, UK) solver, are employed to simulate the mid-stance phase of gait using a patient-specific natural hip joint, and a comparison is performed with the standard point load muscle approach. It is concluded that physiological joint loading is not accurately represented by simplistic muscle point loading conditions; however, when contact pressures are of sole interest, simplifying assumptions with regard to muscular forces may be valid. Copyright © 2014 John Wiley & Sons, Ltd.

Numerical simulation of convective heat transfer of nonhomogeneous nanofluid using Buongiorno model

NASA Astrophysics Data System (ADS)

Sayyar, Ramin Onsor; Saghafian, Mohsen

2017-08-01

The aim is to study the assessment of the flow and convective heat transfer of laminar developing flow of Al2O3-water nanofluid inside a vertical tube. A finite volume method procedure on a structured grid was used to solve the governing partial differential equations. The adopted model (Buongiorno model) assumes that the nanofluid is a mixture of a base fluid and nanoparticles, with the relative motion caused by Brownian motion and thermophoretic diffusion. The results showed the distribution of nanoparticles remained almost uniform except in a region near the hot wall where nanoparticles volume fraction were reduced as a result of thermophoresis. The simulation results also indicated there is an optimal volume fraction about 1-2% of the nanoparticles at each Reynolds number for which the maximum performance evaluation criteria can be obtained. The difference between Nusselt number and nondimensional pressure drop calculated based on two phase model and the one calculated based on single phase model was less than 5% at all nanoparticles volume fractions and can be neglected. In natural convection, for 4% of nanoparticles volume fraction, in Gr = 10 more than 15% enhancement of Nusselt number was achieved but in Gr = 300 it was less than 1%.

A highly accurate dynamic contact angle algorithm for drops on inclined surface based on ellipse-fitting.

PubMed

Xu, Z N; Wang, S Y

2015-02-01

To improve the accuracy in the calculation of dynamic contact angle for drops on the inclined surface, a significant number of numerical drop profiles on the inclined surface with different inclination angles, drop volumes, and contact angles are generated based on the finite difference method, a least-squares ellipse-fitting algorithm is used to calculate the dynamic contact angle. The influences of the above three factors are systematically investigated. The results reveal that the dynamic contact angle errors, including the errors of the left and right contact angles, evaluated by the ellipse-fitting algorithm tend to increase with inclination angle/drop volume/contact angle. If the drop volume and the solid substrate are fixed, the errors of the left and right contact angles increase with inclination angle. After performing a tremendous amount of computation, the critical dimensionless drop volumes corresponding to the critical contact angle error are obtained. Based on the values of the critical volumes, a highly accurate dynamic contact angle algorithm is proposed and fully validated. Within nearly the whole hydrophobicity range, it can decrease the dynamic contact angle error in the inclined plane method to less than a certain value even for different types of liquids.

A network-analysis-based comparative study of the throughput behavior of polymer melts in barrier screw geometries

NASA Astrophysics Data System (ADS)

Aigner, M.; Köpplmayr, T.; Kneidinger, C.; Miethlinger, J.

2014-05-01

Barrier screws are widely used in the plastics industry. Due to the extreme diversity of their geometries, describing the flow behavior is difficult and rarely done in practice. We present a systematic approach based on networks that uses tensor algebra and numerical methods to model and calculate selected barrier screw geometries in terms of pressure, mass flow, and residence time. In addition, we report the results of three-dimensional simulations using the commercially available ANSYS Polyflow software. The major drawbacks of three-dimensional finite-element-method (FEM) simulations are that they require vast computational power and, large quantities of memory, and consume considerable time to create a geometric model created by computer-aided design (CAD) and complete a flow calculation. Consequently, a modified 2.5-dimensional finite volume method, termed network analysis is preferable. The results obtained by network analysis and FEM simulations correlated well. Network analysis provides an efficient alternative to complex FEM software in terms of computing power and memory consumption. Furthermore, typical barrier screw geometries can be parameterized and used for flow calculations without timeconsuming CAD-constructions.

Resonances from lattice QCD

DOE PAGES

Briceno, Raul A.

2018-03-26

The spectrum of hadron is mainly composed as shortly-lived states (resonance) that decay onto two or more hadrons. These resonances play an important role in a variety of phenomenologically significant processes. In this talk, I give an overview on the present status of a rigorous program for studying of resonances and their properties using lattice QCD. I explain the formalism needed for extracting resonant amplitudes from the finite-volume spectra. From these one can extract the masses and widths of resonances. I present some recent examples that illustrate the power of these ideas. I then explain similar formalism that allows formore » the determination of resonant electroweak amplitudes from finite-volume matrix elements. I use the recent calculation of the πγ* → ππ amplitude as an example illustrating the power of this formalism. From such amplitudes one can determine transition form factors of resonances. I close by reviewing on-going efforts to generalize these ideas to increasingly complex reactions and I then give a outlook of the field.« less

Resonances from lattice QCD

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

Briceno, Raul A.

The spectrum of hadron is mainly composed as shortly-lived states (resonance) that decay onto two or more hadrons. These resonances play an important role in a variety of phenomenologically significant processes. In this talk, I give an overview on the present status of a rigorous program for studying of resonances and their properties using lattice QCD. I explain the formalism needed for extracting resonant amplitudes from the finite-volume spectra. From these one can extract the masses and widths of resonances. I present some recent examples that illustrate the power of these ideas. I then explain similar formalism that allows formore » the determination of resonant electroweak amplitudes from finite-volume matrix elements. I use the recent calculation of the πγ* → ππ amplitude as an example illustrating the power of this formalism. From such amplitudes one can determine transition form factors of resonances. I close by reviewing on-going efforts to generalize these ideas to increasingly complex reactions and I then give a outlook of the field.« less

Magnitude of finite-nucleus-size effects in relativistic density functional computations of indirect NMR nuclear spin-spin coupling constants.

PubMed

Autschbach, Jochen

2009-09-14

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

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

Volume dependence of baryon number cumulants and their ratios

DOE PAGES

Almási, Gábor A.; Pisarski, Robert D.; Skokov, Vladimir V.

2017-03-17

Here, we explore the influence of finite-volume effects on cumulants of baryon/quark number fluctuations in a nonperturbative chiral model. In order to account for soft modes, we use the functional renormalization group in a finite volume, using a smooth regulator function in momentum space. We compare the results for a smooth regulator with those for a sharp (or Litim) regulator, and show that in a finite volume, the latter produces spurious artifacts. In a finite volume there are only apparent critical points, about which we compute the ratio of the fourth- to the second-order cumulant of quark number fluctuations. Finally,more » when the volume is sufficiently small the system has two apparent critical points; as the system size decreases, the location of the apparent critical point can move to higher temperature and lower chemical potential.« less

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1974-01-01

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model

NASA Technical Reports Server (NTRS)

Polzin, Kurt A.; Reneau, Jarred P.; Sankaran, Kameshwaran

2011-01-01

A model for pulsed inductive plasma acceleration containing an energy equation to account for the various sources and sinks in such devices is presented. The model consists of a set of circuit equations coupled to an equation of motion and energy equation for the plasma. The latter two equations are obtained for the plasma current sheet by treating it as a one-element finite volume, integrating the equations over that volume, and then matching known terms or quantities already calculated in the model to the resulting current sheet-averaged terms in the equations. Calculations showing the time-evolution of the various sources and sinks in the system are presented to demonstrate the efficacy of the model, with two separate resistivity models employed to show an example of how the plasma transport properties can affect the calculation. While neither resistivity model is fully accurate, the demonstration shows that it is possible within this modeling framework to time-accurately update various plasma parameters.

Order of accuracy of QUICK and related convection-diffusion schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

This report attempts to correct some misunderstandings that have appeared in the literature concerning the order of accuracy of the QUICK scheme for steady-state convective modeling. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the 'curvature' term) is indeed a third-order representation of the finite volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 1/6-factor) is a third-order representation of the finite difference single-point formulation; this can be written in a pseudo-flux difference form. These are both third-order convection schemes; however, the QUICK finite volume convection operator is 33 percent more accurate than the single-point implementation of SPUDS. Another finite volume scheme, writing convective fluxes in terms of cell-average values, requires a 1/6-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux difference form; for third-order accuracy, this requires a curvature factor of 5/24. Diffusion operators are also considered in both single-point and finite volume formulations. Finite volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite volume formulation as it is in single-point.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

Predictions of hydrothermal alteration within near-ridge oceanic crust from coordinated geochemical and fluid flow models

USGS Publications Warehouse

Wetzel, L.R.; Raffensperger, Jeff P.; Shock, E.L.

2001-01-01

Coordinated geochemical and hydrological calculations guide our understanding of the composition, fluid flow patterns, and thermal structure of near-ridge oceanic crust. The case study presented here illustrates geochemical and thermal changes taking place as oceanic crust ages from 0.2 to 1.0 Myr. Using a finite element code, we model fluid flow and heat transport through the upper few hundred meters of an abyssal hill created at an intermediate spreading rate. We use a reaction path model with a customized database to calculate equilibrium fluid compositions and mineral assemblages of basalt and seawater at 500 bars and temperatures ranging from 150 to 400??C. In one scenario, reaction path calculations suggest that volume increases on the order of 10% may occur within portions of the basaltic basement. If this change in volume occurred, it would be sufficient to fill all primary porosity in some locations, effectively sealing off portions of the oceanic crust. Thermal profiles resulting from fluid flow simulations indicate that volume changes along this possible reaction path occur primarily within the first 0.4 Myr of crustal aging. ?? 2001 Elsevier Science B.V. All rights reserved.

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

Summer Research Program (1992). Summer Faculty Research Program (SFRP) Reports. Volume 2. Armstrong Laboratory

DTIC Science & Technology

1992-12-01

desirable. In this study, the proposed model consists of a thick-walled, highly deformable elastic tube in which the blood flow is described by linearized ...presented a mechanical model consisting of linearized Navier-Stokes and finite elasticity equations to predict blood pooling under acceleration stress... linear multielement model of the cardiovascular system which can calculate blood pressures and flows at any point in the cardio- vascular system. It

Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots.

PubMed

Busch, Martin H J; Vollmann, Wolfgang; Grönemeyer, Dietrich H W

2006-05-26

Active magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach (1/4) of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to. First an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants. The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor. The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q V(ind) < 2 cm3) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q V(ind) > 10 cm3). Such resonators exclude patients from exactly the MRI investigation these devices are made for.

Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots

PubMed Central

Busch, Martin HJ; Vollmann, Wolfgang; Grönemeyer, Dietrich HW

2006-01-01

Background Active magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach ¼ of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to. Methods First an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants. Results The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor. Conclusion The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q Vind < 2 cm3) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q Vind > 10 cm3). Such resonators exclude patients from exactly the MRI investigation these devices are made for. PMID:16729878

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

Kicker, Dwayne Curtis; Herrick, Courtney G; Zeitler, Todd

The numerical code DRSPALL (from direct release spallings) is written to calculate the volume of Waste Isolation Pilot Plant solid waste subject to material failure and transport to the surface (i.e., spallings) as a result of a hypothetical future inadvertent drilling intrusion into the repository. An error in the implementation of the DRSPALL finite difference equations was discovered and documented in a software problem report in accordance with the quality assurance procedure for software requirements. This paper describes the corrections to DRSPALL and documents the impact of the new spallings data from the modified DRSPALL on previous performance assessment calculations.more » Updated performance assessments result in more simulations with spallings, which generally translates to an increase in spallings releases to the accessible environment. Total normalized radionuclide releases using the modified DRSPALL data were determined by forming the summation of releases across each potential release pathway, namely borehole cuttings and cavings releases, spallings releases, direct brine releases, and transport releases. Because spallings releases are not a major contributor to the total releases, the updated performance assessment calculations of overall mean complementary cumulative distribution functions for total releases are virtually unchanged. Therefore, the corrections to the spallings volume calculation did not impact Waste Isolation Pilot Plant performance assessment calculation results.« less

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone.

PubMed

Vafaeian, B; El-Rich, M; El-Bialy, T; Adeeb, S

2014-08-01

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone. Copyright © 2014 Elsevier B.V. All rights reserved.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Radiative Heat Transfer in Finite Cylindrical Enclosures with Nonhomogeneous Participating Media

NASA Technical Reports Server (NTRS)

Hsu, Pei-Feng; Ku, Jerry C.

1994-01-01

Results of a numerical solution for radiative heat transfer in homogeneous and nonhomogeneous participating media are presented. The geometry of interest is a finite axisymmetric cylindrical enclosure. The integral formulation for radiative transport is solved by the YIX method. A three-dimensional solution scheme is applied to two-dimensional axisymmetric geometry to simplify kernel calculations and to avoid difficulties associated with treating boundary conditions. As part of the effort to improve modeling capabilities for turbulent jet diffusion flames, predicted distributions for flame temperature and soot volume fraction are used to calculate radiative heat transfer from soot particles in such flames. It is shown that the nonhomogeneity of radiative property has very significant effects. The peak value of the divergence of radiative heat flux could be underestimated by 2 factor of 7 if a mean homogeneous radiative property is used. Since recent studies have shown that scattering by soot agglomerates is significant in flames, the effect of magnitude of scattering is also investigated and found to be nonnegligible.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU

NASA Astrophysics Data System (ADS)

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ˜600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ˜0.25 s/excitation source.

The Impact of Varying the Physics Grid Resolution Relative to the Dynamical Core Resolution in CAM-SE-CSLAM

NASA Astrophysics Data System (ADS)

Herrington, A. R.; Lauritzen, P. H.; Reed, K. A.

2017-12-01

The spectral element dynamical core of the Community Atmosphere Model (CAM) has recently been coupled to an approximately isotropic, finite-volume grid per implementation of the conservative semi-Lagrangian multi-tracer transport scheme (CAM-SE-CSLAM; Lauritzen et al. 2017). In this framework, the semi-Lagrangian transport of tracers are computed on the finite-volume grid, while the adiabatic dynamics are solved using the spectral element grid. The physical parameterizations are evaluated on the finite-volume grid, as opposed to the unevenly spaced Gauss-Lobatto-Legendre nodes of the spectral element grid. Computing the physics on the finite-volume grid reduces numerical artifacts such as grid imprinting, possibly because the forcing terms are no longer computed at element boundaries where the resolved dynamics are least smooth. The separation of the physics grid and the dynamics grid allows for a unique opportunity to understand the resolution sensitivity in CAM-SE-CSLAM. The observed large sensitivity of CAM to horizontal resolution is a poorly understood impediment to improved simulations of regional climate using global, variable resolution grids. Here, a series of idealized moist simulations are presented in which the finite-volume grid resolution is varied relative to the spectral element grid resolution in CAM-SE-CSLAM. The simulations are carried out at multiple spectral element grid resolutions, in part to provide a companion set of simulations, in which the spectral element grid resolution is varied relative to the finite-volume grid resolution, but more generally to understand if the sensitivity to the finite-volume grid resolution is consistent across a wider spectrum of resolved scales. Results are interpreted in the context of prior ideas regarding resolution sensitivity of global atmospheric models.

Micellar hexagonal phases in lyotropic liquid crystals

NASA Astrophysics Data System (ADS)

Amaral, L. Q.; Gulik, A.; Itri, R.; Mariani, P.

1992-09-01

The hexagonal cell parameter a of the system sodium dodecyl lauryl sulfate and water as a function of volume concentration cv in phase Hα shows the functional behavior expected for micelles of finite length: a~c-1/3v. The interpretation of x-ray data based on finite micelles leads to an alternative description of the hexagonal phase Hα: spherocylindrical micelles of constant radius with length that may grow along the range of the Hα phase. Results are compared with recent statistical-mechanical calculations for the isotropic I-Hα transition. The absence of diffraction in the direction perpendicular to the hexagonal plane is ascribed to polydispersity of micellar length, which also is a necessary condition for the occurrence of direct I-Hα transitions.

Local D3/D7 μ-SPLIT SUSY, 125 GeV Higgs and Large Volume Ricci-Flat Swiss-Cheese Metrics:. a Brief Review

NASA Astrophysics Data System (ADS)

Misra, Aalok

In this paper, we review briefly recent progress made in realizing local(ized around a mobile spacetime filling D3-brane in) D3/D7 μ-split Supersymmetry in (the large volume limit of Type IIB) String Theory (compactified on Swiss-Cheese Calabi-Yau orientifolds) as well as obtaining a 125 GeV (light) Higgs in the same setup. We also discuss obtaining the geometric Kähler potential (and hence the Ricci-flat metric) for the Swiss-Cheese Calabi-Yau in the large volume limit using the Donaldson's algorithm and intuition from GLSM-based calculations — we present new results for Swiss-Cheese Calabi-Yau (used in the setup) metrics at points finitely away from the "big" divisor.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

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

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Thermodynamics of hydrogen-helium mixtures at high pressure and finite temperature

NASA Technical Reports Server (NTRS)

Hubbard, W. B.

1972-01-01

A technique is reviewed for calculating thermodynamic quantities for mixtures of light elements at high pressure, in the metallic state. Ensemble averages are calculated with Monte Carlo techniques and periodic boundary conditions. Interparticle potentials are assumed to be coulombic, screened by the electrons in dielectric function theory. This method is quantitatively accurate for alloys at pressures above about 10 Mbar. An alloy of equal parts hydrogen and helium by mass appears to remain liquid and mixed for temperatures above about 3000 K, at pressures of about 15 Mbar. The additive volume law is satisfied to within about 10%, but the Gruneisen equation of state gives poor results. A calculation at 1300 K shows evidence of a hydrogen-helium phase separation.

Statistical mechanics of free particles on space with Lie-type noncommutativity

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H.

2010-07-01

Effects of Lie-type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally, specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.

PLIF Temperature and Velocity Distributions in Laminar Hypersonic Flat-plate Flow

NASA Technical Reports Server (NTRS)

OByrne, S.; Danehy, P. M.; Houwing, A. F. P.

2003-01-01

Rotational temperature and velocity distributions have been measured across a hypersonic laminar flat-plate boundary layer, using planar laser-induced fluorescence. The measurements are compared to a finite-volume computation and a first-order boundary layer computation, assuming local similarity. Both computations produced similar temperature distributions and nearly identical velocity distributions. The disagreement between calculations is ascribed to the similarity solution not accounting for leading-edge displacement effects. The velocity measurements agreed to within the measurement uncertainty of 2 % with both calculated distributions. The peak measured temperature was 200 K lower than the computed values. This discrepancy is tentatively ascribed to vibrational relaxation in the boundary layer.

Resonances in Coupled π K - η K Scattering from Quantum Chromodynamics

DOE PAGES

Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; ...

2014-10-01

Using first-principles calculation within Quantum Chromodynamics, we are able to reproduce the pattern of experimental strange resonances which appear as complex singularities within coupled πK, ηK scattering amplitudes. We make use of numerical computation within the lattice discretized approach to QCD, extracting the energy dependence of scattering amplitudes through their relation- ship to the discrete spectrum of the theory in a finite-volume, which we map out in unprecedented detail.

Flowfield predictions for multiple body launch vehicles

NASA Technical Reports Server (NTRS)

Deese, Jerry E.; Pavish, D. L.; Johnson, Jerry G.; Agarwal, Ramesh K.; Soni, Bharat K.

1992-01-01

A method is developed for simulating inviscid and viscous flow around multicomponent launch vehicles. Grids are generated by the GENIE general-purpose grid-generation code, and the flow solver is a finite-volume Runge-Kutta time-stepping method. Turbulence effects are simulated using Baldwin and Lomax (1978) turbulence model. Calculations are presented for three multibody launch vehicle configurations: one with two small-diameter solid motors, one with nine small-diameter solid motors, and one with three large-diameter solid motors.

A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2010-11-01

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.

Stochastic density functional theory at finite temperatures

NASA Astrophysics Data System (ADS)

Cytter, Yael; Rabani, Eran; Neuhauser, Daniel; Baer, Roi

2018-03-01

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

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

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

A novel contact model of piezoelectric traveling wave rotary ultrasonic motors with the finite volume method.

PubMed

Renteria-Marquez, I A; Renteria-Marquez, A; Tseng, B T L

2018-06-06

The operating principle of the piezoelectric traveling wave rotary ultrasonic motor is based on two energy conversion processes: the generation of the stator traveling wave and the rectification of the stator movement through the stator-rotor contact mechanism. This paper presents a methodology to model in detail the stator-rotor contact interface of these motors. A contact algorithm that couples a model of the stator which is discretized with the finite volume method and an analytical model of the rotor is presented. The outputs of the proposed model are the normal and tangential force distribution produced at the stator-rotor contact interface, contact length, height and shape of the stator traveling wave and rotor speed. The torque-speed characteristic of the USR60 is calculated with the proposed model, and the results of the model are compared versus the real torque-speed of the motor. A good agreement between the proposed model results and the torque-speed characteristic of the USR60 was observed. Copyright © 2018 Elsevier B.V. All rights reserved.

Calculations of turbulent separated flows

NASA Technical Reports Server (NTRS)

Zhu, J.; Shih, T. H.

1993-01-01

A numerical study of incompressible turbulent separated flows is carried out by using two-equation turbulence models of the K-epsilon type. On the basis of realizability analysis, a new formulation of the eddy-viscosity is proposed which ensures the positiveness of turbulent normal stresses - a realizability condition that most existing two-equation turbulence models are unable to satisfy. The present model is applied to calculate two backward-facing step flows. Calculations with the standard K-epsilon model and a recently developed RNG-based K-epsilon model are also made for comparison. The calculations are performed with a finite-volume method. A second-order accurate differencing scheme and sufficiently fine grids are used to ensure the numerical accuracy of solutions. The calculated results are compared with the experimental data for both mean and turbulent quantities. The comparison shows that the present model performs quite well for separated flows.

Coupled Structural, Thermal, Phase-Change and Electromagnetic Analysis for Superconductors. Volume 1

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermal and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. This volume, Volume 1, describes mostly formulations for specific problems. Volume 2 describes generalization of those formulations.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Lattice study of finite volume effect in HVP for muon g-2

NASA Astrophysics Data System (ADS)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

Conservative and bounded volume-of-fluid advection on unstructured grids

NASA Astrophysics Data System (ADS)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a hexahedral, wedge and tetrahedral primal mesh, in three-dimensions. Comparisons are made with the adaptation of a conventional unsplit VOF advection scheme to our collocated node-based flow solver. Depending on the choice in the nominal flux polyhedron, the NIFPA scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude. For the nominal flux polyhedra which demonstrate second-order accuracy on all tests and meshes, the NIFPA method's cost was comparable to the traditional topologically complex second-order accurate VOF advection scheme.

Finite-size effects in simulations of electrolyte solutions under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Thompson, Jeffrey; Sanchez, Isaac

The equilibrium properties of charged systems with periodic boundary conditions may exhibit pronounced system-size dependence due to the long range of the Coulomb force. As shown by others, the leading-order finite-size correction to the Coulomb energy of a charged fluid confined to a periodic box of volume V may be derived from sum rules satisfied by the charge-charge correlations in the thermodynamic limit V -> ∞ . In classical systems, the relevant sum rule is the Stillinger-Lovett second-moment (or perfect screening) condition. This constraint implies that for large V, periodicity induces a negative bias of -kB T(2 V) - 1 in the total Coulomb energy density of a homogeneous classical charged fluid of given density and temperature. We present a careful study of the impact of such finite-size effects on the calculation of solute chemical potentials from explicit-solvent molecular simulations of aqueous electrolyte solutions. National Science Foundation Graduate Research Fellowship Program, Grant No. DGE-1610403.

Finite Element Simulation of Shot Peening: Prediction of Residual Stresses and Surface Roughness

NASA Astrophysics Data System (ADS)

Gariépy, Alexandre; Perron, Claude; Bocher, Philippe; Lévesque, Martin

Shot peening is a surface treatment that consists of bombarding a ductile surface with numerous small and hard particles. Each impact creates localized plastic strains that permanently stretch the surface. Since the underlying material constrains this stretching, compressive residual stresses are generated near the surface. This process is commonly used in the automotive and aerospace industries to improve fatigue life. Finite element analyses can be used to predict residual stress profiles and surface roughness created by shot peening. This study investigates further the parameters and capabilities of a random impact model by evaluating the representative volume element and the calculated stress distribution. Using an isotropic-kinematic hardening constitutive law to describe the behaviour of AA2024-T351 aluminium alloy, promising results were achieved in terms of residual stresses.

Numerical simulation and experimental investigation about internal and external flows†

NASA Astrophysics Data System (ADS)

Wang, Tao; Yang, Guowei; Huang, Guojun; Zhou, Liandi

2006-06-01

In this paper, TASCflow3D is used to solve inner and outer 3D viscous incompressible turbulent flow (Re=5.6×106) around axisymmetric body with duct. The governing equation is a RANS equation with standard k ɛ turbulence model. The discrete method used is a finite volume method based on the finite element approach. In this method, the description of geometry is very flexible and at the same time important conservative properties are retained. The multi-block and algebraic multi-grid techniques are used for the convergence acceleration. Agreement between experimental results and calculation is good. It indicates that this novel approach can be used to simulate complex flow such as the interaction between rotor and stator or propulsion systems containing tip clearance and cavitation.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble.

PubMed

Gross, Markus; Gambassi, Andrea; Dietrich, S

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Tooth Eruption Results from Bone Remodelling Driven by Bite Forces Sensed by Soft Tissue Dental Follicles: A Finite Element Analysis

PubMed Central

Sarrafpour, Babak; Swain, Michael; Li, Qing; Zoellner, Hans

2013-01-01

Intermittent tongue, lip and cheek forces influence precise tooth position, so we here examine the possibility that tissue remodelling driven by functional bite-force-induced jaw-strain accounts for tooth eruption. Notably, although a separate true ‘eruptive force’ is widely assumed, there is little direct evidence for such a force. We constructed a three dimensional finite element model from axial computerized tomography of an 8 year old child mandible containing 12 erupted and 8 unerupted teeth. Tissues modelled included: cortical bone, cancellous bone, soft tissue dental follicle, periodontal ligament, enamel, dentine, pulp and articular cartilage. Strain and hydrostatic stress during incisive and unilateral molar bite force were modelled, with force applied via medial and lateral pterygoid, temporalis, masseter and digastric muscles. Strain was maximal in the soft tissue follicle as opposed to surrounding bone, consistent with follicle as an effective mechanosensor. Initial numerical analysis of dental follicle soft tissue overlying crowns and beneath the roots of unerupted teeth was of volume and hydrostatic stress. To numerically evaluate biological significance of differing hydrostatic stress levels normalized for variable finite element volume, ‘biological response units’ in Nmm were defined and calculated by multiplication of hydrostatic stress and volume for each finite element. Graphical representations revealed similar overall responses for individual teeth regardless if incisive or right molar bite force was studied. There was general compression in the soft tissues over crowns of most unerupted teeth, and general tension in the soft tissues beneath roots. Not conforming to this pattern were the unerupted second molars, which do not erupt at this developmental stage. Data support a new hypothesis for tooth eruption, in which the follicular soft tissues detect bite-force-induced bone-strain, and direct bone remodelling at the inner surface of the surrounding bony crypt, with the effect of enabling tooth eruption into the mouth. PMID:23554928

Tooth eruption results from bone remodelling driven by bite forces sensed by soft tissue dental follicles: a finite element analysis.

PubMed

Sarrafpour, Babak; Swain, Michael; Li, Qing; Zoellner, Hans

2013-01-01

Intermittent tongue, lip and cheek forces influence precise tooth position, so we here examine the possibility that tissue remodelling driven by functional bite-force-induced jaw-strain accounts for tooth eruption. Notably, although a separate true 'eruptive force' is widely assumed, there is little direct evidence for such a force. We constructed a three dimensional finite element model from axial computerized tomography of an 8 year old child mandible containing 12 erupted and 8 unerupted teeth. Tissues modelled included: cortical bone, cancellous bone, soft tissue dental follicle, periodontal ligament, enamel, dentine, pulp and articular cartilage. Strain and hydrostatic stress during incisive and unilateral molar bite force were modelled, with force applied via medial and lateral pterygoid, temporalis, masseter and digastric muscles. Strain was maximal in the soft tissue follicle as opposed to surrounding bone, consistent with follicle as an effective mechanosensor. Initial numerical analysis of dental follicle soft tissue overlying crowns and beneath the roots of unerupted teeth was of volume and hydrostatic stress. To numerically evaluate biological significance of differing hydrostatic stress levels normalized for variable finite element volume, 'biological response units' in Nmm were defined and calculated by multiplication of hydrostatic stress and volume for each finite element. Graphical representations revealed similar overall responses for individual teeth regardless if incisive or right molar bite force was studied. There was general compression in the soft tissues over crowns of most unerupted teeth, and general tension in the soft tissues beneath roots. Not conforming to this pattern were the unerupted second molars, which do not erupt at this developmental stage. Data support a new hypothesis for tooth eruption, in which the follicular soft tissues detect bite-force-induced bone-strain, and direct bone remodelling at the inner surface of the surrounding bony crypt, with the effect of enabling tooth eruption into the mouth.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

NASA Astrophysics Data System (ADS)

Gross, Markus; Gambassi, Andrea; Dietrich, S.

