Finite-Size Effects of Binary Mutual Diffusion Coefficients from Molecular Dynamics

PubMed Central

2018-01-01

Molecular dynamics simulations were performed for the prediction of the finite-size effects of Maxwell-Stefan diffusion coefficients of molecular mixtures and a wide variety of binary Lennard–Jones systems. A strong dependency of computed diffusivities on the system size was observed. Computed diffusivities were found to increase with the number of molecules. We propose a correction for the extrapolation of Maxwell–Stefan diffusion coefficients to the thermodynamic limit, based on the study by Yeh and Hummer (J. Phys. Chem. B, 2004, 108, 15873−15879). The proposed correction is a function of the viscosity of the system, the size of the simulation box, and the thermodynamic factor, which is a measure for the nonideality of the mixture. Verification is carried out for more than 200 distinct binary Lennard–Jones systems, as well as 9 binary systems of methanol, water, ethanol, acetone, methylamine, and carbon tetrachloride. Significant deviations between finite-size Maxwell–Stefan diffusivities and the corresponding diffusivities at the thermodynamic limit were found for mixtures close to demixing. In these cases, the finite-size correction can be even larger than the simulated (finite-size) Maxwell–Stefan diffusivity. Our results show that considering these finite-size effects is crucial and that the suggested correction allows for reliable computations. PMID:29664633

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows.

PubMed

Manneville, Paul

2009-02-01

By use of a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-->laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number Rlow, whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond Rlow.

Stretching Diagnostics and Mixing Properties In The Stratosphere

NASA Astrophysics Data System (ADS)

Legras, B.; Shuckburgh, E.

The "finite size Lyapunov exponent" and the "effective diffusivity" are two diagnos- tics of mixing which have been recently introduced to investigate atmospheric flows. Both have been used to successfully identify the barriers to transport, for instance at the edge of the stratospheric polar vortex. Here we compare the two diagnostics in detail. The equivalent length has the advantage of arising as a mixing quantification from a rigid theoretical framework, however it has the disadvantage of being an aver- age quantity (the average around a tracer contour). The finite size Lyapunov exponent may be defined at any point in the flow, and quantifies the stretching properties expe- rienced by a fluid parcel both in its past and future evolution. In particular, the lines of maximum stretching at any time delineate the building blocks of the chaotic stirring. However the interpretation of the finite size Lyapunov exponent as a mixing time is less direct and depends on the alignment of tracer contours with the stretching lines.

Inertial objects in complex flows

NASA Astrophysics Data System (ADS)

Syed, Rayhan; Ho, George; Cavas, Samuel; Bao, Jialun; Yecko, Philip

2017-11-01

Chaotic Advection and Finite Time Lyapunov Exponents both describe stirring and transport in complex and time-dependent flows, but FTLE analysis has been largely limited to either purely kinematic flow models or high Reynolds number flow field data. The neglect of dynamic effects in FTLE and Lagrangian Coherent Structure studies has stymied detailed information about the role of pressure, Coriolis effects and object inertia. We present results of laboratory and numerical experiments on time-dependent and multi-gyre Stokes flows. In the lab, a time-dependent effectively two-dimensional low Re flow is used to distinguish transport properties of passive tracer from those of small paramagnetic spheres. Companion results of FTLE calculations for inertial particles in a time-dependent multi-gyre flow are presented, illustrating the critical roles of density, Stokes number and Coriolis forces on their transport. Results of Direct Numerical Simulations of fully resolved inertial objects (spheroids) immersed in a three dimensional (ABC) flow show the role of shape and finite size in inertial transport at small finite Re. We acknowledge support of NSF DMS-1418956.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Generalized Knudsen Number for Unsteady Fluid Flow.

PubMed

Kara, V; Yakhot, V; Ekinci, K L

2017-02-17

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Generalized Knudsen Number for Unsteady Fluid Flow

NASA Astrophysics Data System (ADS)

Kara, V.; Yakhot, V.; Ekinci, K. L.

2017-02-01

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

NASA Astrophysics Data System (ADS)

Costa, Pedro; Picano, Francesco; Brandt, Luca; Breugem, Wim-Paul

2018-05-01

We use interface-resolved simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, at the same solid volume fraction of 20% and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (PRL 117, 134501), a particle-wall layer is responsible for deviations of the statistics from what is observed in the continuum limit where the suspension is modeled as a Newtonian fluid with an effective viscosity. Here we investigate the fluid and particle dynamics in this layer and in the bulk. In the particle-wall layer, the near wall inhomogeneity has an influence on the suspension micro-structure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the flow scaling laws in to second-order Eulerian statistics in the homogeneous suspension region away from the wall. Finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that 1-point dispersion is dominated by particle-turbulence (and not particle-particle) interactions, while differences in 2-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions.

ANALYTICAL SOLUTION TO SATURATED FLOW IN A FINITE STRATIFIED AQUIFER

EPA Science Inventory

An analytical solution for the flow of water in a saturated-stratified aquitard-aquifer-aquitard system of finite length is presented. The analytical solution assumes one-dimensional horizontal flow in the aquifer and two-dimensional flow in the aquitards. Several examples are gi...

Lagrangian analysis of multiscale particulate flows with the particle finite element method

NASA Astrophysics Data System (ADS)

Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy

2014-05-01

We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

Moving Computational Domain Method and Its Application to Flow Around a High-Speed Car Passing Through a Hairpin Curve

NASA Astrophysics Data System (ADS)

Watanabe, Koji; Matsuno, Kenichi

This paper presents a new method for simulating flows driven by a body traveling with neither restriction on motion nor a limit of a region size. In the present method named 'Moving Computational Domain Method', the whole of the computational domain including bodies inside moves in the physical space without the limit of region size. Since the whole of the grid of the computational domain moves according to the movement of the body, a flow solver of the method has to be constructed on the moving grid system and it is important for the flow solver to satisfy physical and geometric conservation laws simultaneously on moving grid. For this issue, the Moving-Grid Finite-Volume Method is employed as the flow solver. The present Moving Computational Domain Method makes it possible to simulate flow driven by any kind of motion of the body in any size of the region with satisfying physical and geometric conservation laws simultaneously. In this paper, the method is applied to the flow around a high-speed car passing through a hairpin curve. The distinctive flow field driven by the car at the hairpin curve has been demonstrated in detail. The results show the promising feature of the method.

A hydrodynamic model for granular material flows including segregation effects

NASA Astrophysics Data System (ADS)

Gilberg, Dominik; Klar, Axel; Steiner, Konrad

2017-06-01

The simulation of granular flows including segregation effects in large industrial processes using particle methods is accurate, but very time-consuming. To overcome the long computation times a macroscopic model is a natural choice. Therefore, we couple a mixture theory based segregation model to a hydrodynamic model of Navier-Stokes-type, describing the flow behavior of the granular material. The granular flow model is a hybrid model derived from kinetic theory and a soil mechanical approach to cover the regime of fast dilute flow, as well as slow dense flow, where the density of the granular material is close to the maximum packing density. Originally, the segregation model has been formulated by Thornton and Gray for idealized avalanches. It is modified and adapted to be in the preferred form for the coupling. In the final coupled model the segregation process depends on the local state of the granular system. On the other hand, the granular system changes as differently mixed regions of the granular material differ i.e. in the packing density. For the modeling process the focus lies on dry granular material flows of two particle types differing only in size but can be easily extended to arbitrary granular mixtures of different particle size and density. To solve the coupled system a finite volume approach is used. To test the model the rotational mixing of small and large particles in a tumbler is simulated.

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

Least-squares finite element solutions for three-dimensional backward-facing step flow

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Hou, Lin-Jun; Lin, Tsung-Liang

1993-01-01

Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.

Wake-Driven Dynamics of Finite-Sized Buoyant Spheres in Turbulence

NASA Astrophysics Data System (ADS)

Mathai, Varghese; Prakash, Vivek N.; Brons, Jon; Sun, Chao; Lohse, Detlef

2015-09-01

Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle's density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace this reversed trend back to the growing contribution from wake-induced forces, unaccounted for in current particle models in turbulence. Our findings highlight the need for improved multiphysics based models that account for particle wake effects for a faithful representation of buoyant-sphere dynamics in turbulence.

The constructal law of design and evolution in nature

PubMed Central

Bejan, Adrian; Lorente, Sylvie

2010-01-01

Constructal theory is the view that (i) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered by a principle (the constructal law): ‘for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it’. This law is about the necessity of design to occur, and about the time direction of the phenomenon: the tape of the design evolution ‘movie’ runs such that existing configurations are replaced by globally easier flowing configurations. The constructal law has two useful sides: the prediction of natural phenomena and the strategic engineering of novel architectures, based on the constructal law, i.e. not by mimicking nature. We show that the emergence of scaling laws in inanimate (geophysical) flow systems is the same phenomenon as the emergence of allometric laws in animate (biological) flow systems. Examples are lung design, animal locomotion, vegetation, river basins, turbulent flow structure, self-lubrication and natural multi-scale porous media. This article outlines the place of the constructal law as a self-standing law in physics, which covers all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes. Nature is configured to flow and move as a conglomerate of ‘engine and brake’ designs. PMID:20368252

The constructal law of design and evolution in nature.

PubMed

Bejan, Adrian; Lorente, Sylvie

2010-05-12

Constructal theory is the view that (i) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered by a principle (the constructal law): 'for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it'. This law is about the necessity of design to occur, and about the time direction of the phenomenon: the tape of the design evolution 'movie' runs such that existing configurations are replaced by globally easier flowing configurations. The constructal law has two useful sides: the prediction of natural phenomena and the strategic engineering of novel architectures, based on the constructal law, i.e. not by mimicking nature. We show that the emergence of scaling laws in inanimate (geophysical) flow systems is the same phenomenon as the emergence of allometric laws in animate (biological) flow systems. Examples are lung design, animal locomotion, vegetation, river basins, turbulent flow structure, self-lubrication and natural multi-scale porous media. This article outlines the place of the constructal law as a self-standing law in physics, which covers all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes. Nature is configured to flow and move as a conglomerate of 'engine and brake' designs.

The nature of the laning transition in two dimensions

NASA Astrophysics Data System (ADS)

Glanz, T.; Löwen, H.

2012-11-01

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures (‘lanes’) characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262 144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed Finite Elements

NASA Astrophysics Data System (ADS)

Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L.

2000-11-01

In this paper we describe a fast parallel method for solving highly ill-conditioned saddle-point systems arising from mixed finite element simulations of stochastic partial differential equations (PDEs) modelling flow in heterogeneous media. Each realisation of these stochastic PDEs requires the solution of the linear first-order velocity-pressure system comprising Darcy's law coupled with an incompressibility constraint. The chief difficulty is that the permeability may be highly variable, especially when the statistical model has a large variance and a small correlation length. For reasonable accuracy, the discretisation has to be extremely fine. We solve these problems by first reducing the saddle-point formulation to a symmetric positive definite (SPD) problem using a suitable basis for the space of divergence-free velocities. The reduced problem is solved using parallel conjugate gradients preconditioned with an algebraically determined additive Schwarz domain decomposition preconditioner. The result is a solver which exhibits a good degree of robustness with respect to the mesh size as well as to the variance and to physically relevant values of the correlation length of the underlying permeability field. Numerical experiments exhibit almost optimal levels of parallel efficiency. The domain decomposition solver (DOUG, http://www.maths.bath.ac.uk/~parsoft) used here not only is applicable to this problem but can be used to solve general unstructured finite element systems on a wide range of parallel architectures.

Size-dependent chemical transformation, structural phase-change, and optical properties of nanowires

PubMed Central

Piccione, Brian; Agarwal, Rahul; Jung, Yeonwoong; Agarwal, Ritesh

2013-01-01

Nanowires offer a unique approach for the bottom up assembly of electronic and photonic devices with the potential of integrating photonics with existing technologies. The anisotropic geometry and mesoscopic length scales of nanowires also make them very interesting systems to study a variety of size-dependent phenomenon where finite size effects become important. We will discuss the intriguing size-dependent properties of nanowire systems with diameters in the 5 – 300 nm range, where finite size and interfacial phenomena become more important than quantum mechanical effects. The ability to synthesize and manipulate nanostructures by chemical methods allows tremendous versatility in creating new systems with well controlled geometries, dimensions and functionality, which can then be used for understanding novel processes in finite-sized systems and devices. PMID:23997656

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time.

PubMed

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

2017-06-01

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations.

PubMed

Nick, H M; Paluszny, A; Blunt, M J; Matthai, S K

2011-11-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density.

On accuracy of the wave finite element predictions of wavenumbers and power flow: A benchmark problem

NASA Astrophysics Data System (ADS)

Søe-Knudsen, Alf; Sorokin, Sergey

2011-06-01

This rapid communication is concerned with justification of the 'rule of thumb', which is well known to the community of users of the finite element (FE) method in dynamics, for the accuracy assessment of the wave finite element (WFE) method. An explicit formula linking the size of a window in the dispersion diagram, where the WFE method is trustworthy, with the coarseness of a FE mesh employed is derived. It is obtained by the comparison of the exact Pochhammer-Chree solution for an elastic rod having the circular cross-section with its WFE approximations. It is shown that the WFE power flow predictions are also valid within this window.

High frequency dynamic engine simulation. [TF-30 engine

NASA Technical Reports Server (NTRS)

Schuerman, J. A.; Fischer, K. E.; Mclaughlin, P. W.

1977-01-01

A digital computer simulation of a mixed flow, twin spool turbofan engine was assembled to evaluate and improve the dynamic characteristics of the engine simulation to disturbance frequencies of at least 100 Hz. One dimensional forms of the dynamic mass, momentum and energy equations were used to model the engine. A TF30 engine was simulated so that dynamic characteristics could be evaluated against results obtained from testing of the TF30 engine at the NASA Lewis Research Center. Dynamic characteristics of the engine simulation were improved by modifying the compression system model. Modifications to the compression system model were established by investigating the influence of size and number of finite dynamic elements. Based on the results of this program, high frequency engine simulations using finite dynamic elements can be assembled so that the engine dynamic configuration is optimum with respect to dynamic characteristics and computer execution time. Resizing of the compression systems finite elements improved the dynamic characteristics of the engine simulation but showed that additional refinements are required to obtain close agreement simulation and actual engine dynamic characteristics.

Hydrodynamic fractionation of finite size gold nanoparticle clusters.

PubMed

Tsai, De-Hao; Cho, Tae Joon; DelRio, Frank W; Taurozzi, Julian; Zachariah, Michael R; Hackley, Vincent A

2011-06-15

We demonstrate a high-resolution in situ experimental method for performing simultaneous size classification and characterization of functional gold nanoparticle clusters (GNCs) based on asymmetric-flow field flow fractionation (AFFF). Field emission scanning electron microscopy, atomic force microscopy, multi-angle light scattering (MALS), and in situ ultraviolet-visible optical spectroscopy provide complementary data and imagery confirming the cluster state (e.g., dimer, trimer, tetramer), packing structure, and purity of fractionated populations. An orthogonal analysis of GNC size distributions is obtained using electrospray-differential mobility analysis (ES-DMA). We find a linear correlation between the normalized MALS intensity (measured during AFFF elution) and the corresponding number concentration (measured by ES-DMA), establishing the capacity for AFFF to quantify the absolute number concentration of GNCs. The results and corresponding methodology summarized here provide the proof of concept for general applications involving the formation, isolation, and in situ analysis of both functional and adventitious nanoparticle clusters of finite size. © 2011 American Chemical Society

Finite-size scaling of eigenstate thermalization

NASA Astrophysics Data System (ADS)

Beugeling, W.; Moessner, R.; Haque, Masudul

2014-04-01

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law D-1/2 with the dimension D of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions. Numerical Analysis in Continuous Time

NASA Astrophysics Data System (ADS)

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors the rare trajectories of interest. However, such algorithms are plagued by finite simulation time- and finite population size- effects that can render their use delicate. Using the continuous-time cloning algorithm, we analyze the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. We use these scalings in order to propose a numerical approach which allows to extract the infinite-time and infinite-size limit of these estimators.

Unexpected finite size effects in interfacial systems: Why bigger is not always better—Increase in uncertainty of surface tension with bulk phase width

NASA Astrophysics Data System (ADS)

Longford, Francis G. J.; Essex, Jonathan W.; Skylaris, Chris-Kriton; Frey, Jeremy G.

2018-06-01

We present an unexpected finite size effect affecting interfacial molecular simulations that is proportional to the width-to-surface-area ratio of the bulk phase Ll/A. This finite size effect has a significant impact on the variance of surface tension values calculated using the virial summation method. A theoretical derivation of the origin of the effect is proposed, giving a new insight into the importance of optimising system dimensions in interfacial simulations. We demonstrate the consequences of this finite size effect via a new way to estimate the surface energetic and entropic properties of simulated air-liquid interfaces. Our method is based on macroscopic thermodynamic theory and involves comparing the internal energies of systems with varying dimensions. We present the testing of these methods using simulations of the TIP4P/2005 water forcefield and a Lennard-Jones fluid model of argon. Finally, we provide suggestions of additional situations, in which this finite size effect is expected to be significant, as well as possible ways to avoid its impact.

Non-steady peristaltic propulsion with exponential variable viscosity: a study of transport through the digestive system.

PubMed

Tripathi, Dharmendra; Pandey, S K; Siddiqui, Abdul; Bég, O Anwar

2014-01-01

A theoretical study is presented for transient peristaltic flow of an incompressible fluid with variable viscosity in a finite length cylindrical tube as a simulation of transport in physiological vessels and biomimetic peristaltic pumps. The current axisymmetric analysis is qualitatively similar to two-dimensional analysis but exhibits quantitative variations. The current analysis is motivated towards further elucidating the physiological migration of gastric suspensions (food bolus) in the human digestive system. It also applies to variable viscosity industrial fluid (waste) peristaltic pumping systems. First, an axisymmetric model is analysed in the limit of large wavelength ([Formula: see text]) and low Reynolds number ([Formula: see text]) for axial velocity, radial velocity, pressure, hydromechanical efficiency and stream function in terms of radial vibration of the wall ([Formula: see text]), amplitude of the wave ([Formula: see text]), averaged flow rate ([Formula: see text]) and variable viscosity ([Formula: see text]). Subsequently, the peristaltic flow of a fluid with an exponential viscosity model is examined, which is based on the analytical solutions for pressure, wall shear stress, hydromechanical efficiency and streamline patterns in the finite length tube. The results are found to correlate well with earlier studies using a constant viscosity formulation. This study reveals some important features in the flow characteristics including the observation that pressure as well as both number and size of lower trapped bolus increases. Furthermore, the study indicates that hydromechanical efficiency reduces with increasing magnitude of viscosity parameter.