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ɛ =4 -d , where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ɛ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Monolithic ceramic analysis using the SCARE program

NASA Technical Reports Server (NTRS)

Manderscheid, Jane M.

1988-01-01

The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.

SCARE: A post-processor program to MSC/NASTRAN for the reliability analysis of structural ceramic components

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.

1985-01-01

A computer program was developed for calculating the statistical fast fracture reliability and failure probability of ceramic components. The program includes the two-parameter Weibull material fracture strength distribution model, using the principle of independent action for polyaxial stress states and Batdorf's shear-sensitive as well as shear-insensitive crack theories, all for volume distributed flaws in macroscopically isotropic solids. Both penny-shaped cracks and Griffith cracks are included in the Batdorf shear-sensitive crack response calculations, using Griffith's maximum tensile stress or critical coplanar strain energy release rate criteria to predict mixed mode fracture. Weibull material parameters can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and fracture data. The reliability prediction analysis uses MSC/NASTRAN stress, temperature and volume output, obtained from the use of three-dimensional, quadratic, isoparametric, or axisymmetric finite elements. The statistical fast fracture theories employed, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Exact finite volume expectation values of \\overline{Ψ}Ψ in the massive Thirring model from light-cone lattice correlators

NASA Astrophysics Data System (ADS)

Hegedűs, Árpád

2018-03-01

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

Progress on the three-particle quantization condition

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

Briceno, Raul; Hansen, Mawell T.; Sharpe, Stephen R.

2016-10-01

We report progress on extending the relativistic model-independent quantization condition for three particles, derived previously by two of us, to a broader class of theories, as well as progress on checking the formalism. In particular, we discuss the extension to include the possibility of 2->3 and 3->2 transitions and the calculation of the finite-volume energy shift of an Efimov-like three-particle bound state. The latter agrees with the results obtained previously using non-relativistic quantum mechanics.

Establishing the Basis for Validated Predictions of Highly Non-Equilibrium Flows. (With 9 Attachments)

DTIC Science & Technology

1993-10-14

expansion in Figure 8, a finite rate chemistry, inviscid flow solution was calculated using a One Dimensional Kinetics ( ODK ) computer program2 0...T Temperature range (K) 300 < T < 2000 Units cm3 mo-L’ sec-, [able 2: Reaction rate used in ODK compuiations. Working Gas 12 Stagnation pressure (atm...and proceeding to shorter wavelengths. The laser beam was focused on the probed volume with a 30 cm focal length lens. The LIF signal was collected in

Development of Finite Element Forulations for High-Fidelity Polycrystals and Damage Avoidance in Friction Stir Welding

DTIC Science & Technology

2010-07-26

evolving Voce hardness at the end of each bending and straightening cycle. The value contoured is the element average Voce hardness calculated by volume...cycle is shown in Figure 18. These results show that the gradient hardness is on the order of 10% of the Voce hardness. Increasing the gradient...the models or to the Voce hardness patterns. There are notable changes between the fully bent and fully straightened deformations that indicate a

Implementation of a Pseudo-Bending Seismic Travel-Time Calculator in a Distributed Parallel Computing Environment

DTIC Science & Technology

2008-09-01

algorithms that have been proposed to accomplish it fall into three broad categories. Eikonal solvers (e.g., Vidale, 1988, 1990; Podvin and Lecomte, 1991...difference eikonal solvers, the FMM algorithm works by following a wavefront as it moves across a volume of grid points, updating the travel times in...the grid according to the eikonal differential equation, using a second-order finite-difference scheme. We chose to use FMM for our comparison because

Interactive real time flow simulations

NASA Technical Reports Server (NTRS)

Sadrehaghighi, I.; Tiwari, S. N.

1990-01-01

An interactive real time flow simulation technique is developed for an unsteady channel flow. A finite-volume algorithm in conjunction with a Runge-Kutta time stepping scheme was developed for two-dimensional Euler equations. A global time step was used to accelerate convergence of steady-state calculations. A raster image generation routine was developed for high speed image transmission which allows the user to have direct interaction with the solution development. In addition to theory and results, the hardware and software requirements are discussed.

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

Implementation of different turbulence model to find proper model to estimate aerodynamic properties of airfoils

NASA Astrophysics Data System (ADS)

Sogukpinar, Haci; Bozkurt, Ismail

2018-02-01

In this paper, aerodynamic calculations of NACA 4 series airfoil of 0012 are performed by using Finite-Volume Method and obtained results are compared with experimental data to correlate the numerical accuracy of CFD approximation. Then other airfoils are simulated with k-ɛ, k-w Spalart-Allmaras and SST model. The governing equations are the Reynolds-Averaged-Navier-Stokes (RANS) equations. The performance of different airfoils (NACA 0008, 0009, 0010, 0012, 0015, 0018, 0021, 0024) at different angle of attack are investigated and compared with most used turbulence models for industrial applications. According to the results of the comparison of numerical calculations and experimental data, k-w and SST models are considered to be closest to experimental results for the calculation of the lift coefficient.

Transonic cascade flow calculations using non-periodic C-type grids

NASA Technical Reports Server (NTRS)

Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

1991-01-01

A new kind of C-type grid is proposed for turbomachinery flow calculations. This grid is nonperiodic on the wake and results in minimum skewness for cascades with high turning and large camber. Euler and Reynolds averaged Navier-Stokes equations are discretized on this type of grid using a finite volume approach. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. Jameson's explicit Runge-Kutta scheme is adopted for the integration in time, and computational efficiency is achieved through accelerating strategies such as multigriding and residual smoothing. A detailed numerical study was performed for a turbine rotor and for a vane. A grid dependence analysis is presented and the effect of artificial dissipation is also investigated. Comparison of calculations with experiments clearly demonstrates the advantage of the proposed grid.

Slave finite elements for nonlinear analysis of engine structures, volume 1

NASA Technical Reports Server (NTRS)

Gellin, S.

1991-01-01

A 336 degrees of freedom slave finite element processing capability to analyze engine structures under severe thermomechanical loading is presented. Description of the theoretical development and demonstration of that element is presented in this volume.

A Linear Electromagnetic Piston Pump

NASA Astrophysics Data System (ADS)

Hogan, Paul H.

Advancements in mobile hydraulics for human-scale applications have increased demand for a compact hydraulic power supply. Conventional designs couple a rotating electric motor to a hydraulic pump, which increases the package volume and requires several energy conversions. This thesis investigates the use of a free piston as the moving element in a linear motor to eliminate multiple energy conversions and decrease the overall package volume. A coupled model used a quasi-static magnetic equivalent circuit to calculate the motor inductance and the electromagnetic force acting on the piston. The force was an input to a time domain model to evaluate the mechanical and pressure dynamics. The magnetic circuit model was validated with finite element analysis and an experimental prototype linear motor. The coupled model was optimized using a multi-objective genetic algorithm to explore the parameter space and maximize power density and efficiency. An experimental prototype linear pump coupled pistons to an off-the-shelf linear motor to validate the mechanical and pressure dynamics models. The magnetic circuit force calculation agreed within 3% of finite element analysis, and within 8% of experimental data from the unoptimized prototype linear motor. The optimized motor geometry also had good agreement with FEA; at zero piston displacement, the magnetic circuit calculates optimized motor force within 10% of FEA in less than 1/1000 the computational time. This makes it well suited to genetic optimization algorithms. The mechanical model agrees very well with the experimental piston pump position data when tuned for additional unmodeled mechanical friction. Optimized results suggest that an improvement of 400% of the state of the art power density is attainable with as high as 85% net efficiency. This demonstrates that a linear electromagnetic piston pump has potential to serve as a more compact and efficient supply of fluid power for the human scale.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU.

PubMed

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ∼0.25  s/excitation source. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Levine, J. N.

1971-01-01

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Predicting Bone Mechanical State During Recovery After Long-Duration Skeletal Unloading Using QCT and Finite Element Modeling

NASA Technical Reports Server (NTRS)

Chang, Katarina L.; Pennline, James A.

2013-01-01

During long-duration missions at the International Space Station, astronauts experience weightlessness leading to skeletal unloading. Unloading causes a lack of a mechanical stimulus that triggers bone cellular units to remove mass from the skeleton. A mathematical system of the cellular dynamics predicts theoretical changes to volume fractions and ash fraction in response to temporal variations in skeletal loading. No current model uses image technology to gather information about a skeletal site s initial properties to calculate bone remodeling changes and then to compare predicted bone strengths with the initial strength. The goal of this study is to use quantitative computed tomography (QCT) in conjunction with a computational model of the bone remodeling process to establish initial bone properties to predict changes in bone mechanics during bone loss and recovery with finite element (FE) modeling. Input parameters for the remodeling model include bone volume fraction and ash fraction, which are both computed from the QCT images. A non-destructive approach to measure ash fraction is also derived. Voxel-based finite element models (FEM) created from QCTs provide initial evaluation of bone strength. Bone volume fraction and ash fraction outputs from the computational model predict changes to the elastic modulus of bone via a two-parameter equation. The modulus captures the effect of bone remodeling and functions as the key to evaluate of changes in strength. Application of this time-dependent modulus to FEMs and composite beam theory enables an assessment of bone mechanics during recovery. Prediction of bone strength is not only important for astronauts, but is also pertinent to millions of patients with osteoporosis and low bone density.

Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels

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

Liu, Jinn-Liang, E-mail: jinnliu@mail.nhcue.edu.tw; Eisenberg, Bob, E-mail: beisenbe@rush.edu

2014-12-14

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part ofmore » the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. The classical Gibbs entropy is extended to a new entropy form — called Gibbs-Fermi entropy — that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10{sup 8}-fold range of Ca{sup 2+} concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to study a variety of physical mechanisms ranging from binding, to permeation, blocking, flexibility, and charge/space competition of the channel.« less

Improved estimates of partial volume coefficients from noisy brain MRI using spatial context.

PubMed

Manjón, José V; Tohka, Jussi; Robles, Montserrat

2010-11-01

This paper addresses the problem of accurate voxel-level estimation of tissue proportions in the human brain magnetic resonance imaging (MRI). Due to the finite resolution of acquisition systems, MRI voxels can contain contributions from more than a single tissue type. The voxel-level estimation of this fractional content is known as partial volume coefficient estimation. In the present work, two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods. Concretely, a novel Markov Random Field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non-local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation. In addition, a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes. Based on the obtained results, the main conclusions are that (1) both Markov Random Field modelling and non-local means filtering improved the partial volume coefficient estimation results, and (2) non-local means filtering was the better of the two strategies for partial volume coefficient estimation. Copyright 2010 Elsevier Inc. All rights reserved.

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross-sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. Model predictions are compared to experimental data for developed flow in triangular duct, trapezoidal duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with the measured data.

Navier-Stokes turbine heat transfer predictions using two-equation turbulence closures

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Arnone, Andrea

1992-01-01

Navier-Stokes calculations were carried out in order to predict the heat-transfer rates on turbine blades. The calculations were performed using TRAF2D which is a k-epsilon, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using Coakley's q-omega and Chien's k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a nonperiodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the SSME high-pressure fuel turbine. The comparison serves to highlight the weaknesses of the turbulence models for use in turbomachinery heat-transfer calculations.

Simulation-aided constitutive law development - Assessment of low triaxiality void nucleation models via extended finite element method

NASA Astrophysics Data System (ADS)

Zhao, Jifeng; Kontsevoi, Oleg Y.; Xiong, Wei; Smith, Jacob

2017-05-01

In this work, a multi-scale computational framework has been established in order to investigate, refine and validate constitutive behaviors in the context of the Gurson-Tvergaard-Needleman (GTN) void mechanics model. The eXtended Finite Element Method (XFEM) has been implemented in order to (1) develop statistical volume elements (SVE) of a matrix material with subscale inclusions and (2) to simulate the multi-void nucleation process due to interface debonding between the matrix and particle phases. Our analyses strongly suggest that under low stress triaxiality the nucleation rate of the voids f˙ can be well described by a normal distribution function with respect to the matrix equivalent stress (σe), as opposed to that proposed (σbar + 1 / 3σkk) in the original form of the single void GTN model. The modified form of the multi-void nucleation model has been validated based on a series of numerical experiments with different loading conditions, material properties, particle shape/size and spatial distributions. The utilization of XFEM allows for an invariant finite element mesh to represent varying microstructures, which implies suitability for drastically reducing complexity in generating the finite element discretizations for large stochastic arrays of microstructure configurations. The modified form of the multi-void nucleation model is further applied to study high strength steels by incorporating first principles calculations. The necessity of using a phenomenological interface separation law has been fully eliminated and replaced by the physics-based cohesive relationship obtained from Density Functional Theory (DFT) calculations in order to provide an accurate macroscopic material response.

A novel simulation theory and model system for multi-field coupling pipe-flow system

NASA Astrophysics Data System (ADS)

Chen, Yang; Jiang, Fan; Cai, Guobiao; Xu, Xu

2017-09-01

Due to the lack of a theoretical basis for multi-field coupling in many system-level models, a novel set of system-level basic equations for flow/heat transfer/combustion coupling is put forward. Then a finite volume model of quasi-1D transient flow field for multi-species compressible variable-cross-section pipe flow is established by discretising the basic equations on spatially staggered grids. Combining with the 2D axisymmetric model for pipe-wall temperature field and specific chemical reaction mechanisms, a finite volume model system is established; a set of specific calculation methods suitable for multi-field coupling system-level research is structured for various parameters in this model; specific modularisation simulation models can be further derived in accordance with specific structures of various typical components in a liquid propulsion system. This novel system can also be used to derive two sub-systems: a flow/heat transfer two-field coupling pipe-flow model system without chemical reaction and species diffusion; and a chemical equilibrium thermodynamic calculation-based multi-field coupling system. The applicability and accuracy of two sub-systems have been verified through a series of dynamic modelling and simulations in earlier studies. The validity of this system is verified in an air-hydrogen combustion sample system. The basic equations and the model system provide a unified universal theory and numerical system for modelling and simulation and even virtual testing of various pipeline systems.

Robust design of microchannel cooler

NASA Astrophysics Data System (ADS)

He, Ye; Yang, Tao; Hu, Li; Li, Leimin

2005-12-01

Microchannel cooler has offered a new method for the cooling of high power diode lasers, with the advantages of small volume, high efficiency of thermal dissipation and low cost when mass-produced. In order to reduce the sensitivity of design to manufacture errors or other disturbances, Taguchi method that is one of robust design method was chosen to optimize three parameters important to the cooling performance of roof-like microchannel cooler. The hydromechanical and thermal mathematical model of varying section microchannel was calculated using finite volume method by FLUENT. A special program was written to realize the automation of the design process for improving efficiency. The optimal design is presented which compromises between optimal cooling performance and its robustness. This design method proves to be available.

π π → π γ * amplitude and the resonant ρ → π γ * transition from lattice QCD

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

Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.

2016-06-01

We present a determination of themore » $P$-wave $$\\pi\\pi\\to\\pi\\gamma^\\star$$ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-L\\"uscher formalism. We determine the amplitude for a range of discrete values of the $$\\pi\\pi$$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $$\\rho$$ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the $$\\rho$$ pole extract the $$\\rho\\to\\gamma^\\star\\pi$$ transition form factor. This calculation, at $$m_\\pi\\approx 400$$~MeV, is the first time a form factor of a hadron resonance has been calculated within a first-principles approach to QCD.« less

Viscous wing theory development. Volume 1: Analysis, method and results

NASA Technical Reports Server (NTRS)

Chow, R. R.; Melnik, R. E.; Marconi, F.; Steinhoff, J.

1986-01-01

Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers.

A finite-volume module for all-scale Earth-system modelling at ECMWF

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Malardel, Sylvie; Smolarkiewicz, Piotr

2017-04-01

We highlight recent advancements in the development of the finite-volume module (FVM) (Smolarkiewicz et al., 2016) for the IFS at ECMWF. FVM represents an alternative dynamical core that complements the operational spectral dynamical core of the IFS with new capabilities. Most notably, these include a compact-stencil finite-volume discretisation, flexible meshes, conservative non-oscillatory transport and all-scale governing equations. As a default, FVM solves the compressible Euler equations in a geospherical framework (Szmelter and Smolarkiewicz, 2010). The formulation incorporates a generalised terrain-following vertical coordinate. A hybrid computational mesh, fully unstructured in the horizontal and structured in the vertical, enables efficient global atmospheric modelling. Moreover, a centred two-time-level semi-implicit integration scheme is employed with 3D implicit treatment of acoustic, buoyant, and rotational modes. The associated 3D elliptic Helmholtz problem is solved using a preconditioned Generalised Conjugate Residual approach. The solution procedure employs the non-oscillatory finite-volume MPDATA advection scheme that is bespoke for the compressible dynamics on the hybrid mesh (Kühnlein and Smolarkiewicz, 2017). The recent progress of FVM is illustrated with results of benchmark simulations of intermediate complexity, and comparison to the operational spectral dynamical core of the IFS. C. Kühnlein, P.K. Smolarkiewicz: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics, J. Comput. Phys. (2017), in press. P.K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kühnlein, G. Mozdzynski, J. Szmelter, N.P. Wedi: A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys. 314 (2016) 287-304. J. Szmelter, P.K. Smolarkiewicz: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229 (2010) 4980-4995.

Dynamic modeling of photothermal interactions for laser-induced interstitial thermotherapy: parameter sensitivity analysis.

PubMed

Jiang, S C; Zhang, X X

2005-12-01

A two-dimensional model was developed to model the effects of dynamic changes in the physical properties on tissue temperature and damage to simulate laser-induced interstitial thermotherapy (LITT) treatment procedures with temperature monitoring. A modified Monte Carlo method was used to simulate photon transport in the tissue in the non-uniform optical property field with the finite volume method used to solve the Pennes bioheat equation to calculate the temperature distribution and the Arrhenius equation used to predict the thermal damage extent. The laser light transport and the heat transfer as well as the damage accumulation were calculated iteratively at each time step. The influences of different laser sources, different applicator sizes, and different irradiation modes on the final damage volume were analyzed to optimize the LITT treatment. The numerical results showed that damage volume was the smallest for the 1,064-nm laser, with much larger, similar damage volumes for the 980- and 850-nm lasers at normal blood perfusion rates. The damage volume was the largest for the 1,064-nm laser with significantly smaller, similar damage volumes for the 980- and 850-nm lasers with temporally interrupted blood perfusion. The numerical results also showed that the variations in applicator sizes, laser powers, heating durations and temperature monitoring ranges significantly affected the shapes and sizes of the thermal damage zones. The shapes and sizes of the thermal damage zones can be optimized by selecting different applicator sizes, laser powers, heating duration times, temperature monitoring ranges, etc.

Experimental validation of a numerical 3-D finite model applied to wind turbines design under vibration constraints: TREVISE platform

NASA Astrophysics Data System (ADS)

Sellami, Takwa; Jelassi, Sana; Darcherif, Abdel Moumen; Berriri, Hanen; Mimouni, Med Faouzi

2018-04-01

With the advancement of wind turbines towards complex structures, the requirement of trusty structural models has become more apparent. Hence, the vibration characteristics of the wind turbine components, like the blades and the tower, have to be extracted under vibration constraints. Although extracting the modal properties of blades is a simple task, calculating precise modal data for the whole wind turbine coupled to its tower/foundation is still a perplexing task. In this framework, this paper focuses on the investigation of the structural modeling approach of modern commercial micro-turbines. Thus, the structural model a complex designed wind turbine, which is Rutland 504, is established based on both experimental and numerical methods. A three-dimensional (3-D) numerical model of the structure was set up based on the finite volume method (FVM) using the academic finite element analysis software ANSYS. To validate the created model, experimental vibration tests were carried out using the vibration test system of TREVISE platform at ECAM-EPMI. The tests were based on the experimental modal analysis (EMA) technique, which is one of the most efficient techniques for identifying structures parameters. Indeed, the poles and residues of the frequency response functions (FRF), between input and output spectra, were calculated to extract the mode shapes and the natural frequencies of the structure. Based on the obtained modal parameters, the numerical designed model was up-dated.

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Total decay and transition rates from LQCD

NASA Astrophysics Data System (ADS)

Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel

2018-03-01

We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. In addition, we discuss possible extensions of our approach and, as an example application, prospects for applying the formalism to study the onset of deep-inelastic scattering. More details are given in the published version of this work, Ref. [1].

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

Exact mode volume and Purcell factor of open optical systems

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Langbein, W.

2016-12-01

The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows an analytic treatment, reducing the Purcell factor and other observables to sums over eigenmode resonances. Calculating the mode volumes requires a correct normalization of the modes. We introduce an exact normalization of modes, not relying on perfectly matched layers. We present an analytic theory of the Purcell effect based on this exact mode normalization and the resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings. We furthermore verify the applicability of the normalization to numerically determined modes of a finite dielectric cylinder.

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

Wight, L.; Zaslawsky, M.

Two approaches for calculating soil structure interaction (SSI) are compared: finite element and lumped mass. Results indicate that the calculations with the lumped mass method are generally conservative compared to those obtained by the finite element method. They also suggest that a closer agreement between the two sets of calculations is possible, depending on the use of frequency-dependent soil springs and dashpots in the lumped mass calculations. There is a total lack of suitable guidelines for implementing the lumped mass method of calculating SSI, which leads to the conclusion that the finite element method is generally superior for calculative purposes.

Two-particle multichannel systems in a finite volume with arbitrary spin

DOE PAGES

Briceno, Raul A.

2014-04-08

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the rangemore » of the interaction is set by the inverse of the pion mass, m π, and as a result the formalism presented is suitable for m πL>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.« less

Modeling dam-break flows using finite volume method on unstructured grid

USDA-ARS?s Scientific Manuscript database

Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

Improved Design of Tunnel Supports : Volume 3 : Finite Element Analysis of the Peachtree Center Station in Atlanta

DOT National Transportation Integrated Search

1980-06-01

Volume 3 contains the application of the three-dimensional (3-D) finite element program, Automatic Dynamic Incremental Nonlinear Analysis (ADINA), which was designed to replace the traditional 2-D plane strain analysis, to a specific location. The lo...

Regional teleseismic body-wave tomography with component-differential finite-frequency sensitivity kernels

NASA Astrophysics Data System (ADS)

Yu, Y.; Shen, Y.; Chen, Y. J.

2015-12-01

By using ray theory in conjunction with the Born approximation, Dahlen et al. [2000] computed 3-D sensitivity kernels for finite-frequency seismic traveltimes. A series of studies have been conducted based on this theory to model the mantle velocity structure [e.g., Hung et al., 2004; Montelli et al., 2004; Ren and Shen, 2008; Yang et al., 2009; Liang et al., 2011; Tang et al., 2014]. One of the simplifications in the calculation of the kernels is the paraxial assumption, which may not be strictly valid near the receiver, the region of interest in regional teleseismic tomography. In this study, we improve the accuracy of traveltime sensitivity kernels of the first P arrival by eliminating the paraxial approximation. For calculation efficiency, the traveltime table built by the Fast Marching Method (FMM) is used to calculate both the wave vector and the geometrical spreading at every grid in the whole volume. The improved kernels maintain the sign, but with different amplitudes at different locations. We also find that when the directivity of the scattered wave is being taken into consideration, the differential sensitivity kernel of traveltimes measured at the vertical and radial component of the same receiver concentrates beneath the receiver, which can be used to invert for the structure inside the Earth. Compared with conventional teleseismic tomography, which uses the differential traveltimes between two stations in an array, this method is not affected by instrument response and timing errors, and reduces the uncertainty caused by the finite dimension of the model in regional tomography. In addition, the cross-dependence of P traveltimes to S-wave velocity anomaly is significant and sensitive to the structure beneath the receiver. So with the component-differential finite-frequency sensitivity kernel, the anomaly of both P-wave and S-wave velocity and Vp/Vs ratio can be achieved at the same time.

Isovector and flavor-diagonal charges of the nucleon

NASA Astrophysics Data System (ADS)

Gupta, Rajan; Bhattacharya, Tanmoy; Jang, Yong-Chull; Lin, Huey-Wen; Yoon, Boram

2018-03-01

We present an update on the status of the calculations of isovector and flavor-diagonal charges of the nucleon. The calculations of the isovector charges are being done using ten 2+1+1-flavor HISQ ensembles generated by the MILC collaboration covering the range of lattice spacings a ≈ 0.12, 0.09, 0.06 fm and pion masses Mπ ≈ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and three-states fits to the three-point correlators. The calculations of the disconnected diagrams needed to estimate flavor-diagonal charges are being done on a subset of six ensembles using the stocastic method. Final results are obtained using a simultaneous fit in M2π, the lattice spacing a and the finite volume parameter MπL keeping only the leading order corrections.

Anharmonic effects in the quantum cluster equilibrium method

NASA Astrophysics Data System (ADS)

von Domaros, Michael; Perlt, Eva

2017-03-01

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

A constrained modulus reconstruction technique for breast cancer assessment.

PubMed

Samani, A; Bishop, J; Plewes, D B

2001-09-01

A reconstruction technique for breast tissue elasticity modulus is described. This technique assumes that the geometry of normal and suspicious tissues is available from a contrast-enhanced magnetic resonance image. Furthermore, it is assumed that the modulus is constant throughout each tissue volume. The technique, which uses quasi-static strain data, is iterative where each iteration involves modulus updating followed by stress calculation. Breast mechanical stimulation is assumed to be done by two compressional rigid plates. As a result, stress is calculated using the finite element method based on the well-controlled boundary conditions of the compression plates. Using the calculated stress and the measured strain, modulus updating is done element-by-element based on Hooke's law. Breast tissue modulus reconstruction using simulated data and phantom modulus reconstruction using experimental data indicate that the technique is robust.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

NASA Astrophysics Data System (ADS)

Ye, Qian; Lin, Haoze

2017-07-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.

Compositeness of hadron resonances in finite volume

NASA Astrophysics Data System (ADS)

Tsuchida, Yujiro; Hyodo, Tetsuo

2018-05-01

We develop a theoretical framework to quantify the structure of unstable hadron resonances. With the help of the corresponding system in a finite volume, we define the compositeness of resonance states which can be interpreted as a probability. This framework is used to study the structure of the scalar mesons f0(980 ) and a0(980 ) . In both mesons, the K ¯K component dominates about a half of the wave function. The method is also applied to the Λ (1405 ) resonance. We argue that a single energy level in finite volume represents the two eigenstates in infinite volume. The K ¯N component of Λ (1405 ) , including contributions from both eigenstates, is found to be 58%, and the rest is composed of the π Σ and other channels.

Multi-scale Methods in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Polyzou, W. N.; Michlin, Tracie; Bulut, Fatih

2018-05-01

Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale m{sub IR}

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

Bornyakov, V. G.; Mitrjushkin, V. K.; Mueller-Preussker, M.

2010-03-01

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found themore » Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.« less

Strange Quark Magnetic Moment of the Nucleon at the Physical Point.

PubMed

Sufian, Raza Sabbir; Yang, Yi-Bo; Alexandru, Andrei; Draper, Terrence; Liang, Jian; Liu, Keh-Fei

2017-01-27

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of 0.051  GeV^{2}≲Q^{2}≲1.31  GeV^{2}. The finite lattice spacing and finite volume corrections are included in a global fit with 24 valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment G_{M}^{s}(0)=-0.064(14)(09)μ_{N}. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius ⟨r_{s}^{2}⟩_{E}=-0.0043(16)(14)  fm^{2}.