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.

Predator-prey Encounter Rates in Turbulent Environments: Consequences of Inertia Effects and Finite Sizes

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

Pecseli, H. L.; Trulsen, J.

2009-10-08

Experimental as well as theoretical studies have demonstrated that turbulence can play an important role for the biosphere in marine environments, in particular also by affecting prey-predator encounter rates. Reference models for the encounter rates rely on simplifying assumptions of predators and prey being described as point particles moving passively with the local flow velocity. Based on simple arguments that can be tested experimentally we propose corrections for the standard expression for the encounter rates, where now finite sizes and Stokes drag effects are included.

Effect of vehicular size on chain-reaction crash

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

2015-11-01

We present the dynamic model of the chain-reaction crash to take account of the vehicular size. Drivers brake according to taillights of the forward vehicle. We investigate the effect of the vehicular size on the chain-reaction crash (multiple-vehicle collision) in the traffic flow controlled by taillights. In the multiple-vehicle collision, the first crash induces more collisions. We investigate how the first collision induces the chain-reaction crash numerically. We derive, analytically, the transition points and the region maps for the chain-reaction crash in the traffic flow of vehicles with finite sizes. We clarify the effect of the vehicular size on the multiple-vehicle collision.

The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime

NASA Astrophysics Data System (ADS)

Loisel, Vincent; Abbas, Micheline; Masbernat, Olivier; Climent, Eric

2013-12-01

The presence of finite-size particles in a channel flow close to the laminar-turbulent transition is simulated with the Force Coupling Method which allows two-way coupling with the flow dynamics. Spherical particles with channel height-to-particle diameter ratio of 16 are initially randomly seeded in a fluctuating flow above the critical Reynolds number corresponding to single phase flow relaminarization. When steady-state is reached, the particle volume fraction is homogeneously distributed in the channel cross-section (ϕ ≅ 5%) except in the near-wall region where it is larger due to inertia-driven migration. Turbulence statistics (intensity of velocity fluctuations, small-scale vortical structures, wall shear stress) calculated in the fully coupled two-phase flow simulations are compared to single-phase flow data in the transition regime. It is observed that particles increase the transverse r.m.s. flow velocity fluctuations and they break down the flow coherent structures into smaller, more numerous and sustained eddies, preventing the flow to relaminarize at the single-phase critical Reynolds number. When the Reynolds number is further decreased and the suspension flow becomes laminar, the wall friction coefficient recovers the evolution of the laminar single-phase law provided that the suspension viscosity is used in the Reynolds number definition. The residual velocity fluctuations in the suspension correspond to a regime of particulate shear-induced agitation.

Computations of Drop Collision and Coalescence

NASA Technical Reports Server (NTRS)

Tryggvason, Gretar; Juric, Damir; Nas, Selman; Mortazavi, Saeed

1996-01-01

Computations of drops collisions, coalescence, and other problems involving drops are presented. The computations are made possible by a finite difference/front tracking technique that allows direct solutions of the Navier-Stokes equations for a multi-fluid system with complex, unsteady internal boundaries. This method has been used to examine the various collision modes for binary collisions of drops of equal size, mixing of two drops of unequal size, behavior of a suspension of drops in linear and parabolic shear flows, and the thermal migration of several drops. The key results from these simulations are reviewed. Extensions of the method to phase change problems and preliminary results for boiling are also shown.

Parallel solution of high-order numerical schemes for solving incompressible flows

NASA Technical Reports Server (NTRS)

Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.

1993-01-01

A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.

Fictitious domain method for fully resolved reacting gas-solid flow simulation

NASA Astrophysics Data System (ADS)

Zhang, Longhui; Liu, Kai; You, Changfu

2015-10-01

Fully resolved simulation (FRS) for gas-solid multiphase flow considers solid objects as finite sized regions in flow fields and their behaviours are predicted by solving equations in both fluid and solid regions directly. Fixed mesh numerical methods, such as fictitious domain method, are preferred in solving FRS problems and have been widely researched. However, for reacting gas-solid flows no suitable fictitious domain numerical method has been developed. This work presents a new fictitious domain finite element method for FRS of reacting particulate flows. Low Mach number reacting flow governing equations are solved sequentially on a regular background mesh. Particles are immersed in the mesh and driven by their surface forces and torques integrated on immersed interfaces. Additional treatments on energy and surface reactions are developed. Several numerical test cases validated the method and a burning carbon particles array falling simulation proved the capability for solving moving reacting particle cluster problems.

Excited-state quantum phase transitions in systems with two degrees of freedom: Level density, level dynamics, thermal properties

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

Stránský, Pavel; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510, México, D.F.; Macek, Michal

2014-06-15

Quantum systems with a finite number of freedom degrees f develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f, particularly f=2, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition. --more » Highlights: •ESQPTs found in infinite-size limit of systems with low numbers of freedom degrees f. •ESQPTs related to non-analytical evolutions of classical phase–space properties. •ESQPT signatures analyzed for general f, particularly f=2, extending known case f=1. •ESQPT signatures identified in smoothened density and flow of energy spectrum. •ESQPTs shown to induce a new type of thermodynamic anomalies.« less

Inertial flow regimes of the suspension of finite size particles

NASA Astrophysics Data System (ADS)

Lashgari, Iman; Picano, Francesco; Brandt, Luca

2015-03-01

We study inertial flow regimes of the suspensions of finite size neutrally buoyant particles. These suspensions experience three different regimes by varying the Reynolds number, Re , and particle volume fraction, Φ. At low values of Re and Φ, flow is laminar-like where viscous stress is the dominating term in the stress budget. At high Re and relatively small Φ, the flow is turbulent-like where Reynolds stress has the largest contribution to the total stress. At high Φ, the flow regime is as a form of inertial shear-thickening characterized by a significant enhancement in the wall shear stress not due to the increment of Reynolds stress but to the particle stress. We further analyze the local behavior of the suspension in the three different regimes by studying the particle dispersion and collisions. Turbulent cases shows higher level of particle dispersion and higher values of the collision kernel (the radial distribution function times the particle relative velocity as a function of the distance between the particles) than those of the inertial shear-thickening regimes providing additional evidence of two different transport mechanisms in the Bagnoldian regime. Support from the European Research Council (ERC) is acknowledged.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

NASA Astrophysics Data System (ADS)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Criticality in finite dynamical networks

NASA Astrophysics Data System (ADS)

Rohlf, Thimo; Gulbahce, Natali; Teuscher, Christof

2007-03-01

It has been shown analytically and experimentally that both random boolean and random threshold networks show a transition from ordered to chaotic dynamics at a critical average connectivity Kc in the thermodynamical limit [1]. By looking at the statistical distributions of damage spreading (damage sizes), we go beyond this extensively studied mean-field approximation. We study the scaling properties of damage size distributions as a function of system size N and initial perturbation size d(t=0). We present numerical evidence that another characteristic point, Kd exists for finite system sizes, where the expectation value of damage spreading in the network is independent of the system size N. Further, the probability to obtain critical networks is investigated for a given system size and average connectivity k. Our results suggest that, for finite size dynamical networks, phase space structure is very complex and may not exhibit a sharp order-disorder transition. Finally, we discuss the implications of our findings for evolutionary processes and learning applied to networks which solve specific computational tasks. [1] Derrida, B. and Pomeau, Y. (1986), Europhys. Lett., 1, 45-49

Effects of finite spatial resolution on quantitative CBF images from dynamic PET

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

Phelps, M.E.; Huang, S.C.; Mahoney, D.K.

1985-05-01

The finite spatial resolution of PET causes the time-activity responses on pixels around the boundaries between gray and white matter regions to contain kinetic components from tissues of different CBF's. CBF values estimated from kinetics of such mixtures are underestimated because of the nonlinear relationship between the time-activity response and the estimated CBF. Computer simulation is used to investigate these effects on phantoms of circular structures and realistic brain slice in terms of object size and quantitative CBF values. The CBF image calculated is compared to the case of having resolution loss alone. Results show that the size of amore » high flow region in the CBF image is decreased while that of a low flow region is increased. For brain phantoms, the qualitative appearance of CBF images is not seriously affected, but the estimated CBF's are underestimated by 11 to 16 percent in local gray matter regions (of size 1 cm/sup 2/) with about 14 percent reduction in global CBF over the whole slice. It is concluded that the combined effect of finite spatial resolution and the nonlinearity in estimating CBF from dynamic PET is quite significant and must be considered in processing and interpreting quantitative CBF images.« less

Comparison of Accuracy and Performance for Lattice Boltzmann and Finite Difference Simulations of Steady Viscous Flow

NASA Astrophysics Data System (ADS)

Noble, David R.; Georgiadis, John G.; Buckius, Richard O.

1996-07-01

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 05% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 139 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.

A Finite Layer Formulation for Groundwater Flow to Horizontal Wells.

PubMed

Xu, Jin; Wang, Xudong

2016-09-01

A finite layer approach for the general problem of three-dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three-layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems. © 2016, National Ground Water Association.

Many-body localization in disorder-free systems: The importance of finite-size constraints

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

Papić, Z., E-mail: zpapic@perimeterinstitute.ca; Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5; Stoudenmire, E. Miles

2015-11-15

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that variousmore » bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.« less

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows.

DTIC Science & Technology

1986-09-01

respectively. Here h is a parameter which is usually related to the size of the grid associated with the finite element partitioning of Q. Then one... grid and of not at least performing serious mesh refinement studies. It also points out the usefulness of rigorous results concerning the stability...overconstrained the .1% approximate velocity field. However, by employing different grids for the ’z pressure and velocity fields, the linear-constant

Phase equilibria in polymer blend thin films: A Hamiltonian approach

NASA Astrophysics Data System (ADS)

Souche, M.; Clarke, N.

2009-12-01

We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films.

Simulation of two-dimensional adjustable liquid gradient refractive index (L-GRIN) microlens

NASA Astrophysics Data System (ADS)

Le, Zichun; Wu, Xiang; Sun, Yunli; Du, Ying

2017-07-01

In this paper, a two-dimensional liquid gradient refractive index (L-GRIN) microlens is designed which can be used in adjusting focusing direction and focal spot of light beam. Finite element method (FEM) is used to simulate the convection diffusion process happening in core inlet flow and cladding inlet flow. And the ray tracing method shows us the light beam focusing effect including the extrapolation of focal length and output beam spot size. When the flow rates of the core and cladding fluids are held the same between the internal and external, left and right, and upper and lower inlets, the focal length varied from 313 μm to 53.3 μm while the flow rate of liquids ranges from 500 pL/s to 10,000 pL/s. While the core flow rate is bigger than the cladding inlet flow rate, the light beam will focus on a light spot with a tunable size. By adjusting the ratio of cladding inlet flow rate including Qright/Qleft and Qup/Qdown, we get the adjustable two-dimensional focus direction rather than the one-dimensional focusing. In summary, by adjusting the flow rate of core inlet and cladding inlet, the focal length, output beam spot and focusing direction of the input light beam can be manipulated. We suppose this kind of flexible microlens can be used in integrated optics and lab-on-a-chip system.

Propagation of a finite bubble in a Hele-Shaw channel of variable depth

NASA Astrophysics Data System (ADS)

Juel, Anne; Franco-Gomez, Andres; Thompson, Alice; Hazel, Andrew

2017-11-01

We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred rail is introduced to provide a small axially-uniform depth constriction. We demonstrate experimentally that this channel geometry can be used as a passive sorting device. Single air bubbles carried within silicone oil are generally transported on one side of the rail. However, for flow rates marginally larger than a critical value, a narrow band of bubble sizes on the order of the rail width can propagate over the rail, while bubbles of other sizes segregate to the side of the rail. The width of this band of bubble sizes increases with flow rate and the size of the most stable bubble can be tuned by varying the rail width. We present a depth-averaged theory which reveals that the mechanism relies on a non-trivial interaction between capillary and viscous forces that is fully dynamic, rather than being a simple modification of capillary static solutions. In contrast, for larger bubbles and sufficiently large imposed flow rates, we find that initially centred bubbles do not converge onto a steady mode of propagation. Instead they transiently explore weakly unstable steady modes, an evolution which results in their break-up and eventual settling into a steady state of changed topology. The financial support of CONICYT and the Leverhulme Trust are gratefully acknowledged.

Extreme value statistics and finite-size scaling at the ecological extinction/laminar-turbulence transition

NASA Astrophysics Data System (ADS)

Shih, Hong-Yan; Goldenfeld, Nigel

Experiments on transitional turbulence in pipe flow seem to show that turbulence is a transient metastable state since the measured mean lifetime of turbulence puffs does not diverge asymptotically at a critical Reynolds number. Yet measurements reveal that the lifetime scales with Reynolds number in a super-exponential way reminiscent of extreme value statistics, and simulations and experiments in Couette and channel flow exhibit directed percolation type scaling phenomena near a well-defined transition. This universality class arises from the interplay between small-scale turbulence and a large-scale collective zonal flow, which exhibit predator-prey behavior. Why is asymptotically divergent behavior not observed? Using directed percolation and a stochastic individual level model of predator-prey dynamics related to transitional turbulence, we investigate the relation between extreme value statistics and power law critical behavior, and show that the paradox is resolved by carefully defining what is measured in the experiments. We theoretically derive the super-exponential scaling law, and using finite-size scaling, show how the same data can give both super-exponential behavior and power-law critical scaling.

Numerical analysis of finite Debye-length effects in induced-charge electro-osmosis.

PubMed

Gregersen, Misha Marie; Andersen, Mathias Baekbo; Soni, Gaurav; Meinhart, Carl; Bruus, Henrik

2009-06-01

For a microchamber filled with a binary electrolyte and containing a flat unbiased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that, compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e., for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.

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

Altabet, Y. Elia; Debenedetti, Pablo G., E-mail: pdebene@princeton.edu; Stillinger, Frank H.

In particle systems with cohesive interactions, the pressure-density relationship of the mechanically stable inherent structures sampled along a liquid isotherm (i.e., the equation of state of an energy landscape) will display a minimum at the Sastry density ρ{sub S}. The tensile limit at ρ{sub S} is due to cavitation that occurs upon energy minimization, and previous characterizations of this behavior suggested that ρ{sub S} is a spinodal-like limit that separates all homogeneous and fractured inherent structures. Here, we revisit the phenomenology of Sastry behavior and find that it is subject to considerable finite-size effects, and the development of the inherentmore » structure equation of state with system size is consistent with the finite-size rounding of an athermal phase transition. What appears to be a continuous spinodal-like point at finite system sizes becomes discontinuous in the thermodynamic limit, indicating behavior akin to a phase transition. We also study cavitation in glassy packings subjected to athermal expansion. Many individual expansion trajectories averaged together produce a smooth equation of state, which we find also exhibits features of finite-size rounding, and the examples studied in this work give rise to a larger limiting tension than for the corresponding landscape equation of state.« less

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

Numerical study of 3D flow structure near a cylinder piercing turbulent free-convection boundary layer on a vertical plate

NASA Astrophysics Data System (ADS)

Levchenya, A. M.; Smirnov, E. M.; Zhukovskaya, V. D.

2018-05-01

The present contribution covers RANS-based simulation of 3D flow near a cylinder introduced into turbulent vertical-plate free-convection boundary layer. Numerical solutions were obtained with a finite-volume Navier-Stokes code of second-order accuracy using refined grids. Peculiarities of the flow disturbed by the obstacle are analyzed. Cylinder-diameter effect on the horseshoe vortex size and its position is evaluated.

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

NASA Astrophysics Data System (ADS)

Flores-Sola, Emilio J.; Berche, Bertrand; Kenna, Ralph; Weigel, Martin

2015-01-01

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour by simulating one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

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

A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model

USGS Publications Warehouse

McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing; Lu, Guoping

1988-01-01

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

Parallel Simulation of Three-Dimensional Free Surface Fluid Flow Problems

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

BAER,THOMAS A.; SACKINGER,PHILIP A.; SUBIA,SAMUEL R.

1999-10-14

Simulation of viscous three-dimensional fluid flow typically involves a large number of unknowns. When free surfaces are included, the number of unknowns increases dramatically. Consequently, this class of problem is an obvious application of parallel high performance computing. We describe parallel computation of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact fines. The Galerkin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-staticmore » solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of unknowns. Other issues discussed are the proper constraints appearing along the dynamic contact line in three dimensions. Issues affecting efficient parallel simulations include problem decomposition to equally distribute computational work among a SPMD computer and determination of robust, scalable preconditioners for the distributed matrix systems that must be solved. Solution continuation strategies important for serial simulations have an enhanced relevance in a parallel coquting environment due to the difficulty of solving large scale systems. Parallel computations will be demonstrated on an example taken from the coating flow industry: flow in the vicinity of a slot coater edge. This is a three dimensional free surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another region. As such, a significant fraction of the computational time is devoted to processing boundary data. Discussion focuses on parallel speed ups for fixed problem size, a class of problems of immediate practical importance.« less

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

NASA Astrophysics Data System (ADS)

Zschocke, Fabian; Vojta, Matthias

2015-07-01

Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static Z2 gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by F. L. Pedrocchi, S. Chesi, and D. Loss [Phys. Rev. B 84, 165414 (2011), 10.1103/PhysRevB.84.165414]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR line shape. We also predict a transition to a random-flux state with increasing disorder.

Structural weights analysis of advanced aerospace vehicles using finite element analysis

NASA Technical Reports Server (NTRS)

Bush, Lance B.; Lentz, Christopher A.; Rehder, John J.; Naftel, J. Chris; Cerro, Jeffrey A.

1989-01-01

A conceptual/preliminary level structural design system has been developed for structural integrity analysis and weight estimation of advanced space transportation vehicles. The system includes a three-dimensional interactive geometry modeler, a finite element pre- and post-processor, a finite element analyzer, and a structural sizing program. Inputs to the system include the geometry, surface temperature, material constants, construction methods, and aerodynamic and inertial loads. The results are a sized vehicle structure capable of withstanding the static loads incurred during assembly, transportation, operations, and missions, and a corresponding structural weight. An analysis of the Space Shuttle external tank is included in this paper as a validation and benchmark case of the system.

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1997-01-01

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

Development of new vibration energy flow analysis software and its applications to vehicle systems

NASA Astrophysics Data System (ADS)

Kim, D.-J.; Hong, S.-Y.; Park, Y.-H.

2005-09-01

The Energy flow analysis (EFA) offers very promising results in predicting the noise and vibration responses of system structures in medium-to-high frequency ranges. We have developed the Energy flow finite element method (EFFEM) based software, EFADSC++ R4, for the vibration analysis. The software can analyze the system structures composed of beam, plate, spring-damper, rigid body elements and many other components developed, and has many useful functions in analysis. For convenient use of the software, the main functions of the whole software are modularized into translator, model-converter, and solver. The translator module makes it possible to use finite element (FE) model for the vibration analysis. The model-converter module changes FE model into energy flow finite element (EFFE) model, and generates joint elements to cover the vibrational attenuation in the complex structures composed of various elements and can solve the joint element equations by using the wave tra! nsmission approach very quickly. The solver module supports the various direct and iterative solvers for multi-DOF structures. The predictions of vibration for real vehicles by using the developed software were performed successfully.

Ion sound instability driven by the ion flows

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

Koshkarov, O., E-mail: koshkarov.alexandr@usask.ca; Smolyakov, A. I.; National Research Centre

2015-05-15

Ion sound instabilities driven by the ion flow in a system of a finite length are considered by analytical and numerical methods. The ion sound waves are modified by the presence of stationary ion flow resulting in negative and positive energy modes. The instability develops due to coupling of negative and positive energy modes mediated by reflections from the boundary. It is shown that the wave dispersion due to deviation from quasineutrality is crucial for the stability. In finite length system, the dispersion is characterized by the length of the system measured in units of the Debye length. The instabilitymore » is studied analytically and the results are compared with direct, initial value numerical simulations.« less

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers.

PubMed

Rosén, T; Einarsson, J; Nordmark, A; Aidun, C K; Lundell, F; Mehlig, B

2015-12-01

We numerically analyze the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem, we compute the linear stability of the log-rolling orbit at small shear Reynolds number Re(a). As Re(a)→0 and as the box size of the system tends to infinity, we find good agreement between the numerical results and earlier analytical predictions valid to linear order in Re(a) for the case of an unbounded shear. The numerical stability analysis indicates that there are substantial finite-size corrections to the analytical results obtained for the unbounded system. We also compare the analytical results to results of lattice Boltzmann simulations to analyze the stability of the tumbling orbit at shear Reynolds numbers of order unity. Theory for an unbounded system at infinitesimal shear Reynolds number predicts a bifurcation of the tumbling orbit at aspect ratio λ(c)≈0.137 below which tumbling is stable (as well as log rolling). The simulation results show a bifurcation line in the λ-Re(a) plane that reaches λ≈0.1275 at the smallest shear Reynolds number (Re(a)=1) at which we could simulate with the lattice Boltzmann code, in qualitative agreement with the analytical results.

Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength

NASA Astrophysics Data System (ADS)

Hong, Hyunsuk

2017-07-01

We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984), 10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν ¯=5 /4 . Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ =1 /4 , which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007), 10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν ¯=5 /2 . On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν ¯=5 /4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.

Transformation-Induced, Geometrically Necessary, Dislocation-Based Flow Curve Modeling of Dual-Phase Steels: Effect of Grain Size

NASA Astrophysics Data System (ADS)

Ramazani, Ali; Mukherjee, Krishnendu; Prahl, Ulrich; Bleck, Wolfgang

2012-10-01

The flow behavior of dual-phase (DP) steels is modeled on the finite-element method (FEM) framework on the microscale, considering the effect of the microstructure through the representative volume element (RVE) approach. Two-dimensional RVEs were created from microstructures of experimentally obtained DP steels with various ferrite grain sizes. The flow behavior of single phases was modeled through the dislocation-based work-hardening approach. The volume change during austenite-to-martensite transformation was modeled, and the resultant prestrained areas in the ferrite were considered to be the storage place of transformation-induced, geometrically necessary dislocations (GNDs). The flow curves of DP steels with varying ferrite grain sizes, but constant martensite fractions, were obtained from the literature. The flow curves of simulations that take into account the GND are in better agreement with those of experimental flow curves compared with those of predictions without consideration of the GND. The experimental results obeyed the Hall-Petch relationship between yield stress and flow stress and the simulations predicted this as well.

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.

Dissipative models of colliding stellar winds - I. Effects of thermal conduction in wide binary systems

NASA Astrophysics Data System (ADS)

Myasnikov, A. V.; Zhekov, S. A.

1998-11-01

The influence of electron thermal conduction on the 2D gas dynamics of colliding stellar winds is investigated. It is shown that, as a result of the non-linear dependence of the electron thermal flux on the temperature, the pre-heating zones (in which the hot gas in the interaction region heats the cool winds in front of the shocks) have finite sizes. The dependence of the problem of the structure of the flow in the interaction region on the dimensionless parameters is studied, and a simple expression is derived for the size of the pre-heating zones at the axis of symmetry. It is shown that small values of the thermal conductivity do not suppress the Kelvin-Helmholtz instability if the adiabatic flow is subject to it. Further studies, both numerical and analytical, in this direction will be of great interest. The influence of thermal conduction on the X-ray emission from the interaction region is also estimated.

Numerical simulation of turbulence in the presence of shear

NASA Technical Reports Server (NTRS)

Shaanan, S.; Ferziger, J. H.; Reynolds, W. C.

1975-01-01

The numerical calculations are presented of the large eddy structure of turbulent flows, by use of the averaged Navier-Stokes equations, where averages are taken over spatial regions small compared to the size of the computational grid. The subgrid components of motion are modeled by a local eddy-viscosity model. A new finite-difference scheme is proposed to represent the nonlinear average advective term which has fourth-order accuracy. This scheme exhibits several advantages over existing schemes with regard to the following: (1) the scheme is compact as it extends only one point away in each direction from the point to which it is applied; (2) it gives better resolution for high wave-number waves in the solution of Poisson equation, and (3) it reduces programming complexity and computation time. Examples worked out in detail are the decay of isotropic turbulence, homogeneous turbulent shear flow, and homogeneous turbulent shear flow with system rotation.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

A cavitation transition in the energy landscape of simple cohesive liquids and glasses

NASA Astrophysics Data System (ADS)

Altabet, Y. Elia; Stillinger, Frank H.; Debenedetti, Pablo G.

2016-12-01

In particle systems with cohesive interactions, the pressure-density relationship of the mechanically stable inherent structures sampled along a liquid isotherm (i.e., the equation of state of an energy landscape) will display a minimum at the Sastry density ρS. The tensile limit at ρS is due to cavitation that occurs upon energy minimization, and previous characterizations of this behavior suggested that ρS is a spinodal-like limit that separates all homogeneous and fractured inherent structures. Here, we revisit the phenomenology of Sastry behavior and find that it is subject to considerable finite-size effects, and the development of the inherent structure equation of state with system size is consistent with the finite-size rounding of an athermal phase transition. What appears to be a continuous spinodal-like point at finite system sizes becomes discontinuous in the thermodynamic limit, indicating behavior akin to a phase transition. We also study cavitation in glassy packings subjected to athermal expansion. Many individual expansion trajectories averaged together produce a smooth equation of state, which we find also exhibits features of finite-size rounding, and the examples studied in this work give rise to a larger limiting tension than for the corresponding landscape equation of state.

Finite micro-tab system for load control on a wind turbine

NASA Astrophysics Data System (ADS)

Bach, A. B.; Lennie, M.; Pechlivanoglou, G.; Nayeri, C. N.; Paschereit, C. O.

2014-06-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

Parallel Computation and Visualization of Three-dimensional, Time-dependent, Thermal Convective Flows

NASA Technical Reports Server (NTRS)

Wang, P.; Li, P.

1998-01-01

A high-resolution numerical study on parallel systems is reported on three-dimensional, time-dependent, thermal convective flows. A parallel implentation on the finite volume method with a multigrid scheme is discussed, and a parallel visualization systemm is developed on distributed systems for visualizing the flow.

Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process

PubMed Central

Corral, Álvaro; Garcia-Millan, Rosalba; Font-Clos, Francesc

2016-01-01

The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary. PMID:27584596

Point-to-point connectivity prediction in porous media using percolation theory

NASA Astrophysics Data System (ADS)

Tavagh-Mohammadi, Behnam; Masihi, Mohsen; Ganjeh-Ghazvini, Mostafa

2016-10-01

The connectivity between two points in porous media is important for evaluating hydrocarbon recovery in underground reservoirs or toxic migration in waste disposal. For example, the connectivity between a producer and an injector in a hydrocarbon reservoir impact the fluid dispersion throughout the system. The conventional approach, flow simulation, is computationally very expensive and time consuming. Alternative method employs percolation theory. Classical percolation approach investigates the connectivity between two lines (representing the wells) in 2D cross sectional models whereas we look for the connectivity between two points (representing the wells) in 2D aerial models. In this study, site percolation is used to determine the fraction of permeable regions connected between two cells at various occupancy probabilities and system sizes. The master curves of mean connectivity and its uncertainty are then generated by finite size scaling. The results help to predict well-to-well connectivity without need to any further simulation.

Identification of PARMA Models and Their Application to the Modeling of River flows

NASA Astrophysics Data System (ADS)

Tesfaye, Y. G.; Meerschaert, M. M.; Anderson, P. L.

2004-05-01

The generation of synthetic river flow samples that can reproduce the essential statistical features of historical river flows is essential to the planning, design and operation of water resource systems. Most river flow series are periodically stationary; that is, their mean and covariance functions are periodic with respect to time. We employ a periodic ARMA (PARMA) model. The innovation algorithm can be used to obtain parameter estimates for PARMA models with finite fourth moment as well as infinite fourth moment but finite variance. Anderson and Meerschaert (2003) provide a method for model identification when the time series has finite fourth moment. This article, an extension of the previous work by Anderson and Meerschaert, demonstrates the effectiveness of the technique using simulated data. An application to monthly flow data for the Frazier River in British Columbia is also included to illustrate the use of these methods.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

The effects of exercise on blood flow with reference to the human cardiovascular system: a finite element study

NASA Technical Reports Server (NTRS)

Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

1992-01-01

This paper reports on a theoretical investigation into the effects of vasomotion on blood through the human cardiovascular system. The finite element method has been used to analyse the model. Vasoconstriction and vasodilation may be effected either through the action of the central nervous system or autoregulation. One of the conditions responsible for vasomotion is exercise. The proposed model has been solved and quantitative results of flows and pressures due to changing the conductances of specific networks of arterioles, capillaries and venules comprising the arms, legs, stomach and their combinations have been obtained.

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.

Sedimentation of finite-size particles in quiescent and turbulent environments

NASA Astrophysics Data System (ADS)

Brandt, Luca; Fornari, Walter; Picano, Francesco

2015-11-01

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows. We present Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to study the behavior of finite-size particles in homogeneous isotropic turbulence. The particle radius is approximately 6 Komlogorov lengthscales, the volume fraction 0.5% and 1% and the density ratio 1.02. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reduction with respect to a single particle in quiescent fluid is about 12% in dilute conditions. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated to the intermittent fast sedimentation of particle pairs in drafting-kissing-tumbling motions. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulas and show that non stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment. This work was supported by the European Research Council Grant No. ERC-2013- CoG-616186, TRITOS.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

1D-3D coupling for hydraulic system transient simulations

NASA Astrophysics Data System (ADS)

Wang, Chao; Nilsson, Håkan; Yang, Jiandong; Petit, Olivier

2017-01-01

This work describes a coupling between the 1D method of characteristics (MOC) and the 3D finite volume method of computational fluid dynamics (CFD). The coupling method is applied to compressible flow in hydraulic systems. The MOC code is implemented as a set of boundary conditions in the OpenFOAM open source CFD software. The coupling is realized by two linear equations originating from the characteristics equation and the Riemann constant equation, respectively. The coupling method is validated using three simple water hammer cases and several coupling configurations. The accuracy and robustness are investigated with respect to the mesh size ratio across the interface, and 3D flow features close to the interface. The method is finally applied to the transient flow caused by the closing and opening of a knife valve (gate) in a pipe, where the flow is driven by the difference in free surface elevation between two tanks. A small region surrounding the moving gate is resolved by CFD, using a dynamic mesh library, while the rest of the system is modeled by MOC. Minor losses are included in the 1D region, corresponding to the contraction of the flow from the upstream tank into the pipe, a separate stationary flow regulation valve, and a pipe bend. The results are validated with experimental data. A 1D solution is provided for comparison, using the static gate characteristics obtained from steady-state CFD simulations.

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Implicit method for the computation of unsteady flows on unstructured grids

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, D. J.

1995-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Asta, Adelchi J.; Levesque, Maximilien; Vuilleumier, Rodolphe; Rotenberg, Benjamin

2017-06-01

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t-3 /2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

The finite element method in low speed aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1975-01-01

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

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.

Membrane emulsification to produce perfume microcapsules

NASA Astrophysics Data System (ADS)

Pan, Xuemiao

Microencapsulation is an efficient technology to deliver perfume oils from consumer products onto the surface of fabrics. Microcapsules having uniform size/mechanical strength, may provide better release performance. Membrane emulsification in a dispersion cell followed by in-situ polymerization was used to prepare narrow size distribution melamine-formaldehyde (MF) microcapsules containing several types of oil-based fragrances or ingredients. Investigated in this study are the parameters impacting to the size and size distribution of the droplets and final MF microcapsules. A pilot plant-scale cross-flow membrane system was also used to produce MF microcapsules, demonstrating that the membrane emulsification process has potential to be scaled up for industrial applications. In this study, health and environmental friendly poly (methyl methacrylate) (PMMA) microcapsules with narrow size distribution were also prepared for the first time using the dispersion cell membrane emulsification system. Characterization methods previously used for thin-shell microcapsules were expanded to analyse microcapsules with thick shells. The intrinsic mechanical properties of thick shells were determined using a micromanipulation technique and finite element analysis (FEM). The microcapsules structure was also considered in the determination of the permeability and diffusivity of the perfume oils in good solvents..

Interface-Resolving Simulation of Collision Efficiency of Cloud Droplets

NASA Astrophysics Data System (ADS)

Wang, Lian-Ping; Peng, Cheng; Rosa, Bodgan; Onishi, Ryo

2017-11-01

Small-scale air turbulence could enhance the geometric collision rate of cloud droplets while large-scale air turbulence could augment the diffusional growth of cloud droplets. Air turbulence could also enhance the collision efficiency of cloud droplets. Accurate simulation of collision efficiency, however, requires capture of the multi-scale droplet-turbulence and droplet-droplet interactions, which has only been partially achieved in the recent past using the hybrid direct numerical simulation (HDNS) approach. % where Stokes disturbance flow is assumed. The HDNS approach has two major drawbacks: (1) the short-range droplet-droplet interaction is not treated rigorously; (2) the finite-Reynolds number correction to the collision efficiency is not included. In this talk, using two independent numerical methods, we will develop an interface-resolved simulation approach in which the disturbance flows are directly resolved numerically, combined with a rigorous lubrication correction model for near-field droplet-droplet interaction. This multi-scale approach is first used to study the effect of finite flow Reynolds numbers on the droplet collision efficiency in still air. Our simulation results show a significant finite-Re effect on collision efficiency when the droplets are of similar sizes. Preliminary results on integrating this approach in a turbulent flow laden with droplets will also be presented. This work is partially supported by the National Science Foundation.

Many-body delocalization in a strongly disordered system with long-range interactions: Finite-size scaling

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-03-01

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1 /Rα is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N . The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d -dimensional system including the absence of localization in the infinite system at α <2 d and a universal scaling of a critical energy disordering Wc∝N2/d -α d .

Scaling the low-shear pulsatile TORVAD for pediatric heart failure

PubMed Central

Gohean, Jeffrey R.; Larson, Erik R.; Hsi, Brian H.; Kurusz, Mark; Smalling, Richard W.; Longoria, Raul G.

2016-01-01

This article provides an overview of the design challenges associated with scaling the low-shear pulsatile TORVAD ventricular assist device (VAD) for treating pediatric heart failure. A cardiovascular system model was used to determine that a 15 ml stroke volume device with a maximum flow rate of 4 L/min can provide full support to pediatric patients with body surface areas between 0.6 to 1.5 m2. Low shear stress in the blood is preserved as the device is scaled down and remains at least two orders of magnitude less than continuous flow VADs. A new magnetic linkage coupling the rotor and piston has been optimized using a finite element model (FEM) resulting in increased heat transfer to the blood while reducing the overall size of TORVAD. Motor FEM has also been used to reduce motor size and improve motor efficiency and heat transfer. FEM analysis predicts no more than 1°C temperature rise on any blood or tissue contacting surface of the device. The iterative computational approach established provides a methodology for developing a TORVAD platform technology with various device sizes for supporting the circulation of infants to adults. PMID:27832001

Scaling the Low-Shear Pulsatile TORVAD for Pediatric Heart Failure.

PubMed

Gohean, Jeffrey R; Larson, Erik R; Hsi, Brian H; Kurusz, Mark; Smalling, Richard W; Longoria, Raul G

This article provides an overview of the design challenges associated with scaling the low-shear pulsatile TORVAD ventricular assist device (VAD) for treating pediatric heart failure. A cardiovascular system model was used to determine that a 15 ml stroke volume device with a maximum flow rate of 4 L/min can provide full support to pediatric patients with body surface areas between 0.6 and 1.5 m. Low-shear stress in the blood is preserved as the device is scaled down and remains at least two orders of magnitude less than continuous flow VADs. A new magnetic linkage coupling the rotor and piston has been optimized using a finite element model (FEM) resulting in increased heat transfer to the blood while reducing the overall size of TORVAD. Motor FEM has also been used to reduce motor size and improve motor efficiency and heat transfer. FEM analysis predicts no more than 1°C temperature rise on any blood or tissue contacting surface of the device. The iterative computational approach established provides a methodology for developing a TORVAD platform technology with various device sizes for supporting the circulation of infants to adults.