A three-dimensional transient mixed hybrid finite element model for superabsorbent polymers with strain-dependent permeability.

PubMed

Yu, Cong; Malakpoor, Kamyar; Huyghe, Jacques M

2018-05-16

A hydrogel is a cross-linked polymer network with water as solvent. Industrially widely used superabsorbent polymers (SAP) are partially neutralized sodium polyacrylate hydrogels. The extremely large degree of swelling is one of the most distinctive characteristics of such hydrogels, as the volume increase can be about 30 times its original volume when exposed to physiological solution. The large deformation resulting from the swelling demands careful numerical treatment. In this work, we present a biphasic continuum-level swelling model using the mixed hybrid finite element method (MHFEM) in three dimensions. The hydraulic permeability is highly dependent on the swelling ratio, resulting in values that are orders of magnitude apart from each other. The property of the local mass conservation of MHFEM contributes to a more accurate calculation of the deformation as the permeability across the swelling gel in a transient state is highly non-uniform. We show that the proposed model is able to simulate the free swelling of a random-shaped gel and the squeezing of fluid out of a swollen gel. Finally, we make use of the proposed numerical model to study the onset of surface instability in transient swelling.

Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

NASA Technical Reports Server (NTRS)

Casper, Jay; Dorrepaal, J. Mark

1990-01-01

The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

Convergence speeding up in the calculation of the viscous flow about an airfoil

NASA Technical Reports Server (NTRS)

Radespiel, R.; Rossow, C.

1988-01-01

A finite volume method to solve the three dimensional Navier-Stokes equations was developed. It is based on a cell-vertex scheme with central differences and explicit Runge-Kutta time steps. A good convergence for a stationary solution was obtained by the use of local time steps, implicit smoothing of the residues, a multigrid algorithm, and a carefully controlled artificial dissipative term. The method is illustrated by results for transonic profiles and airfoils. The method allows a routine solution of the Navier-Stokes equations.

Constitutive Modeling of Piezoelectric Polymer Composites

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Gates, Tom (Technical Monitor)

2003-01-01

A new modeling approach is proposed for predicting the bulk electromechanical properties of piezoelectric composites. The proposed model offers the same level of convenience as the well-known Mori-Tanaka method. In addition, it is shown to yield predicted properties that are, in most cases, more accurate or equally as accurate as the Mori-Tanaka scheme. In particular, the proposed method is used to determine the electromechanical properties of four piezoelectric polymer composite materials as a function of inclusion volume fraction. The predicted properties are compared to those calculated using the Mori-Tanaka and finite element methods.

Numerical investigation of self-sustained oscillations in the flow over the spiked blunt body

NASA Astrophysics Data System (ADS)

Konstantin, Babarykin

2018-05-01

Numerical simulation of the supersonic turbulent flow around spike-tipped cylindrical body is carried out. The self-sustained oscillating flow picture is studied. For the simulations the ANSYS Fluent finite-volume solver is employed, the calculations are performed mainly for 2d axisymmetric case, and some simulations are made in 3d version. The freestream Mach number is 2,22, the cases of sharp and obtuse needle of different length are considered. The numerical results are obtained using different turbulence models, are compared with experimental data.

Mathematical Simulation of Drying Process of Fibrous Material

NASA Astrophysics Data System (ADS)

Blejchař, Tomáš; Raška, Jiří; Jablonská, Jana

2018-06-01

The article describes mathematical simulation of flowing air through porous zone and water vaporisation from mentioned porous area which actually represents dried fibrous material - cotton towel. Simulation is based on finite volume method. Wet towel is placed in pipe and hot air flow through the towel. Water from towel is evaporated. Simulation of airflow through porous element is described first. Eulerian multiphase model is then used for simulation of water vaporisation from porous medium. Results of simulation are compared with experiment. Ansys Fluent 13.0 was used for calculation.

Thermomechanical CSM analysis of a superheater tube in transient state

NASA Astrophysics Data System (ADS)

Taler, Dawid; Madejski, Paweł

2011-12-01

The paper presents a thermomechanical computational solid mechanics analysis (CSM) of a pipe "double omega", used in the steam superheaters in circulating fluidized bed (CFB) boilers. The complex cross-section shape of the "double omega" tubes requires more precise analysis in order to prevent from failure as a result of the excessive temperature and thermal stresses. The results have been obtained using the finite volume method for transient state of superheater. The calculation was carried out for the section of pipe made of low-alloy steel.

SAM-CE; A Three Dimensional Monte Carlo Code for the Dolution of the Forward Neutron and Forward and Adjoint Gamma Ray Transport Equations. Revision C

DTIC Science & Technology

1974-07-31

Multiple scoring regions are permitted and these may be either finite volume regions or point detectors or both. Other sccres of interest, e.g., collision... Multiplicities ...... . . . . 43 2,3.5.2 Photon Production Cross Sections. . 44 2.3.5.3 Anisotropy of Photon Production . . 44 2.3.5.4 Continuous...hepting, count rates, etc., are calculated as functions of energy, time and position. Multiple scoring regions are permitted and these may be either

Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 1: Computational technique

NASA Technical Reports Server (NTRS)

Marconi, F.; Salas, M.; Yaeger, L.

1976-01-01

A numerical procedure has been developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second order accurate finite difference scheme is used to integrate the three dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.

Computer program for calculating full potential transonic, quasi-three-dimensional flow through a rotating turbomachinery blade row

NASA Technical Reports Server (NTRS)

Farrell, C. A.

1982-01-01

A fast, reliable computer code is described for calculating the flow field about a cascade of arbitrary two dimensional airfoils. The method approximates the three dimensional flow in a turbomachinery blade row by correcting for stream tube convergence and radius change in the throughflow direction. A fully conservative solution of the full potential equation is combined with the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. The instructions required to set up and use the code are included. The name of the code is QSONIC. A numerical example is also given to illustrate the output of the program.

Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 2: Code description

NASA Technical Reports Server (NTRS)

Marconi, F.; Yaeger, L.

1976-01-01

A numerical procedure was developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.

Turbofan forced mixer-nozzle internal flowfield. Volume 3: A computer code for 3-D mixing in axisymmetric nozzles

NASA Technical Reports Server (NTRS)

Kreskovsky, J. P.; Briley, W. R.; Mcdonald, H.

1982-01-01

A finite difference method is developed for making detailed predictions of three dimensional subsonic turbulent flow in turbofan lobe mixers. The governing equations are solved by a forward-marching solution procedure which corrects an inviscid potential flow solution for viscous and thermal effects, secondary flows, total pressure distortion and losses, internal flow blockage and pressure drop. Test calculations for a turbulent coaxial jet flow verify that the turbulence model performs satisfactorily for this relatively simple flow. Lobe mixer flows are presented for two geometries typical of current mixer design. These calculations included both hot and cold flow conditions, and both matched and mismatched Mach number and total pressure in the fan and turbine streams.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 1: Theory and validations

NASA Technical Reports Server (NTRS)

Baker, A. J.; Iannelli, G. S.; Manhardt, Paul D.; Orzechowski, J. A.

1993-01-01

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 2: FEMNAS user guide

NASA Technical Reports Server (NTRS)

Manhardt, Paul D.; Orzechowski, J. A.; Baker, A. J.

1992-01-01

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

Development of a hip joint model for finite volume simulations.

PubMed

Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A

2014-01-01

This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

DOE PAGES

Barnard, Richard C.; Frank, Martin; Krycki, Kai

2016-02-09

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P N) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose depositionmore » depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.« less

Vertical solidification of dendritic binary alloys

NASA Technical Reports Server (NTRS)

Heinrich, J. C.; Felicelli, S.; Poirier, D. R.

1991-01-01

Three numerical techniques are employed to analyze the influence of thermosolutal convection on defect formation in directionally solidified (DS) alloys. The finite-element models are based on the Boussinesq approximation and include the plane-front model and two plane-front models incorporating special dendritic regions. In the second model the dendritic region has a time-independent volume fraction of liquid, and in the last model the dendritic region evolves as local conditions dictate. The finite-element models permit the description of nonlinear thermosolutal convection by treating the dendritic regions as porous media with variable porosities. The models are applied to lead-tin alloys including DS alloys, and severe segregation phenomena such as freckles and channels are found to develop in the DS alloys. The present calculations and the permeability functions selected are shown to predict behavior in the dendritic regions that qualitatively matches that observed experimentally.

Clustering and pasta phases in nuclear density functional theory

DOE PAGES

Schuetrumpf, Bastian; Zhang, Chunli; Nazarewicz, Witold

2017-05-23

Nuclear density functional theory is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we usemore » the concept of nucleon localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.« less

Finite-size effects in surface-enhanced Raman scattering in noble-metal nanoparticles: a semiclassical approach.

PubMed

Pustovit, Vitaliy N; Shahbazyan, Tigran V

2006-06-01

We study finite-size effects in surface-enhanced Raman scattering (SERS) from molecules adsorbed on small metal particles. Within an electromagnetic description of SERS, the enhancement of the Raman signal originates from the local field of the surface plasmon resonance in a nanoparticle. With decreasing particle sizes, this enhancement is reduced due to the size-dependent Landau damping of the surface plasmon. We show that, in small noble-metal particles, the reduction of interband screening in the surface layer leads to an additional increase in the local field acting on a molecule close to the metal surface. The overall size dependence of Raman signal enhancement is determined by the interplay between Landau damping and underscreening effects. Our calculations, based on a two-region model, show that the role of the surface layer increases for smaller nanoparticle sizes due to a larger volume fraction of the underscreened region.

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

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

Schuetrumpf, Bastian; Zhang, Chunli; Nazarewicz, Witold

Nuclear density functional theory is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we usemore » the concept of nucleon localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.« less

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Dunn, Patrick

1995-01-01

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

PBSM3D: A finite volume, scalar-transport blowing snow model for use with variable resolution meshes

NASA Astrophysics Data System (ADS)

Marsh, C.; Wayand, N. E.; Pomeroy, J. W.; Wheater, H. S.; Spiteri, R. J.

2017-12-01

Blowing snow redistribution results in heterogeneous snowcovers that are ubiquitous in cold, windswept environments. Capturing this spatial and temporal variability is important for melt and runoff simulations. Point scale blowing snow transport models are difficult to apply in fully distributed hydrological models due to landscape heterogeneity and complex wind fields. Many existing distributed snow transport models have empirical wind flow and/or simplified wind direction algorithms that perform poorly in calculating snow redistribution where there are divergent wind flows, sharp topography, and over large spatial extents. Herein, a steady-state scalar transport model is discretized using the finite volume method (FVM), using parameterizations from the Prairie Blowing Snow Model (PBSM). PBSM has been applied in hydrological response units and grids to prairie, arctic, glacier, and alpine terrain and shows a good capability to represent snow redistribution over complex terrain. The FVM discretization takes advantage of the variable resolution mesh in the Canadian Hydrological Model (CHM) to ensure efficient calculations over small and large spatial extents. Variable resolution unstructured meshes preserve surface heterogeneity but result in fewer computational elements versus high-resolution structured (raster) grids. Snowpack, soil moisture, and streamflow observations were used to evaluate CHM-modelled outputs in a sub-arctic and an alpine basin. Newly developed remotely sensed snowcover indices allowed for validation over large basins. CHM simulations of snow hydrology were improved by inclusion of the blowing snow model. The results demonstrate the key role of snow transport processes in creating pre-melt snowcover heterogeneity and therefore governing post-melt soil moisture and runoff generation dynamics.

Flow studies in canine artery bifurcations using a numerical simulation method.

PubMed

Xu, X Y; Collins, M W; Jones, C J

1992-11-01

Three-dimensional flows through canine femoral bifurcation models were predicted under physiological flow conditions by solving numerically the time-dependent three-dimensional Navier-stokes equations. In the calculations, two models were assumed for the blood, those of (a) a Newtonian fluid, and (b) a non-Newtonian fluid obeying the power law. The blood vessel wall was assumed to be rigid this being the only approximation to the prediction model. The numerical procedure utilized a finite volume approach on a finite element mesh to discretize the equations, and the code used (ASTEC) incorporated the SIMPLE velocity-pressure algorithm in performing the calculations. The predicted velocity profiles were in good qualitative agreement with the in vivo measurements recently obtained by Jones et al. The non-Newtonian effects on the bifurcation flow field were also investigated, and no great differences in velocity profiles were observed. This indicated that the non-Newtonian characteristics of the blood might not be an important factor in determining the general flow patterns for these bifurcations, but could have local significance. Current work involves modeling wall distensibility in an empirically valid manner. Predictions accommodating these will permit a true quantitative comparison with experiment.

The finite ground plane effect on the microstrip antenna radiation patterns

NASA Technical Reports Server (NTRS)

Huang, J.

1983-01-01

The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)

2002-01-01

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Demonstration Of Ultra HI-FI (UHF) Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2004-01-01

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Wigner analysis of three dimensional pupil with finite lateral aperture

PubMed Central

Chen, Hsi-Hsun; Oh, Se Baek; Zhai, Xiaomin; Tsai, Jui-Chang; Cao, Liang-Cai; Barbastathis, George; Luo, Yuan

2015-01-01

A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions. PMID:25836443

Sanity check for NN bound states in lattice QCD with Lüscher's finite volume formula - Disclosing Symptoms of Fake Plateaux -

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Doi, Takumi; Iritani, Takumi

2018-03-01

The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Lüscher's finite volume formula [1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4-5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansions (EREs) in NPL2013 violate the physical pole condition. (iv) Their comment is partly based on new data and analysis different from the original ones. (v) Their new ERE does not satisfy the Lüscher's finite volume formula.

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Finite Element Analysis of Walking Beam of a New Compound Adjustment Balance Pumping Unit

NASA Astrophysics Data System (ADS)

Wu, Jufei; Wang, Qian; Han, Yunfei

2017-12-01

In this paper, taking the designer of the new compound balance pumping unit beam as our research target, the three-dimensional model is established by Solid Works, the load and the constraint are determined. ANSYS Workbench is used to analyze the tail and the whole of the beam, the stress and deformation are obtained to meet the strength requirements. The finite element simulation and theoretical calculation of the moment of the center axis beam are carried out. The finite element simulation results are compared with the calculated results of the theoretical mechanics model to verify the correctness of the theoretical calculation. Finally, the finite element analysis is consistent with the theoretical calculation results. The theoretical calculation results are preferable, and the bending moment value provides the theoretical reference for the follow-up optimization and research design.

Equation of state for neutron stars. Some recent developments

NASA Astrophysics Data System (ADS)

Haensel, P.; Fortin, M.

2017-12-01

Calculations using the chiral effective field theory (ChEFT) indicate that the four-body force contribution to the equation of state (EOS) of pure neutron matter (PNM) at the nuclear density n 0 is negligibly small. However, the overall uncertainty in the EOS of PNM at n 0 remains ∼ 20%. Relativistic mean field (RMF) calculations with in-medium scaling, and including hyperons and Δ resonances, can be made consistent with recent nuclear and astrophysical constraints. Dirac-Brueckner-Hartree-Fock calculations with some medium dependence of the nuclear interaction yield neutron star (NS) models with hyperonic cores consistent with 2 M⊙ stars and agreeing with the saturation parameters of nuclear matter. Many unified EOS for the NS crust and core were calculated, and are reviewed here. The effect of the finite size of baryons on the EOS, its treatment via the excluded-volume approximation, and its relevance for the hypothetical hybrid-star twins at ∼ 2 M⊙ are dicussed.

Foam structure :from soap froth to solid foams.

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

Kraynik, Andrew Michael

2003-01-01

The properties of solid foams depend on their structure, which usually evolves in the fluid state as gas bubbles expand to form polyhedral cells. The characteristic feature of foam structure-randomly packed cells of different sizes and shapes-is examined in this article by considering soap froth. This material can be modeled as a network of minimal surfaces that divide space into polyhedral cells. The cell-level geometry of random soap froth is calculated with Brakke's Surface Evolver software. The distribution of cell volumes ranges from monodisperse to highly polydisperse. Topological and geometric properties, such as surface area and edge length, of themore » entire foam and individual cells, are discussed. The shape of struts in solid foams is related to Plateau borders in liquid foams and calculated for different volume fractions of material. The models of soap froth are used as templates to produce finite element models of open-cell foams. Three-dimensional images of open-cell foams obtained with x-ray microtomography allow virtual reconstruction of skeletal structures that compare well with the Surface Evolver simulations of soap-froth geometry.« less

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

NASA Technical Reports Server (NTRS)

Chen, Yen-Sen; Shang, Huan-Min; Liaw, Paul; Wang, Ten-See

1996-01-01

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory

NASA Astrophysics Data System (ADS)

Lee, Jong-Wan

2015-05-01

We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.

State relations for a two-phase mixture of reacting explosives and applications

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

Kubota, Shiro; Saburi, Tei; Ogata, Yuji

2007-10-15

To assess the assumptions behind the two phase mixture rule for reacting explosives, the shock-to-detonation transition process was calculated for high explosives using a finite difference method. An ignition and growth model and the Jones-Wilkins-Lee (JWL) equations of state were employed. The simple mixture rule assumes that the reacting explosive is a simple mixture of the reactant and product components. Four different assumptions, such as that of thermal equilibrium and isotropy, were adopted to calculate the pressure. The main purpose of this paper is to present the answer to the question of why the numerical results of shock-initiation are insensitivemore » to the assumptions adopted. The equations of state for reactants and products were assessed by considering plots of the specific internal energy E and specific volume V. If the slopes of the constant-pressure lines for both components in the E-V plane are almost the same, it is demonstrated that the numerical results are insensitive to the assumptions adopted. We have found that the relation for the specific volumes of the two components can be approximately expressed by a single curve of the specific volume of the reactant vs that of the products. We discuss this relationship in terms of the results of the numerical simulation. (author)« less

A full potential inverse method based on a density linearization scheme for wing design

NASA Technical Reports Server (NTRS)

Shankar, V.

1982-01-01

A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.

Simulation of vaporization in low fluence nanosecond laser ablation of aluminum alloy

NASA Astrophysics Data System (ADS)

Song, Chaoqun; Dong, Shiyun; Yan, Shixing; Li, Enzhong; Xu, Binshi; He, Peng

2018-03-01

This paper presents a multi-phase flow model for the nanosecond laser ablation of aluminum alloy at a low fluence based on finite volume method, considering gravity, recoil pressure, buoyancy and surface tension to describe vaporization. Actual morphology of ablation crater was measured by a laser scanning confocal microscope to verify the model. Results show that vaporization is the main ablation mechanism for 100ns laser ablation at low fluences, and the peak temperature is only 50% of critical temperature. Both the experimental and calculated crater have a wall-like bulge around the rim, as a result of impact of recoil pressure and resolidification of pushed liquid metal. The calculated depth and diameter of crater are in good agreement with the corresponding experimental measurement indicating the feasibility of the model.

Control of Leakage Flow by Triple Squealer Configuration in Axial Flow Turbine

NASA Astrophysics Data System (ADS)

El-Ghandour, Mohamed; Ibrahim, Mohammed K.; Mori, Koichi; Nakamura, Yoshiaki

A new turbine blade tip shape called triple squealer is proposed. This shape is based on the conventional double squealer, and the cavity on the tip surface is divided into two parts by using a third squealer along the blade camber line. The effect of the ratio of groove depth to span (GDS ratio) was investigated. The flat-tip case (baseline case) and double-squealer case were calculated for comparison. In-house, unstructured, 3D, Navier-Stokes, finite volume, multiblock code with DES (Detached Eddy Simulation) as turbulence model was used to calculate the flow field around the tip. The computational results show that the reduction in the mass flow rate of the leakage flow for the triple squealer is 15.69% compared to the flat-tip case.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

Energy Losses Estimation During Pulsed-Laser Seam Welding

NASA Astrophysics Data System (ADS)

Sebestova, Hana; Havelkova, Martina; Chmelickova, Hana

2014-06-01

The finite-element tool SYSWELD (ESI Group, Paris, France) was adapted to simulate pulsed-laser seam welding. Besides temperature field distribution, one of the possible outputs of the welding simulation is the amount of absorbed power necessary to melt the required material volume including energy losses. Comparing absorbed or melting energy with applied laser energy, welding efficiencies can be calculated. This article presents achieved results of welding efficiency estimation based on the assimilation both experimental and simulation output data of the pulsed Nd:YAG laser bead on plate welding of 0.6-mm-thick AISI 304 stainless steel sheets using different beam powers.

Gravity and the membrane-solution interface: theoretical investigations.

PubMed

Schatz, A; Linke-Hommes, A

1989-01-01

The theory of concentration and potential variations at interfaces is applied to the membrane-solution interface to calculate density variations. The theory is modified to take care of the finite ion volumes in electrolytes. Our model is a phospholipid membrane with a surface charge density of -4.824*10(-6)(As/cm2) in contact with solutions of KCl, NaCl, CaCl2, and mixtures. Maximal density variations of about 4*10(-2)(G/cm3) were found in surface layers between the membrane and the solutions. The extension of the layers is in the range of 1 to 6 nm.

SCISEAL: A CFD code for analysis of fluid dynamic forces in seals

NASA Technical Reports Server (NTRS)

Athavale, Mahesh; Przekwas, Andrzej

1994-01-01

A viewgraph presentation is made of the objectives, capabilities, and test results of the computer code SCISEAL. Currently, the seal code has: a finite volume, pressure-based integration scheme; colocated variables with strong conservation approach; high-order spatial differencing, up to third-order; up to second-order temporal differencing; a comprehensive set of boundary conditions; a variety of turbulence models and surface roughness treatment; moving grid formulation for arbitrary rotor whirl; rotor dynamic coefficients calculated by the circular whirl and numerical shaker methods; and small perturbation capabilities to handle centered and eccentric seals.

NΩ interaction from two approaches in lattice QCD

NASA Astrophysics Data System (ADS)

Etminan, Faisal; Firoozabadi, Mohammad Mehdi

2014-10-01

We compare the standard finite volume method by Lüscher with the potential method by HAL QCD collaboration, by calculating the ground state energy of N(nucleon)-Ω(Omega) system in 5 S2 channel. We employ 2+1 flavor full QCD configurations on a (1.9 fm)3×3.8 fm lattice at the lattice spacing a≃0.12 fm, whose ud(s) quark mass corresponds to mπ = 875(1) (mK = 916(1)) MeV. We have found that both methods give reasonably consistent results that there is one NΩ bound state at this parameter.

3D highly heterogeneous thermal model of pineal gland in-vitro study for electromagnetic exposure using finite volume method

NASA Astrophysics Data System (ADS)

Cen, Wei; Hoppe, Ralph; Lu, Rongbo; Cai, Zhaoquan; Gu, Ning

2017-08-01

In this paper, the relationship between electromagnetic power absorption and temperature distributions inside highly heterogeneous biological samples was accurately determinated using finite volume method. An in-vitro study on pineal gland that is responsible for physiological activities was for the first time simulated to illustrate effectiveness of the proposed method.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Statistical Optics

NASA Astrophysics Data System (ADS)

Goodman, Joseph W.

2000-07-01

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Hsu, Andrew T.

1989-01-01

A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

Post-1906 stress recovery of the San Andreas fault system calculated from three-dimensional finite element analysis

USGS Publications Warehouse

Parsons, T.

2002-01-01

The M = 7.8 1906 San Francisco earthquake cast a stress shadow across the San Andreas fault system, inhibiting other large earthquakes for at least 75 years. The duration of the stress shadow is a key question in San Francisco Bay area seismic hazard assessment. This study presents a three-dimensional (3-D) finite element simulation of post-1906 stress recovery. The model reproduces observed geologic slip rates on major strike-slip faults and produces surface velocity vectors comparable to geodetic measurements. Fault stressing rates calculated with the finite element model are evaluated against numbers calculated using deep dislocation slip. In the finite element model, tectonic stressing is distributed throughout the crust and upper mantle, whereas tectonic stressing calculated with dislocations is focused mostly on faults. In addition, the finite element model incorporates postseismic effects such as deep afterslip and viscoelastic relaxation in the upper mantle. More distributed stressing and postseismic effects in the finite element model lead to lower calculated tectonic stressing rates and longer stress shadow durations (17-74 years compared with 7-54 years). All models considered indicate that the 1906 stress shadow was completely erased by tectonic loading no later than 1980. However, the stress shadow still affects present-day earthquake probability. Use of stressing rate parameters calculated with the finite element model yields a 7-12% reduction in 30-year probability caused by the 1906 stress shadow as compared with calculations not incorporating interactions. The aggregate interaction-based probability on selected segments (not including the ruptured San Andreas fault) is 53-70% versus the noninteraction range of 65-77%.

Two-nucleon higher partial-wave scattering from lattice QCD

DOE PAGES

Berkowitz, Evan; Kurth, Thorsten; Nicholson, Amy; ...

2016-12-14

Here, we present a determination of nucleon-nucleon scattering phase shifts for L>0. The S,P,D and F phase shifts for both the spin-triplet and spin-singlet channels are computed for the first time with lattice Quantum ChromoDynamics. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. In order to demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to m π=m K≈800~MeV. Two spatial volumes of V ≈ (3.5 fm) 3 and V ≈more » (4.6 fm) 3 were used. Furthermore, the finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.« less

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

Chakraborty, Bipasha; Davies, C. T. H.; de Oliveira, P. G.

We determine the contribution to the anomalous magnetic moment of the muon from themore » $$\\alpha^2_{\\mathrm{QED}}$$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $$a_{\\mu}^{\\mathrm{HVP,LO}}$$ of $667(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $$a_{\\mu}$$ and the Standard Model of 3$$\\sigma$$.« less

Isoscalar ππ Scattering and the σ Meson Resonance from QCD.

PubMed

Briceño, Raul A; Dudek, Jozef J; Edwards, Robert G; Wilson, David J

2017-01-13

We present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum, we obtain the S-wave phase shift up to the KK[over ¯] threshold. Calculations are performed at two values of the u, d quark mass corresponding to m_{π}=236,391  MeV, and the resulting amplitudes are described in terms of a σ meson which evolves from a bound state below the ππ threshold at the heavier quark mass to a broad resonance at the lighter quark mass.

Higher order cumulants in colorless partonic plasma

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

Cherif, S.; Laboratoire de Physique et de Mathématiques Appliquées; Ahmed, M. A. A.

2016-06-10

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to themore » thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.« less

The fcc - bcc structural transition: I. A band theoretical study for Li, K, Rb, Ca, Sr, and the transition metals Ti and V

NASA Astrophysics Data System (ADS)

Sliwko, V. L.; Mohn, P.; Schwarz, K.; Blaha, P.

1996-02-01

Employing a high-precision band structure method (FP LAPW - full potential linearized augmented plane wave) we calculate the total energy variation along the tetragonal distortion path connecting the body centred cubic (bcc) and the face centred cubic (fcc) structures. The total energy along this Bain transformation is calculated, varying c/a and volume, providing a first-principles energy surface which has two minima as a function of c/a. These are shallow and occur for the sp metals at the two cubic structures, while Ti (V) has a minimum at fcc (bcc) but a saddle point (i.e. a minimum in volume and a maximum with respect to c/a) at the other cubic structure. These features can be analysed in terms of an interplay between the Madelung contribution and the band energies. Our total energy results allow us to calculate the elastic constants 0953-8984/8/7/006/img1 and 0953-8984/8/7/006/img2 and to study the influence of pressure on the phase stability. These energy surfaces will be used in part II of this paper to investigate finite-temperature effects by mapping them to a Landau - Ginzburg expansion.

Extrusion Process by Finite Volume Method Using OpenFoam Software

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

Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose

The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Incorporation of Condensation Heat Transfer in a Flow Network Code

NASA Technical Reports Server (NTRS)

Anthony, Miranda; Majumdar, Alok

2002-01-01

Pure water is distilled from waste water in the International Space Station. The distillation assembly consists of an evaporator, a compressor and a condenser. Vapor is periodically purged from the condenser to avoid vapor accumulation. Purged vapor is condensed in a tube by coolant water prior to entering the purge pump. The paper presents a condensation model of purged vapor in a tube. This model is based on the Finite Volume Method. In the Finite Volume Method, the flow domain is discretized into multiple control volumes and a simultaneous analysis is performed.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Moore, John; Nicholson, Stephen; Moore, Joan G.

1986-01-01

The development of a computational capability to handle viscous flow with an explicit time-marching method based on the finite volume approach is summarized. Emphasis is placed on the extensions to the computational procedure which allow the handling of shock induced separation and large regions of strong backflow. Appendices contain abstracts of papers and whole reports generated during the contract period.

Numerical approach for finite volume three-body interaction

NASA Astrophysics Data System (ADS)

Guo, Peng; Gasparian, Vladimir

2018-01-01

In the present work, we study a numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise δ -function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when the strength of short-range interactions are set equal for all pairs.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Rocket Based Combined Cycle Exchange Inlet Performance Estimation at Supersonic Speeds

NASA Astrophysics Data System (ADS)

Murzionak, Aliaksandr

A method to estimate the performance of an exchange inlet for a Rocket Based Combined Cycle engine is developed. This method is to be used for exchange inlet geometry optimization and as such should be able to predict properties that can be used in the design process within a reasonable amount of time to allow multiple configurations to be evaluated. The method is based on a curve fit of the shocks developed around the major components of the inlet using solutions for shocks around sharp cones and 2D estimations of the shocks around wedges with blunt leading edges. The total pressure drop across the estimated shocks as well as the mass flow rate through the exchange inlet are calculated. The estimations for a selected range of free-stream Mach numbers between 1.1 and 7 are compared against numerical finite volume method simulations which were performed using available commercial software (Ansys-CFX). The total pressure difference between the two methods is within 10% for the tested Mach numbers of 5 and below, while for the Mach 7 test case the difference is 30%. The mass flow rate on average differs by less than 5% for all tested cases with the maximum difference not exceeding 10%. The estimation method takes less than 3 seconds on 3.0 GHz single core processor to complete the calculations for a single flight condition as oppose to over 5 days on 8 cores at 2.4 GHz system while using 3D finite volume method simulation with 1.5 million elements mesh. This makes the estimation method suitable for the use with exchange inlet geometry optimization algorithm.

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

NASA Technical Reports Server (NTRS)

Felici, Helene Marie

1992-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Simulation studies of vestibular macular afferent-discharge patterns using a new, quasi-3-D finite volume method

NASA Technical Reports Server (NTRS)

Ross, M. D.; Linton, S. W.; Parnas, B. R.

2000-01-01

A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Haque, Najmul; Mustafa, Munshi G.; Strickland, Michael

2016-03-01

In a previous paper [N. Haque et al., J. High Energy Phys. 05 (2014) 27], we calculated the three-loop thermodynamic potential of QCD at finite temperature T and quark chemical potentials μq using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and finite baryon, strangeness, and isospin chemical potentials μB, μS, and μI. We calculate the pressure at nonzero μB and μI with μS=0 , and the energy density, the entropy density, the trace anomaly, and the speed of sound at nonzero μI with μB=μS=0 . The second- and fourth-order isospin susceptibilities are calculated at μB=μS=μI=0 . Our results can be directly compared to lattice QCD without Taylor expansions around μq=0 since QCD has no sign problem at μB=μS=0 and finite isospin chemical potential μI.

76 FR 53497 - Florida Power and Light Company; St. Lucie Plant, Units 1 and 2; Environmental Assessment and...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-26

... Appendix G to the Code for calculating K IM factors, and instead applies FEM [finite element modeling..., Units 1 and 2 are calculated using the CE NSSS finite element modeling methods. The Need for the... Society of Mechanical Engineers (ASME) Code, Section XI, Appendix G) or determined by applying finite...

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

NASA Astrophysics Data System (ADS)

Moraleda, Joaquín; Segurado, Javier; LLorca, Javier

2009-09-01

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10-40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time "quasi-exact" results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.

Moduli thermalization and finite temperature effects in "big" divisor large volume D3/ D7 Swiss-cheese compactification

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2011-01-01

In the context of Type IIB compactified on a large volume Swiss-Cheese orientifold in the presence of a mobile space-time filling D3-brane and stacks of fluxed D7-branes wrapping the "big" divisor Σ B of a Swiss-Cheese Calabi Yau in WCP 4[1, 1, 1, 6, 9], we explore various implications of moduli dynamics and discuss their couplings and decay into MSSM (-like) matter fields early in the history of universe to reach thermal equilibrium. Like finite temperature effects in O'KKLT, we observe that the local minimum of zero-temperature effective scalar potential is stable against any finite temperature corrections (up to two-loops) in large volume scenarios as well. Also we find that moduli are heavy enough to avoid any cosmological moduli problem.

The unstaggered extension to GFDL's FV3 dynamical core on the cubed-sphere

NASA Astrophysics Data System (ADS)

Chen, X.; Lin, S. J.; Harris, L.

2017-12-01

Finite-volume schemes have become popular for atmospheric transport since they provide intrinsic mass conservation to constituent species. Many CFD codes use unstaggered discretizations for finite volume methods with an approximate Riemann solver. However, this approach is inefficient for geophysical flows due to the complexity of the Riemann solver. We introduce a Low Mach number Approximate Riemann Solver (LMARS) simplified using assumptions appropriate for atmospheric flows: the wind speed is much slower than the sound speed, weak discontinuities, and locally uniform sound wave velocity. LMARS makes possible a Riemann-solver-based dynamical core comparable in computational efficiency to many current dynamical cores. We will present a 3D finite-volume dynamical core using LMARS in a cubed-sphere geometry with a vertically Lagrangian discretization. Results from standard idealized test cases will be discussed.

Large Diameter Femoral Heads Impose Significant Alterations on the Strains Developed on Femoral Component and Bone: A Finite Element Analysis

PubMed Central

Theodorou, E.G; Provatidis, C.G; Babis, G.C; Georgiou, C.S; Megas, P.D

2011-01-01

Total Hip Arthroplasty aims at fully recreating a functional hip joint. Over the past years modular implant systems have become common practice and are widely used, due to the surgical options they provide. In addition Big Femoral Heads have also been implemented in the process, providing more flexibility for the surgeon. The current study aims at investigating the effects that femoral heads of bigger diameter may impose on the mechanical behavior of the bone-implant assembly. Using data acquired by Computed Tomographies and a Coordinate Measurement Machine, a cadaveric femur and a Profemur-E modular stem were fully digitized, leading to a three dimensional finite element model in ANSYS Workbench. Strains and stresses were then calculated, focusing on areas of clinical interest, based on Gruen zones: the calcar and the corresponding below the greater trochanter area in the proximal femur, the stem tip region and a profile line along linea aspera. The performed finite elements analysis revealed that the use of large diameter heads produces significant changes in strain development within the bone volume, especially in the lateral side. The application of Frost’s law in bone remodeling, validated the hypothesis that for all diameters normal bone growth occurs. However, in the calcar area lower strain values were recorded, when comparing with the reference model featuring a 28mm femoral head. Along line aspera and for the stem tip area, higher values were recorded. Finally, stresses calculated on the modular neck revealed increased values, but without reaching the yield strength of the titanium alloy used. PMID:21792381

Large diameter femoral heads impose significant alterations on the strains developed on femoral component and bone: a finite element analysis.

PubMed

Theodorou, E G; Provatidis, C G; Babis, G C; Georgiou, C S; Megas, P D

2011-01-01

Total Hip Arthroplasty aims at fully recreating a functional hip joint. Over the past years modular implant systems have become common practice and are widely used, due to the surgical options they provide. In addition Big Femoral Heads have also been implemented in the process, providing more flexibility for the surgeon. The current study aims at investigating the effects that femoral heads of bigger diameter may impose on the mechanical behavior of the bone-implant assembly. Using data acquired by Computed Tomographies and a Coordinate Measurement Machine, a cadaveric femur and a Profemur-E modular stem were fully digitized, leading to a three dimensional finite element model in ANSYS Workbench. Strains and stresses were then calculated, focusing on areas of clinical interest, based on Gruen zones: the calcar and the corresponding below the greater trochanter area in the proximal femur, the stem tip region and a profile line along linea aspera. The performed finite elements analysis revealed that the use of large diameter heads produces significant changes in strain development within the bone volume, especially in the lateral side. The application of Frost's law in bone remodeling, validated the hypothesis that for all diameters normal bone growth occurs. However, in the calcar area lower strain values were recorded, when comparing with the reference model featuring a 28mm femoral head. Along line aspera and for the stem tip area, higher values were recorded. Finally, stresses calculated on the modular neck revealed increased values, but without reaching the yield strength of the titanium alloy used.

Finite Beta Boundary Magnetic Fields of NCSX

NASA Astrophysics Data System (ADS)

Grossman, A.; Kaiser, T.; Mioduszewski, P.

2004-11-01

The magnetic field between the plasma surface and wall of the National Compact Stellarator (NCSX), which uses quasi-symmetry to combine the best features of the tokamak and stellarator in a configuration of low aspect ratio is mapped via field line tracing in a range of finite beta in which part of the rotational transform is generated by the bootstrap current. We adopt the methodology developed for W7-X, in which an equilibrium solution is computed by an inverse equilibrium solver based on an energy minimizing variational moments code, VMEC2000[1], which solves directly for the shape of the flux surfaces given the external coils and their currents as well as a bootstrap current provided by a separate transport calculation. The VMEC solution and the Biot-Savart vacuum fields are coupled to the magnetic field solver for finite-beta equilibrium (MFBE2001)[2] code to determine the magnetic field on a 3D grid over a computational domain. It is found that the edge plasma is more stellarator-like, with a complex 3D structure, and less like the ordered 2D symmetric structure of a tokamak. The field lines make a transition from ergodically covering a surface to ergodically covering a volume, as the distance from the last closed magnetic surface is increased. The results are compared with the PIES[3] calculations. [1] S.P. Hirshman et al. Comput. Phys. Commun. 43 (1986) 143. [2] E. Strumberger, et al. Nucl. Fusion 42 (2002) 827. [3] A.H. Reiman and H.S. Greenside, Comput. Phys. Commun. 43, 157 (1986).

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames. Volume 4

NASA Technical Reports Server (NTRS)

Ku, Jerry C.; Tong, Li; Greenberg, Paul S.

1996-01-01

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two p electrons using all-electron explicitly correlated Gaussian basis functions

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

Sharkey, Keeper L.; Pavanello, Michele; Bubin, Sergiy

2009-12-15

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.

Communication: Finite size correction in periodic coupled cluster theory calculations of solids.

PubMed

Liao, Ke; Grüneis, Andreas

2016-10-14

We present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Møller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 × 2 × 2 and 3 × 3 × 3 k-point meshes only.

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The methodology used to implement structural sensitivity calculations into a major, general-purpose finite-element analysis system (SPAR) is described. This implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calculating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of SPAR are also discussed.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

A design tool for direct and non-stochastic calculations of near-field radiative transfer in complex structures: The NF-RT-FDTD algorithm

NASA Astrophysics Data System (ADS)

Didari, Azadeh; Pinar Mengüç, M.

2017-08-01

Advances in nanotechnology and nanophotonics are inextricably linked with the need for reliable computational algorithms to be adapted as design tools for the development of new concepts in energy harvesting, radiative cooling, nanolithography and nano-scale manufacturing, among others. In this paper, we provide an outline for such a computational tool, named NF-RT-FDTD, to determine the near-field radiative transfer between structured surfaces using Finite Difference Time Domain method. NF-RT-FDTD is a direct and non-stochastic algorithm, which accounts for the statistical nature of the thermal radiation and is easily applicable to any arbitrary geometry at thermal equilibrium. We present a review of the fundamental relations for far- and near-field radiative transfer between different geometries with nano-scale surface and volumetric features and gaps, and then we discuss the details of the NF-RT-FDTD formulation, its application to sample geometries and outline its future expansion to more complex geometries. In addition, we briefly discuss some of the recent numerical works for direct and indirect calculations of near-field thermal radiation transfer, including Scattering Matrix method, Finite Difference Time Domain method (FDTD), Wiener Chaos Expansion, Fluctuating Surface Current (FSC), Fluctuating Volume Current (FVC) and Thermal Discrete Dipole Approximations (TDDA).

Finite element validation of stress intensity factor calculation models for thru-thickness and thumb-nail cracks in double edge notch specimens

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

Beres, W.; Koul, A.K.

1994-09-01

Stress intensity factors for thru-thickness and thumb-nail cracks in the double edge notch specimens, containing two different notch radius (R) to specimen width (W) ratios (R/W = 1/8 and 1/16), are calculated through finite element analysis. The finite element results are compared with predictions based on existing empirical models for SIF calculations. The effects of a change in R/W ratio on SIF of thru-thickness and thumb-nail cracks are also discussed. 34 refs.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

Equivalent Circuit Parameter Calculation of Interior Permanent Magnet Motor Involving Iron Loss Resistance Using Finite Element Method

NASA Astrophysics Data System (ADS)

Yamazaki, Katsumi

In this paper, we propose a method to calculate the equivalent circuit parameters of interior permanent magnet motors including iron loss resistance using the finite element method. First, the finite element analysis considering harmonics and magnetic saturation is carried out to obtain time variations of magnetic fields in the stator and the rotor core. Second, the iron losses of the stator and the rotor are calculated from the results of the finite element analysis with the considerations of harmonic eddy current losses and the minor hysteresis losses of the core. As a result, we obtain the equivalent circuit parameters i.e. the d-q axis inductance and the iron loss resistance as functions of operating condition of the motor. The proposed method is applied to an interior permanent magnet motor to calculate the characteristics based on the equivalent circuit obtained by the proposed method. The calculated results are compared with the experimental results to verify the accuracy.

Experimental analysis and simulation calculation of the inductances of loosely coupled transformer

NASA Astrophysics Data System (ADS)

Kerui, Chen; Yang, Han; Yan, Zhang; Nannan, Gao; Ying, Pei; Hongbo, Li; Pei, Li; Liangfeng, Guo

2017-11-01

The experimental design of iron-core wireless power transmission system is designed, and an experimental model of loosely coupled transformer is built. Measuring the air gap on both sides of the transformer 15mm inductor under the parameters. The feasibility and feasibility of using the finite element method to calculate the coil inductance parameters of the loosely coupled transformer are analyzed. The system was modeled by ANSYS, and the magnetic field was calculated by finite element method, and the inductance parameters were calculated. The finite element method is used to calculate the inductive parameters of the loosely coupled transformer, and the basis for the accurate compensation of the capacitance of the wireless power transmission system is established.

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

NASA Technical Reports Server (NTRS)

Gloss, R. J.

1971-01-01

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

Direct Density Functional Energy Minimization using an Tetrahedral Finite Element Grid

NASA Astrophysics Data System (ADS)

Vaught, A.; Schmidt, K. E.; Chizmeshya, A. V. G.

1998-03-01

We describe an O(N) (N proportional to volume) technique for solving electronic structure problems using the finite element method (FEM). A real--space tetrahedral grid is used as a basis to represent the electronic density, of a free or periodic system and Poisson's equation is solved as a boundary value problem. Nuclear cusps are treated using a local grid consisting of radial elements. These features facilitate the implementation of complicated energy functionals and permit a direct (constrained) energy minimization with respect to the density. We demonstrate the usefulness of the scheme by calculating the binding trends and polarizabilities of a number of atoms and molecules using a number of recently proposed non--local, orbital--free kinetic energy functionals^1,2. Scaling behavior, computational efficiency and the generalization to band--structure will also be discussed. indent 0 pt øbeylines øbeyspaces skip 0 pt ^1 P. Garcia-Gonzalez, J.E. Alvarellos and E. Chacon, Phys. Rev. B 54, 1897 (1996). ^2 A. J. Thakkar, Phys.Rev.B 46, 6920 (1992).

ANSYS duplicate finite-element checker routine

NASA Technical Reports Server (NTRS)

Ortega, R.

1995-01-01

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

Turbulent piloted partially-premixed flames with varying levels of O2/N2: stability limits and PDF calculations

NASA Astrophysics Data System (ADS)

Juddoo, Mrinal; Masri, Assaad R.; Pope, Stephen B.

2011-12-01

This paper reports measured stability limits and PDF calculations of piloted, turbulent flames of compressed natural gas (CNG) partially-premixed with either pure oxygen, or with varying levels of O2/N2. Stability limits are presented for flames of CNG fuel premixed with up to 20% oxygen as well as CNG-O2-N2 fuel where the O2 content is varied from 8 to 22% by volume. Calculations are presented for (i) Sydney flame B [Masri et al. 1988] which uses pure CNG as well as flames B15 to B25 where the CNG is partially-premixed with 15-25% oxygen by volume, respectively and (ii) Sandia methane-air (1:3 by volume) flame E [Barlow et al. 2005] as well as new flames E15 and E25 that are partially-premixed with 'reconstituted air' where the O2 content in nitrogen is 15 and 25% by volume, respectively. The calculations solve a transported PDF of composition using a particle-based Monte Carlo method and employ the EMST mixing model as well as detailed chemical kinetics. The addition of oxygen to the fuel increases stability, shortens the flames, broadens the reaction zone, and shifts the stoichiometric mixture fraction towards the inner side of the jet. It is found that for pure CNG flames where the reaction zone is narrow (∼0.1 in mixture fraction space), the PDF calculations fail to reproduce the correct level of local extinction on approach to blow-off. A broadening in the reaction zone up to about 0.25 in mixture fraction space is needed for the PDF/EMST approach to be able to capture these finite-rate chemistry effects. It is also found that for the same level of partial premixing, increasing the O2/N2 ratio increases the maximum levels of CO and NO but shifts the peak to richer mixture fractions. Over the range of oxygenation investigated here, stability limits have shown to improve almost linearly with increasing oxygen levels in the fuel and with increasing the contribution of release rate from the pilot.

Calculation of compressible boundary layer flow about airfoils by a finite element/finite difference method

NASA Technical Reports Server (NTRS)

Strong, Stuart L.; Meade, Andrew J., Jr.

1992-01-01

Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.

Phase transition for the system of finite volume in the ϕ4 theory in the Tsallis nonextensive statistics

NASA Astrophysics Data System (ADS)

Ishihara, Masamichi

2018-04-01

We studied the effects of nonextensivity on the phase transition for the system of finite volume V in the ϕ4 theory in the Tsallis nonextensive statistics of entropic parameter q and temperature T, when the deviation from the Boltzmann-Gibbs (BG) statistics, |q ‑ 1|, is small. We calculated the condensate and the effective mass to the order q ‑ 1 with the normalized q-expectation value under the free particle approximation with zero bare mass. The following facts were found. The condensate Φ divided by v, Φ/v, at q (v is the value of the condensate at T = 0) is smaller than that at q‧ for q > q‧ as a function of Tph/v which is the physical temperature Tph divided by v. The physical temperature Tph is related to the variation of the Tsallis entropy and the variation of the internal energies, and Tph at q = 1 coincides with T. The effective mass decreases, reaches minimum, and increases after that, as Tph increases. The effective mass at q > 1 is lighter than the effective mass at q = 1 at low physical temperature and heavier than the effective mass at q = 1 at high physical temperature. The effects of the nonextensivity on the physical quantity as a function of Tph become strong as |q ‑ 1| increases. The results indicate the significance of the definition of the expectation value, the definition of the physical temperature, and the constraints for the density operator, when the terms including the volume of the system are not negligible.

Hadronic vacuum polarization contribution to aμ from full lattice QCD

NASA Astrophysics Data System (ADS)

Chakraborty, Bipasha; Davies, C. T. H.; de Oliveira, P. G.; Koponen, J.; Lepage, G. P.; van de Water, R. S.; Hpqcd Collaboration

2017-08-01

We determine the contribution to the anomalous magnetic moment of the muon from the αQED2 hadronic vacuum polarization diagram using full lattice QCD and including u /d quarks with physical masses for the first time. We use gluon field configurations that include u , d , s and c quarks in the sea at multiple values of the lattice spacing, multiple u /d masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for aμHVP ,LO of 667 (6 )(12 )×10-10, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of aμ and the Standard Model of 3 σ .

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

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

Kong, Bo; Fox, Rodney O.; Feng, Heng

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE PAGES

Kong, Bo; Fox, Rodney O.; Feng, Heng; ...

2017-02-16

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

A Statistics-Based Cracking Criterion of Resin-Bonded Silica Sand for Casting Process Simulation

NASA Astrophysics Data System (ADS)

Wang, Huimin; Lu, Yan; Ripplinger, Keith; Detwiler, Duane; Luo, Alan A.

2017-02-01

Cracking of sand molds/cores can result in many casting defects such as veining. A robust cracking criterion is needed in casting process simulation for predicting/controlling such defects. A cracking probability map, relating to fracture stress and effective volume, was proposed for resin-bonded silica sand based on Weibull statistics. Three-point bending test results of sand samples were used to generate the cracking map and set up a safety line for cracking criterion. Tensile test results confirmed the accuracy of the safety line for cracking prediction. A laboratory casting experiment was designed and carried out to predict cracking of a cup mold during aluminum casting. The stress-strain behavior and the effective volume of the cup molds were calculated using a finite element analysis code ProCAST®. Furthermore, an energy dispersive spectroscopy fractographic examination of the sand samples confirmed the binder cracking in resin-bonded silica sand.

Isoscalar π π Scattering and the σ Meson Resonance from QCD

DOE PAGES

Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.; ...

2017-01-09

Here, we present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. We also compute the hadronic correlation functions including all required quark propagation diagrams. From these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the S-wave phase-shift up to the Kmore » $$\\bar{K}$$ threshold. Calculations are performed at two values of the u, d quark mass corresponding to m π = 236, 391 MeV and the resulting amplitudes are described in terms of a σ meson which evolves from a bound-state below ππ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.« less

Computational analysis of species transport and electrochemical characteristics of a MOLB-type SOFC

NASA Astrophysics Data System (ADS)

Hwang, J. J.; Chen, C. K.; Lai, D. Y.

A multi-physics model coupling electrochemical kinetics with fluid dynamics has been developed to simulate the transport phenomena in mono-block-layer built (MOLB) solid oxide fuel cells (SOFC). A typical MOLB module is composed of trapezoidal flow channels, corrugated positive electrode-electrolyte-negative electrode (PEN) plates, and planar inter-connecters. The control volume-based finite difference method is employed for calculation, which is based on the conservation of mass, momentum, energy, species, and electric charge. In the porous electrodes, the flow momentum is governed by a Darcy model with constant porosity and permeability. The diffusion of reactants follows the Bruggman model. The chemistry within the plates is described via surface reactions with a fixed surface-to-volume ratio, tortuosity and average pore size. Species transports as well as the local variations of electrochemical characteristics, such as overpotential and current density distributions in the electrodes of an MOLB SOFC, are discussed in detail.

A comparison of the finite difference and finite element methods for heat transfer calculations

NASA Technical Reports Server (NTRS)

Emery, A. F.; Mortazavi, H. R.

1982-01-01

The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.

Continuum kinetic modeling of the tokamak plasma edge

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

Dorf, M. A.; Dorr, M. R.; Hittinger, J. A.

2016-05-15

The first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalous radial transport.

Parallel computing using a Lagrangian formulation

NASA Technical Reports Server (NTRS)

Liou, May-Fun; Loh, Ching Yuen

1991-01-01

A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.

Parallel computing using a Lagrangian formulation

NASA Technical Reports Server (NTRS)

Liou, May-Fun; Loh, Ching-Yuen

1992-01-01

This paper adopts a new Lagrangian formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.

Numerical simulation of water evaporation inside vertical circular tubes

NASA Astrophysics Data System (ADS)

Ocłoń, Paweł; Nowak, Marzena; Majewski, Karol

2013-10-01

In this paper the results of simplified numerical analysis of water evaporation in vertical circular tubes are presented. The heat transfer in fluid domain (water or wet steam) and solid domain (tube wall) is analyzed. For the fluid domain the temperature field is calculated solving energy equation using the Control Volume Method and for the solid domain using the Finite Element Method. The heat transfer between fluid and solid domains is conjugated using the value of heat transfer coefficient from evaporating liquid to the tube wall. It is determined using the analytical Steiner-Taborek correlation. The pressure changes in fluid are computed using Friedel model.

Coincidental match of numerical simulation and physics

NASA Astrophysics Data System (ADS)

Pierre, B.; Gudmundsson, J. S.

2010-08-01

Consequences of rapid pressure transients in pipelines range from increased fatigue to leakages and to complete ruptures of pipeline. Therefore, accurate predictions of rapid pressure transients in pipelines using numerical simulations are critical. State of the art modelling of pressure transient in general, and water hammer in particular include unsteady friction in addition to the steady frictional pressure drop, and numerical simulations rely on the method of characteristics. Comparison of rapid pressure transient calculations by the method of characteristics and a selected high resolution finite volume method highlights issues related to modelling of pressure waves and illustrates that matches between numerical simulations and physics are purely coincidental.

Numerical Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1996-01-01

A numerical method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a Lagrangian particle tracking scheme, and the inter-phase momentum exchange is described by the Particle-In-Cell scheme. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.

Estimation of supersonic fighter jet airfoil data and low speed aerodynamic analysis of airfoil section at the Mach number 0.15

NASA Astrophysics Data System (ADS)

Sogukpinar, Haci

2018-02-01

In this paper, some of the NACA 64A series airfoils data are estimated and aerodynamic properties are calculated to facilitate great understandings effect of relative thickness on the aerodynamic performance of the airfoil by using COMSOL software. 64A201-64A204 airfoils data are not available in literature therefore 64A210 data are used as reference data to estimate 64A201, 64A202, 64A203, 64A204 airfoil configurations. Numerical calculations are then conducted with the angle of attack from -12° to +16° by using k-w turbulence model based on the finite-volume approach. The lift and drag coefficient are one of the most important parameters in studying the airplane performance. Therefore lift, drag and pressure coefficient around selected airfoil are calculated and compared at the Reynolds numbers of 6 × 106 and also stalling characteristics of airfoil section are investigated and presented numerically.

Transcranial Magnetic Stimulation: An Automated Procedure to Obtain Coil-specific Models for Field Calculations.

PubMed

Madsen, Kristoffer H; Ewald, Lars; Siebner, Hartwig R; Thielscher, Axel

2015-01-01

Field calculations for transcranial magnetic stimulation (TMS) are increasingly implemented online in neuronavigation systems and in more realistic offline approaches based on finite-element methods. They are often based on simplified and/or non-validated models of the magnetic vector potential of the TMS coils. To develop an approach to reconstruct the magnetic vector potential based on automated measurements. We implemented a setup that simultaneously measures the three components of the magnetic field with high spatial resolution. This is complemented by a novel approach to determine the magnetic vector potential via volume integration of the measured field. The integration approach reproduces the vector potential with very good accuracy. The vector potential distribution of a standard figure-of-eight shaped coil determined with our setup corresponds well with that calculated using a model reconstructed from x-ray images. The setup can supply validated models for existing and newly appearing TMS coils. Copyright © 2015 Elsevier Inc. All rights reserved.

The NATA code; theory and analysis. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Bade, W. L.; Yos, J. M.

1975-01-01

The NATA code is a computer program for calculating quasi-one-dimensional gas flow in axisymmetric nozzles and rectangular channels, primarily to describe conditions in electric archeated wind tunnels. The program provides solutions based on frozen chemistry, chemical equilibrium, and nonequilibrium flow with finite reaction rates. The shear and heat flux on the nozzle wall are calculated and boundary layer displacement effects on the inviscid flow are taken into account. The program contains compiled-in thermochemical, chemical kinetic and transport cross section data for high-temperature air, CO2-N2-Ar mixtures, helium, and argon. It calculates stagnation conditions on axisymmetric or two-dimensional models and conditions on the flat surface of a blunt wedge. Included in the report are: definitions of the inputs and outputs; precoded data on gas models, reactions, thermodynamic and transport properties of species, and nozzle geometries; explanations of diagnostic outputs and code abort conditions; test problems; and a user's manual for an auxiliary program (NOZFIT) used to set up analytical curvefits to nozzle profiles.

Exploratory Lattice QCD Study of the Rare Kaon Decay K^{+}→π^{+}νν[over ¯].

PubMed

Bai, Ziyuan; Christ, Norman H; Feng, Xu; Lawson, Andrew; Portelli, Antonin; Sachrajda, Christopher T

2017-06-23

We report a first, complete lattice QCD calculation of the long-distance contribution to the K^{+}→π^{+}νν[over ¯] decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics, there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.