Parallel Simulation of Three-Dimensional Free-Surface Fluid Flow Problems

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

BAER,THOMAS A.; SUBIA,SAMUEL R.; SACKINGER,PHILIP A.

2000-01-18

We describe parallel simulations of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact lines. The Galerlin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of problem unknowns. Issues concerning the proper constraints along the solid-fluid dynamic contact line inmore » three dimensions are discussed. Parallel computations are carried out for an example taken from the coating flow industry, flow in the vicinity of a slot coater edge. This is a three-dimensional free-surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another part of the flow domain. Discussion focuses on parallel speedups for fixed problem size, a class of problems of immediate practical importance.« less

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

PubMed Central

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

2013-01-01

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol−1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol−1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning. PMID:24320250

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects.

PubMed

Rocklin, Gabriel J; Mobley, David L; Dill, Ken A; Hünenberger, Philippe H

2013-11-14

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

NASA Astrophysics Data System (ADS)

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

2013-11-01

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol-1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol-1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Finite Element Modeling of Non-linear Coupled Interacting Fault System

NASA Astrophysics Data System (ADS)

Xing, H. L.; Zhang, J.; Wyborn, D.

2009-04-01

PANDAS - Parallel Adaptive static/dynamic Nonlinear Deformation Analysis System - a novel supercomputer simulation tool is developed for simulating the highly non-linear coupled geomechanical-fluid flow-thermal systems involving heterogeneously fractured geomaterials. PANDAS includes the following key components: Pandas/Pre, ESyS_Crustal, Pandas/Thermo, Pandas/Fluid and Pandas/Post as detailed in the following: • Pandas/Pre is developed to visualise the microseismicity events recorded during the hydraulic stimulation process to further evaluate the fracture location and evolution and geological setting of a certain reservoir, and then generate the mesh by it and/or other commercial graphics software (such as Patran) for the further finite element analysis of various cases; The Delaunay algorithm is applied as a suitable method for mesh generation using such a point set; • ESyS_Crustal is a finite element code developed for the interacting fault system simulation, which employs the adaptive static/dynamic algorithm to simulate the dynamics and evolution of interacting fault systems and processes that are relevant on short to mediate time scales in which several dynamic phenomena related with stick-slip instability along the faults need to be taken into account, i.e. (a). slow quasi-static stress accumulation, (b) rapid dynamic rupture, (c) wave propagation and (d) corresponding stress redistribution due to the energy release along the multiple fault boundaries; those are needed to better describe ruputure/microseimicity/earthquake related phenomena with applications in earthquake forecasting, hazard quantification, exploration, and environmental problems. It has been verified with various available experimental results[1-3]; • Pandas/Thermo is a finite element method based module for the thermal analysis of the fractured porous media; the temperature distribution is calculated from the heat transfer induced by the thermal boundary conditions without/with the coupled fluid effects and the geomechanical energy conversion for the pure/coupled thermal analysis. • Pandas/Fluid is a finite element method based module for simulating the fluid flow in the fractured porous media; the fluid flow velocity and pressure are calculated from energy equilibrium equations without/together with the coupling effects of the thermal and solid rock deformation for an independent/coupled fluid flow analysis; • Pandas/Post is to visualise the simulation results through the integration of VTK and/or Patran. All the above modules can be used independently/together to simulate individual/coupled phenomena (such as interacting fault system dynamics, heat flow and fluid flow) without/with coupling effects. PANDAS has been applied to the following issues: • visualisation of the microseismic events to monitor and determine where/how the underground rupture proceeds during a hydraulic stimulation, to generate the mesh using the recorded data for determining the domain of the ruptured zone and to evaluate the material parameters (i.e. the permeability) for the further numerical analysis; • interacting fault system simulation to determine the relevant complicated dynamic rupture process. • geomechanical-fluid flow coupling analysis to investigate the interactions between fluid flow and deformation in the fractured porous media under different loading conditions. • thermo-fluid flow coupling analysis of a fractured geothermal reservoir system. PANDAS will be further developed for a multiscale simulation of multiphase dynamic behaviour for a certain fractured geothermal reservoir. More details and additional application examples will be given during the presentation. References [1] Xing, H. L., Makinouchi, A. and Mora, P. (2007). Finite element modeling of interacting fault system, Physics of the Earth and Planetary Interiors, 163, 106-121.doi:10.1016/j.pepi.2007.05.006 [2] Xing, H. L., Mora, P., Makinouchi, A. (2006). An unified friction description and its application to simulation of frictional instability using finite element method. Philosophy Magazine, 86, 3453-3475 [3] Xing, H. L., Mora, P.(2006). Construction of an intraplate fault system model of South Australia, and simulation tool for the iSERVO institute seed project.. Pure and Applied Geophysics. 163, 2297-2316. DOI 10.1007/s00024-006-0127-x

Thermocapillary flow contribution to dropwise condensation heat transfer

NASA Astrophysics Data System (ADS)

Phadnis, Akshay; Rykaczewski, Konrad

2017-11-01

With recent developments of durable hydrophobic materials potentially enabling industrial applications of dropwise condensation, accurate modeling of heat transfer during this phase change process is becoming increasingly important. Classical steady state models of dropwise condensation are based on the integration of heat transfer through individual droplets over the entire drop size distribution. These models consider only the conduction heat transfer inside the droplets. However, simple scaling arguments suggest that thermocapillary flows might exist in such droplets. In this work, we used Finite Element heat transfer model to quantify the effect of Marangoni flow on dropwise condensation heat transfer of liquids with a wide range of surface tensions ranging from water to pentane. We confirmed that the Marangoni flow is present for a wide range of droplet sizes, but only has quantifiable effects on heat transfer in drops larger than 10 µm. By integrating the single drop heat transfer simulation results with drop size distribution for the cases considered, we demonstrated that Marangoni flow contributes a 10-30% increase in the overall heat transfer coefficient over conduction only model.

Least-squares finite element method for fluid dynamics

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1989-01-01

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Application of program generation technology in solving heat and flow problems

NASA Astrophysics Data System (ADS)

Wan, Shui; Wu, Bangxian; Chen, Ningning

2007-05-01

Based on a new DIY concept for software development, an automatic program-generating technology attached on a software system called as Finite Element Program Generator (FEPG) provides a platform of developing programs, through which a scientific researcher can submit his special physico-mathematical problem to the system in a more direct and convenient way for solution. For solving flow and heat problems by using finite element method, the stabilization technologies and fraction-step methods are adopted to overcome the numerical difficulties caused mainly due to the dominated convection. A couple of benchmark problems are given in this paper as examples to illustrate the usage and the superiority of the automatic program generation technique, including the flow in a lid-driven cavity, the starting flow in a circular pipe, the natural convection in a square cavity, and the flow past a circular cylinder, etc. They are also shown as the verification of the algorithms.

Semianalytical computation of path lines for finite-difference models

USGS Publications Warehouse

Pollock, D.W.

1988-01-01

A semianalytical particle tracking method was developed for use with velocities generated from block-centered finite-difference ground-water flow models. Based on the assumption that each directional velocity component varies linearly within a grid cell in its own coordinate directions, the method allows an analytical expression to be obtained describing the flow path within an individual grid cell. Given the intitial position of a particle anywhere in a cell, the coordinates of any other point along its path line within the cell, and the time of travel between them, can be computed directly. For steady-state systems, the exit point for a particle entering a cell at any arbitrary location can be computed in a single step. By following the particle as it moves from cell to cell, this method can be used to trace the path of a particle through any multidimensional flow field generated from a block-centered finite-difference flow model. -Author

Effects of finite-size particles on the turbulent flows in a square duct

NASA Astrophysics Data System (ADS)

Yu, Zhaosheng; Lin, Zhaowu; Shao, Xueming; Wang, Lian-Ping

2015-11-01

Fully resolved numerical simulations of the particle-laden turbulent flows in a square duct are performed with a direct-forcing fictitious domain method. The effects of the finite-size particles on the mean and root-mean-square (RMS) velocities are investigated at the friction Reynolds number of 150 (based on the friction velocity and half duct width) and the particle volume fractions ranging from 0.78% to 7.07%. For the neutrally buoyant case, our results show that the mean secondary flow is enhanced and its circulation center shifts closer to the center of the duct cross-section when the particles are added. The reason for the particle effect on the mean secondary flow is analyzed by examining the terms in the mean streamwise vorticity equation. The particles enhance the wall-tangential component of the RMS velocity (i.e. Reynolds normal stress) more than its wall-normal component in the near-wall region near the corners, resulting in the enhancement in the gradients of the normal stress difference, which we think is mainly responsible for the enhancement in the mean secondary flow. The particles accumulate preferentially in the near-corner region in the neutrally buoyant case. In addition, the effects of particle sedimentation are examined at different Shields numbers. The work was supported by the National Natural Science Foundation of China (11372275) and Research Fund for the Doctoral Program of Higher Education of China (20130101110035).

Lesion size estimator of cardiac radiofrequency ablation at different common locations with different tip temperatures.

PubMed

Lai, Yu-Chi; Choy, Young Bin; Haemmerich, Dieter; Vorperian, Vicken R; Webster, John G

2004-10-01

Finite element method (FEM) analysis has become a common method to analyze the lesion formation during temperature-controlled radiofrequency (RF) cardiac ablation. We present a process of FEM modeling a system including blood, myocardium, and an ablation catheter with a thermistor embedded at the tip. The simulation used a simple proportional-integral (PI) controller to control the entire process operated in temperature-controlled mode. Several factors affect the lesion size such as target temperature, blood flow rate, and application time. We simulated the time response of RF ablation at different locations by using different target temperatures. The applied sites were divided into two groups each with a different convective heat transfer coefficient. The first group was high-flow such as the atrioventricular (AV) node and the atrial aspect of the AV annulus, and the other was low-flow such as beneath the valve or inside the coronary sinus. Results showed the change of lesion depth and lesion width with time, under different conditions. We collected data for all conditions and used it to create a database. We implemented a user-interface, the lesion size estimator, where the user enters set temperature and location. Based on the database, the software estimated lesion dimensions during different applied durations. This software could be used as a first-step predictor to help the electrophysiologist choose treatment parameters.

Bacterial aggregation and biofilm formation in a vortical flow

PubMed Central

Yazdi, Shahrzad; Ardekani, Arezoo M.

2012-01-01

Bacterial aggregation and patchiness play an important role in a variety of ecological processes such as competition, adaptation, epidemics, and succession. Here, we demonstrate that hydrodynamics of their environment can lead to their aggregation. This is specially important since microbial habitats are rarely at rest (e.g., ocean, blood stream, flow in porous media, and flow through membrane filtration processes). In order to study the dynamics of bacterial collection in a vortical flow, we utilize a microfluidic system to mimic some of the important microbial conditions at ecologically relevant spatiotemporal scales. We experimentally demonstrate the formation of “ring”-shaped bacterial collection patterns and subsequently the formation of biofilm streamers in a microfluidic system. Acoustic streaming of a microbubble is used to generate a vortical flow in a microchannel. Due to bacteria's finite-size, the microorganisms are directed to closed streamlines and trapped in the vortical flow. The collection of bacteria in the vortices occurs in a matter of seconds, and unexpectedly, triggers the formation of biofilm streamers within minutes. Swimming bacteria have a competitive advantage to respond to their environmental conditions. In order to investigate the role of bacterial motility on the rate of collection, two strains of Escherichia coli bacteria with different motilities are used. We show that the bacterial collection in a vortical flow is strongly pronounced for high motile bacteria. PMID:24339847

Vibration analysis of large centrifugal pump rotors

NASA Astrophysics Data System (ADS)

Y Zhao, W.; Ge, J. G.; Ma, D.; Li, C. M.; Bao, S. B.

2013-12-01

Through the critical speed of centrifugal pumps, internal flow field and the force of the impeller, we analyze centrifugal pump vibration. Using finite element analysis software ANSYS to calculate the natural frequency of the rotor system and the critical speed; with the help of the Fluent software to simulate pump internal flow field, we conclude that speed increase will not cause intense vibration of the fluid in the pump. Using unsteady numerical simulation we discovered that in an impeller suffering transient radial force cyclical change periodically, as well as the frequency size determined by the product of the impeller speed and number of blades, resonance phenomena should make impeller to transient radial force frequency. If wanting to avoid pump resonance when it is running away, the transient radial force frequency should avoid the frequency range which can cause resonance.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

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.

Percolation Thresholds in Angular Grain media: Drude Directed Infiltration

NASA Astrophysics Data System (ADS)

Priour, Donald

Pores in many realistic systems are not well delineated channels, but are void spaces among grains impermeable to charge or fluid flow which comprise the medium. Sparse grain concentrations lead to permeable systems, while concentrations in excess of a critical density block bulk fluid flow. We calculate percolation thresholds in porous materials made up of randomly placed (and oriented) disks, tetrahedrons, and cubes. To determine if randomly generated finite system samples are permeable, we deploy virtual tracer particles which are scattered (e.g. specularly) by collisions with impenetrable angular grains. We hasten the rate of exploration (which would otherwise scale as ncoll1 / 2 where ncoll is the number of collisions with grains if the tracers followed linear trajectories) by considering the tracer particles to be charged in conjunction with a randomly directed uniform electric field. As in the Drude treatment, where a succession of many scattering events leads to a constant drift velocity, tracer displacements on average grow linearly in ncoll. By averaging over many disorder realizations for a variety of systems sizes, we calculate the percolation threshold and critical exponent which characterize the phase transition.

Hierarchical organization as a diagnostic approach to volcano mechanics: Validation on Piton de la Fournaise

NASA Astrophysics Data System (ADS)

Grasso, J. R.; Bachèlery, P.

Self-organized systems are often used to describe natural phenomena where power laws and scale invariant geometry are observed. The Piton de la Fournaise volcano shows power-law behavior in many aspects. These include the temporal distribution of eruptions, the frequency-size distributions of induced earthquakes, dikes, fissures, lava flows and interflow periods, all evidence of self-similarity over a finite scale range. We show that the bounds to scale-invariance can be used to derive geomechanical constraints on both the volcano structure and the volcano mechanics. We ascertain that the present magma bodies are multi-lens reservoirs in a quasi-eruptive condition, i.e. a marginally critical state. The scaling organization of dynamic fluid-induced observables on the volcano, such as fluid induced earthquakes, dikes and surface fissures, appears to be controlled by underlying static hierarchical structure (geology) similar to that proposed for fluid circulations in human physiology. The emergence of saturation lengths for the scalable volcanic observable argues for the finite scalability of complex naturally self-organized critical systems, including volcano dynamics.

Three-dimensional finite amplitude electroconvection in dielectric liquids

NASA Astrophysics Data System (ADS)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Spiral vortices and Taylor vortices in the annulus between rotating cylinders and the effect of an axial flow.

PubMed

Hoffmann, Ch; Lücke, M; Pinter, A

2004-05-01

We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter rotating as well as with corotating cylinders. The full, time dependent Navier Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation, and stability behavior between spiral vortices with azimuthal wave numbers M=+/-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1, 0, and 1 vortex structures are changed by an externally imposed axial through flow with Reynolds numbers in the range -40< or =Re< or =40. Among other things we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.

A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner

NASA Technical Reports Server (NTRS)

Watson, W. R.

1977-01-01

Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.

Preconditioning and the limit to the incompressible flow equations

NASA Technical Reports Server (NTRS)

Turkel, E.; Fiterman, A.; Vanleer, B.

1993-01-01

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

Meta-ecosystem dynamics and functioning on finite spatial networks

PubMed Central

Marleau, Justin N.; Guichard, Frédéric; Loreau, Michel

2014-01-01

The addition of spatial structure to ecological concepts and theories has spurred integration between sub-disciplines within ecology, including community and ecosystem ecology. However, the complexity of spatial models limits their implementation to idealized, regular landscapes. We present a model meta-ecosystem with finite and irregular spatial structure consisting of local nutrient–autotrophs–herbivores ecosystems connected through spatial flows of materials and organisms. We study the effect of spatial flows on stability and ecosystem functions, and provide simple metrics of connectivity that can predict these effects. Our results show that high rates of nutrient and herbivore movement can destabilize local ecosystem dynamics, leading to spatially heterogeneous equilibria or oscillations across the meta-ecosystem, with generally increased meta-ecosystem primary and secondary production. However, the onset and the spatial scale of these emergent dynamics depend heavily on the spatial structure of the meta-ecosystem and on the relative movement rate of the autotrophs. We show how this strong dependence on finite spatial structure eludes commonly used metrics of connectivity, but can be predicted by the eigenvalues and eigenvectors of the connectivity matrix that describe the spatial structure and scale. Our study indicates the need to consider finite-size ecosystems in meta-ecosystem theory. PMID:24403323

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.

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.

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Modifications to the modular three-dimensional finite-difference ground-water flow model used for the Columbia Plateau Regional Aquifer-System Analysis, Washington, Oregon, and Idaho

USGS Publications Warehouse

Hansen, A.J.

1993-01-01

The report documents modifications to the U.S. Geological Survey's modular three-dimensional finite-difference ground-water flow model used for a regional aquifer-system analysis of the Columbia Plateau. The report, which describes the concepts and mathematical basis for the modifications, is intended for potential users who are familiar with the original modular model. The modifications permit flow from a layer to any adjacent layer, allow the model to retain a cell of a layer that has been cut completely through by a canyon, and allow placing ground-water flow barriers on only specified branch conductances; a special version of the modified model uses a convergent grid. The report describes the data-input items that this modified model must read.