Exploratory Lattice QCD Study of the Rare Kaon Decay K+→π+ν ν ¯

NASA Astrophysics Data System (ADS)

Bai, Ziyuan; Christ, Norman H.; Feng, Xu; Lawson, Andrew; Portelli, Antonin; Sachrajda, Christopher T.; Rbc-Ukqcd Collaboration

2017-06-01

We report a first, complete lattice QCD calculation of the long-distance contribution to the K+→π+ν ν ¯ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics, there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.

An analysis of the nucleon spectrum from lattice partially-quenched QCD

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

W. Armour; Allton, C. R.; Leinweber, Derek B.

2010-09-01

The chiral extrapolation of the nucleon mass, Mn, is investigated using data coming from 2-flavour partially-quenched lattice simulations. The leading one-loop corrections to the nucleon mass are derived for partially-quenched QCD. A large sample of lattice results from the CP-PACS Collaboration is analysed, with explicit corrections for finite lattice spacing artifacts. The extrapolation is studied using finite range regularised chiral perturbation theory. The analysis also provides a quantitative estimate of the leading finite volume corrections. It is found that the discretisation, finite-volume and partial quenching effects can all be very well described in this framework, producing an extrapolated value ofmore » Mn in agreement with experiment. This procedure is also compared with extrapolations based on polynomial forms, where the results are less encouraging.« less

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

Micromechanics effects in creep of metal-matrix composites

NASA Astrophysics Data System (ADS)

Davis, L. C.; Allison, J. E.

1995-12-01

The creep of metal-matrix composites is analyzed by finite element techniques. An axisymmetric unit-cell model with spherical reinforcing particles is used. Parameters appropriate to TiC particles in a precipitation-hardened (2219) Al matrix are chosen. The effects of matrix plasticity and residual stresses on the creep of the composite are calculated. We confirm (1) that the steady-state rate is independent of the particle elastic moduli and the matrix elastic and plastic properties, (2) that the ratio of composite to matrix steady-state rates depends only on the volume fraction and geometry of the reinforcing phase, and (3) that this ratio can be determined from a calculation of the stress-strain relation for the geometrically identical composite (same phase volume and geometry) with rigid particles in the appropriate power-law hardening matrix. The values of steady-state creep are compared to experimental ones (Krajewski et al.). Continuum mechanics predictions give a larger reduction of the composite creep relative to the unreinforced material than measured, suggesting that the effective creep rate of the matrix is larger than in unreinforced precipitation-hardened Al due to changes in microstructure, dislocation density, or creep mechanism. Changes in matrix creep properties are also suggested by the comparison of calculated and measured creep strain rates in the primary creep regime, where significantly different time dependencies are found. It is found that creep calculations performed for a timeindependent matrix creep law can be transformed to obtain the creep for a time-dependent creep law.

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.

Multidimensional directional flux weighted upwind scheme for multiphase flow modeling in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Jin, G.

2012-12-01

Multiphase flow modeling is an important numerical tool for a better understanding of transport processes in the fields including, but not limited to, petroleum reservoir engineering, remedy of ground water contamination, and risk evaluation of greenhouse gases such as CO2 injected into deep saline reservoirs. However, accurate numerical modeling for multiphase flow remains many challenges that arise from the inherent tight coupling and strong non-linear nature of the governing equations and the highly heterogeneous media. The existence of counter current flow which is caused by the effect of adverse relative mobility contrast and gravitational and capillary forces will introduce additional numerical instability. Recently multipoint flux approximation (MPFA) has become a subject of extensive research and has been demonstrated with great success in reducing considerable grid orientation effects compared to the conventional single point upstream (SPU) weighting scheme, especially in higher dimensions. However, the present available MPFA schemes are mathematically targeted to certain types of grids in two dimensions, a more general form of MPFA scheme is needed for both 2-D and 3-D problems. In this work a new upstream weighting scheme based on multipoint directional incoming fluxes is proposed which incorporates full permeability tensor to account for the heterogeneity of the porous media. First, the multiphase governing equations are decoupled into an elliptic pressure equation and a hyperbolic or parabolic saturation depends on whether the gravitational and capillary pressures are presented or not. Next, a dual secondary grid (called finite volume grid) is formulated from a primary grid (called finite element grid) to create interaction regions for each grid cell over the entire simulation domain. Such a discretization must ensure the conservation of mass and maintain the continuity of the Darcy velocity across the boundaries between neighboring interaction regions. The pressure field is then implicitly calculated from the pressure equation, which in turn results in the derived velocity field for directional flux calculation at each grid node. Directional flux at the center of each interaction surface is also calculated by interpolation from the element nodal fluxes using shape functions. The MPFA scheme is performed by a specific linear combination of all incoming fluxes into the upstream cell represented by either nodal fluxes or interpolated surface boundary fluxes to produce an upwind directional fluxed weighted relative mobility at the center of the interaction region boundary. Such an upwind weighted relative mobility is then used for calculating the saturations of each fluid phase explicitly. The proposed upwind weighting scheme has been implemented into a mixed finite element-finite volume (FE-FV) method, which allows for handling complex reservoir geometry with second-order accuracies in approximating primary variables. The numerical solver has been tested with several bench mark test problems. The application of the proposed scheme to migration path analysis of CO2 injected into deep saline reservoirs in 3-D has demonstrated its ability and robustness in handling multiphase flow with adverse mobility contrast in highly heterogeneous porous media.

Static and dynamic structural-sensitivity derivative calculations in the finite-element-based Engineering Analysis Language (EAL) system

NASA Technical Reports Server (NTRS)

Camarda, C. J.; Adelman, H. M.

1984-01-01

The implementation of static and dynamic structural-sensitivity derivative calculations in a general purpose, finite-element computer program denoted the Engineering Analysis Language (EAL) System is described. Derivatives are calculated with respect to structural parameters, specifically, member sectional properties including thicknesses, cross-sectional areas, and moments of inertia. Derivatives are obtained for displacements, stresses, vibration frequencies and mode shapes, and buckling loads and mode shapes. Three methods for calculating derivatives are implemented (analytical, semianalytical, and finite differences), and comparisons of computer time and accuracy are made. Results are presented for four examples: a swept wing, a box beam, a stiffened cylinder with a cutout, and a space radiometer-antenna truss.

Thermal residual stresses in silicon-carbide/titanium (0/90) laminate

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1992-01-01

The current work formulated a micromechanical analysis of a cross-ply laminate and calculated the thermal residual stress in a very thick (0/90)(sub 2n) silicon-carbide/titanium laminate. Results were also shown for a unidirectional laminate of the same material. Discrete fiber-matrix models assuming a rectangular array of fibers with a fiber volume fraction of 32.5 percent and a three-dimensional, finite-element analysis were used. Significant differences in the trends and magnitudes for the fiber, matrix, and interface stresses were calculated for unidirectional and (0/90) models. Larger hoop stresses calculated for the (0/90) model indicate that it may be more susceptible to radial cracking when subjected to mechanical loading than the unidirectional model. The axial stresses in the matrix were calculated to be slightly larger for the (0/90) model. The compressive axial stresses in the fiber were significantly larger in the (0/90) model. The presence of the cross-ply in the (0/90) model reduced the constraint on the fiber, producing radial interface stresses that were less compressive, which could lead to earlier failure of the fiber-matrix interface.

The NATA code: Theory and analysis, volume 1. [user manuals (computer programming) - gas dynamics, wind tunnels

NASA Technical Reports Server (NTRS)

Bade, W. L.; Yos, J. M.

1975-01-01

A computer program for calculating quasi-one-dimensional gas flow in axisymmetric and two-dimensional nozzles and rectangular channels is presented. Flow is assumed to start from a state of thermochemical equilibrium at a high temperature in an upstream reservoir. The program provides solutions based on frozen chemistry, chemical equilibrium, and nonequilibrium flow with finite reaction rates. Electronic nonequilibrium effects can be included using a two-temperature model. An approximate laminar boundary layer calculation is given for the shear and heat flux on the nozzle wall. Boundary layer displacement effects on the inviscid flow are considered also. Chemical equilibrium and transport property calculations are provided by subroutines. The code contains precoded thermochemical, chemical kinetic, and transport cross section data for high-temperature air, CO2-N2-Ar mixtures, helium, and argon. It provides calculations of the stagnation conditions on axisymmetric or two-dimensional models, and of the conditions on the flat surface of a blunt wedge. The primary purpose of the code is to describe the flow conditions and test conditions in electric arc heated wind tunnels.

Calculation methods for compressible turbulent boundary layers, 1976

NASA Technical Reports Server (NTRS)

Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.

1977-01-01

Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2015-02-24

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less

A time-accurate finite volume method valid at all flow velocities

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1993-01-01

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Evolution of relative magnetic helicity. New boundary conditions for the vector potential

NASA Astrophysics Data System (ADS)

Yang, Shangbin; Büchner, Jörg; Skála, Jan; Zhang, Hongqi

2018-05-01

Context. For a better understanding of the dynamics of the solar corona, it is important to analyse the evolution of the helicity of the magnetic field. Since the helicity cannot be directly determined by observations, we have recently proposed a method to calculate the relative magnetic helicity in a finite volume for a given magnetic field, which however required the flux to be balanced separately on all the sides of the considered volume. Aims: We developed a scheme to obtain the vector potential in a volume without the above restriction at the boundary. We studied the dissipation and escape of relative magnetic helicity from an active region. Methods: In order to allow finite magnetic fluxes through the boundaries, a Coulomb gauge was constructed that allows for global magnetic flux balance. The property of sinusoidal function was used to obtain the vector potentials at the 12 edges of the considered rectangular volume extending above an active region. We tested and verified our method in a theoretical fore-free magnetic field model. Results: We applied the new method to the former calculation data and found a difference of less than 1.2%. We also applied our method to the magnetic field above active region NOAA 11429 obtained by a new photospheric-data-driven magnetohydrodynamics (MHD) model code GOEMHD3. We analysed the magnetic helicity evolution in the solar corona using our new method. We find that the normalized magnetic helicity (H/Φ2) is equal to -0.038 when fast magnetic reconnection is triggered. This value is comparable to the previous value (-0.029) in the MHD simulations when magnetic reconnection happened and the observed normalized magnetic helicity (-0.036) from the eruption of newly emerging active regions. We find that only 8% of the accumulated magnetic helicity is dissipated after it is injected through the bottom boundary. This is in accordance with the Woltjer conjecture. Only 2% of the magnetic helicity injected from the bottom boundary escapes through the corona. This is consistent with the observation of magnetic clouds, which could take magnetic helicity into the interplanetary space. In the case considered here, several halo coronal mass ejections (CMEs) and two X-class solar flares originate from this active region.

Incompressibility in finite nuclei and nuclear matter

NASA Astrophysics Data System (ADS)

Stone, J. R.; Stone, N. J.; Moszkowski, S. A.

2014-04-01

The incompressibility (compression modulus) K0 of infinite symmetric nuclear matter at saturation density has become one of the major constraints on mean-field models of nuclear many-body systems as well as of models of high density matter in astrophysical objects and heavy-ion collisions. It is usually extracted from data on the giant monopole resonance (GMR) or calculated using theoretical models. We present a comprehensive reanalysis of recent data on GMR energies in even-even 112-124Sn and 106,100-116Cd and earlier data on 58≤A≤208 nuclei. The incompressibility of finite nuclei KA is calculated from experimental GMR energies and expressed in terms of A-1/3 and the asymmetry parameter β =(N-Z)/A as a leptodermous expansion with volume, surface, isospin, and Coulomb coefficients Kvol, Ksurf, Kτ, and KCoul. Only data consistent with the scaling approximation, leading to a fast converging leptodermous expansion, with negligible higher-order-term contributions to KA, were used in the present analysis. Assuming that the volume coefficient Kvol is identified with K0, the KCoul=-(5.2±0.7) MeV and the contribution from the curvature term KcurvA-2/3 in the expansion is neglected, compelling evidence is found for K0 to be in the range 250

Finite size effects in the thermodynamics of a free neutral scalar field

NASA Astrophysics Data System (ADS)

Parvan, A. S.

2018-04-01

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.

Low-order modelling of shallow water equations for sensitivity analysis using proper orthogonal decomposition

NASA Astrophysics Data System (ADS)

Zokagoa, Jean-Marie; Soulaïmani, Azzeddine

2012-06-01

This article presents a reduced-order model (ROM) of the shallow water equations (SWEs) for use in sensitivity analyses and Monte-Carlo type applications. Since, in the real world, some of the physical parameters and initial conditions embedded in free-surface flow problems are difficult to calibrate accurately in practice, the results from numerical hydraulic models are almost always corrupted with uncertainties. The main objective of this work is to derive a ROM that ensures appreciable accuracy and a considerable acceleration in the calculations so that it can be used as a surrogate model for stochastic and sensitivity analyses in real free-surface flow problems. The ROM is derived using the proper orthogonal decomposition (POD) method coupled with Galerkin projections of the SWEs, which are discretised through a finite-volume method. The main difficulty of deriving an efficient ROM is the treatment of the nonlinearities involved in SWEs. Suitable approximations that provide rapid online computations of the nonlinear terms are proposed. The proposed ROM is applied to the simulation of hypothetical flood flows in the Bordeaux breakwater, a portion of the 'Rivière des Prairies' located near Laval (a suburb of Montreal, Quebec). A series of sensitivity analyses are performed by varying the Manning roughness coefficient and the inflow discharge. The results are satisfactorily compared to those obtained by the full-order finite volume model.

Masses and sigma terms of doubly charmed baryons up to O (p4) in manifestly Lorentz-invariant baryon chiral perturbation theory

NASA Astrophysics Data System (ADS)

Yao, De-Liang

2018-02-01

We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order [i.e., O (p4) ] in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite-volume corrections. Up to O (p3) , all relevant low-energy constants can be well determined. As a consequence, we obtain the physical values for the masses of Ξc c and Ωc c baryons by extrapolating to the physical limit. Our determination of the Ξc c mass is consistent with the recent experimental value by LHCb Collaboration, however, larger than the one by SELEX Collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the Ξc c and Ωc c states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of O (p4) order, where more unknown constants are involved, when more data are available for unphysical pion masses.

Efficient and robust compositional two-phase reservoir simulation in fractured media

NASA Astrophysics Data System (ADS)

Zidane, A.; Firoozabadi, A.

2015-12-01

Compositional and compressible two-phase flow in fractured media has wide applications including CO2 injection. Accurate simulations are currently based on the discrete fracture approach using the cross-flow equilibrium model. In this approach the fractures and a small part of the matrix blocks are combined to form a grid cell. The major drawback is low computational efficiency. In this work we use the discrete-fracture approach to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross-flow equilibrium in the fractures (FCFE). This allows using large matrix elements in the neighborhood of the fractures. We solve the fracture transport equations implicitly to overcome the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. Our implicit approach is based on calculation of the derivative of the molar concentration of component i in phase (cαi ) with respect to the total molar concentration (ci ) at constant volume V and temperature T. This contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix, and a finite volume (FV) discretization in the fractures. In large scale problems the proposed approach is orders of magnitude faster than the existing models.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Three-Dimensional Viscous Flow Analysis for Moving Bodies Past Fixed Structures

DTIC Science & Technology

1988-05-13

BELLEVUE, WA 98n)05 Research Triangle Park, UC 27709-2211 6Sý. NAME Of FUNDING I PONSORING O Ib. C’FFICE SYMBOL 9 . PROCUREMENT INSTRUMENT IPENTIFICATION...34 otheor sditico Grs IMa ý; pl S- Three- Dimvensio:.iýal Viscrous Flow Analysis for Moving Bodies Past Fixed Structures Fina.11Report, Kelton M. Peery and...Recommendations 40 List of Figures 1 Finite-Volume Mesh ......... ......................... 8 2 Finite-Volume Cell ....... ............................ 9 3

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

An installed nacelle design code using a multiblock Euler solver. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

An efficient multiblock Euler design code was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design driver based on a direct iterative surface curvature method developed at LaRC. A general multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler Equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design driver successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings. The capability and efficiency of the code was demonstrated through the design of both an isolated nacelle and an installed nacelle at various flow conditions. Information on the execution of the computer program is provided in volume 2.

A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method

NASA Astrophysics Data System (ADS)

Shams, Mosayeb; Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko

2018-03-01

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier-Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier-Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas.

Decomposition of the Seismic Source Using Numerical Simulations and Observations of Nuclear Explosions

DTIC Science & Technology

2017-05-31

SUBJECT TERMS nonlinear finite element calculations, nuclear explosion monitoring, topography 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18...3D North Korea calculations........ Figure 6. The CRAM 3D finite element outer grid (left) is rectangular......................... Figure 7. Stress...Figure 6. The CRAM 3D finite element outer grid (left) is rectangular. The inner grid (center) is shaped to match the shape of the explosion shock wave

Interfacial ion solvation: Obtaining the thermodynamic limit from molecular simulations

NASA Astrophysics Data System (ADS)

Cox, Stephen J.; Geissler, Phillip L.

2018-06-01

Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting finite size effects can be substantial and may attenuate very slowly with increasing system size, as shown by previous work on dilute ions in bulk aqueous solution. Here we examine corrections for such effects, with an emphasis on solvation near interfaces. Our central assumption follows the perspective of Hünenberger and McCammon [J. Chem. Phys. 110, 1856 (1999)]: Long-wavelength solvent response underlying finite size effects should be well described by reduced models like dielectric continuum theory, whose size dependence can be calculated straightforwardly. Applied to an ion in a periodic slab of liquid coexisting with vapor, this approach yields a finite size correction for solvation free energies that differs in important ways from results previously derived for bulk solution. For a model polar solvent, we show that this new correction quantitatively accounts for the variation of solvation free energy with volume and aspect ratio of the simulation cell. Correcting periodic slab results for an aqueous system requires an additional accounting for the solvent's intrinsic charge asymmetry, which shifts electric potentials in a size-dependent manner. The accuracy of these finite size corrections establishes a simple method for a posteriori extrapolation to the thermodynamic limit and also underscores the realism of dielectric continuum theory down to the nanometer scale.

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

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

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

Neutral Kaon Mixing from Lattice QCD

NASA Astrophysics Data System (ADS)

Bai, Ziyuan

In this work, we report the lattice calculation of two important quantities which emerge from second order, K0 - K¯0 mixing : DeltaMK and epsilonK. The RBC-UKQCD collaboration has performed the first calculation of DeltaMK with unphysical kinematics [1]. We now extend this calculation to near-physical and physical ensembles. In these physical or near-physical calculations, the two-pion energies are below the kaon threshold, and we have to examine the two-pion intermediate states contribution to DeltaMK, as well as the enhanced finite volume corrections arising from these two-pion intermediate states. We also report the ?rst lattice calculation of the long-distance contribution to the indirect CP violation parameter, the epsilonK. This calculation involves the treatment of a short-distance, ultra-violet divergence that is absent in the calculation of DeltaMK, and we will report our techniques for correcting this divergence on the lattice. In this calculation, we used unphysical quark masses on the same ensemble that we used in [1]. Therefore, rather than providing a physical result, this calculation demonstrates the technique for calculating epsilonK, and provides an approximate understanding the size of the long-distance contributions. Various new techniques are employed in this work, such as the use of All-Mode-Averaging (AMA), the All-to-All (A2A) propagators and the use of super-jackknife method in analyzing the data.

Periodic Inclusion—Matrix Microstructures with Constant Field Inclusions

NASA Astrophysics Data System (ADS)

Liu, Liping; James, Richard D.; Leo, Perry H.

2007-04-01

We find a class of special microstructures consisting of a periodic array of inclusions, with the special property that constant magnetization (or eigenstrain) of the inclusion implies constant magnetic field (or strain) in the inclusion. The resulting inclusions, which we term E-inclusions, have the same property in a finite periodic domain as ellipsoids have in infinite space. The E-inclusions are found by mapping the magnetostatic or elasticity equations to a constrained minimization problem known as a free-boundary obstacle problem. By solving this minimization problem, we can construct families of E-inclusions with any prescribed volume fraction between zero and one. In two dimensions, our results coincide with the microstructures first introduced by Vigdergauz,[1,2] while in three dimensions, we introduce a numerical method to calculate E-inclusions. E-inclusions extend the important role of ellipsoids in calculations concerning phase transformations and composite materials.

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Expansion and improvement of the FORMA system for response and load analysis. Volume 2C: Listings, finite element FORMA subroutines

NASA Technical Reports Server (NTRS)

Wohlen, R. L.

1976-01-01

A listing of the source deck of each finite element FORMA subroutine is given to remove the 'black-box' aura of the subroutines so that the analyst may better understand the detailed operations of each subroutine. The FORTRAN 4 programming language is used in all finite element FORMA subroutines.

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

Bolt clampup relaxation in a graphite/epoxy laminate

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Crews, J. H., Jr.

1982-01-01

A simple bolted joint was analyzed to calculate bolt clampup relaxation for a graphite/epoxy (T300/5208) laminate. A viscoelastic finite element analysis of a double-lap joint with a steel bolt was conducted. Clampup forces were calculated for various steady-state temperature-moisture conditions using a 20-year exposure duration. The finite element analysis predicted that clampup forces relax even for the room-temperature-dry condition. The relaxations were 8, 13, 20, and 30 percent for exposure durations of 1 day, 1 month, 1 year, and 20 years, respectively. As expected, higher temperatures and moisture levels each increased the relaxation rate. The combined viscoelastic effects of steady-state temperature and moisture appeared to be additive. From the finite-element analysis, a simple equation was developed for clampup force relaxation. This generalized equation was used to calculate clampup forces for the same temperature-moisture conditions as used in the finite-element analysis. The two sets of calculated results agreed well.

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...

Numerical Cerebrospinal System Modeling in Fluid-Structure Interaction.

PubMed

Garnotel, Simon; Salmon, Stéphanie; Balédent, Olivier

2018-01-01

Cerebrospinal fluid (CSF) stroke volume in the aqueduct is widely used to evaluate CSF dynamics disorders. In a healthy population, aqueduct stroke volume represents around 10% of the spinal stroke volume while intracranial subarachnoid space stroke volume represents 90%. The amplitude of the CSF oscillations through the different compartments of the cerebrospinal system is a function of the geometry and the compliances of each compartment, but we suspect that it could also be impacted be the cardiac cycle frequency. To study this CSF distribution, we have developed a numerical model of the cerebrospinal system taking into account cerebral ventricles, intracranial subarachnoid spaces, spinal canal and brain tissue in fluid-structure interactions. A numerical fluid-structure interaction model is implemented using a finite-element method library to model the cerebrospinal system and its interaction with the brain based on fluid mechanics equations and linear elasticity equations coupled in a monolithic formulation. The model geometry, simplified in a first approach, is designed in accordance with realistic volume ratios of the different compartments: a thin tube is used to mimic the high flow resistance of the aqueduct. CSF velocity and pressure and brain displacements are obtained as simulation results, and CSF flow and stroke volume are calculated from these results. Simulation results show a significant variability of aqueduct stroke volume and intracranial subarachnoid space stroke volume in the physiological range of cardiac frequencies. Fluid-structure interactions are numerous in the cerebrospinal system and difficult to understand in the rigid skull. The presented model highlights significant variations of stroke volumes under cardiac frequency variations only.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Nyx: Adaptive mesh, massively-parallel, cosmological simulation code

NASA Astrophysics Data System (ADS)

Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun

2017-12-01

Nyx code solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D Eulerian grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the code calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.

Continuum kinetic modeling of the tokamak plasma edge

DOE PAGES

Dorf, M. A.; Dorr, M.; Rognlien, T.; ...

2016-03-10

In this study, the first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasmatransport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalousmore » radial transport.« less

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

NASA Technical Reports Server (NTRS)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.

Redshifted and blueshifted photoluminescence emission of InAs/InP quantum dots upon amorphization of phase change material.

PubMed

Humam, Nurrul Syafawati Binti; Sato, Yu; Takahashi, Motoki; Kanazawa, Shohei; Tsumori, Nobuhiro; Regreny, Philippe; Gendry, Michel; Saiki, Toshiharu

2014-06-16

We present the mechanisms underlying the redshifted and blueshifted photoluminescence (PL) of quantum dots (QDs) upon amorphization of phase change material (PCM). We calculated the stress and energy shift distribution induced by volume expansion using finite element method. Simulation result reveals that redshift is obtained beneath the flat part of amorphous mark, while blueshift is obtained beneath the edge region of amorphous mark. Simulation result is accompanied by two experimental studies; two-dimensional PL intensity mapping of InAs/InP QD sample deposited by a layer of PCM, and an analysis on the relationship between PL intensity ratio and energy shift were performed.

Measurement of gas diffusion coefficient in liquid-saturated porous media using magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Song, Yongchen; Hao, Min; Zhao, Yuechao; Zhang, Liang

2014-12-01

In this study, the dual-chamber pressure decay method and magnetic resonance imaging (MRI) were used to dynamically visualize the gas diffusion process in liquid-saturated porous media, and the relationship of concentration-distance for gas diffusing into liquid-saturated porous media at different times were obtained by MR images quantitative analysis. A non-iterative finite volume method was successfully applied to calculate the local gas diffusion coefficient in liquid-saturated porous media. The results agreed very well with the conventional pressure decay method, thus it demonstrates that the method was feasible of determining the local diffusion coefficient of gas in liquid-saturated porous media at different times during diffusion process.

Nucleon Axial and Electromagnetic Form Factors

NASA Astrophysics Data System (ADS)

Jang, Yong-Chull; Bhattacharya, Tanmoy; Gupta, Rajan; Lin, Huey-Wen; Yoon, Boram

2018-03-01

We present results for the isovector axial, induced pseudoscalar, electric, and magnetic form factors of the nucleon. The calculations were done using 2 + 1 + 1-flavor HISQ ensembles generated by the MILC collaboration with lattice spacings a ≈ 0.12, 0.09, 0.06 fm and pion masses Mπ ≈ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and by comparing two-versus three-states in three-point correlators. The Q2 behavior is analyzed using the model independent z-expansion and the dipole ansatz. Final results for the charge radii and magnetic moment are obtained using a simultaneous fit in Mπ, lattice spacing a and finite volume.

Aerodynamic Heating Computations for Projectiles. Volume 2. Swept Wing Calculations Using the Planar Version of the ABRES Shape Change Code (PLNRASCC)

DTIC Science & Technology

1984-06-01

Mt n o ro " g < - OD-O)C 0N v : _grI40N40 O I0 eeg gr, Wn *, c.M b-C N Z ý VN dN N C4 C4 C4 e"Ř!02AWVý 00 0 P- 1( or . . . . . . . . . i...the ABRES Shape Change Code (ASCC)," Acurex Report TM -80-31/AS, July 1980. 3. M. J. Abbett, "Finite Difference Solution of the Subsonic/Supersonic...Development Command US Army AMCCOM Technical Support Activity ATTN: DRSMC- TDC (D) ATTN: DELSD-L DRSMC-TSS (D) Fort Monmouth, NJ 07703 DRSMC-LCA-F (D) Mr. 0

A singular finite element technique for calculating continuum damping of Alfvén eigenmodes

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

Bowden, G. W.; Hole, M. J.

2015-02-15

Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode inmore » a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.« less

Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

NASA Technical Reports Server (NTRS)

Mei, Chuh; Shen, Mo-How

1987-01-01

Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Hurricane Forecasting with the High-resolution NASA Finite-volume General Circulation Model

NASA Technical Reports Server (NTRS)

Atlas, R.; Reale, O.; Shen, B.-W.; Lin, S.-J.; Chern, J.-D.; Putman, W.; Lee, T.; Yeh, K.-S.; Bosilovich, M.; Radakovich, J.

2004-01-01

A high-resolution finite-volume General Circulation Model (fvGCM), resulting from a development effort of more than ten years, is now being run operationally at the NASA Goddard Space Flight Center and Ames Research Center. The model is based on a finite-volume dynamical core with terrain-following Lagrangian control-volume discretization and performs efficiently on massive parallel architectures. The computational efficiency allows simulations at a resolution of a quarter of a degree, which is double the resolution currently adopted by most global models in operational weather centers. Such fine global resolution brings us closer to overcoming a fundamental barrier in global atmospheric modeling for both weather and climate, because tropical cyclones and even tropical convective clusters can be more realistically represented. In this work, preliminary results of the fvGCM are shown. Fifteen simulations of four Atlantic tropical cyclones in 2002 and 2004 are chosen because of strong and varied difficulties presented to numerical weather forecasting. It is shown that the fvGCM, run at the resolution of a quarter of a degree, can produce very good forecasts of these tropical systems, adequately resolving problems like erratic track, abrupt recurvature, intense extratropical transition, multiple landfall and reintensification, and interaction among vortices.