Unified gas-kinetic scheme with multigrid convergence for rarefied flow study

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2017-09-01

The unified gas kinetic scheme (UGKS) is based on direct modeling of gas dynamics on the mesh size and time step scales. With the modeling of particle transport and collision in a time-dependent flux function in a finite volume framework, the UGKS can connect the flow physics smoothly from the kinetic particle transport to the hydrodynamic wave propagation. In comparison with the direct simulation Monte Carlo (DSMC) method, the current equation-based UGKS can implement implicit techniques in the updates of macroscopic conservative variables and microscopic distribution functions. The implicit UGKS significantly increases the convergence speed for steady flow computations, especially in the highly rarefied and near continuum regimes. In order to further improve the computational efficiency, for the first time, a geometric multigrid technique is introduced into the implicit UGKS, where the prediction step for the equilibrium state and the evolution step for the distribution function are both treated with multigrid acceleration. More specifically, a full approximate nonlinear system is employed in the prediction step for fast evaluation of the equilibrium state, and a correction linear equation is solved in the evolution step for the update of the gas distribution function. As a result, convergent speed has been greatly improved in all flow regimes from rarefied to the continuum ones. The multigrid implicit UGKS (MIUGKS) is used in the non-equilibrium flow study, which includes microflow, such as lid-driven cavity flow and the flow passing through a finite-length flat plate, and high speed one, such as supersonic flow over a square cylinder. The MIUGKS shows 5-9 times efficiency increase over the previous implicit scheme. For the low speed microflow, the efficiency of MIUGKS is several orders of magnitude higher than the DSMC. Even for the hypersonic flow at Mach number 5 and Knudsen number 0.1, the MIUGKS is still more than 100 times faster than the DSMC method for obtaining a convergent steady state solution.

Investigation of Liner Characteristics in the NASA Langley Curved Duct Test Rig

NASA Technical Reports Server (NTRS)

Gerhold, Carl H.; Brown, Martha C.; Watson, Willie R.; Jones, Michael G.

2007-01-01

The Curved Duct Test Rig (CDTR), which is designed to investigate propagation of sound in a duct with flow, has been developed at NASA Langley Research Center. The duct incorporates an adaptive control system to generate a tone in the duct at a specific frequency with a target Sound Pressure Level and a target mode shape. The size of the duct, the ability to isolate higher order modes, and the ability to modify the duct configuration make this rig unique among experimental duct acoustics facilities. An experiment is described in which the facility performance is evaluated by measuring the sound attenuation by a sample duct liner. The liner sample comprises one wall of the liner test section. Sound in tones from 500 to 2400 Hz, with modes that are parallel to the liner surface of order 0 to 5, and that are normal to the liner surface of order 0 to 2, can be generated incident on the liner test section. Tests are performed in which sound is generated without axial flow in the duct and with flow at a Mach number of 0.275. The attenuation of the liner is determined by comparing the sound power in a hard wall section downstream of the liner test section to the sound power in a hard wall section upstream of the liner test section. These experimentally determined attenuations are compared to numerically determined attenuations calculated by means of a finite element analysis code. The code incorporates liner impedance values educed from measured data from the NASA Langley Grazing Incidence Tube, a test rig that is used for investigating liner performance with flow and with (0,0) mode incident grazing. The analytical and experimental results compare favorably, indicating the validity of the finite element method and demonstrating that finite element prediction tools can be used together with experiment to characterize the liner attenuation.

A finite area scheme for shallow granular flows on three-dimensional surfaces

NASA Astrophysics Data System (ADS)

Rauter, Matthias

2017-04-01

Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

Airflow structures and nano-particle deposition in a human upper airway model

NASA Astrophysics Data System (ADS)

Zhang, Z.; Kleinstreuer, C.

2004-07-01

Considering a human upper airway model, or equivalently complex internal flow conduits, the transport and deposition of nano-particles in the 1-150 nm diameter range are simulated and analyzed for cyclic and steady flow conditions. Specifically, using a commercial finite-volume software with user-supplied programs as a solver, the Euler-Euler approach for the fluid-particle dynamics is employed with a low-Reynolds-number k- ω model for laminar-to-turbulent airflow and the mass transfer equation for dispersion of nano-particles or vapors. Presently, the upper respiratory system consists of two connected segments of a simplified human cast replica, i.e., the oral airways from the mouth to the trachea (Generation G0) and an upper tracheobronchial tree model of G0-G3. Experimentally validated computational fluid-particle dynamics results show the following: (i) transient effects in the oral airways appear most prominently during the decelerating phase of the inspiratory cycle; (ii) selecting matching flow rates, total deposition fractions of nano-size particles for cyclic inspiratory flow are not significantly different from those for steady flow; (iii) turbulent fluctuations which occur after the throat can persist downstream to at least Generation G3 at medium and high inspiratory flow rates (i.e., Qin⩾30 l/min) due to the enhancement of flow instabilities just upstream of the flow dividers; however, the effects of turbulent fluctuations on nano-particle deposition are quite minor in the human upper airways; (iv) deposition of nano-particles occurs to a relatively greater extent around the carinal ridges when compared to the straight tubular segments in the bronchial airways; (v) deposition distributions of nano-particles vary with airway segment, particle size, and inhalation flow rate, where the local deposition is more uniformly distributed for large-size particles (say, dp=100 nm) than for small-size particles (say, dp=1 nm); (vi) dilute 1 nm particle suspensions behave like certain (fuel) vapors which have the same diffusivities; and (vii) new correlations for particle deposition as a function of a diffusion parameter are most useful for global lung modeling.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

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.

Space-time least-squares finite element method for convection-reaction system with transformed variables

PubMed Central

Nam, Jaewook

2011-01-01

We present a method to solve a convection-reaction system based on a least-squares finite element method (LSFEM). For steady-state computations, issues related to recirculation flow are stated and demonstrated with a simple example. The method can compute concentration profiles in open flow even when the generation term is small. This is the case for estimating hemolysis in blood. Time-dependent flows are computed with the space-time LSFEM discretization. We observe that the computed hemoglobin concentration can become negative in certain regions of the flow; it is a physically unacceptable result. To prevent this, we propose a quadratic transformation of variables. The transformed governing equation can be solved in a straightforward way by LSFEM with no sign of unphysical behavior. The effect of localized high shear on blood damage is shown in a circular Couette-flow-with-blade configuration, and a physiological condition is tested in an arterial graft flow. PMID:21709752

A fast numerical method for ideal fluid flow in domains with multiple stirrers

NASA Astrophysics Data System (ADS)

Nasser, Mohamed M. S.; Green, Christopher C.

2018-03-01

A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field—given a particular distribution of any finite number of stirrers of specified shape and speed—can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

External mean flow influence on sound transmission through finite clamped double-wall sandwich panels

NASA Astrophysics Data System (ADS)

Liu, Yu; Catalan, Jean-Cédric

2017-09-01

This paper studies the influence of an external mean flow on the sound transmission through finite clamped double-wall sandwich panels lined with poroelastic materials. Biot's theory is employed to describe wave propagation in poroelastic materials and various configurations of coupling the poroelastic layer to the facing plates are considered. The clamped boundary of finite panels are dealt with by the modal superposition theory and the weighted residual (Garlekin) method, leading to a matrix equation solution for the sound transmission loss (STL) through the structure. The theoretical model is validated against existing theories of infinite sandwich panels with and without an external flow. The numerical results of a single incident wave show that the external mean flow has significant effects on the STL which are coupled with the clamped boundary effect dominating in the low-frequency range. The external mean flow also influences considerably the limiting incidence angle of the panel system and the effect of the incidence angle on the STL. However, the influences of the azimuthal angle and the external flow orientation are negligible.

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

DOE PAGES

Hu, Rui

2017-03-27

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

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

Hu, Rui

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less

Parametric Optimization of Thermoelectric Generators for Waste Heat Recovery

NASA Astrophysics Data System (ADS)

Huang, Shouyuan; Xu, Xianfan

2016-10-01

This paper presents a methodology for design optimization of thermoelectric-based waste heat recovery systems called thermoelectric generators (TEGs). The aim is to maximize the power output from thermoelectrics which are used as add-on modules to an existing gas-phase heat exchanger, without negative impacts, e.g., maintaining a minimum heat dissipation rate from the hot side. A numerical model is proposed for TEG coupled heat transfer and electrical power output. This finite-volume-based model simulates different types of heat exchangers, i.e., counter-flow and cross-flow, for TEGs. Multiple-filled skutterudites and bismuth-telluride-based thermoelectric modules (TEMs) are applied, respectively, in higher and lower temperature regions. The response surface methodology is implemented to determine the optimized TEG size along and across the flow direction and the height of thermoelectric couple legs, and to analyze their covariance and relative sensitivity. A genetic algorithm is employed to verify the globality of the optimum. The presented method will be generally useful for optimizing heat-exchanger-based TEG performance.

Experimental assessment of spanwise-oscillating dielectric electroactive surfaces for turbulent drag reduction in an air channel flow

NASA Astrophysics Data System (ADS)

Gatti, Davide; Güttler, Andreas; Frohnapfel, Bettina; Tropea, Cameron

2015-05-01

In the present work, wall oscillations for turbulent skin friction drag reduction are realized in an air turbulent duct flow by means of spanwise-oscillating active surfaces based on dielectric electroactive polymers. The actuator system produces spanwise wall velocity oscillations of 820 mm/s semi-amplitude at its resonance frequency of 65 Hz while consuming an active power of a few 100 mW. The actuators achieved a maximum integral drag reduction of 2.4 %. The maximum net power saving, budget of the power benefit and cost of the control, was measured for the first time with wall oscillations. Though negative, the net power saving is order of magnitudes higher than what has been estimated in previous studies. Two new direct numerical simulations of turbulent channel flow show that the finite size of the actuator only partially explains the lower values of integral drag reduction typically achieved in laboratory experiments compared to numerical simulations.

Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

The constructal law and the evolution of design in nature.

PubMed

Bejan, Adrian; Lorente, Sylvie

2011-10-01

The constructal law accounts for the universal phenomenon of generation and evolution of design (configuration, shape, structure, pattern, rhythm). This phenomenon is observed across the board, in animate, inanimate and human systems. The constructal law states the time direction of the evolutionary design phenomenon. It defines the concept of design evolution in physics. Along with the first and second law, the constructal law elevates thermodynamics to a science of systems with configuration. In this article we review the more recent work of our group, with emphasis on the advances made with the constructal law in the natural sciences. Highlighted are the oneness of animate and inanimate designs, the origin of finite-size organs on animals and vehicles, the flow of stresses as the generator of design in solid structures (skeletons, vegetation), the universality and rigidity of hierarchy in all flow systems, and the global design of human flows. Noteworthy is the tapestry of distributed energy systems, which balances nodes of production with networks of distribution on the landscape, and serves as key to energy sustainability and empowerment. At the global level, the constructal law accounts for the geography and design of human movement, wealth and communications. Copyright © 2011 Elsevier B.V. All rights reserved.

Finite-time braiding exponents

NASA Astrophysics Data System (ADS)

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

Finite-time braiding exponents.

PubMed

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Groundwater dynamics in a two-dimensional aquifer

NASA Astrophysics Data System (ADS)

Jules, Valentin; Devauchelle, Olivier; Lajeunesse, Eric

2017-11-01

During a rain event, water infiltrates into the ground where it flows slowly towards a river. The time scale and the geometry of this flow control the chemical composition and the discharge of the river. We use a tank filled with glass beads to simulate this process in a simplified laboratory experiment. A sprinkler pipe generates rain, which infiltrates into the porous material. Groundwater exits this laboratory aquifer through a side of the tank. Guérin et al. (2014) investigated the case of a quasi-horizontal flow. In nature, however, groundwater often follows non-horizontal flowlines. To create a vertical flow, we place the outlet of our experiment high above its bottom. We find that, during rainfall, the discharge Q increases as the rainfall rate R times the square root of time t (Q Rt 1 / 2). This laboratory aquifer thus responds linearly to the forcing. However, long after the rain has stopped, the discharge decreases as the inverse square of time (Q t-2), although linear systems of finite size typically relax exponentially. We investigate this surprising behavior using a combination of complex analysis and numerical methods.

ISSM: Ice Sheet System Model

NASA Technical Reports Server (NTRS)

Larour, Eric; Schiermeier, John E.; Seroussi, Helene; Morlinghem, Mathieu

2013-01-01

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Modeling erosion and sedimentation coupled with hydrological and overland flow processes at the watershed scale

NASA Astrophysics Data System (ADS)

Kim, Jongho; Ivanov, Valeriy Y.; Katopodes, Nikolaos D.

2013-09-01

A novel two-dimensional, physically based model of soil erosion and sediment transport coupled to models of hydrological and overland flow processes has been developed. The Hairsine-Rose formulation of erosion and deposition processes is used to account for size-selective sediment transport and differentiate bed material into original and deposited soil layers. The formulation is integrated within the framework of the hydrologic and hydrodynamic model tRIBS-OFM, Triangulated irregular network-based, Real-time Integrated Basin Simulator-Overland Flow Model. The integrated model explicitly couples the hydrodynamic formulation with the advection-dominated transport equations for sediment of multiple particle sizes. To solve the system of equations including both the Saint-Venant and the Hairsine-Rose equations, the finite volume method is employed based on Roe's approximate Riemann solver on an unstructured grid. The formulation yields space-time dynamics of flow, erosion, and sediment transport at fine scale. The integrated model has been successfully verified with analytical solutions and empirical data for two benchmark cases. Sensitivity tests to grid resolution and the number of used particle sizes have been carried out. The model has been validated at the catchment scale for the Lucky Hills watershed located in southeastern Arizona, USA, using 10 events for which catchment-scale streamflow and sediment yield data were available. Since the model is based on physical laws and explicitly uses multiple types of watershed information, satisfactory results were obtained. The spatial output has been analyzed and the driving role of topography in erosion processes has been discussed. It is expected that the integrated formulation of the model has the promise to reduce uncertainties associated with typical parameterizations of flow and erosion processes. A potential for more credible modeling of earth-surface processes is thus anticipated.

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

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.

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

Scaling, Microstructure and Dynamic Fracture

NASA Astrophysics Data System (ADS)

Minich, Roger W.; Kumar, Mukul; Schwarz, Adam; Cazamias, James

2006-07-01

The relationship between pullback velocity and impact velocity is studied for different microstructures in Cu. A size distribution of potential nucleation sites is derived under the conditions of an applied stochastic stress field. The size distribution depends on the amplitude of the stress fluctuations, which may be proportional to the flow stress thereby providing a connection between plastic flow and microvoid nucleation rate. The pullback velocity in turn depends on the nucleation rate resulting in a prediction for the relationship between pullback velocity and flow stress. The theory is compared to results from Cu on Cu gas-gun experiments (10-50 GPa) with different microstructures. The scaling law relating pullback velocity and impact velocity is incorporated into a 1D finite difference code and is shown to reproduce the experimental data with one adjustable parameter, the nucleation exponent, Γ.

Four-way coupling of a three-dimensional debris flow solver to a Lagrangian Particle Simulation: method and first results

NASA Astrophysics Data System (ADS)

von Boetticher, Albrecht; Rickenmann, Dieter; McArdell, Brian; Kirchner, James W.

2017-04-01

Debris flows are dense flowing mixtures of water, clay, silt, sand and coarser particles. They are a common natural hazard in mountain regions and frequently cause severe damage. Modeling debris flows to design protection measures is still challenging due to the complex interactions within the inhomogeneous material mixture, and the sensitivity of the flow process to the channel geometry. The open-source, OpenFOAM-based finite-volume debris flow model debrisInterMixing (von Boetticher et al, 2016) defines rheology parameters based on the material properties of the debris flow mixture to reduce the number of free model parameters. As a simplification in this first model version, gravel was treated as a Coulomb-viscoplastic fluid, neglecting grain-to-grain collisions and the coupling between the coarser gravel grains and the interstitial fluid. Here we present an extension of that solver, accounting for the particle-to-particle and particle-to-boundary contacts with a Lagrangian Particle Simulation composed of spherical grains and a user-defined grain size distribution. The grain collisions of the Lagrangian particles add granular flow behavior to the finite-volume simulation of the continuous phases. The two-way coupling exchanges momentum between the phase-averaged flow in a finite volume cell, and among all individual particles contained in that cell, allowing the user to choose from a number of different drag models. The momentum exchange is implemented in the momentum equation and in the pressure equation (ensuring continuity) of the so-called PISO-loop, resulting in a stable 4-way coupling (particle-to-particle, particle-to-boundary, particle-to-fluid and fluid-to-particle) that represents the granular and viscous flow behavior of debris flow material. We will present simulations that illustrate the relative benefits and drawbacks of explicitly representing grain collisions, compared to the original debrisInterMixing solver.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

NASA Technical Reports Server (NTRS)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Computational techniques for flows with finite-rate condensation

NASA Technical Reports Server (NTRS)

Candler, Graham V.

1993-01-01

A computational method to simulate the inviscid two-dimensional flow of a two-phase fluid was developed. This computational technique treats the gas phase and each of a prescribed number of particle sizes as separate fluids which are allowed to interact with one another. Thus, each particle-size class is allowed to move through the fluid at its own velocity at each point in the flow field. Mass, momentum, and energy are exchanged between each particle class and the gas phase. It is assumed that the particles do not collide with one another, so that there is no inter-particle exchange of momentum and energy. However, the particles are allowed to grow, and therefore, they may change from one size class to another. Appropriate rates of mass, momentum, and energy exchange between the gas and particle phases and between the different particle classes were developed. A numerical method was developed for use with this equation set. Several test cases were computed and show qualitative agreement with previous calculations.

The effect of a finite focal spot size on location dependent detectability in a fan beam CT system

NASA Astrophysics Data System (ADS)

Kim, Byeongjoon; Baek, Jongduk

2017-03-01

A finite focal spot size is one of the sources to degrade the resolution performance in a fan beam CT system. In this work, we investigated the effect of the finite focal spot size on signal detectability. For the evaluation, five spherical objects with diameters of 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm were used. The optical focal spot size viewed at the iso-center was a 1 mm (height) × 1 mm (width) with a target angle of 7 degrees, corresponding to an 8.21 mm (i.e., 1 mm / sin (7°)) focal spot length. Simulated projection data were acquired using 8 × 8 source lets, and reconstructed by Hanning weighted filtered backprojection. For each spherical object, the detectability was calculated at (0 mm, 0 mm) and (0 mm, 200 mm) using two image quality metrics: pixel signal to noise ratio (SNR) and detection SNR. For all signal sizes, the pixel SNR is higher at the iso-center since the noise variance at the off-center is much higher than that at the iso-center due to the backprojection weightings used in direct fan beam reconstruction. In contrast, detection SNR shows similar values for different spherical objects except 1 mm and 2 mm diameter spherical objects. Overall, the results indicate the resolution loss caused by the finite focal spot size degrades the detection performance, especially for small objects with less than 2 mm diameter.

Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers

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

Abbas, M., E-mail: micheline.abbas@ensiacet.fr; CNRS, Fédération de recherche FERMaT, CNRS, 31400, Toulouse; Magaud, P.

2014-12-15

The migration of neutrally buoyant finite sized particles in a Newtonian square channel flow is investigated in the limit of very low solid volumetric concentration, within a wide range of channel Reynolds numbers Re = [0.07-120]. In situ microscope measurements of particle distributions, taken far from the channel inlet (at a distance several thousand times the channel height), revealed that particles are preferentially located near the channel walls at Re > 10 and near the channel center at Re < 1. Whereas the cross-streamline particle motion is governed by inertia-induced lift forces at high inertia, it seems to be controlledmore » by shear-induced particle interactions at low (but finite) Reynolds numbers, despite the low solid volume fraction (<1%). The transition between both regimes is observed in the range Re = [1-10]. In order to exclude the effect of multi-body interactions, the trajectories of single freely moving particles are calculated thanks to numerical simulations based on the force coupling method. With the deployed numerical tool, the complete particle trajectories are accessible within a reasonable computational time only in the inertial regime (Re > 10). In this regime, we show that (i) the particle undergoes cross-streamline migration followed by a cross-lateral migration (parallel to the wall) in agreement with previous observations, and (ii) the stable equilibrium positions are located at the midline of the channel faces while the diagonal equilibrium positions are unstable. At low flow inertia, the first instants of the numerical simulations (carried at Re = O(1)) reveal that the cross-streamline migration of a single particle is oriented towards the channel wall, suggesting that the particle preferential positions around the channel center, observed in the experiments, are rather due to multi-body interactions.« less

Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

NASA Astrophysics Data System (ADS)

Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K.

2018-02-01

We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.

Polysaccharide characterization by hollow-fiber flow field-flow fractionation with on-line multi-angle static light scattering and differential refractometry.

PubMed

Pitkänen, Leena; Striegel, André M

2015-02-06

Accurate characterization of the molar mass and size of polysaccharides is an ongoing challenge, oftentimes due to architectural diversity but also to the broad molar mass (M) range over which a single polysaccharide can exist and to the ultra-high M of many polysaccharides. Because of the latter, many of these biomacromolecules experience on-column, flow-induced degradation during analysis by size-exclusion and, even, hydrodynamic chromatography (SEC and HDC, respectively). The necessity for gentler fractionation methods has, to date, been addressed employing asymmetric flow field-flow fractionation (AF4). Here, we introduce the coupling of hollow-fiber flow field-flow fractionation (HF5) to multi-angle static light scattering (MALS) and differential refractometry (DRI) detection for the analysis of polysaccharides. In HF5, less stresses are placed on the macromolecules during separation than in SEC or HDC, and HF5 can offer a higher sensitivity, with less propensity for system overloading and analyte aggregation, than generally found in AF4. The coupling to MALS and DRI affords the determination of absolute, calibration-curve-independent molar mass averages and dispersities. Results from the present HF5/MALS/DRI experiments with dextrans, pullulans, and larch arabinogalactan were augmented with hydrodynamic radius (RH) measurements from off-line quasi-elastic light scattering (QELS) and by RH distribution calculations and fractogram simulations obtained via a finite element analysis implementation of field-flow fractionation theory by commercially available software. As part of this study, we have investigated analyte recovery in HF5 and also possible reasons for discrepancies between calculated and simulated results vis-à-vis experimentally determined data. Published by Elsevier B.V.

Ground-water flow in the New Jersey Coastal Plain

USGS Publications Warehouse

Martin, Mary

1998-01-01

Ground-water flow in 10 aquifers and 9 intervening confining units of the New Jersey Coastal Plain was simulated as part of the Regional Aquifer System Analysis. Data on aquifer and confining unit characteristics and on pumpage and water levels from 1918 through 1980 were incorporated into a multilayer finite-difference model. The report describes the conceptual hydrogeologic model of the unstressed flow systems, the methods and approach used in simulating flow, and the results of the simulations.

Development of stable low-electroosmotic mobility coatings. [for use in electrophoresis systems in space

NASA Technical Reports Server (NTRS)

Vanderhoff, J. W.; Micale, F. J.

1979-01-01

Long-time rinsings of the Z6040-methlycellulose coating used successfully on the ASTP MA=011 experiment indicate the permanency of this coating is inadequate for continuous flowing systems. Two approaches are described for developing coatings which are stable under continuous fluid movement and which exhibit finite and predictable electroosmotic mobility values while being effective on different types of surfaces, such as glass, plastics, and ceramic alumina, such as is currently used as the electrophoresis channel in the GE-SPAR-CPE apparatus. The surface charge modification of polystyrene latex, especially by protein absorption, to be used as model materials for ground-based electrophoresis experiments, and the preliminary work directed towards the seeded polymerization of large-particle-size monodisperse latexes in a microgravity environment are discussed.

Finite-time barriers to reaction front propagation

NASA Astrophysics Data System (ADS)

Locke, Rory; Mahoney, John; Mitchell, Kevin

2015-11-01

Front propagation in advection-reaction-diffusion systems gives rise to rich geometric patterns. It has been shown for time-independent and time-periodic fluid flows that invariant manifolds, termed burning invariant manifolds (BIMs), serve as one-sided dynamical barriers to the propagation of reaction front. More recently, theoretical work has suggested that one-sided barriers, termed burning Lagrangian Coherent structures (bLCSs), exist for fluid velocity data prescribed over a finite time interval, with no assumption on the time-dependence of the flow. In this presentation, we use a time-varying fluid ``wind'' in a double-vortex channel flow to demonstrate that bLCSs form the (locally) most attracting or repelling fronts.

Scaling laws and bulk-boundary decoupling in heat flow.

PubMed

del Pozo, Jesús J; Garrido, Pedro L; Hurtado, Pablo I

2015-03-01

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows one to measure the marginal anomaly of the heat conductivity predicted for hard disks.

A finite-element model for simulation of two-dimensional steady-state ground-water flow in confined aquifers

USGS Publications Warehouse

Kuniansky, E.L.

1990-01-01

A computer program based on the Galerkin finite-element method was developed to simulate two-dimensional steady-state ground-water flow in either isotropic or anisotropic confined aquifers. The program may also be used for unconfined aquifers of constant saturated thickness. Constant head, constant flux, and head-dependent flux boundary conditions can be specified in order to approximate a variety of natural conditions, such as a river or lake boundary, and pumping well. The computer program was developed for the preliminary simulation of ground-water flow in the Edwards-Trinity Regional aquifer system as part of the Regional Aquifer-Systems Analysis Program. Results of the program compare well to analytical solutions and simulations .from published finite-difference models. A concise discussion of the Galerkin method is presented along with a description of the program. Provided in the Supplemental Data section are a listing of the computer program, definitions of selected program variables, and several examples of data input and output used in verifying the accuracy of the program.

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2016-04-01

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

Unjamming a granular hopper by vibration

NASA Astrophysics Data System (ADS)

Janda, A.; Maza, D.; Garcimartín, A.; Kolb, E.; Lanuza, J.; Clément, E.

2009-07-01

We present an experimental study of the outflow of a hopper continuously vibrated by a piezoelectric device. Outpouring of grains can be achieved for apertures much below the usual jamming limit observed for non-vibrated hoppers. Granular flow persists down to the physical limit of one grain diameter, a limit reached for a finite vibration amplitude. For the smaller orifices, we observe an intermittent regime characterized by alternated periods of flow and blockage. Vibrations do not significantly modify the flow rates both in the continuous and the intermittent regime. The analysis of the statistical features of the flowing regime shows that the flow time significantly increases with the vibration amplitude. However, at low vibration amplitude and small orifice sizes, the jamming time distribution displays an anomalous statistics.

Solid-liquid surface tensions of critical nuclei and nucleation barriers from a phase-field-crystal study of a model binary alloy using finite system sizes.

PubMed

Choudhary, Muhammad Ajmal; Kundin, Julia; Emmerich, Heike; Oettel, Martin

2014-08-01

Phase-field-crystal (PFC) modeling has emerged as a computationally efficient tool to address crystal growth phenomena on atomistic length and diffusive time scales. We use a two-dimensional phase-field-crystal model for a binary system based on Elder et al. [Phys. Rev. B 75, 064107 (2007)] to study critical nuclei and their liquid-solid phase boundaries, in particular the nucleus size dependence of the liquid-solid interface tension as well as of the nucleation barrier. Critical nuclei are stabilized in finite systems of various sizes, however, the extracted interface tension as function of the nucleus radius r is independent of system size. We suggest a phenomenological expression to describe the dependence of the extracted interface tension on the nucleus radius r for the liquid-solid system. Moreover, the numerical PFC results show that this dependency can not be fully described by the nonclassical Tolman formula.

Simulating root-induced rhizosphere deformation and its effect on water flow

NASA Astrophysics Data System (ADS)

Aravena, J. E.; Ruiz, S.; Mandava, A.; Regentova, E. E.; Ghezzehei, T.; Berli, M.; Tyler, S. W.

2011-12-01

Soil structure in the rhizosphere is influenced by root activities, such as mucilage production, microbial activity and root growth. Root growth alters soil structure by moving and deforming soil aggregates, affecting water and nutrient flow from the bulk soil to the root surface. In this study, we utilized synchrotron X-ray micro-tomography (XMT) and finite element analysis to quantify the effect of root-induced compaction on water flow through the rhizosphere to the root surface. In a first step, finite element meshes of structured soil around the root were created by processing rhizosphere XMT images. Then, soil deformation by root expansion was simulated using COMSOL Multiphysics° (Version 4.2) considering the soil an elasto-plastic porous material. Finally, fluid flow simulations were carried out on the deformed mesh to quantify the effect of root-induced compaction on water flow to the root surface. We found a 31% increase in water flow from the bulk soil to the root due to a 56% increase in root diameter. Simulations also show that the increase of root-soil contact area was the dominating factor with respect to the calculated increase in water flow. Increase of inter-aggregate contacts in size and number were observed within a couple of root diameters away from the root surface. But their influence on water flow was, in this case, rather limited compared to the immediate soil-root contact.

The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory

PubMed Central

Bosbach, Wolfram A.

2015-01-01

Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603

Documentation of a finite-element two-layer model for simulation of ground-water flow

USGS Publications Warehouse

Mallory, Michael J.

1979-01-01

This report documents a finite-element model for simulation of ground-water flow in a two-aquifer system where the two aquifers are coupled by a leakage term that represents flow through a confining layer separating the two aquifers. The model was developed by Timothy J. Durbin (U.S. Geological Survey) for use in ground-water investigations in southern California. The documentation assumes that the reader is familiar with the physics of ground-water flow, numerical methods of solving partial-differential equations, and the FORTRAN IV computer language. It was prepared as part of the investigations made by the U.S. Geological Survey in cooperation with the San Bernardino Valley Municipal Water District. (Kosco-USGS)

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.

Self-Organized Criticality and Scaling in Lifetime of Traffic Jams

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

1995-01-01

The deterministic cellular automaton 184 (the one-dimensional asymmetric simple-exclusion model with parallel dynamics) is extended to take into account injection or extraction of particles. The model presents the traffic flow on a highway with inflow or outflow of cars.Introducing injection or extraction of particles into the asymmetric simple-exclusion model drives the system asymptotically into a steady state exhibiting a self-organized criticality. The typical lifetime of traffic jams scales as \\cong Lν with ν=0.65±0.04. It is shown that the cumulative distribution Nm (L) of lifetimes satisfies the finite-size scaling form Nm (L) \\cong L-1 f(m/Lν).

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.

1993-01-01

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Elastic collapse in disordered isostatic networks

NASA Astrophysics Data System (ADS)

Moukarzel, C. F.

2012-02-01

Isostatic networks are minimally rigid and therefore have, generically, nonzero elastic moduli. Regular isostatic networks have finite moduli in the limit of large sizes. However, numerical simulations show that all elastic moduli of geometrically disordered isostatic networks go to zero with system size. This holds true for positional as well as for topological disorder. In most cases, elastic moduli decrease as inverse power laws of system size. On directed isostatic networks, however, of which the square and cubic lattices are particular cases, the decrease of the moduli is exponential with size. For these, the observed elastic weakening can be quantitatively described in terms of the multiplicative growth of stresses with system size, giving rise to bulk and shear moduli of order e-bL. The case of sphere packings, which only accept compressive contact forces, is considered separately. It is argued that these have a finite bulk modulus because of specific correlations in contact disorder, introduced by the constraint of compressivity. We discuss why their shear modulus, nevertheless, is again zero for large sizes. A quantitative model is proposed that describes the numerically measured shear modulus, both as a function of the loading angle and system size. In all cases, if a density p>0 of overconstraints is present, as when a packing is deformed by compression or when a glass is outside its isostatic composition window, all asymptotic moduli become finite. For square networks with periodic boundary conditions, these are of order \\sqrt{p} . For directed networks, elastic moduli are of order e-c/p, indicating the existence of an "isostatic length scale" of order 1/p.

Global Culture: A Noise Induced Transition in Finite Systems

NASA Astrophysics Data System (ADS)

Klemm, Konstantin; Eguíluz, Victor M.; Toral, Raúl; San Miguel, Maxi

2003-04-01

We analyze Axelrod's model for the unbiased transmission of culture in the presence of noise. In a one-dimensional lattice, the dynamics is described in terms of a Lyapunov potential, where the disordered configurations are metastable states of the dynamics. In a two-dimensional lattice the dynamics is governed by the average relaxation time T for perturbations to the homogeneous configuration. If the noise rate is smaller than 1/T, the perturbations drive the system to a completely ordered configuration, whereas the system remains disordered for larger noise rates. Based on a mean-field approximation we obtain the average relaxation time T(N) = Nln(N) for system size N. Thus in the limit of infinite system size the system is disordered for any finite noise rate.

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.

Comparisons of Particle Tracking Techniques and Galerkin Finite Element Methods in Flow Simulations on Watershed Scales

NASA Astrophysics Data System (ADS)

Shih, D.; Yeh, G.

2009-12-01

This paper applies two numerical approximations, the particle tracking technique and Galerkin finite element method, to solve the diffusive wave equation in both one-dimensional and two-dimensional flow simulations. The finite element method is one of most commonly approaches in numerical problems. It can obtain accurate solutions, but calculation times may be rather extensive. The particle tracking technique, using either single-velocity or average-velocity tracks to efficiently perform advective transport, could use larger time-step sizes than the finite element method to significantly save computational time. Comparisons of the alternative approximations are examined in this poster. We adapt the model WASH123D to examine the work. WASH123D is an integrated multimedia, multi-processes, physics-based computational model suitable for various spatial-temporal scales, was first developed by Yeh et al., at 1998. The model has evolved in design capability and flexibility, and has been used for model calibrations and validations over the course of many years. In order to deliver a locally hydrological model in Taiwan, the Taiwan Typhoon and Flood Research Institute (TTFRI) is working with Prof. Yeh to develop next version of WASH123D. So, the work of our preliminary cooperationx is also sketched in this poster.

Tree-Level Hydrodynamic Approach for Improved Stomatal Conductance Parameterization

NASA Astrophysics Data System (ADS)

Mirfenderesgi, G.; Bohrer, G.; Matheny, A. M.; Ivanov, V. Y.

2014-12-01

The land-surface models do not mechanistically resolve hydrodynamic processes within the tree. The Finite-Elements Tree-Crown Hydrodynamics model version 2 (FETCH2) is based on the pervious FETCH model approach, but with finite difference numerics, and simplified single-beam conduit system. FETCH2 simulates water flow through the tree as a simplified system of porous media conduits. It explicitly resolves spatiotemporal hydraulic stresses throughout the tree's vertical extent that cannot be easily represented using other stomatal-conductance models. Empirical equations relate water potential at the stem to stomata conductance at leaves connected to the stem (through unresolved branches) at that height. While highly simplified, this approach bring some realism to the simulation of stomata conductance because the stomata can respond to stem water potential, rather than an assumed direct relationship with soil moisture, as is currently the case in almost all models. By enabling mechanistic simulation of hydrological traits, such as xylem conductivity, conductive area per DBH, vertical distribution of leaf area and maximal and minimal water content in the xylem, and their effect of the dynamics of water flow in the tree system, the FETCH2 modeling system enhanced our understanding of the role of hydraulic limitations on an experimental forest plot short-term water stresses that lead to tradeoffs between water and light availability for transpiring leaves in forest ecosystems. FETCH2 is particularly suitable to resolve the effects of structural differences between tree and species and size groups, and the consequences of differences in hydraulic strategies of different species. We leverage on a large dataset of sap flow from 60 trees of 4 species at our experimental plot at the University of Michigan Biological Station. Comparison of the sap flow and transpiration patterns in this site and an undisturbed control site shows significant difference in hydraulic strategies between species which affect their response to the disturbance. We used FETCH2 to conduct a sensitivity analysis of the total stand-level transpiration to the inter-specific differences in hydraulic strategies and used the results to reflect on the future trajectory of the forest, in terms of species composition and transpiration.

Modeling Physical Processes at the Nanoscale—Insight into Self-Organization of Small Systems (abstract)

NASA Astrophysics Data System (ADS)

Proykova, Ana

2009-04-01

Essential contributions have been made in the field of finite-size systems of ingredients interacting with potentials of various ranges. Theoretical simulations have revealed peculiar size effects on stability, ground state structure, phases, and phase transformation of systems confined in space and time. Models developed in the field of pure physics (atomic and molecular clusters) have been extended and successfully transferred to finite-size systems that seem very different—small-scale financial markets, autoimmune reactions, and social group reactions to advertisements. The models show that small-scale markets diverge unexpectedly fast as a result of small fluctuations; autoimmune reactions are sequences of two discontinuous phase transitions; and social groups possess critical behavior (social percolation) under the influence of an external field (advertisement). Some predicted size-dependent properties have been experimentally observed. These findings lead to the hypothesis that restrictions on an object's size determine the object's total internal (configuration) and external (environmental) interactions. Since phases are emergent phenomena produced by self-organization of a large number of particles, the occurrence of a phase in a system containing a small number of ingredients is remarkable.