CFD flowfield simulation of Delta Launch Vehicles in a power-on configuration

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Gielda, T. P.; Soni, B. K.; Deese, J. E.; Agarwal, R. K.

1993-01-01

This paper summarizes recent work at McDonnell Douglas Aerospace (MDA) to develop and validate computational fluid dynamic (CFD) simulations of under expanded rocket plume external flowfields for multibody expendable launch vehicles (ELVs). Multi engine reacting gas flowfield predictions of ELV base pressures are needed to define vehicle base drag and base heating rates for sizing external nozzle and base region insulation thicknesses. Previous ELV design programs used expensive multibody power-on wind tunnel tests that employed chamber/nozzle injected high pressure cold or hot-air. Base heating and pressure measurements were belatedly made during the first flights of past ELV's to correct estimates from semi-empirical engineering models or scale model tests. Presently, CFD methods for use in ELV design are being jointly developed at the Space Transportation Division (MDA-STD) and New Aircraft Missiles Division (MDA-NAMD). An explicit three dimensional, zonal, finite-volume, full Navier-Stokes (FNS) solver with finite rate hydrocarbon/air and aluminum combustion kinetics was developed to accurately compute ELV power-on flowfields. Mississippi State University's GENIE++ general purpose interactive grid generation code was chosen to create zonal, finite volume viscous grids. Axisymmetric, time dependent, turbulent CFD simulations of a Delta DSV-2A vehicle with a MB-3 liquid main engine burning RJ-1/LOX were first completed. Hydrocarbon chemical kinetics and a k-epsilon turbulence model were employed and predictions were validated with flight measurements of base pressure and temperature. Zonal internal/external grids were created for a Delta DSV-2C vehicle with a MB-3 and three Castor-1 solid motors burning and a Delta-2 with an RS-27 main engine (LOX/RP-1) and 9 GEM's attached/6 burning. Cold air, time dependent FNS calculations were performed for DSV-2C during 1992. Single phase simulations that employ finite rate hydrocarbon and aluminum (solid fuel) combustion chemistry are currently in progress. Reliable and efficient Eulerian algorithms are needed to model two phase (solid-gas) momentum and energy transfer mechanisms for solid motor fuel combustion products.

Modeling the purging of dense fluid from a street canyon driven by an interfacial mixing flow and skimming flow

NASA Astrophysics Data System (ADS)

Baratian-Ghorghi, Z.; Kaye, N. B.

2013-07-01

An experimental study is presented to investigate the mechanism of flushing a trapped dense contaminant from a canyon by turbulent boundary layer flow. The results of a series of steady-state experiments are used to parameterize the flushing mechanisms. The steady-state experimental results for a canyon with aspect ratio one indicate that dense fluid is removed from the canyon by two different processes, skimming of dense fluid from the top of the dense layer; and by an interfacial mixing flow that mixes fresh fluid down into the dense lower layer (entrainment) while mixing dense fluid into the flow above the canyon (detrainment). A model is developed for the time varying buoyancy profile within the canyon as a function of the Richardson number which parameterizes both the interfacial mixing and skimming processes observed. The continuous release steady-state experiments allowed for the direct measurement of the skimming and interfacial mixing flow rates for any layer depth and Richardson number. Both the skimming rate and the interfacial mixing rate were found to be power-law functions of the Richardson number of the layer. The model results were compared to the results of previously published finite release experiments [Z. Baratian-Ghorghi and N. B. Kaye, Atmos. Environ. 60, 392-402 (2012)], 10.1016/j.atmosenv.2012.06.077. A high degree of consistency was found between the finite release data and the continuous release data. This agreement acts as an excellent check on the measurement techniques used, as the finite release data was based on curve fitting through buoyancy versus time data, while the continuous release data was calculated directly by measuring the rate of addition of volume and buoyancy once a steady-state was established. Finally, a system of ordinary differential equations is presented to model the removal of dense fluid from the canyon based on empirical correlations of the skimming and interfacial mixing taken form the steady-state experiments. The ODE model predicts well the time taken for a finite volume of dense fluid to be flushed from a canyon.

CFD flowfield simulation of Delta Launch Vehicles in a power-on configuration

NASA Astrophysics Data System (ADS)

Pavish, D. L.; Gielda, T. P.; Soni, B. K.; Deese, J. E.; Agarwal, R. K.

1993-07-01

This paper summarizes recent work at McDonnell Douglas Aerospace (MDA) to develop and validate computational fluid dynamic (CFD) simulations of under expanded rocket plume external flowfields for multibody expendable launch vehicles (ELVs). Multi engine reacting gas flowfield predictions of ELV base pressures are needed to define vehicle base drag and base heating rates for sizing external nozzle and base region insulation thicknesses. Previous ELV design programs used expensive multibody power-on wind tunnel tests that employed chamber/nozzle injected high pressure cold or hot-air. Base heating and pressure measurements were belatedly made during the first flights of past ELV's to correct estimates from semi-empirical engineering models or scale model tests. Presently, CFD methods for use in ELV design are being jointly developed at the Space Transportation Division (MDA-STD) and New Aircraft Missiles Division (MDA-NAMD). An explicit three dimensional, zonal, finite-volume, full Navier-Stokes (FNS) solver with finite rate hydrocarbon/air and aluminum combustion kinetics was developed to accurately compute ELV power-on flowfields. Mississippi State University's GENIE++ general purpose interactive grid generation code was chosen to create zonal, finite volume viscous grids. Axisymmetric, time dependent, turbulent CFD simulations of a Delta DSV-2A vehicle with a MB-3 liquid main engine burning RJ-1/LOX were first completed. Hydrocarbon chemical kinetics and a k-epsilon turbulence model were employed and predictions were validated with flight measurements of base pressure and temperature. Zonal internal/external grids were created for a Delta DSV-2C vehicle with a MB-3 and three Castor-1 solid motors burning and a Delta-2 with an RS-27 main engine (LOX/RP-1) and 9 GEM's attached/6 burning. Cold air, time dependent FNS calculations were performed for DSV-2C during 1992. Single phase simulations that employ finite rate hydrocarbon and aluminum (solid fuel) combustion chemistry are currently in progress. Reliable and efficient Eulerian algorithms are needed to model two phase (solid-gas) momentum and energy transfer mechanisms for solid motor fuel combustion products.

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

NASA Technical Reports Server (NTRS)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling

NASA Astrophysics Data System (ADS)

Ito, Kosuke; Hayashi, Masahito

2018-01-01

In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.

Gradient corrections to the exchange-correlation free energy

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-07

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures abovemore » 10 000 K.« less

Heat Transfer during Blanching and Hydrocooling of Broccoli Florets.

PubMed

Iribe-Salazar, Rosalina; Caro-Corrales, José; Hernández-Calderón, Óscar; Zazueta-Niebla, Jorge; Gutiérrez-Dorado, Roberto; Carrazco-Escalante, Marco; Vázquez-López, Yessica

2015-12-01

The objective of this work was to simulate heat transfer during blanching (90 °C) and hydrocooling (5 °C) of broccoli florets (Brassica oleracea L. Italica) and to evaluate the impact of these processes on the physicochemical and nutrimental quality properties. Thermophysical properties (thermal conductivity [line heat source], specific heat capacity [differential scanning calorimetry], and bulk density [volume displacement]) of stem and inflorescence were measured as a function of temperature (5, 10, 20, 40, 60, and 80 °C). The activation energy and the frequency factor (Arrhenius model) of these thermophysical properties were calculated. A 3-dimensional finite element model was developed to predict the temperature history at different points inside the product. Comparison of the theoretical and experimental temperature histories was carried out. Quality parameters (firmness, total color difference, and vitamin C content) and peroxidase activity were measured. The satisfactory validation of the finite element model allows the prediction of temperature histories and profiles under different process conditions, which could lead to an eventual optimization aimed to minimize the nutritional and sensorial losses in broccoli florets. © 2015 Institute of Food Technologists®

Heat Transfer Issues in Finite Element Analysis of Bounding Accidents in PPCS Models

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

Pampin, R.; Karditsas, P.J.

2005-05-15

Modelling of temperature excursions in structures of conceptual power plants during hypothetical worst-case accidents has been performed within the European Power Plant Conceptual Study (PPCS). A new, 3D finite elements (FE) based tool, coupling the different calculations to the same tokamak geometry, has been extensively used to conduct the neutron transport, activation and thermal analyses for all PPCS plant models. During a total loss of cooling, the usual assumption for the bounding accident, passive removal of the decay heat from activated materials depends on conduction and radiation heat exchange between components. This paper presents and discusses results obtained during themore » PPCS bounding accident thermal analyses, examining the following issues: (a) radiation heat exchange between the inner surfaces of the tokamak, (b) the presence of air within the cryostat volume, and the heat flow arising from the circulation pattern provided by temperature differences between various parts, and (c) the thermal conductivity of pebble beds, and its degradation due to exposure to neutron irradiation, affecting the heat transfer capability and thermal response of a blanket based on these components.« less

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

NASA Technical Reports Server (NTRS)

Lin, Ray-Quing; Kuang, Weijia

2011-01-01

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

Three-Dimensional Finite-Element Simulation for a Thermoelectric Generator Module

NASA Astrophysics Data System (ADS)

Hu, Xiaokai; Takazawa, Hiroyuki; Nagase, Kazuo; Ohta, Michihiro; Yamamoto, Atsushi

2015-10-01

A three-dimensional closed-circuit numerical model of a thermoelectric generator (TEG) module has been constructed with COMSOL® Multiphysics to verify a module test system. The Seebeck, Peltier, and Thomson effects and Joule heating are included in the thermoelectric conversion model. The TEG model is employed to simulate the operation of a 16-leg TEG module based on bismuth telluride with temperature-dependent material properties. The module is mounted on a test platform, and simulated by combining the heat conduction process and thermoelectric conversion process. Simulation results are obtained for the terminal voltage, output power, heat flow, and efficiency as functions of the electric current; the results are compared with measurement data. The Joule and Thomson heats in all the thermoelectric legs, as functions of the electric current, are calculated by finite-element volume integration over the entire legs. The Peltier heat being pumped at the hot side and released at the cold side of the module are also presented in relation to the electric current. The energy balance relations between heat and electricity are verified to support the simulation.

Method to study complex systems of mesons in lattice QCD

DOE PAGES

Detmold, William; Savage, Martin J.

2010-07-30

Correlation functions involving many hadrons allow finite density systems to be explored with Lattice QCD. Recently, systems with up to 12more » $$\\pi^+$$'s or $K^+$'s have been studied to determine the the $3$-$$\\pi^+$$ and $3$-$K^+$ interactions and the corresponding chemical potential has been determined as a function of density in each case. We derive recursion relations between correlation functions that allow us to extend this work to systems of arbitrary numbers of mesons and to systems containing arbitrary different types of mesons such as $$\\pi^+$$'s, $K^+$'s, $D^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and the study of high-density systems. Systems comprised of up to N=12 m mesons can be explored with Lattice QCD calculations utilizing $m$ different sources for the quark propagators. As the recursion relations require only a small, N-independent, number of operations to derive the N+1 meson contractions from the N meson contractions, they are compuationally feasible.« less

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

On 3-D inelastic analysis methods for hot section components. Volume 1: Special finite element models

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1987-01-01

This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.

Effects of Pore Distributions on Ductility of Thin-Walled High Pressure Die-Cast Magnesium

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

Choi, Kyoo Sil; Li, Dongsheng; Sun, Xin

2013-06-01

In this paper, a microstructure-based three-dimensional (3D) finite element modeling method is adopted to investigate the effects of porosity in thin-walled high pressure die-cast (HPDC) Magnesium alloys on their ductility. For this purpose, the cross-sections of AM60 casting samples are first examined using optical microscope and X-ray tomography to obtain the general information on the pore distribution features. The experimentally observed pore distribution features are then used to generate a series of synthetic microstructure-based 3D finite element models with different pore volume fractions and pore distribution features. Shear and ductile damage models are adopted in the finite element analyses tomore » induce the fracture by element removal, leading to the prediction of ductility. The results in this study show that the ductility monotonically decreases as the pore volume fraction increases and that the effect of ‘skin region’ on the ductility is noticeable under the condition of same local pore volume fraction in the center region of the sample and its existence can be beneficial for the improvement of ductility. The further synthetic microstructure-based 3D finite element analyses are planned to investigate the effects of pore size and pore size distribution.« less

ρ-VOF: An interface sharpening method for gas-liquid flow simulation

NASA Astrophysics Data System (ADS)

Wang, Jiantao; Liu, Gang; Jiang, Xiong; Mou, Bin

2018-05-01

The study on simulation of compressible gas-liquid flow remains open. Popular methods are either confined to incompressible flow regime, or inevitably induce smear of the free interface. A new finite volume method for compressible two-phase flow simulation is contributed for this subject. First, the “heterogeneous equilibrium” assumption is introduced to the control volume, by hiring free interface reconstruction technology, the distribution of each component in the control volume is achieved. Next, AUSM+-up (advection upstream splitting method) scheme is employed to calculate the convective fluxes and pressure fluxes, with the contact discontinuity characteristic considered, followed by the update of the whole flow field. The new method features on density-based pattern and interface reconstruction technology from VOF (volume of fluid), thus we name it “ρ-VOF method”. Inherited from AUSM families and VOF, ρ-VOF behaves as an all-speed method, capable of simulating shock in gas-liquid flow, and preserving the sharpness of the free interface. Gas-liquid shock tube is simulated to evaluate the method, from which good agreement is obtained between the predicted results and those of the cited literature, meanwhile, sharper free interface is identified. Finally, the capability and validity of ρ-VOF method can be concluded in compressible gas-liquid flow simulation.

Finite element method for calculating spectral and optical characteristics of axially symmetric quantum dots

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Vinitsky, S. I.; Derbov, V. L.; Hai, L. L.; Kazaryan, E. M.; Sarkisyan, H. A.

2018-04-01

We present new calculation schemes using high-order finite element method implemented on unstructured grids with triangle elements for solving boundary-value problems that describe axially symmetric quantum dots. The efficiency of the algorithms and software is demonstrated by benchmark calculations of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in conical and spheroidal impenetrable quantum dots.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

FLUX-CORRECTED TRANSPORT TECHNIQUE FOR OPEN CHANNEL FLOW. (R825200)

EPA Science Inventory

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second- and higher-order s...

Definition of NASTRAN sets by use of parametric geometry

NASA Technical Reports Server (NTRS)

Baughn, Terry V.; Tiv, Mehran

1989-01-01

Many finite element preprocessors describe finite element model geometry with points, lines, surfaces and volumes. One method for describing these basic geometric entities is by use of parametric cubics which are useful for representing complex shapes. The lines, surfaces and volumes may be discretized for follow on finite element analysis. The ability to limit or selectively recover results from the finite element model is extremely important to the analyst. Equally important is the ability to easily apply boundary conditions. Although graphical preprocessors have made these tasks easier, model complexity may not lend itself to easily identify a group of grid points desired for data recovery or application of constraints. A methodology is presented which makes use of the assignment of grid point locations in parametric coordinates. The parametric coordinates provide a convenient ordering of the grid point locations and a method for retrieving the grid point ID's from the parent geometry. The selected grid points may then be used for the generation of the appropriate set and constraint cards.

Electron-phonon coupling from finite differences

NASA Astrophysics Data System (ADS)

Monserrat, Bartomeu

2018-02-01

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Uranium phase diagram from first principles

NASA Astrophysics Data System (ADS)

Yanilkin, Alexey; Kruglov, Ivan; Migdal, Kirill; Oganov, Artem; Pokatashkin, Pavel; Sergeev, Oleg

2017-06-01

The work is devoted to the investigation of uranium phase diagram up to pressure of 1 TPa and temperature of 15 kK based on density functional theory. First of all the comparison of pseudopotential and full potential calculations is carried out for different uranium phases. In the second step, phase diagram at zero temperature is investigated by means of program USPEX and pseudopotential calculations. Stable and metastable structures with close energies are selected. In order to obtain phase diagram at finite temperatures the preliminary selection of stable phases is made by free energy calculation based on small displacement method. For remaining candidates the accurate values of free energy are obtained by means of thermodynamic integration method (TIM). For this purpose quantum molecular dynamics are carried out at different volumes and temperatures. Interatomic potentials based machine learning are developed in order to consider large systems and long times for TIM. The potentials reproduce the free energy with the accuracy 1-5 meV/atom, which is sufficient for prediction of phase transitions. The equilibrium curves of different phases are obtained based on free energies. Melting curve is calculated by modified Z-method with developed potential.

Simulations of nanocrystals under pressure: combining electronic enthalpy and linear-scaling density-functional theory.

PubMed

Corsini, Niccolò R C; Greco, Andrea; Hine, Nicholas D M; Molteni, Carla; Haynes, Peter D

2013-08-28

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)], it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.

Simulations of nanocrystals under pressure: Combining electronic enthalpy and linear-scaling density-functional theory

NASA Astrophysics Data System (ADS)

Corsini, Niccolò R. C.; Greco, Andrea; Hine, Nicholas D. M.; Molteni, Carla; Haynes, Peter D.

2013-08-01

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)], 10.1103/PhysRevLett.94.145501, it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.

Control volume analyses of glottal flow using a fully-coupled numerical fluid-structure interaction model

NASA Astrophysics Data System (ADS)

Yang, Jubiao; Krane, Michael; Zhang, Lucy

2013-11-01

Vocal fold vibrations and the glottal jet are successfully simulated using the modified Immersed Finite Element method (mIFEM), a fully coupled dynamics approach to model fluid-structure interactions. A self-sustained and steady vocal fold vibration is captured given a constant pressure input at the glottal entrance. The flow rates at different axial locations in the glottis are calculated, showing small variations among them due to the vocal fold motion and deformation. To further facilitate the understanding of the phonation process, two control volume analyses, specifically with Bernoulli's equation and Newton's 2nd law, are carried out for the glottal flow based on the simulation results. A generalized Bernoulli's equation is derived to interpret the correlations between the velocity and pressure temporally and spatially along the center line which is a streamline using a half-space model with symmetry boundary condition. A specialized Newton's 2nd law equation is developed and divided into terms to help understand the driving mechanism of the glottal flow.

A Lagrangian discontinuous Galerkin hydrodynamic method

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

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

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

Ahmed, A.; Chadwick, T.; Makhlouf, M.

This paper deals with the effects of various solidification variables such as cooling rate, temperature gradient, solidification rate, etc. on the microstructure and shrinkage defects in aluminum alloy (A356) castings. The effects are first predicted using commercial solidification modeling softwares and then verified experimentally. For this work, the authors are considering a rectangular bar cast in a sand mold. Simulation is performed using SIMULOR, a finite volume based casting simulation program. Microstructural variables such as dendritic arm spacing (DAS) and defects (percentage porosity) are calculated from the temperature fields, cooling rate, solidification time, etc. predicted by the computer softwares. Themore » same variables are then calculated experimentally in the foundry. The test piece is cast in a resin (Sodium Silicate) bonded sand mold and the DAS and porosity variables are calculated using Scanning Electron Microscopy and Image Analysis. The predictions from the software are compared with the experimental results. The results are presented and critically analyzed to determine the quality of the predicted results. The usefulness of the commercial solidification modeling softwares as a tool for the foundry are also discussed.« less

Pinning Susceptibility at the Jamming Transition

NASA Astrophysics Data System (ADS)

Graves, Amy; Padgett, Elliot; Goodrich, Carl; Liu, Andrea

2013-03-01

Jamming in the presence of fixed or pinned obstacles, representing quenched disorder, is a situation of both practical and theoretical interest. We study the jamming of soft, bidisperse discs in which a subset of discs are pinned while the remaining particles equilibrate around them at a given volume fraction. The obstacles provide a supporting structure for the jammed configuration which not only lowers the jamming threshold, ϕJ, but affects the coordination number and other parameters of interest as the critical point is approached. In the limit of low obstacle density, one can calculate a pinning susceptibility χP, analogous to the magnetic susceptibility, with obstacle density playing the role of the magnetic field. The pinning susceptibility is thus expected to diverge in the thermodynamic limit as χP ~| ϕ -ϕJ | -γP . Finite-size scaling calculations allow us to confirm this and calculate the critical exponent, γP. Acknowledgement is made to the Donors of the Petrolium Research Fund administered by the American Chemical Society, Swarthmore College's Eugene M. Lang Faculty Fellowship, NSF grant DMR-1062638 and DOE grant DE-FG02-05ER46199.

A Lagrangian discontinuous Galerkin hydrodynamic method

DOE PAGES

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

2017-12-11

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

Closed-form analysis of fiber-matrix interface stresses under thermo-mechanical loadings

NASA Technical Reports Server (NTRS)

Naik, Rajiv A.; Crews, John H., Jr.

1992-01-01

Closed form techniques for calculating fiber matrix (FM) interface stresses, using repeating square and diamond regular arrays, were presented for a unidirectional composite under thermo-mechanical loadings. An Airy's stress function micromechanics approach from the literature, developed for calculating overall composite moduli, was extended in the present study to compute FM interface stresses for a unidirectional graphite/epoxy (AS4/3501-6) composite under thermal, longitudinal, transverse, transverse shear, and longitudinal shear loadings. Comparison with finite element results indicate excellent agreement of the FM interface stresses for the square array. Under thermal and longitudinal loading, the square array has the same FM peak stresses as the diamond array. The square array predicted higher stress concentrations under transverse normal and longitudinal shear loadings than the diamond array. Under transverse shear loading, the square array had a higher stress concentration while the diamond array had a higher radial stress concentration. Stress concentration factors under transverse shear and longitudinal shear loadings were very sensitive to fiber volume fraction. The present analysis provides a simple way to calculate accurate FM interface stresses for both the square and diamond array configurations.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

Simulation of all-scale atmospheric dynamics on unstructured meshes

NASA Astrophysics Data System (ADS)

Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng

2016-10-01

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

The Influence of Reconstruction Kernel on Bone Mineral and Strength Estimates Using Quantitative Computed Tomography and Finite Element Analysis.

PubMed

Michalski, Andrew S; Edwards, W Brent; Boyd, Steven K

2017-10-17

Quantitative computed tomography has been posed as an alternative imaging modality to investigate osteoporosis. We examined the influence of computed tomography convolution back-projection reconstruction kernels on the analysis of bone quantity and estimated mechanical properties in the proximal femur. Eighteen computed tomography scans of the proximal femur were reconstructed using both a standard smoothing reconstruction kernel and a bone-sharpening reconstruction kernel. Following phantom-based density calibration, we calculated typical bone quantity outcomes of integral volumetric bone mineral density, bone volume, and bone mineral content. Additionally, we performed finite element analysis in a standard sideways fall on the hip loading configuration. Significant differences for all outcome measures, except integral bone volume, were observed between the 2 reconstruction kernels. Volumetric bone mineral density measured using images reconstructed by the standard kernel was significantly lower (6.7%, p < 0.001) when compared with images reconstructed using the bone-sharpening kernel. Furthermore, the whole-bone stiffness and the failure load measured in images reconstructed by the standard kernel were significantly lower (16.5%, p < 0.001, and 18.2%, p < 0.001, respectively) when compared with the image reconstructed by the bone-sharpening kernel. These data suggest that for future quantitative computed tomography studies, a standardized reconstruction kernel will maximize reproducibility, independent of the use of a quantitative calibration phantom. Copyright © 2017 The International Society for Clinical Densitometry. Published by Elsevier Inc. All rights reserved.

A normal mode treatment of semi-diurnal body tides on an aspherical, rotating and anelastic Earth

NASA Astrophysics Data System (ADS)

Lau, Harriet C. P.; Yang, Hsin-Ying; Tromp, Jeroen; Mitrovica, Jerry X.; Latychev, Konstantin; Al-Attar, David

2015-08-01

Normal mode treatments of the Earth's body tide response were developed in the 1980s to account for the effects of Earth rotation, ellipticity, anelasticity and resonant excitation within the diurnal band. Recent space-geodetic measurements of the Earth's crustal displacement in response to luni-solar tidal forcings have revealed geographical variations that are indicative of aspherical deep mantle structure, thus providing a novel data set for constraining deep mantle elastic and density structure. In light of this, we make use of advances in seismic free oscillation literature to develop a new, generalized normal mode theory for the tidal response within the semi-diurnal and long-period tidal band. Our theory involves a perturbation method that permits an efficient calculation of the impact of aspherical structure on the tidal response. In addition, we introduce a normal mode treatment of anelasticity that is distinct from both earlier work in body tides and the approach adopted in free oscillation seismology. We present several simple numerical applications of the new theory. First, we compute the tidal response of a spherically symmetric, non-rotating, elastic and isotropic Earth model and demonstrate that our predictions match those based on standard Love number theory. Second, we compute perturbations to this response associated with mantle anelasticity and demonstrate that the usual set of seismic modes adopted for this purpose must be augmented by a family of relaxation modes to accurately capture the full effect of anelasticity on the body tide response. Finally, we explore aspherical effects including rotation and we benchmark results from several illustrative case studies of aspherical Earth structure against independent finite-volume numerical calculations of the semi-diurnal body tide response. These tests confirm the accuracy of the normal mode methodology to at least the level of numerical error in the finite-volume predictions. They also demonstrate that full coupling of normal modes, rather than group coupling, is necessary for accurate predictions of the body tide response.

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

NASA Astrophysics Data System (ADS)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

A combined registration and finite element analysis method for fast estimation of intraoperative brain shift; phantom and animal model study.

PubMed

Mohammadi, Amrollah; Ahmadian, Alireza; Rabbani, Shahram; Fattahi, Ehsan; Shirani, Shapour

2017-12-01

Finite element models for estimation of intraoperative brain shift suffer from huge computational cost. In these models, image registration and finite element analysis are two time-consuming processes. The proposed method is an improved version of our previously developed Finite Element Drift (FED) registration algorithm. In this work the registration process is combined with the finite element analysis. In the Combined FED (CFED), the deformation of whole brain mesh is iteratively calculated by geometrical extension of a local load vector which is computed by FED. While the processing time of the FED-based method including registration and finite element analysis was about 70 s, the computation time of the CFED was about 3.2 s. The computational cost of CFED is almost 50% less than similar state of the art brain shift estimators based on finite element models. The proposed combination of registration and structural analysis can make the calculation of brain deformation much faster. Copyright © 2016 John Wiley & Sons, Ltd.

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Study on Edge Thickening Flow Forming Using the Finite Elements Analysis

NASA Astrophysics Data System (ADS)

Kim, Young Jin; Park, Jin Sung; Cho, Chongdu

2011-08-01

This study is to examine the forming features of flow stress property and the incremental forming method with increasing the thickness of material. Recently, the optimized forming method is widely studied through the finite element analysis to optimize forming process conditions in many different forming fields. The optimal forming method should be adopted to meet geometric requirements as the reduction in volume per unit length of material such as forging, rolling, spinning etc. However conventional studies have not dealt with issue regarding volume per unit length. For the study we use the finite element method and model a gear part of an automotive engine flywheel as the study model, which is a weld assembly of a plate and a gear with respective different thickness. In simulation of the present study, a optimized forming condition for gear machining, considering the thickness of the outer edge of flywheel is studied using the finite elements analysis for the increasing thickness of the forming method. It is concluded from the study that forming method to increase the thickness per unit length for gear machining is reasonable using the finite elements analysis and forming test.

Method for calculating the aerodynamic loading on an oscillating finite wing in subsonic and sonic flow

NASA Technical Reports Server (NTRS)

Runyan, Harry L; Woolston, Donald S

1957-01-01

A method is presented for calculating the loading on a finite wing oscillating in subsonic or sonic flow. The method is applicable to any plan form and may be used for determining the loading on deformed wings. The procedure is approximate and requires numerical integration over the wing surface.

Solution of the neutronics code dynamic benchmark by finite element method

NASA Astrophysics Data System (ADS)

Avvakumov, A. V.; Vabishchevich, P. N.; Vasilev, A. O.; Strizhov, V. F.

2016-10-01

The objective is to analyze the dynamic benchmark developed by Atomic Energy Research for the verification of best-estimate neutronics codes. The benchmark scenario includes asymmetrical ejection of a control rod in a water-type hexagonal reactor at hot zero power. A simple Doppler feedback mechanism assuming adiabatic fuel temperature heating is proposed. The finite element method on triangular calculation grids is used to solve the three-dimensional neutron kinetics problem. The software has been developed using the engineering and scientific calculation library FEniCS. The matrix spectral problem is solved using the scalable and flexible toolkit SLEPc. The solution accuracy of the dynamic benchmark is analyzed by condensing calculation grid and varying degree of finite elements.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

Transport properties of bilayer graphene due to charged impurity scattering: Temperature-dependent screening and substrate effects

NASA Astrophysics Data System (ADS)

Linh, Dang Khanh; Khanh, Nguyen Quoc

2018-03-01

We calculate the zero-temperature conductivity of bilayer graphene (BLG) impacted by Coulomb impurity scattering using four different screening models: unscreened, Thomas-Fermi (TF), overscreened and random phase approximation (RPA). We also calculate the conductivity and thermal conductance of BLG using TF, zero- and finite-temperature RPA screening functions. We find large differences between the results of the models and show that TF and finite-temperature RPA give similar results for diffusion thermopower Sd. Using the finite-temperature RPA, we calculate temperature and density dependence of Sd in BLG on SiO2, HfO2 substrates and suspended BLG for different values of interlayer distance c and distance between the first layer and the substrate d.

Quality-assurance study of the special - purpose finite-element program - SPECTROM: I. Thermal, thermoelastic, and viscoelastic problems. [Comparison with MARC-CDC

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

Wagner, R.A.

1980-12-01

This comparison study involves a preliminary verification of finite element calculations. The methodology of the comparison study consists of solving four example problems with both the SPECTROM finite element program and the MARC-CDC general purpose finite element program. The results show close agreement for all example problems.

A modified 3D algorithm for road traffic noise attenuation calculations in large urban areas.

PubMed

Wang, Haibo; Cai, Ming; Yao, Yifan

2017-07-01

The primary objective of this study is the development and application of a 3D road traffic noise attenuation calculation algorithm. First, the traditional empirical method does not address problems caused by non-direct occlusion by buildings and the different building heights. In contrast, this study considers the volume ratio of the buildings and the area ratio of the projection of buildings adjacent to the road. The influence of the ground affection is analyzed. The insertion loss due to barriers (infinite length and finite barriers) is also synthesized in the algorithm. Second, the impact of different road segmentation is analyzed. Through the case of Pearl River New Town, it is recommended that 5° is the most appropriate scanning angle as the computational time is acceptable and the average error is approximately 3.1 dB. In addition, the algorithm requires only 1/17 of the time that the beam tracking method requires at the cost of more imprecise calculation results. Finally, the noise calculation for a large urban area with a high density of buildings shows the feasibility of the 3D noise attenuation calculation algorithm. The algorithm is expected to be applied in projects requiring large area noise simulations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Electronic and thermodynamic properties of layered Hf2Sfrom first-principles calculations

NASA Astrophysics Data System (ADS)

Nandadasa, Chandani; Yoon, Mina; Kim, Seong-Gon; Erwin, Steve; Kim, Sungho; Kim, Sung Wng; Lee, Kimoon

Theoretically we explored two stable phases of inorganic fullerene-like structure of the layered dihafnium sulfide (Hf2 S) . We investigated structural and electronic properties of the two phases of Hf2 S by using first-principles calculations. Our calculation identifies experimentally observed anti-NbS2 structure of Hf2 S . Our electronic calculation results indicate that the density of states of anti- NbS2 structure of Hf2 S at fermi level is less than that of the other phase of Hf2 S . To study the relative stability of different phases at finite temperature Helmholtz free energies of two phases are obtained using density functional theory and density functional perturbation theory. The free energy of the anti-NbS2 structure of Hf2 S always lies below the free energy of the other phase by confirming the most stable structure of Hf2 S . The phonon dispersion, phonon density of states including partial density of states and total density of states are obtained within density functional perturbation theory. Our calculated zero-pressure phonon dispersion curves confirm that the thermodynamic stability of Hf2 S structures. For further investigation of thermodynamic properties, the temperature dependency of thermal expansion, heat capacities at constant pressure and volume are evaluated within the quasiharmonic approximations (QHA).

Structural Acoustic Physics Based Modeling of Curved Composite Shells

DTIC Science & Technology

2017-09-19

Results show that the finite element computational models accurately match analytical calculations, and that the composite material studied in this...products. 15. SUBJECT TERMS Finite Element Analysis, Structural Acoustics, Fiber-Reinforced Composites, Physics-Based Modeling 16. SECURITY...2 4 FINITE ELEMENT MODEL DESCRIPTION

Finite element analysis of thrust angle contact ball slewing bearing

NASA Astrophysics Data System (ADS)

Deng, Biao; Guo, Yuan; Zhang, An; Tang, Shengjin

2017-12-01

In view of the large heavy slewing bearing no longer follows the rigid ring hupothesis under the load condition, the entity finite element model of thrust angular contact ball bearing was established by using finite element analysis software ANSYS. The boundary conditions of the model were set according to the actual condition of slewing bearing, the internal stress state of the slewing bearing was obtained by solving and calculation, and the calculated results were compared with the numerical results based on the rigid ring assumption. The results show that more balls are loaded in the result of finite element method, and the maximum contact stresses between the ball and raceway have some reductions. This is because the finite element method considers the ferrule as an elastic body. The ring will produce structure deformation in the radial plane when the heavy load slewing bearings are subjected to external loads. The results of the finite element method are more in line with the actual situation of the slewing bearing in the engineering.

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Exact solutions of a two parameter flux model and cryobiological applications.

PubMed

Benson, James D; Chicone, Carmen C; Critser, John K

2005-06-01

Solute-solvent transmembrane flux models are used throughout biological sciences with applications in plant biology, cryobiology (transplantation and transfusion medicine), as well as circulatory and kidney physiology. Using a standard two parameter differential equation model of solute and solvent transmembrane flux described by Jacobs [The simultaneous measurement of cell permeability to water and to dissolved substances, J. Cell. Comp. Physiol. 2 (1932) 427-444], we determine the functions that describe the intracellular water volume and moles of intracellular solute for every time t and every set of initial conditions. Here, we provide several novel biophysical applications of this theory to important biological problems. These include using this result to calculate the value of cell volume excursion maxima and minima along with the time at which they occur, a novel result that is of significant relevance to the addition and removal of permeating solutes during cryopreservation. We also present a methodology that produces extremely accurate sum of squares estimates when fitting data for cellular permeability parameter values. Finally, we show that this theory allows a significant increase in both accuracy and speed of finite element methods for multicellular volume simulations, which has critical clinical biophysical applications in cryosurgical approaches to cancer treatment.

Numerical Modeling of Cavitating Venturi: A Flow Control Element of Propulsion System

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Saxon, Jeff (Technical Monitor)

2002-01-01

In a propulsion system, the propellant flow and mixture ratio could be controlled either by variable area flow control valves or by passive flow control elements such as cavitating venturies. Cavitating venturies maintain constant propellant flowrate for fixed inlet conditions (pressure and temperature) and wide range of outlet pressures, thereby maintain constant, engine thrust and mixture ratio. The flowrate through the venturi reaches a constant value and becomes independent of outlet pressure when the pressure at throat becomes equal to vapor pressure. In order to develop a numerical model of propulsion system, it is necessary to model cavitating venturies in propellant feed systems. This paper presents a finite volume model of flow network of a cavitating venturi. The venturi was discretized into a number of control volumes and mass, momentum and energy conservation equations in each control volume are simultaneously solved to calculate one-dimensional pressure, density, and flowrate and temperature distribution. The numerical model predicts cavitations at the throat when outlet pressure was gradually reduced. Once cavitation starts, with further reduction of downstream pressure, no change in flowrate is found. The numerical predictions have been compared with test data and empirical equation based on Bernoulli's equation.

One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization

NASA Astrophysics Data System (ADS)

Zacharias, Marios; Giustino, Feliciano

Electron-phonon interactions are of fundamental importance in the study of the optical properties of solids at finite temperatures. Here we present a new first-principles computational technique based on the Williams-Lax theory for performing predictive calculations of the optical spectra, including quantum zero-point renormalization and indirect absorption. The calculation of the Williams-Lax optical spectra is computationally challenging, as it involves the sampling over all possible nuclear quantum states. We develop an efficient computational strategy for performing ''one-shot'' finite-temperature calculations. These require only a single optimal configuration of the atomic positions. We demonstrate our methodology for the case of Si, C, and GaAs, yielding absorption coefficients in good agreement with experiment. This work opens the way for systematic calculations of optical spectra at finite temperature. This work was supported by the UK EPSRC (EP/J009857/1 and EP/M020517/) and the Leverhulme Trust (RL-2012-001), and the Graphene Flagship (EU-FP7-604391).

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

DOE PAGES

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

2017-04-18

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

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

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

Correlation of predicted and measured thermal stresses on an advanced aircraft structure with dissimilar materials. [hypersonic heating simulation

NASA Technical Reports Server (NTRS)

Jenkins, J. M.

1979-01-01

Additional information was added to a growing data base from which estimates of finite element model complexities can be made with respect to thermal stress analysis. The manner in which temperatures were smeared to the finite element grid points was examined from the point of view of the impact on thermal stress calculations. The general comparison of calculated and measured thermal stresses is guite good and there is little doubt that the finite element approach provided by NASTRAN results in correct thermal stress calculations. Discrepancies did exist between measured and calculated values in the skin and the skin/frame junctures. The problems with predicting skin thermal stress were attributed to inadequate temperature inputs to the structural model rather than modeling insufficiencies. The discrepancies occurring at the skin/frame juncture were most likely due to insufficient modeling elements rather than temperature problems.

Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

NASA Technical Reports Server (NTRS)

Yeh, Kao-San; Lin, Shian-Jiann; Rood, Richard B.

2002-01-01

We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

Coupled discrete element and finite volume solution of two classical soil mechanics problems

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

Chen, Feng; Drumm, Eric; Guiochon, Georges A

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier-Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAMmore » for the computational fluid dynamics. The particle-fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.« less

Minimizing finite-volume discretization errors on polyhedral meshes

NASA Astrophysics Data System (ADS)

Mouly, Quentin; Evrard, Fabien; van Wachem, Berend; Denner, Fabian

2017-11-01

Tetrahedral meshes are widely used in CFD to simulate flows in and around complex geometries, as automatic generation tools now allow tetrahedral meshes to represent arbitrary domains in a relatively accessible manner. Polyhedral meshes, however, are an increasingly popular alternative. While tetrahedron have at most four neighbours, the higher number of neighbours per polyhedral cell leads to a more accurate evaluation of gradients, essential for the numerical resolution of PDEs. The use of polyhedral meshes, nonetheless, introduces discretization errors for finite-volume methods: skewness and non-orthogonality, which occur with all sorts of unstructured meshes, as well as errors due to non-planar faces, specific to polygonal faces with more than three vertices. Indeed, polyhedral mesh generation algorithms cannot, in general, guarantee to produce meshes free of non-planar faces. The presented work focuses on the quantification and optimization of discretization errors on polyhedral meshes in the context of finite-volume methods. A quasi-Newton method is employed to optimize the relevant mesh quality measures. Various meshes are optimized and CFD results of cases with known solutions are presented to assess the improvements the optimization approach can provide.

Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume

DOE PAGES

Hansen, Maxwell; Briceno, Raul

2015-10-01

We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volumemore » $$\\textbf{0}\\rightarrow\\textbf{2}$$ and $$\\textbf{1}\\rightarrow\\textbf{2}$$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $$N+\\mathcal{J}~\\rightarrow~(N\\pi,N\\eta,N\\eta',\\Sigma K,\\Lambda K)$$ transitions, where $$\\mathcal{J}$$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.« less

Second order tensor finite element

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

1990-01-01

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

Hybrid finite volume-finite element model for the numerical analysis of furrow irrigation and fertigation

USDA-ARS?s Scientific Manuscript database

Although slowly abandoned in developed countries, furrow irrigation systems continue to be a dominant irrigation method in developing countries. Numerical models represent powerful tools to assess irrigation and fertigation efficiency. While several models have been proposed in the past, the develop...

Very Large Data Volumes Analysis of Collaborative Systems with Finite Number of States

ERIC Educational Resources Information Center

Ivan, Ion; Ciurea, Cristian; Pavel, Sorin

2010-01-01

The collaborative system with finite number of states is defined. A very large database is structured. Operations on large databases are identified. Repetitive procedures for collaborative systems operations are derived. The efficiency of such procedures is analyzed. (Contains 6 tables, 5 footnotes and 3 figures.)

Boundary Element Method in a Self-Gravitating Elastic Half-Space and Its Application to Deformation Induced by Magma Chambers

NASA Astrophysics Data System (ADS)

Fang, M.; Hager, B. H.

2014-12-01

In geophysical applications the boundary element method (BEM) often carries the essential physics in addition to being an efficient numerical scheme. For use of the BEM in a self-gravitating uniform half-space, we made extra effort and succeeded in deriving the fundamental solution analytically in closed-form. A problem that goes deep into the heart of the classic BEM is encountered when we try to apply the new fundamental solution in BEM for deformation field induced by a magma chamber or a fluid-filled reservoir. The central issue of the BEM is the singular integral arising from determination of the boundary values. A widely employed technique is to rescale the singular boundary point into a small finite volume and then shrink it to extract the limits. This operation boils down to the calculation of the so-called C-matrix. Authors in the past take the liberty of either adding or subtracting a small volume. By subtracting a small volume, the C-matrix is (1/2)I on a smooth surface, where I is the identity matrix; by adding a small volume, we arrive at the same C-matrix in the form of I - (1/2)I. This evenness is a result of the spherical symmetry of Kelvin's fundamental solution employed. When the spherical symmetry is broken by gravity, the C-matrix is polarized. And we face the choice between right and wrong, for adding and subtracting a small volume yield different C-matrices. Close examination reveals that both derivations, addition and subtraction of a small volume, are ad hoc. To resolve the issue we revisit the Somigliana identity with a new derivation and careful step-by-step anatomy. The result proves that even though both adding and subtracting a small volume appear to twist the original boundary, only addition essentially modifies the original boundary and consequently modifies the physics of the original problem in a subtle way. The correct procedure is subtraction. We complete a new BEM theory by introducing in full analytical form what we call the singular stress tensor for the fundamental solution. We partition the stress tensor of the fundamental solution into a singular part and a regular part. In this way all singular integrals systematically shift into the easy singular stress tensor. Applications of this new BEM to deformation and gravitational perturbation induced by magma chambers of finite volume will be presented.

Mechanical Strength of the Proximal Femur After Arthroscopic Osteochondroplasty for Femoroacetabular Impingement: Finite Element Analysis and 3-Dimensional Image Analysis.

PubMed

Oba, Masatoshi; Kobayashi, Naomi; Inaba, Yutaka; Choe, Hyonmin; Ike, Hiroyuki; Kubota, So; Saito, Tomoyuki

2018-06-21

To examine the influence of femoral neck resection on the mechanical strength of the proximal femur in actual surgery. Eighteen subjects who received arthroscopic cam resection for cam-type femoroacetabular impingement (FAI) were included. Finite element analyses (FEAs) were performed to calculate changes in simulative fracture load between pre- and postoperative femur models. The finite element femur models were constructed from computed tomographic images; thus, the models represented the shape of the original femur, including the bone resection site. Three-dimensional image analysis of the bone resection site was performed to identify morphometric factors that affect strength in the postoperative femur model. Four oblique sagittal planes running perpendicular to the femoral neck axis were used as reference planes to measure the bone resection site. At the transcervical reference plane, both the bone resection depth and the cross-sectional area at the resection site correlated strongly with postoperative changes in the simulated fracture load (R 2  = 0.6, P = .0001). However, only resection depth was significantly correlated with the simulated fracture load at the reference plane for the head-neck junction. The resected bone volume did not correlate with the postoperative changes in the simulated fracture load. The results of our FEA suggest that the bone resection depth measured at the head-neck junction and transcervical reference plane correlates with fracture risk after osteochondroplasty. By contrast, bone resection at more proximal areas did not have a significant effect on the postoperative femur model strength in our FEA. The total volume of resected bone was also not significantly correlated with postoperative changes in femur model strength. This biomechanical study using FEA suggest that there is a risk of femoral neck fracture after arthroscopic cam resection, particularly when the resected lesion is located distally. Copyright © 2018 Arthroscopy Association of North America. Published by Elsevier Inc. All rights reserved.

Three-Dimensional Analysis of Voids in AM60B Magnesium Tensile Bars Using Computed Tomography Imagery

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

Waters, A M

2001-05-01

In an effort to increase automobile fuel efficiency as well as decrease the output of harmful greenhouse gases, the automotive industry has recently shown increased interest in cast light metals such as magnesium alloys in an effort to increase weight savings. Currently several magnesium alloys such as AZ91 and AM60B are being used in structural applications for automobiles. However, these magnesium alloys are not as well characterized as other commonly used structural metals such as aluminum. This dissertation presents a methodology to nondestructively quantify damage accumulation due to void behavior in three dimensions in die-cast magnesium AM60B tensile bars asmore » a function of mechanical load. Computed tomography data was acquired after tensile bars were loaded up to and including failure, and analyzed to characterize void behavior as it relates to damage accumulation. Signal and image processing techniques were used along with a cluster labeling routine to nondestructively quantify damage parameters in three dimensions. Void analyses were performed including void volume distribution characterization, nearest neighbor distance calculations, shape parameters, and volumetric renderings of voids in the alloy. The processed CT data was used to generate input files for use in finite element simulations, both two- and three-dimensional. The void analyses revealed that the overwhelming source of failure in each tensile bar was a ring of porosity within each bar, possibly due to a solidification front inherent to the casting process. The measured damage parameters related to void nucleation, growth, and coalescence were shown to contribute significantly to total damage accumulation. Void volume distributions were characterized using a Weibull function, and the spatial distributions of voids were shown to be clustered. Two-dimensional finite element analyses of the tensile bars were used to fine-tune material damage models and a three-dimensional mesh of an extracted portion of one tensile bar including voids was generated from CT data and used as input to a finite element analysis.« less

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

1996-01-01

Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

Nonlinear mesomechanics of composites with periodic microstructure

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Jordan, Eric H.; Freed, Alan D.

1989-01-01

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

Accurate green water loads calculation using naval hydro pack

NASA Astrophysics Data System (ADS)

Jasak, H.; Gatin, I.; Vukčević, V.

2017-12-01

An extensive verification and validation of Finite Volume based CFD software Naval Hydro based on foam-extend is presented in this paper for green water loads. Two-phase numerical model with advanced methods for treating the free surface is employed. Pressure loads on horizontal deck of Floating Production Storage and Offloading vessel (FPSO) model are compared to experimental results from [1] for three incident regular waves. Pressure peaks and integrals of pressure in time are measured on ten different locations on deck for each case. Pressure peaks and integrals are evaluated as average values among the measured incident wave periods, where periodic uncertainty is assessed for both numerical and experimental results. Spatial and temporal discretization refinement study is performed providing numerical discretization uncertainties.

Detailed Aerodynamic Analysis of a Shrouded Tail Rotor Using an Unstructured Mesh Flow Solver

NASA Astrophysics Data System (ADS)

Lee, Hee Dong; Kwon, Oh Joon

The detailed aerodynamics of a shrouded tail rotor in hover has been numerically studied using a parallel inviscid flow solver on unstructured meshes. The numerical method is based on a cell-centered finite-volume discretization and an implicit Gauss-Seidel time integration. The calculation was made for a single blade by imposing a periodic boundary condition between adjacent rotor blades. The grid periodicity was also imposed at the periodic boundary planes to avoid numerical inaccuracy resulting from solution interpolation. The results were compared with available experimental data and those from a disk vortex theory for validation. It was found that realistic three-dimensional modeling is important for the prediction of detailed aerodynamics of shrouded rotors including the tip clearance gap flow.

A closer look at the physical and optical properties of gold nanostars: an experimental and computational study

DOE PAGES

Tsoulos, T. V.; Han, L.; Weir, J.; ...

2017-02-22

A combined experimental and computational study was carried out to design a semi-empirical method to determine the volume, surface area, and extinction coefficients of gold nanostars. The values obtained were confirmed by reconstructing the nanostar 3D topography through high-tilt TEM tomography and introducing the finite elements in COMSOL Multiphysics through which we have also calculated the morphology-dependent extinction coefficient. We have, for the first time, modeled the heat losses of a real, experimentally synthesized nanostar, and found the plasmon resonances to be in excellent agreement with those obtained experimentally. Furthermore, we believe that our approach could substantially improve the applicabilitymore » of this remarkable nanomaterial.« less

CFD comparison with centrifugal compressor measurements on a wide operating range

NASA Astrophysics Data System (ADS)

Le Sausse, P.; Fabrie, P.; Arnou, D.; Clunet, F.

2013-04-01

Centrifugal compressors are widely used in industrial applications thanks to their high efficiency. They are able to provide a wide operating range before reaching the flow barrier or surge limits. Performances and range are described by compressor maps obtained experimentally. After a description of performance test rig, this article compares measured centrifugal compressor performances with computational fluid dynamics results. These computations are performed at steady conditions with R134a refrigerant as fluid. Navier-Stokes equations, coupled with k-ɛ turbulence model, are solved by the commercial software ANSYS-CFX by means of volume finite method. Input conditions are varied in order to calculate several speed lines. Theoretical isentropic efficiency and theoretical surge line are finally compared to experimental data.

On a phase field approach for martensitic transformations in a crystal plastic material at a loaded surface

NASA Astrophysics Data System (ADS)

Schmitt, Regina; Kuhn, Charlotte; Müller, Ralf

2017-07-01

A continuum phase field model for martensitic transformations is introduced, including crystal plasticity with different slip systems for the different phases. In a 2D setting, the transformation-induced eigenstrain is taken into account for two martensitic orientation variants. With aid of the model, the phase transition and its dependence on the volume change, crystal plastic material behavior, and the inheritance of plastic deformations from austenite to martensite are studied in detail. The numerical setup is motivated by the process of cryogenic turning. The resulting microstructure qualitatively coincides with an experimentally obtained martensite structure. For the numerical calculations, finite elements together with global and local implicit time integration scheme are employed.

Improved modeling of turbulent forced convection heat transfer in straight ducts

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

Rokni, M.; Sunden, B.

1999-08-01

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in their fully developed state at low Reynolds number. The authors have developed a low Reynolds number version of the nonlinear {kappa}-{epsilon} model combined with the heat flux models of simple eddy diffusivity (SED), low Reynolds number version of generalized gradient diffusion hypothesis (GGDH), and wealth {proportional_to} earning {times} time (WET) in general three-dimensional geometries. The numerical approach is based on the finite volume technique with a nonstaggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with the nonlinear {kappa}-{epsilon} model, combined with themore » Lam-Bremhorst and the Abe-Kondoh-Nagano damping functions for low Reynolds numbers.« less

A closer look at the physical and optical properties of gold nanostars: an experimental and computational study

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

Tsoulos, T. V.; Han, L.; Weir, J.

A combined experimental and computational study was carried out to design a semi-empirical method to determine the volume, surface area, and extinction coefficients of gold nanostars. The values obtained were confirmed by reconstructing the nanostar 3D topography through high-tilt TEM tomography and introducing the finite elements in COMSOL Multiphysics through which we have also calculated the morphology-dependent extinction coefficient. We have, for the first time, modeled the heat losses of a real, experimentally synthesized nanostar, and found the plasmon resonances to be in excellent agreement with those obtained experimentally. Furthermore, we believe that our approach could substantially improve the applicabilitymore » of this remarkable nanomaterial.« less

Type curves for selected problems of flow to wells in confined aquifers

USGS Publications Warehouse

Reed, J.E.

1980-01-01

This report presents type curves and related material for 11 conditions of flow to wells m confined aquifers. These solutions, compiled from hydrologic literature, span an interval of time from Theis (1935) to Papadopulos, Bredehoeft, and Cooper (1973). Solutions are presented for constant discharge, constant drawdown, and variable discharge for pumping wells that fully penetrate leaky and nonleaky aquifers. Solutions for wells that partially penetrate leaky and nonleaky aquifers are included. Also, solutions are included for the effect of finite well radius and the sudden injection of a volume of water for nonleaky aquifers. Each problem includes the partial differential equation, boundary and initial conditions, and solutions. Programs in FORTRAN for calculating additional function values are included for most of the solutions.

Comparison of two- and three-dimensional Navier-Stokes solutions with NASA experimental data for CAST-10 airfoil

NASA Technical Reports Server (NTRS)

Swanson, R. Charles; Radespiel, Rolf; Mccormick, V. Edward

1989-01-01

The two-dimensional (2-D) and three-dimensional Navier-Stokes equations are solved for flow over a NAE CAST-10 airfoil model. Recently developed finite-volume codes that apply a multistage time stepping scheme in conjunction with steady state acceleration techniques are used to solve the equations. Two-dimensional results are shown for flow conditions uncorrected and corrected for wind tunnel wall interference effects. Predicted surface pressures from 3-D simulations are compared with those from 2-D calculations. The focus of the 3-D computations is the influence of the sidewall boundary layers. Topological features of the 3-D flow fields are indicated. Lift and drag results are compared with experimental measurements.

Implementation of the high-order schemes QUICK and LECUSSO in the COMMIX-1C Program

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

Sakai, K.; Sun, J.G.; Sha, W.T.

Multidimensional analysis computer programs based on the finite volume method, such as COMMIX-1C, have been commonly used to simulate thermal-hydraulic phenomena in engineering systems such as nuclear reactors. In COMMIX-1C, the first-order schemes with respect to both space and time are used. In many situations such as flow recirculations and stratifications with steep gradient of velocity and temperature fields, however, high-order difference schemes are necessary for an accurate prediction of the fields. For these reasons, two second-order finite difference numerical schemes, QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and LECUSSO (Local Exact Consistent Upwind Scheme of Second Order), have beenmore » implemented in the COMMIX-1C computer code. The formulations were derived for general three-dimensional flows with nonuniform grid sizes. Numerical oscillation analyses for QUICK and LECUSSO were performed. To damp the unphysical oscillations which occur in calculations with high-order schemes at high mesh Reynolds numbers, a new FRAM (Filtering Remedy and Methodology) scheme was developed and implemented. To be consistent with the high-order schemes, the pressure equation and the boundary conditions for all the conservation equations were also modified to be of second order. The new capabilities in the code are listed. Test calculations were performed to validate the implementation of the high-order schemes. They include the test of the one-dimensional nonlinear Burgers equation, two-dimensional scalar transport in two impinging streams, von Karmann vortex shedding, shear driven cavity flow, Couette flow, and circular pipe flow. The calculated results were compared with available data; the agreement is good.« less

Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media

NASA Astrophysics Data System (ADS)

Quintal, Beatriz; Steeb, Holger; Frehner, Marcel; Schmalholz, Stefan M.

2011-01-01

The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u - p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.

Critical influence of finite rate chemistry and unmixedness on ignition and combustion of supersonic H2-air streams

NASA Technical Reports Server (NTRS)

Evans, J. S.; Schexnayder, C. J., Jr.

1979-01-01

Good agreement has been obtained between published profiles of composition and pitot pressure and the calculated results from a computer program in which finite rate chemistry was used. Significant differences are noted between results calculated using 7 species and 8 reactions and those calculated using 12 species and 25 reactions. Differences are also found between results in which the effect of unmixedness on reaction in turbulent flow is applied or is not applied.

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

continuation of sources and geophones by finite difference (S-G finite - difference migration ), are relatively slow and dip-limited. Compared to S-G... finite - difference migration , the Kirchhoff integral implements prestack migration relatively efficiently and has no dip limitation. Liu .Mlodeling and...for modeling and migration . In this paper, a finite - difference algorithm is used to calculate traveltimes and amplitudes. With the help of

Stochastic properties of radiation-induced DSB: DSB distributions in large scale chromatin loops, the HPRT gene and within the visible volumes of DNA repair foci.