Lattice Boltzmann simulations of liquid crystal particulate flow in a channel with finite anchoring boundary conditions

NASA Astrophysics Data System (ADS)

Zhang, Rui; Roberts, Tyler; de Pablo, Juan; dePablo Team

2014-11-01

Liquid crystals (LC) posses anisotropic viscoelastic properties, and, as such, LC flow can be incredibly complicated. Here we employ a hybrid lattice Boltzmann method (pioneered by Deniston, Yeomans and Cates) to systematically study the hydrodynamics of nematic liquid crystals (LCs) with and without solid particles. This method evolves the velocity field through lattice Boltzmann and the LC-order parameter via a finite-difference solver of the Beris-Edwards equation. The evolution equation of the boundary points with finite anchoring is obtained through Poisson bracket formulation. Our method has been validated by matching the Ericksen-Leslie theory. We demonstrate two applications in the flow alignment regime. We first investigate a hybrid channel flow in which the top and bottom walls have different anchoring directions. By measuring the apparent shear viscosity in terms of Couette flow, we achieve a viscosity inhomogeneous system which may be applicable to nano particle processing. In the other example, we introduce a homeotropic spherical particle to the channel, and focus on the deformations of the defect ring due to anchorings and flow. The results are then compared to the molecular dynamics simulations of a colloid particle in an LC modeled by a Gay-Berne potential.

The development of an erosive burning model for solid rocket motors using direct numerical simulation

NASA Astrophysics Data System (ADS)

McDonald, Brian A.

A method for developing an erosive burning model for use in solid propellant design-and-analysis interior ballistics codes is described and evaluated. Using Direct Numerical Simulation, the primary mechanisms controlling erosive burning (turbulent heat transfer, and finite rate reactions) have been studied independently through the development of models using finite rate chemistry, and infinite rate chemistry. Both approaches are calibrated to strand burn rate data by modeling the propellant burning in an environment with no cross-flow, and adjusting thermophysical properties until the predicted regression rate matches test data. Subsequent runs are conducted where the cross-flow is increased from M = 0.0 up to M = 0.8. The resulting relationship of burn rate increase versus Mach Number is used in an interior ballistics analysis to compute the chamber pressure of an existing solid rocket motor. The resulting predictions are compared to static test data. Both the infinite rate model and the finite rate model show good agreement when compared to test data. The propellant considered is an AP/HTPB with an average AP particle size of 37 microns. The finite rate model shows that as the cross-flow increases, near wall vorticity increases due to the lifting of the boundary caused by the side injection of gases from the burning propellant surface. The point of maximum vorticity corresponds to the outer edge of the APd-binder flame. As the cross-flow increases, the APd-binder flame thickness becomes thinner; however, the point of highest reaction rate moves only slightly closer to the propellant surface. As such, the net increase of heat transfer to the propellant surface due to finite rate chemistry affects is small. This leads to the conclusion that augmentation of thermal transport properties and the resulting heat transfer increase due to turbulence dominates over combustion chemistry in the erosive burning problem. This conclusion is advantageous in the development of future models that can be calibrated to heat transfer conditions without the necessity for finite rate chemistry. These results are considered applicable for propellants with small, evenly distributed AP particles where the assumption of premixed APd-binder gases is reasonable.

On the ab initio calculation of vibrational formation entropy of point defect: the case of the silicon vacancy

NASA Astrophysics Data System (ADS)

Seeberger, Pia; Vidal, Julien

2017-08-01

Formation entropy of point defects is one of the last crucial elements required to fully describe the temperature dependence of point defect formation. However, while many attempts have been made to compute them for very complicated systems, very few works have been carried out such as to assess the different effects of finite size effects and precision on such quantity. Large discrepancies can be found in the literature for a system as primitive as the silicon vacancy. In this work, we have proposed a systematic study of formation entropy for silicon vacancy in its 3 stable charge states: neutral, +2 and -2 for supercells with size not below 432 atoms. Rationalization of the formation entropy is presented, highlighting importance of finite size error and the difficulty to compute such quantities due to high numerical requirement. It is proposed that the direct calculation of formation entropy of VSi using first principles methods will be plagued by very high computational workload (or large numerical errors) and finite size dependent results.

On the formulation and assessment of flamelet-generated manifolds applied to two-phase turbulent combustion

NASA Astrophysics Data System (ADS)

Bojko, Brian T.

Accounting for the effects of finite rate chemistry in reacting flows is intractable when considering the number of species and reactions to be solved for during a large scale flow simulation. This is especially complicated when solid/liquid fuels are also considered. While modeling the reacting boundary layer with the use of finite-rate chemistry may allow for a highly accurate description of the coupling between the flame and fuel surface, it is not tractable in large scale simulations when considering detailed chemical kinetics. It is the goal of this research to investigate a Flamelet-Generated Manifold (FGM) method in order to reduce the finite rate chemistry to a lookup table cataloged by progress variables and queried during runtime. In this study, simplified unsteady 1D flames with mass blowing are considered for a solid biomass fuel where the FGM method is employed as a model reduction strategy for potential application to multidimensional calculations. Two types of FGM are considered. The first are a set of steady-state flames differentiated by their scalar dissipation rate. Results show the use of steady flames produce unacceptable errors compared to the finite-rate chemistry solution, with temperature errors in excess of 45%. To avoid these errors, a new methodology for developing an unsteady FGM (UFGM) is presented that accounts for unsteady diffusion effects and greatly reduces errors in temperature with differences that are under 10%. The FGM modeling is then extended to individual droplet combustion with the development of a Droplet Flamelet-Generated Manifold (DFGM) to account for the effects of finite-rate chemistry of individual droplets. A spherically symmetric droplet model is developed for methanol and aluminum. The inclusion of finite-rate chemistry allows the capturing of the transition from diffusion to kinetically controlled combustion as the droplet diameter decreases. The droplet model is then used to create a DFGM by successively solving the 1D flame equations at varying drop sizes, where the source terms for energy, mixture fraction, and progress variable are cataloged as a function of normalized diameter. A unique coupling of the DFGM and planar UFGM is developed and is used to account for individual and gas phase combustion processes in turbulent combustion situations, such as spray flames, particle laden blasts, etc. The DFGM for the methanol and aluminum droplets are used in mixed Eulerian and Eulerian-Lagrangian formulations of compressible multiphase flows. System level simulations are conducted and compared experimental data for a methanol spray flame and an aluminized blast studied at the Explosives Components Facility (ECF) at Sandia National Laboratories.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

Simulating incompressible flow on moving meshfree grids using General Finite Differences (GFD)

NASA Astrophysics Data System (ADS)

Vasyliv, Yaroslav; Alexeev, Alexander

2016-11-01

We simulate incompressible flow around an oscillating cylinder at different Reynolds numbers using General Finite Differences (GFD) on a meshfree grid. We evolve the meshfree grid by treating each grid node as a particle. To compute velocities and accelerations, we consider the particles at a particular instance as Eulerian observation points. The incompressible Navier-Stokes equations are directly discretized using GFD with boundary conditions enforced using a sharp interface treatment. Cloud sizes are set such that the local approximations use only 16 neighbors. To enforce incompressibility, we apply a semi-implicit approximate projection method. To prevent overlapping particles and formation of voids in the grid, we propose a particle regularization scheme based on a local minimization principle. We validate the GFD results for an oscillating cylinder against the lattice Boltzmann method and find good agreement. Financial support provided by National Science Foundation (NSF) Graduate Research Fellowship, Grant No. DGE-1148903.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

A least-squares finite element method for incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1992-01-01

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

A simulation of the atmospheric cloud physics laboratory to aid in its design and the design of the experiments within the laboratory

NASA Technical Reports Server (NTRS)

Winchester, L. W., Jr.

1980-01-01

Using the finite difference method with overrelaxation, numerical solutions of the steady-state vorticity transport equation were obtained for a continuous flow diffusion chamber of the Hudson-Squires type. The calculation neglected the effects due to temperature, gravity, and saturation. The size and shape of the manifold used to inject the aerosol laden flow were varied to obtain a design which would improve the performance of the chamber from strictly low Reynolds number (less than 20) fluid dynamical considerations.

Eroding dipoles and vorticity growth for Euler flows in {{{R}}}^{3}: the hairpin geometry as a model for finite-time blowup

NASA Astrophysics Data System (ADS)

Childress, Stephen; Gilbert, Andrew D.

2018-02-01

A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as realized in the eroding hairpin excludes a finite time blowup for the corresponding Navier-Stokes model.

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.

A computational study of coherent structures in the wakes of two-dimensional bluff bodies

NASA Astrophysics Data System (ADS)

Pearce, Jeffrey Alan

1988-08-01

The periodic shedding of vortices from bluff bodies was first recognized in the late 1800's. Currently, there is great interest concerning the effect of vortex shedding on structures and on vehicle stability. In the design of bluff structures which will be exposed to a flow, knowledge of the shedding frequency and the amplitude of the aerodynamic forces is critical. The ability to computationally predict parameters associated with periodic vortex shedding is thus a valuable tool. In this study, the periodic shedding of vortices from several bluff body geometries is predicted. The study is conducted with a two-dimensional finite-difference code employed on various grid sizes. The effects of the grid size and time step on the accuracy of the solution are addressed. Strouhal numbers and aerodynamic force coefficients are computed for all of the bodies considered and compared with previous experimental results. Results indicate that the finite-difference code is capable of predicting periodic vortex shedding for all of the geometries tested. Refinement of the finite-difference grid was found to give little improvement in the prediction; however, the choice of time step size was shown to be critical. Predictions of Strouhal numbers were generally accurate, and the calculated aerodynamic forces generally exhibited behavior consistent with previous studies.

A guide for using the transient ground-water flow model of the Death Valley regional ground-water flow system, Nevada and California

USGS Publications Warehouse

Blainey, Joan B.; Faunt, Claudia C.; Hill, Mary C.

2006-01-01

This report is a guide for executing numerical simulations with the transient ground-water flow model of the Death Valley regional ground-water flow system, Nevada and California using the U.S. Geological Survey modular finite-difference ground-water flow model, MODFLOW-2000. Model inputs, including observations of hydraulic head, discharge, and boundary flows, are summarized. Modification of the DVRFS transient ground-water model is discussed for two common uses of the Death Valley regional ground-water flow system model: predictive pumping scenarios that extend beyond the end of the model simulation period (1998), and model simulations with only steady-state conditions.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Impact of magnetic suspension stiffness on aeroelastic compressor rotor vibrations of gas pumping units

NASA Astrophysics Data System (ADS)

Mekhonoshina, E. V.; Modorskii, V. Ya.

2016-10-01

This paper describes simulation of oscillation modes in the elastic rotor supports with the gas-dynamic flow influence on the rotor in the magnetic suspension in the course of computational experiments. The system of engineering analysis ANSYS 15.0 was used as a numerical tool. The finite volume method for gas dynamics and finite element method for evaluating components of the stress-strain state (SSS) were applied for computation. The research varied magnetic suspension rigidity and estimated the SSS components in the system "gas-dynamic flow - compressor rotor - magnetic suspensions." The influence of aeroelastic effects on the impeller and the rotor on the deformability of vibration magnetic suspension was detected.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Surface and finite size effect on fluctuations dynamics in nanoparticles with long-range order

NASA Astrophysics Data System (ADS)

Morozovska, A. N.; Eliseev, E. A.

2010-02-01

The influence of surface and finite size on the dynamics of the order parameter fluctuations and critical phenomena in the three-dimensional (3D)-confined systems with long-range order was not considered theoretically. In this paper, we study the influence of surface and finite size on the dynamics of the order parameter fluctuations in the particles of arbitrary shape. We consider concrete examples of the spherical and cylindrical ferroic nanoparticles within Landau-Ginzburg-Devonshire phenomenological approach. Allowing for the strong surface energy contribution in micro and nanoparticles, the analytical expressions derived for the Ornstein-Zernike correlator of the long-range order parameter spatial-temporal fluctuations, dynamic generalized susceptibility, relaxation times, and correlation radii discrete spectra are different from those known for bulk systems. Obtained analytical expressions for the correlation function of the order parameter spatial-temporal fluctuations in micro and nanosized systems can be useful for the quantitative analysis of the dynamical structural factors determined from magnetic resonance diffraction and scattering spectra. Besides the practical importance of the correlation function for the analysis of the experimental data, derived expressions for the fluctuations strength determine the fundamental limits of phenomenological theories applicability for 3D-confined systems.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

NASA Technical Reports Server (NTRS)

Weilmuenster, K. J.; Hamilton, H. H., II

1979-01-01

A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Predicting the constitutive behavior of semi-solids via a direct finite element simulation: application to AA5182

NASA Astrophysics Data System (ADS)

Phillion, A. B.; Cockcroft, S. L.; Lee, P. D.

2009-07-01

The methodology of direct finite element (FE) simulation was used to predict the semi-solid constitutive behavior of an industrially important aluminum-magnesium alloy, AA5182. Model microstructures were generated that detail key features of the as-cast semi-solid: equiaxed-globular grains of random size and shape, interconnected liquid films, and pores at the triple-junctions. Based on the results of over fifty different simulations, a model-based constitutive relationship which includes the effects of the key microstructure features—fraction solid, grain size and fraction porosity—was derived using regression analysis. This novel constitutive equation was then validated via comparison with both the FE simulations and experimental stress/strain data. Such an equation can now be used to incorporate the effects of microstructure on the bulk semi-solid flow stress within a macro- scale process model.

Particle Size Distributions in Atmospheric Clouds

NASA Technical Reports Server (NTRS)

Paoli, Roberto; Shariff, Karim

2003-01-01

In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.

The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications

NASA Technical Reports Server (NTRS)

Bravo, Ramiro H.; Chen, Ching-Jen

1992-01-01

In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.

Relativistic thermal electron scale instabilities in sheared flow plasma

NASA Astrophysics Data System (ADS)

Miller, Evan D.; Rogers, Barrett N.

2016-04-01

> The linear dispersion relation obeyed by finite-temperature, non-magnetized, relativistic two-fluid plasmas is presented, in the special case of a discontinuous bulk velocity profile and parallel wave vectors. It is found that such flows become universally unstable at the collisionless electron skin-depth scale. Further analyses are performed in the limits of either free-streaming ions or ultra-hot plasmas. In these limits, the system is highly unstable in the parameter regimes associated with either the electron scale Kelvin-Helmholtz instability (ESKHI) or the relativistic electron scale sheared flow instability (RESI) recently highlighted by Gruzinov. Coupling between these modes provides further instability throughout the remaining parameter space, provided both shear flow and temperature are finite. An explicit parameter space bound on the highly unstable region is found.

Dynamical Languages

NASA Astrophysics Data System (ADS)

Xie, Huimin

The following sections are included: * Definition of Dynamical Languages * Distinct Excluded Blocks * Definition and Properties * L and L″ in Chomsky Hierarchy * A Natural Equivalence Relation * Symbolic Flows * Symbolic Flows and Dynamical Languages * Subshifts of Finite Type * Sofic Systems * Graphs and Dynamical Languages * Graphs and Shannon-Graphs * Transitive Languages * Topological Entropy

Effect of Pumping on Groundwater Levels: A Case Study

NASA Astrophysics Data System (ADS)

Sindhu, G.; Vijayachandran, Lekshmi

2018-03-01

Groundwater is a major source for drinking and domestic purposes. Nowadays, extensive pumping has become a major issue of concern since pumping has led to rapid decline in the groundwater table, thus imposing landward gradient, leading to saline water intrusion especially in coastal areas. Groundwater pumping has seen its utmost effect on coastal aquifer systems, where the sea-ward gradient gets disturbed due to anthropogenic influences. Hence, a groundwater flow modelling of an aquifer system is essential for understanding the various hydro-geologic conditions, which can be used to study the responses of the aquifer system with regard to various pumping scenarios. Besides, a model helps to predict the water levels for the future period with respect to changing environment. In this study, a finite element groundwater flow model of a coastal aquifer system at Aakulam, Trivandrum district is developed, calibrated and simulated using the software Finite Element subsurface Flow system (FEFLOW 6.2).This simulated model is then used to predict the groundwater levels for a future 5 year period during pre monsoon and post monsoon season.

Effect of Pumping on Groundwater Levels: A Case Study

NASA Astrophysics Data System (ADS)

Sindhu, G.; Vijayachandran, Lekshmi

2018-06-01

Groundwater is a major source for drinking and domestic purposes. Nowadays, extensive pumping has become a major issue of concern since pumping has led to rapid decline in the groundwater table, thus imposing landward gradient, leading to saline water intrusion especially in coastal areas. Groundwater pumping has seen its utmost effect on coastal aquifer systems, where the sea-ward gradient gets disturbed due to anthropogenic influences. Hence, a groundwater flow modelling of an aquifer system is essential for understanding the various hydro-geologic conditions, which can be used to study the responses of the aquifer system with regard to various pumping scenarios. Besides, a model helps to predict the water levels for the future period with respect to changing environment. In this study, a finite element groundwater flow model of a coastal aquifer system at Aakulam, Trivandrum district is developed, calibrated and simulated using the software Finite Element subsurface Flow system (FEFLOW 6.2).This simulated model is then used to predict the groundwater levels for a future 5 year period during pre monsoon and post monsoon season.

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.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

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

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

The Zombie Instability: Using Numerical Simulation to Design a Laboratory Experiment

NASA Astrophysics Data System (ADS)

Wang, Meng; Pei, Suyang; Jiang, Chung-Hsiang; Hassanzadeh, Pedram; Marcus, Philip

2014-11-01

A new type of finite amplitude-instability has been found in numerical simulations of stratified, rotating, shear flows. The instability occurs via baroclinic critical layers that create linearly unstable vortex layers, which roll-up into vortices. Under the right conditions, those vortices can form a new generation of vortices, resulting in ``vortex self-replication'' that fills the fluid with vortices. Creating this instability in a laboratory would provide further evidence for the existence of the instability, which we first found in numerical simulations of protoplanetary disks. To design a laboratory experiment we need to know how the flow parameters-- shear, rotation and stratification, etc. affect the instability. To build an experiment economically, we also need to know how the finite-amplitude trigger of the instability scales with viscosity and the size of the domain. In this talk, we summarize our findings. We present a map, in terms of the experimentally controllable parameters, that shows where the instability occurs and whether the instability creates a few isolated transient vortices, a few long-lived vortices, or long-lived, self-replicating vortices that fill the entire flow.