PubMed

Ponomarev, Artem L; Costes, Sylvain V; Cucinotta, Francis A

2008-11-01

We computed probabilities to have multiple double-strand breaks (DSB), which are produced in DNA on a regional scale, and not in close vicinity, in volumes matching the size of DNA damage foci, of a large chromatin loop, and in the physical volume of DNA containing the HPRT (human hypoxanthine phosphoribosyltransferase) locus. The model is based on a Monte Carlo description of DSB formation by heavy ions in the spatial context of the entire human genome contained within the cell nucleus, as well as at the gene sequence level. We showed that a finite physical volume corresponding to a visible DNA repair focus, believed to be associated with one DSB, can contain multiple DSB due to heavy ion track structure and the DNA supercoiled topography. A corrective distribution was introduced, which was a conditional probability to have excess DSB in a focus volume, given that there was already one present. The corrective distribution was calculated for 19.5 MeV/amu N ions, 3.77 MeV/amu alpha-particles, 1000 MeV/amu Fe ions, and X-rays. The corrected initial DSB yield from the experimental data on DNA repair foci was calculated. The DSB yield based on the corrective function converts the focus yield into the DSB yield, which is comparable with the DSB yield based on the earlier PFGE experiments. The distribution of DSB within the physical limits of the HPRT gene was analyzed by a similar method as well. This corrective procedure shows the applicability of the model and empowers the researcher with a tool to better analyze focus statistics. The model enables researchers to analyze the DSB yield based on focus statistics in real experimental situations that lack one-to-one focus-to-DSB correspondance.

Program Calculates Forces in Bolted Structural Joints

NASA Technical Reports Server (NTRS)

Buder, Daniel A.

2005-01-01

FORTRAN 77 computer program calculates forces in bolts in the joints of structures. This program is used in conjunction with the NASTRAN finite-element structural-analysis program. A mathematical model of a structure is first created by approximating its load-bearing members with representative finite elements, then NASTRAN calculates the forces and moments that each finite element contributes to grid points located throughout the structure. The user selects the finite elements that correspond to structural members that contribute loads to the joints of interest, and identifies the grid point nearest to each such joint. This program reads the pertinent NASTRAN output, combines the forces and moments from the contributing elements to determine the resultant force and moment acting at each proximate grid point, then transforms the forces and moments from these grid points to the centroids of the affected joints. Then the program uses these joint loads to obtain the axial and shear forces in the individual bolts. The program identifies which bolts bear the greatest axial and/or shear loads. The program also performs a fail-safe analysis in which the foregoing calculations are repeated for a sequence of cases in which each fastener, in turn, is assumed not to transmit an axial force.

Criteria for representing circular arc and sine wave spar webs by non-curved elements

NASA Technical Reports Server (NTRS)

Jenkins, J. M.

1979-01-01

The basic problem of how to simply represent a curved web of a spar in a finite element structural model was addressed. The ratio of flat web to curved web axial deformations and longitudinal rotations were calculated using NASTRAN models. Multiplying factors were developed from these calculations for various web thicknesses. These multiplying factors can be applied directly to the area and moment of inertia inputs of the finite element model. This allows the thermal stress relieving configurations of sine wave and circular arc webs to be simply accounted for in finite element structural models.

Computer program for calculation of complex chemical equilibrium compositions and applications. Part 1: Analysis

NASA Technical Reports Server (NTRS)

Gordon, Sanford; Mcbride, Bonnie J.

1994-01-01

This report presents the latest in a number of versions of chemical equilibrium and applications programs developed at the NASA Lewis Research Center over more than 40 years. These programs have changed over the years to include additional features and improved calculation techniques and to take advantage of constantly improving computer capabilities. The minimization-of-free-energy approach to chemical equilibrium calculations has been used in all versions of the program since 1967. The two principal purposes of this report are presented in two parts. The first purpose, which is accomplished here in part 1, is to present in detail a number of topics of general interest in complex equilibrium calculations. These topics include mathematical analyses and techniques for obtaining chemical equilibrium; formulas for obtaining thermodynamic and transport mixture properties and thermodynamic derivatives; criteria for inclusion of condensed phases; calculations at a triple point; inclusion of ionized species; and various applications, such as constant-pressure or constant-volume combustion, rocket performance based on either a finite- or infinite-chamber-area model, shock wave calculations, and Chapman-Jouguet detonations. The second purpose of this report, to facilitate the use of the computer code, is accomplished in part 2, entitled 'Users Manual and Program Description'. Various aspects of the computer code are discussed, and a number of examples are given to illustrate its versatility.

Numerical Simulations for Landing Gear Noise Generation and Radiation

NASA Technical Reports Server (NTRS)

Morris, Philip J.; Long, Lyle N.

2002-01-01

Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams -Hawkings (FW-H) equation. The time accurate flow data on the surface is obtained using a finite volume flow solver on an unstructured and. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Hawkings code are compared with direct calculations by the flow solver at several observer locations inside the computational domain. The permeable Ffowcs Williams-Hawkings surface predictions match those of the flow solver in the near-field. Far-field noise calculations coincide for both integration surfaces. The increase in drag observed between the two landing gear configurations is reflected in the sound pressure level and directivity mainly in the streamwise direction.

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 2: Unsteady Ducted Propfan Analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1991-01-01

The primary objective was the development of a time dependent 3-D Euler/Navier-Stokes aerodynamic analysis to predict unsteady compressible transonic flows about ducted and unducted propfan propulsion systems at angle of attack. The resulting computer codes are referred to as Advanced Ducted Propfan Analysis Codes (ADPAC). A computer program user's manual is presented for the ADPAC. Aerodynamic calculations were based on a four stage Runge-Kutta time marching finite volume solution technique with added numerical dissipation. A time accurate implicit residual smoothing operator was used for unsteady flow predictions. For unducted propfans, a single H-type grid was used to discretize each blade passage of the complete propeller. For ducted propfans, a coupled system of five grid blocks utilizing an embedded C grid about the cowl leading edge was used to discretize each blade passage. Grid systems were generated by a combined algebraic/elliptic algorithm developed specifically for ducted propfans. Numerical calculations were compared with experimental data for both ducted and unducted flows.

Monte Carlo simulation for kinetic chemotaxis model: An application to the traveling population wave

NASA Astrophysics Data System (ADS)

Yasuda, Shugo

2017-02-01

A Monte Carlo simulation of chemotactic bacteria is developed on the basis of the kinetic model and is applied to a one-dimensional traveling population wave in a microchannel. In this simulation, the Monte Carlo method, which calculates the run-and-tumble motions of bacteria, is coupled with a finite volume method to calculate the macroscopic transport of the chemical cues in the environment. The simulation method can successfully reproduce the traveling population wave of bacteria that was observed experimentally and reveal the microscopic dynamics of bacterium coupled with the macroscopic transports of the chemical cues and bacteria population density. The results obtained by the Monte Carlo method are also compared with the asymptotic solution derived from the kinetic chemotaxis equation in the continuum limit, where the Knudsen number, which is defined by the ratio of the mean free path of bacterium to the characteristic length of the system, vanishes. The validity of the Monte Carlo method in the asymptotic behaviors for small Knudsen numbers is numerically verified.

B{sub K} with two flavors of dynamical overlap fermions

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

Aoki, S.; Riken BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973; Fukaya, H.

2008-05-01

We present a two-flavor QCD calculation of B{sub K} on a 16{sup 3}x32 lattice at a{approx}0.12 fm (or equivalently a{sup -1}=1.67 GeV). Both valence and sea quarks are described by the overlap fermion formulation. The matching factor is calculated nonperturbatively with the so-called RI/MOM scheme. We find that the lattice data are well described by the next-to-leading order (NLO) partially quenched chiral perturbation theory (PQChPT) up to around a half of the strange quark mass (m{sub s}{sup phys}/2). The data at quark masses heavier than m{sub s}{sup phys}/2 are fitted including a part of next-to-next-to-leading order terms. We obtain B{submore » K}{sup MS}(2 GeV)=0.537(4)(40), where the first error is statistical and the second is an estimate of systematic uncertainties from finite volume, fixing topology, the matching factor, and the scale setting.« less

Charmed bottom baryon spectroscopy from lattice QCD

DOE PAGES

Brown, Zachary S.; Detmold, William; Meinel, Stefan; ...

2014-11-19

In this study, we calculate the masses of baryons containing one, two, or three heavy quarks using lattice QCD. We consider all possible combinations of charm and bottom quarks, and compute a total of 36 different states with J P = 1/2 + and J P = 3/2 +. We use domain-wall fermions for the up, down, and strange quarks, a relativistic heavy-quark action for the charm quarks, and nonrelativistic QCD for the bottom quarks. Our analysis includes results from two different lattice spacings and seven different pion masses. We perform extrapolations of the baryon masses to the continuum limitmore » and to the physical pion mass using SU(4|2) heavy-hadron chiral perturbation theory including 1/m Q and finite-volume effects. For the 14 singly heavy baryons that have already been observed, our results agree with the experimental values within the uncertainties. We compare our predictions for the hitherto unobserved states with other lattice calculations and quark-model studies.« less

Influence of Finite Element Software on Energy Release Rates Computed Using the Virtual Crack Closure Technique

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Goetze, Dirk; Ransom, Jonathon (Technical Monitor)

2006-01-01

Strain energy release rates were computed along straight delamination fronts of Double Cantilever Beam, End-Notched Flexure and Single Leg Bending specimens using the Virtual Crack Closure Technique (VCCT). Th e results were based on finite element analyses using ABAQUS# and ANSYS# and were calculated from the finite element results using the same post-processing routine to assure a consistent procedure. Mixed-mode strain energy release rates obtained from post-processing finite elem ent results were in good agreement for all element types used and all specimens modeled. Compared to previous studies, the models made of s olid twenty-node hexahedral elements and solid eight-node incompatible mode elements yielded excellent results. For both codes, models made of standard brick elements and elements with reduced integration did not correctly capture the distribution of the energy release rate acr oss the width of the specimens for the models chosen. The results suggested that element types with similar formulation yield matching results independent of the finite element software used. For comparison, m ixed-mode strain energy release rates were also calculated within ABAQUS#/Standard using the VCCT for ABAQUS# add on. For all specimens mod eled, mixed-mode strain energy release rates obtained from ABAQUS# finite element results using post-processing were almost identical to re sults calculated using the VCCT for ABAQUS# add on.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Calculation of dose distribution in compressible breast tissues using finite element modeling, Monte Carlo simulation and thermoluminescence dosimeters

NASA Astrophysics Data System (ADS)

Mohammadyari, Parvin; Faghihi, Reza; Mosleh-Shirazi, Mohammad Amin; Lotfi, Mehrzad; Rahim Hematiyan, Mohammad; Koontz, Craig; Meigooni, Ali S.

2015-12-01

Compression is a technique to immobilize the target or improve the dose distribution within the treatment volume during different irradiation techniques such as AccuBoost® brachytherapy. However, there is no systematic method for determination of dose distribution for uncompressed tissue after irradiation under compression. In this study, the mechanical behavior of breast tissue between compressed and uncompressed states was investigated. With that, a novel method was developed to determine the dose distribution in uncompressed tissue after irradiation of compressed breast tissue. Dosimetry was performed using two different methods, namely, Monte Carlo simulations using the MCNP5 code and measurements using thermoluminescent dosimeters (TLD). The displacement of the breast elements was simulated using a finite element model and calculated using ABAQUS software. From these results, the 3D dose distribution in uncompressed tissue was determined. The geometry of the model was constructed from magnetic resonance images of six different women volunteers. The mechanical properties were modeled by using the Mooney-Rivlin hyperelastic material model. Experimental dosimetry was performed by placing the TLD chips into the polyvinyl alcohol breast equivalent phantom. The results determined that the nodal displacements, due to the gravitational force and the 60 Newton compression forces (with 43% contraction in the loading direction and 37% expansion in the orthogonal direction) were determined. Finally, a comparison of the experimental data and the simulated data showed agreement within 11.5%  ±  5.9%.

Calculation of dose distribution in compressible breast tissues using finite element modeling, Monte Carlo simulation and thermoluminescence dosimeters.

PubMed

Mohammadyari, Parvin; Faghihi, Reza; Mosleh-Shirazi, Mohammad Amin; Lotfi, Mehrzad; Hematiyan, Mohammad Rahim; Koontz, Craig; Meigooni, Ali S

2015-12-07

Compression is a technique to immobilize the target or improve the dose distribution within the treatment volume during different irradiation techniques such as AccuBoost(®) brachytherapy. However, there is no systematic method for determination of dose distribution for uncompressed tissue after irradiation under compression. In this study, the mechanical behavior of breast tissue between compressed and uncompressed states was investigated. With that, a novel method was developed to determine the dose distribution in uncompressed tissue after irradiation of compressed breast tissue. Dosimetry was performed using two different methods, namely, Monte Carlo simulations using the MCNP5 code and measurements using thermoluminescent dosimeters (TLD). The displacement of the breast elements was simulated using a finite element model and calculated using ABAQUS software. From these results, the 3D dose distribution in uncompressed tissue was determined. The geometry of the model was constructed from magnetic resonance images of six different women volunteers. The mechanical properties were modeled by using the Mooney-Rivlin hyperelastic material model. Experimental dosimetry was performed by placing the TLD chips into the polyvinyl alcohol breast equivalent phantom. The results determined that the nodal displacements, due to the gravitational force and the 60 Newton compression forces (with 43% contraction in the loading direction and 37% expansion in the orthogonal direction) were determined. Finally, a comparison of the experimental data and the simulated data showed agreement within 11.5%  ±  5.9%.

Finite element analysis of notch behavior using a state variable constitutive equation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.

1985-01-01

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.

Three-body spectrum in a finite volume: The role of cubic symmetry

DOE PAGES

Doring, M.; Hammer, H. -W.; Mai, M.; ...

2018-06-15

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Three-body spectrum in a finite volume: The role of cubic symmetry

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

Doring, M.; Hammer, H. -W.; Mai, M.

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics.

PubMed

Brocchini, Maurizio

2013-12-08

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

PubMed Central

Brocchini, Maurizio

2013-01-01

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention. PMID:24353475

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

NASA Astrophysics Data System (ADS)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

DOE PAGES

Xia, Yidong; Wang, Chuanjin; Luo, Hong; ...

2015-12-15

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

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

Xia, Yidong; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

K-theory of locally finite graph C∗-algebras

NASA Astrophysics Data System (ADS)

Iyudu, Natalia

2013-09-01

We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).

Simulation of thin slot spirals and dual circular patch antennas using the finite element method with mixed elements

NASA Technical Reports Server (NTRS)

Gong, Jian; Volakis, John L.; Nurnberger, Michael W.

1995-01-01

This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.

Development of automatic visceral fat volume calculation software for CT volume data.

PubMed

Nemoto, Mitsutaka; Yeernuer, Tusufuhan; Masutani, Yoshitaka; Nomura, Yukihiro; Hanaoka, Shouhei; Miki, Soichiro; Yoshikawa, Takeharu; Hayashi, Naoto; Ohtomo, Kuni

2014-01-01

To develop automatic visceral fat volume calculation software for computed tomography (CT) volume data and to evaluate its feasibility. A total of 24 sets of whole-body CT volume data and anthropometric measurements were obtained, with three sets for each of four BMI categories (under 20, 20 to 25, 25 to 30, and over 30) in both sexes. True visceral fat volumes were defined on the basis of manual segmentation of the whole-body CT volume data by an experienced radiologist. Software to automatically calculate visceral fat volumes was developed using a region segmentation technique based on morphological analysis with CT value threshold. Automatically calculated visceral fat volumes were evaluated in terms of the correlation coefficient with the true volumes and the error relative to the true volume. Automatic visceral fat volume calculation results of all 24 data sets were obtained successfully and the average calculation time was 252.7 seconds/case. The correlation coefficients between the true visceral fat volume and the automatically calculated visceral fat volume were over 0.999. The newly developed software is feasible for calculating visceral fat volumes in a reasonable time and was proved to have high accuracy.

Evaluation of Kirkwood-Buff integrals via finite size scaling: a large scale molecular dynamics study

NASA Astrophysics Data System (ADS)

Dednam, W.; Botha, A. E.

2015-01-01

Solvation of bio-molecules in water is severely affected by the presence of co-solvent within the hydration shell of the solute structure. Furthermore, since solute molecules can range from small molecules, such as methane, to very large protein structures, it is imperative to understand the detailed structure-function relationship on the microscopic level. For example, it is useful know the conformational transitions that occur in protein structures. Although such an understanding can be obtained through large-scale molecular dynamic simulations, it is often the case that such simulations would require excessively large simulation times. In this context, Kirkwood-Buff theory, which connects the microscopic pair-wise molecular distributions to global thermodynamic properties, together with the recently developed technique, called finite size scaling, may provide a better method to reduce system sizes, and hence also the computational times. In this paper, we present molecular dynamics trial simulations of biologically relevant low-concentration solvents, solvated by aqueous co-solvent solutions. In particular we compare two different methods of calculating the relevant Kirkwood-Buff integrals. The first (traditional) method computes running integrals over the radial distribution functions, which must be obtained from large system-size NVT or NpT simulations. The second, newer method, employs finite size scaling to obtain the Kirkwood-Buff integrals directly by counting the particle number fluctuations in small, open sub-volumes embedded within a larger reservoir that can be well approximated by a much smaller simulation cell. In agreement with previous studies, which made a similar comparison for aqueous co-solvent solutions, without the additional solvent, we conclude that the finite size scaling method is also applicable to the present case, since it can produce computationally more efficient results which are equivalent to the more costly radial distribution function method.

Improved Algorithm For Finite-Field Normal-Basis Multipliers

NASA Technical Reports Server (NTRS)

Wang, C. C.

1989-01-01

Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

The basic reproductive number, R0, is one of the most important epidemiological quantities. R0 provides a threshold for elimination and determines when a disease can spread or when a disease will die out. Classically, R0 is calculated assuming an infinite population of identical hosts. Previous work has shown that heterogeneity in the host mixing rate increases R0 in an infinite population. However, it has been suggested that in a finite population, heterogeneity in the mixing rate may actually decrease the finite-population reproductive numbers. Here, we outline a framework for discussing different types of heterogeneity in disease parameters, and how these affect disease spread and control. We calculate "finite-population reproductive numbers" with different types of heterogeneity, and show that in a finite population, heterogeneity has complicated effects on the reproductive number. We find that simple heterogeneity decreases the finite-population reproductive number, whereas heterogeneity in the intrinsic mixing rate (which affects both infectiousness and susceptibility) increases the finite-population reproductive number when R0 is small relative to the size of the population and decreases the finite-population reproductive number when R0 is large relative to the size of the population. Although heterogeneity has complicated effects on the finite-population reproductive numbers, its implications for control are straightforward: when R0 is large relative to the size of the population, heterogeneity decreases the finite-population reproductive numbers, making disease control or elimination easier than predicted by R0. Copyright © 2016 Elsevier Ltd. All rights reserved.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

Statistical properties and condensate fluctuation of attractive Bose gas with finite number of particles

NASA Astrophysics Data System (ADS)

Bera, Sangita; Lekala, Mantile Leslie; Chakrabarti, Barnali; Bhattacharyya, Satadal; Rampho, Gaotsiwe Joel

2017-09-01

'We study the condensate fluctuation and several statistics of weakly interacting attractive Bose gas of 7 Li atoms in harmonic trap. Using exact recursion relation we calculate canonical ensemble partition function and study the thermal evolution of the condensate. As 7 Li condensate is associated with collapse, the number of condensate atom is truly finite and it facilitates to study the condensate in mesoscopic region. Being highly correlated, we utilize the two-body correlated basis function to get the many-body effective potential which is further used to calculate the energy levels. Taking van der Waals interaction as interatomic interaction we calculate several quantities like condensate fraction N, root-mean-square fluctuation δn0 and different orders of central moments. We observe the effect of finite size on the calculation of condensate fluctuations and the effect of attractive interaction over the noninteracting limit. We observe the depletion of the condensate with increase in temperature. The calculated moments nicely exhibit the mesoscopic effect. The sharp fall in the root-mean-square fluctuation near the critical point signifies the possibility of phase transition.

Calculation of reaction forces in the boiler supports using the method of equivalent stiffness of membrane wall.

PubMed

Sertić, Josip; Kozak, Dražan; Samardžić, Ivan

2014-01-01

The values of reaction forces in the boiler supports are the basis for the dimensioning of bearing steel structure of steam boiler. In this paper, the application of the method of equivalent stiffness of membrane wall is proposed for the calculation of reaction forces. The method of equalizing displacement, as the method of homogenization of membrane wall stiffness, was applied. On the example of "Milano" boiler, using the finite element method, the calculation of reactions in the supports for the real geometry discretized by the shell finite element was made. The second calculation was performed with the assumption of ideal stiffness of membrane walls and the third using the method of equivalent stiffness of membrane wall. In the third case, the membrane walls are approximated by the equivalent orthotropic plate. The approximation of membrane wall stiffness is achieved using the elasticity matrix of equivalent orthotropic plate at the level of finite element. The obtained results were compared, and the advantages of using the method of equivalent stiffness of membrane wall for the calculation of reactions in the boiler supports were emphasized.

Method for calculating internal radiation and ventilation with the ADINAT heat-flow code

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

Butkovich, T.R.; Montan, D.N.

1980-04-01

One objective of the spent fuel test in Climax Stock granite (SFTC) is to correctly model the thermal transport, and the changes in the stress field and accompanying displacements from the application of the thermal loads. We have chosen the ADINA and ADINAT finite element codes to do these calculations. ADINAT is a heat transfer code compatible to the ADINA displacement and stress analysis code. The heat flow problem encountered at SFTC requires a code with conduction, radiation, and ventilation capabilities, which the present version of ADINAT does not have. We have devised a method for calculating internal radiation andmore » ventilation with the ADINAT code. This method effectively reproduces the results from the TRUMP multi-dimensional finite difference code, which correctly models radiative heat transport between drift surfaces, conductive and convective thermal transport to and through air in the drifts, and mass flow of air in the drifts. The temperature histories for each node in the finite element mesh calculated with ADINAT using this method can be used directly in the ADINA thermal-mechanical calculation.« less

First-Principles Investigation of Mechanical and Thermodynamic Properties of Nickel Silicides at Finite Temperature

NASA Astrophysics Data System (ADS)

Wen, Zhiqin; Zhao, Yuhong; Hou, Hua; Chen, Liwen

2018-05-01

First-principles calculations are performed to investigate lattice parameters, elastic constants and 3D directional Young's modulus E of nickel silicides (i.e., β-Ni3Si, δ-Ni2Si, θ-Ni2Si, ɛ-NiSi, and θ-Ni2Si), and thermodynamic properties, such as the Debye temperature, heat capacity, volumetric thermal expansion coefficient, at finite temperature are also explored in combination with the quasi-harmonic Debye model. The calculated results are in a good agreement with available experimental and theoretical values. The five compounds demonstrate elastic anisotropy. The dependence on the direction of stiffness is the greatest for δ-Ni2Si and θ-Ni2Si, when the stress is applied, while that for β-Ni3Si is minimal. The bulk modulus B reduces with increasing temperature, implying that the resistance to volume deformation will weaken with temperature, and the capacity gradually descend for the compound sequence of β-Ni3Si > δ-Ni2Si > θ-Ni2Si > ɛ-NiSi > θ-Ni2Si. The temperature dependence of the Debye temperature ΘD is related to the change of lattice parameters, and ΘD gradually decreases for the compound sequence of ɛ-NiSi > β-Ni3Si > δ-Ni2Si > θ-Ni2Si > θ-Ni2Si. The volumetric thermal expansion coefficient αV, isochoric heat capacity and isobaric heat capacity C p of nickel silicides are proportional to T 3 at low temperature, subsequently, αV and C p show modest linear change at high temperature, whereas C v obeys the Dulong-Petit limit. In addition, β-Ni3Si has the largest capability to store or release heat at high temperature. From the perspective of solid state physics, the thermodynamic properties at finite temperature can be used to guide further experimental works and design of novel nickel-silicon alloys.

Nonlinear susceptibilities of finite conjugated organic polymers

NASA Technical Reports Server (NTRS)

Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.

1987-01-01

Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.

Finite geometry effects of field-aligned currents

NASA Technical Reports Server (NTRS)

Fung, Shing F.; Hoffman, R. A.

1992-01-01

Results are presented of model calculations of the magnetic field produced by finite current regions that would be measured by a spaceborne magnetometer. Conditions were examined under which the infinite current sheet approximation can be applied to the calculation of the field-aligned current (FAC) density, using satellite magnetometer data. The accuracy of the three methods used for calculating the current sheet normal direction with respect to the spacecraft trajectory was assessed. It is shown that the model can be used to obtain the position and the orientation of the spacecraft trajectory through the FAC region.

Development of a finite volume two-dimensional model and its application in a bay with two inlets: Mobile Bay, Alabama

NASA Astrophysics Data System (ADS)

Lee, Jun; Lee, Jungwoo; Yun, Sang-Leen; Oh, Hye-Cheol

2017-08-01

The purpose of this study was to develop a two-dimensional shallow water flow model using the finite volume method on a combined unstructured triangular and quadrilateral grid system to simulate coastal, estuarine and river flows. The intercell numerical fluxes were calculated using the classical Osher-Solomon's approximate Riemann solver for the governing conservation laws to be able to handle wetting and drying processes and to capture a tidal bore like phenomenon. The developed model was validated with several benchmark test problems including the two-dimensional dam-break problem. The model results were well agreed with results of other models and experimental results in literature. The unstructured triangular and quadrilateral combined grid system was successfully implemented in the model, thus the developed model would be more flexible when applying in an estuarine system, which includes narrow channels. Then, the model was tested in Mobile Bay, Alabama, USA. The developed model reproduced water surface elevation well as having overall Predictive Skill of 0.98. We found that the primary inlet, Main Pass, only covered 35% of the fresh water exchange while it covered 89% of the total water exchange between the ocean and Mobile Bay. There were also discharge phase difference between MP and the secondary inlet, Pass aux Herons, and this phase difference in flows would act as a critical role in substances' exchange between the eastern Mississippi Sound and the northern Gulf of Mexico through Main Pass and Pass aux Herons in Mobile Bay.

Pretest 3-D finite element modeling of the wedge pillar portion of the WIPP (Waste Isolation Pilot Plant) Geomechanical Evaluation (Room G) in situ experiment. [Waste Isolation Pilot Plant

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

Preece, D.S.

Pretest 3-D finite element calculations have been performed on the wedge pillar portion of the WIPP Geomechanical Evaluation Experiment. The wedge pillar separates two drifts that intersect at an angle of 7.5/sup 0/. Purpose of the experiment is to provide data on the creep behavior of the wedge and progressive failure at the tip. The first set of calculations utilized a symmetry plane on the center-line of the wedge which allowed treatment of the entire configuration by modeling half of the geometry. Two 3-D calculations in this first set were performed with different drift widths to study the influence ofmore » drift size on closure and maximum stress. A cross-section perpendicular to the wedge was also analyzed with 2-D finite element models and the results compared to the 3-D results. In another set of 3-D calculations both drifts were modeled but with less distance between the drifts and the outer boundaries. Results of these calculations are compared with results from the other calculations to better understand the influence of boundary conditions.« less

Pairing mechanism in Bi-O superconductors: A finite-size chain calculation

NASA Astrophysics Data System (ADS)

Aligia, A. A.; Nuez Regueiro, M. D.; Gagliano, E. R.

1989-09-01

We have studied the pairing mechanism in BiO3 systems by calculating the binding energy of a pair of holes in finite Bi-O chains, for parameters that simulate three-dimensional behavior. In agreement with previous results using perturbation theory in the hopping t, for covalent Bi-O binding and parameters for which the parent compound has a disproportionate ground state, pairing induced by the presence of biexcitons is obtained for sufficiently large interatomic Coulomb repulsion. The analysis of appropriate correlation functions shows a rapid metallization of the system as t and the number of holes increase. This fact shrinks the region of parameters for which the finite-size calculations can be trusted without further study. The same model for other parameters yields pairing in two other regimes: bipolaronic and magnetic excitonic.

Renyi Entropy of the Ideal Gas in Finite Momentum Intervals

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.

2003-06-01

Coincidence probabilities of multiparticle events, as measured in finite momentum intervals for Bose and Fermi ideal gas, are calculated and compared with the exact expressions given in statistical physics.