Stabilized finite element methods to simulate the conductances of ion channels

NASA Astrophysics Data System (ADS)

Tu, Bin; Xie, Yan; Zhang, Linbo; Lu, Benzhuo

2015-03-01

We have previously developed a finite element simulator, ichannel, to simulate ion transport through three-dimensional ion channel systems via solving the Poisson-Nernst-Planck equations (PNP) and Size-modified Poisson-Nernst-Planck equations (SMPNP), and succeeded in simulating some ion channel systems. However, the iterative solution between the coupled Poisson equation and the Nernst-Planck equations has difficulty converging for some large systems. One reason we found is that the NP equations are advection-dominated diffusion equations, which causes troubles in the usual FE solution. The stabilized schemes have been applied to compute fluids flow in various research fields. However, they have not been studied in the simulation of ion transport through three-dimensional models based on experimentally determined ion channel structures. In this paper, two stabilized techniques, the SUPG and the Pseudo Residual-Free Bubble function (PRFB) are introduced to enhance the numerical robustness and convergence performance of the finite element algorithm in ichannel. The conductances of the voltage dependent anion channel (VDAC) and the anthrax toxin protective antigen pore (PA) are simulated to validate the stabilization techniques. Those two stabilized schemes give reasonable results for the two proteins, with decent agreement with both experimental data and Brownian dynamics (BD) simulations. For a variety of numerical tests, it is found that the simulator effectively avoids previous numerical instability after introducing the stabilization methods. Comparison based on our test data set between the two stabilized schemes indicates both SUPG and PRFB have similar performance (the latter is slightly more accurate and stable), while SUPG is relatively more convenient to implement.

1 / f α noise and generalized diffusion in random Heisenberg spin systems

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

Agarwal, Kartiek; Demler, Eugene; Martin, Ivar

2015-11-01

We study the “flux-noise” spectrum of random-bond quantum Heisenberg spin systems using a real-space renormalization group (RSRG) procedure that accounts for both the renormalization of the system Hamiltonian and of a generic probe that measures the noise. For spin chains, we find that the dynamical structure factor Sq (f ), at finite wave vector q, exhibits a power-law behavior both at high and low frequencies f , with exponents that are connected to one another and to an anomalous dynamical exponent through relations that differ at T = 0 and T =∞. The low-frequency power-law behavior of the structure factormore » is inherited by any generic probe with a finite bandwidth and is of the form 1/f α with 0.5 < α < 1. An analytical calculation of the structure factor, assuming a limiting distribution of the RG flow parameters (spin size, length, bond strength) confirms numerical findings.More generally, we demonstrate that this form of the structure factor, at high temperatures, is a manifestation of anomalous diffusionwhich directly follows from a generalized spin-diffusion propagator.We also argue that 1/f -noise is intimately connected to many-body-localization at finite temperatures. In two dimensions, the RG procedure is less reliable; however, it becomes convergent for quasi-one-dimensional geometries where we find that one-dimensional 1/f α behavior is recovered at low frequencies; the latter configurations are likely representative of paramagnetic spin networks that produce 1/f α noise in SQUIDs.« less

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

NASA Technical Reports Server (NTRS)

Candler, Graham V.; Johnson, Heath B.; Nompelis, Ioannis; Subbareddy, Pramod K.; Drayna, Travis W.; Gidzak, Vladimyr; Barnhardt, Michael D.

2015-01-01

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

Finite-size scaling for discontinuous nonequilibrium phase transitions

NASA Astrophysics Data System (ADS)

de Oliveira, Marcelo M.; da Luz, M. G. E.; Fiore, Carlos E.

2018-06-01

A finite-size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E 92, 062126 (2015), 10.1103/PhysRevE.92.062126], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities such as response functions, reduced cumulants, and equal area probability distributions are derived from phenomenological arguments. Irrespective of system details, all these quantities scale with the volume, establishing the dependence on size. The approach generality is illustrated through the analysis of different models. The present results are a relevant step in trying to unify the scaling behavior description of nonequilibrium transition processes.

On an interface of the online system for a stochastic analysis of the varied information flows

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

Gorshenin, Andrey K.; MIREA, MGUPI; Kuzmin, Victor Yu.

The article describes a possible approach to the construction of an interface of an online asynchronous system that allows researchers to analyse varied information flows. The implemented stochastic methods are based on the mixture models and the method of moving separation of mixtures. The general ideas of the system functionality are demonstrated on an example for some moments of a finite normal mixture.

Mathematical modeling of influence of ion size effects in an electrolyte in a nanoslit with overlapped EDL

NASA Astrophysics Data System (ADS)

Rajni, Kumar, Prashant

2017-10-01

Many nanofluidic systems are being used in a wide range of applications due to advances in nanotechnology. Due to nanoscale size of the system, the physics involved in the electric double layer and consequently the different phenomena related to it are different than those at microscale. The Poisson-Boltzmann equation governing the electric double layer in the system has many shortcomings such as point sized ions. The inclusion of finite size of ions give rise to various electrokinetic phenomena. Electrocapillarity is one such phenomena where the size effect plays an important role. Theeffect of asymmetric finite ion sizes in nano-confinement in the view of osmotic pressure and electrocapillarity is analyzed. As the confinement width of the system becomes comparable with the Debye length, the overlapped electric double layer (EDL) is influenced and significantly deformed by the steric effects. The osmotic pressure from the modified Poisson-Boltzmann equation in nanoslit is obtained. Due to nonlinear nature of the modified PB equation, the solution is obtained through numerical method. Afterwards, the electrocapillarity due to the steric effect is analyzed under constant surface potential condition at the walls of the nanoslit along with the flat interface assumption.

Lagrangian Coherent Structures, Hyperbolicity, and Lyapunov Exponents

NASA Astrophysics Data System (ADS)

Haller, George

2010-05-01

We review the fundamental physical motivation behind the definition of Lagrangian Coherent Structures (LCS) and show how it leads to the concept of finite-time hyperbolicity in non-autonomous dynamical systems. Using this concept of hyperbolicity, we obtain a self-consistent criterion for the existence of attracting and repelling material surfaces in unsteady fluid flows, such as those in the atmosphere and the ocean. The existence of LCS is often postulated in terms of features of the Finite-Time Lyapunov Exponent (FTLE) field associated with the system. As simple examples show, however, the FTLE field does not necessarily highlight LCS, or may ighlight structures that are not LCS. Under appropriate nondegeneracy conditions, we show that ridges of the FTLE field indeed coincide with LCS in volume-preserving flows. For general flows, we obtain a more general scalar field whose ridges correspond to LCS. We finally review recent applications of LCS techniques to flight safety analysis at Hong Kong International Airport.

Pinching solutions of slender cylindrical jets

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Orellana, Oscar

1993-01-01

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

Modeling Sound Propagation Through Non-Axisymmetric Jets

NASA Technical Reports Server (NTRS)

Leib, Stewart J.

2014-01-01

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

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.

SUPG Finite Element Simulations of Compressible Flows

NASA Technical Reports Server (NTRS)

Kirk, Brnjamin, S.

2006-01-01

The Streamline-Upwind Petrov-Galerkin (SUPG) finite element simulations of compressible flows is presented. The topics include: 1) Introduction; 2) SUPG Galerkin Finite Element Methods; 3) Applications; and 4) Bibliography.

Finite element analysis of transonic flows in cascades: Importance of computational grids in improving accuracy and convergence

NASA Technical Reports Server (NTRS)

Ecer, A.; Akay, H. U.

1981-01-01

The finite element method is applied for the solution of transonic potential flows through a cascade of airfoils. Convergence characteristics of the solution scheme are discussed. Accuracy of the numerical solutions is investigated for various flow regions in the transonic flow configuration. The design of an efficient finite element computational grid is discussed for improving accuracy and convergence.

Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing

NASA Technical Reports Server (NTRS)

Gumbert, Clyde R.; Hou, Gene J.-W.; Newman, Perry A.

2001-01-01

The formulation and implementation of an optimization method called Simultaneous Aerodynamic and Structural Design Optimization (SASDO) is shown as an extension of the Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) method. It is extended by the inclusion of structure element sizing parameters as design variables and Finite Element Method (FEM) analysis responses as constraints. The method aims to reduce the computational expense. incurred in performing shape and sizing optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, FEM structural analysis and sensitivity analysis tools. SASDO is applied to a simple. isolated, 3-D wing in inviscid flow. Results show that the method finds the saine local optimum as a conventional optimization method with some reduction in the computational cost and without significant modifications; to the analysis tools.

On the delay analysis of a TDMA channel with finite buffer capacity

NASA Technical Reports Server (NTRS)

Yan, T.-Y.

1982-01-01

The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.

Chemorheology of reactive systems: Finite element analysis

NASA Technical Reports Server (NTRS)

Douglas, C.; Roylance, D.

1982-01-01

The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Design approach of an aquaculture cage system for deployment in the constructed channel flow environments of a power plant

PubMed Central

Lee, Jihoon; Fredriksson, David W.; DeCew, Judson; Drach, Andrew; Yim, Solomon C.

2018-01-01

This study provides an engineering approach for designing an aquaculture cage system for use in constructed channel flow environments. As sustainable aquaculture has grown globally, many novel techniques have been introduced such as those implemented in the global Atlantic salmon industry. The advent of several highly sophisticated analysis software systems enables the development of such novel engineering techniques. These software systems commonly include three-dimensional (3D) drafting, computational fluid dynamics, and finite element analysis. In this study, a combination of these analysis tools is applied to evaluate a conceptual aquaculture system for potential deployment in a power plant effluent channel. The channel is supposedly clean; however, it includes elevated water temperatures and strong currents. The first portion of the analysis includes the design of a fish cage system with specific net solidities using 3D drafting techniques. Computational fluid dynamics is then applied to evaluate the flow reduction through the system from the previously generated solid models. Implementing the same solid models, a finite element analysis is performed on the critical components to assess the material stresses produced by the drag force loads that are calculated from the fluid velocities. PMID:29897954

Clogging transition of many-particle systems flowing through bottlenecks

NASA Astrophysics Data System (ADS)

Zuriguel, Iker; Parisi, Daniel Ricardo; Hidalgo, Raúl Cruz; Lozano, Celia; Janda, Alvaro; Gago, Paula Alejandra; Peralta, Juan Pablo; Ferrer, Luis Miguel; Pugnaloni, Luis Ariel; Clément, Eric; Maza, Diego; Pagonabarraga, Ignacio; Garcimartín, Angel

2014-12-01

When a large set of discrete bodies passes through a bottleneck, the flow may become intermittent due to the development of clogs that obstruct the constriction. Clogging is observed, for instance, in colloidal suspensions, granular materials and crowd swarming, where consequences may be dramatic. Despite its ubiquity, a general framework embracing research in such a wide variety of scenarios is still lacking. We show that in systems of very different nature and scale -including sheep herds, pedestrian crowds, assemblies of grains, and colloids- the probability distribution of time lapses between the passages of consecutive bodies exhibits a power-law tail with an exponent that depends on the system condition. Consequently, we identify the transition to clogging in terms of the divergence of the average time lapse. Such a unified description allows us to put forward a qualitative clogging state diagram whose most conspicuous feature is the presence of a length scale qualitatively related to the presence of a finite size orifice. This approach helps to understand paradoxical phenomena, such as the faster-is-slower effect predicted for pedestrians evacuating a room and might become a starting point for researchers working in a wide variety of situations where clogging represents a hindrance.

Clogging transition of many-particle systems flowing through bottlenecks

PubMed Central

Zuriguel, Iker; Parisi, Daniel Ricardo; Hidalgo, Raúl Cruz; Lozano, Celia; Janda, Alvaro; Gago, Paula Alejandra; Peralta, Juan Pablo; Ferrer, Luis Miguel; Pugnaloni, Luis Ariel; Clément, Eric; Maza, Diego; Pagonabarraga, Ignacio; Garcimartín, Angel

2014-01-01

When a large set of discrete bodies passes through a bottleneck, the flow may become intermittent due to the development of clogs that obstruct the constriction. Clogging is observed, for instance, in colloidal suspensions, granular materials and crowd swarming, where consequences may be dramatic. Despite its ubiquity, a general framework embracing research in such a wide variety of scenarios is still lacking. We show that in systems of very different nature and scale -including sheep herds, pedestrian crowds, assemblies of grains, and colloids- the probability distribution of time lapses between the passages of consecutive bodies exhibits a power-law tail with an exponent that depends on the system condition. Consequently, we identify the transition to clogging in terms of the divergence of the average time lapse. Such a unified description allows us to put forward a qualitative clogging state diagram whose most conspicuous feature is the presence of a length scale qualitatively related to the presence of a finite size orifice. This approach helps to understand paradoxical phenomena, such as the faster-is-slower effect predicted for pedestrians evacuating a room and might become a starting point for researchers working in a wide variety of situations where clogging represents a hindrance. PMID:25471601

Clogging transition of many-particle systems flowing through bottlenecks.

PubMed

Zuriguel, Iker; Parisi, Daniel Ricardo; Hidalgo, Raúl Cruz; Lozano, Celia; Janda, Alvaro; Gago, Paula Alejandra; Peralta, Juan Pablo; Ferrer, Luis Miguel; Pugnaloni, Luis Ariel; Clément, Eric; Maza, Diego; Pagonabarraga, Ignacio; Garcimartín, Angel

2014-12-04

When a large set of discrete bodies passes through a bottleneck, the flow may become intermittent due to the development of clogs that obstruct the constriction. Clogging is observed, for instance, in colloidal suspensions, granular materials and crowd swarming, where consequences may be dramatic. Despite its ubiquity, a general framework embracing research in such a wide variety of scenarios is still lacking. We show that in systems of very different nature and scale -including sheep herds, pedestrian crowds, assemblies of grains, and colloids- the probability distribution of time lapses between the passages of consecutive bodies exhibits a power-law tail with an exponent that depends on the system condition. Consequently, we identify the transition to clogging in terms of the divergence of the average time lapse. Such a unified description allows us to put forward a qualitative clogging state diagram whose most conspicuous feature is the presence of a length scale qualitatively related to the presence of a finite size orifice. This approach helps to understand paradoxical phenomena, such as the faster-is-slower effect predicted for pedestrians evacuating a room and might become a starting point for researchers working in a wide variety of situations where clogging represents a hindrance.

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

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

Chakrabarty, Aurab, E-mail: aurab.chakrabarty@qatar.tamu.edu; Bouhali, Othmane; Mousseau, Normand

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structuralmore » defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.« less

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

NASA Astrophysics Data System (ADS)

Chakrabarty, Aurab; Bouhali, Othmane; Mousseau, Normand; Becquart, Charlotte S.; El-Mellouhi, Fedwa

2016-08-01

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structural defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

PubMed Central

Baity-Jesi, Marco; Calore, Enrico; Cruz, Andres; Fernandez, Luis Antonio; Gil-Narvión, José Miguel; Gordillo-Guerrero, Antonio; Iñiguez, David; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor; Monforte-Garcia, Jorge; Muñoz Sudupe, Antonio; Navarro, Denis; Parisi, Giorgio; Perez-Gaviro, Sergio; Ricci-Tersenghi, Federico; Ruiz-Lorenzo, Juan Jesus; Schifano, Sebastiano Fabio; Tarancón, Alfonso; Tripiccione, Raffaele; Yllanes, David

2017-01-01

We have performed a very accurate computation of the nonequilibrium fluctuation–dissipation ratio for the 3D Edwards–Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes. PMID:28174274

Finite-size effects and switching times for Moran process with mutation.

PubMed

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

Using MODFLOW drains to simulate groundwater flow in a karst environment

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

Quinn, J.; Tomasko, D.; Glennon, M.A.

1998-07-01

Modeling groundwater flow in a karst environment is both numerically challenging and highly uncertain because of potentially complex flowpaths and a lack of site-specific information. This study presents the results of MODFLOW numerical modeling in which drain cells in a finite-difference model are used as analogs for preferential flowpaths or conduits in karst environments. In this study, conduits in mixed-flow systems are simulated by assigning connected pathways of drain cells from the locations of tracer releases, sinkholes, or other karst features to outlet springs along inferred flowpaths. These paths are determined by the locations of losing stream segments, ephemeral streammore » beds, geophysical surveys, fracture lineaments, or other surficial characteristics, combined with the results of dye traces. The elevations of the drains at the discharge ends of the inferred flowpaths are estimated from field data and are adjusted when necessary during model calibration. To simulate flow in a free-flowing conduit, a high conductance is assigned to each drain to eliminate the need for drain-specific information that would be very difficult to obtain. Calculations were performed for a site near Hohenfels, Germany. The potentiometric surface produced by the simulations agreed well with field data. The head contours in the vicinity of the karst features behaved in a manner consistent with a flow system having both diffuse and conduit components, and the sum of the volumetric flow out of the drain cells agreed closely with spring discharges and stream flows. Because of the success of this approach, it is recommended for regional studies in which little site-specific information (e.g., location, number, size, and conductivity of fractures and conduits) is available, and general flow characteristics are desired.« less

Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

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.

Finite Element Flow Code Optimization on the Cray T3D,

DTIC Science & Technology

1997-04-01

present time, the system is configured with 512 processing elements and 32.8 Cigabytes of memory. Through a gift of time from MSCI and other arrangements, the AHPCRC has limited access to this system.

Fast mean and variance computation of the diffuse sound transmission through finite-sized thick and layered wall and floor systems

NASA Astrophysics Data System (ADS)

Decraene, Carolina; Dijckmans, Arne; Reynders, Edwin P. B.

2018-05-01

A method is developed for computing the mean and variance of the diffuse field sound transmission loss of finite-sized layered wall and floor systems that consist of solid, fluid and/or poroelastic layers. This is achieved by coupling a transfer matrix model of the wall or floor to statistical energy analysis subsystem models of the adjacent room volumes. The modal behavior of the wall is approximately accounted for by projecting the wall displacement onto a set of sinusoidal lateral basis functions. This hybrid modal transfer matrix-statistical energy analysis method is validated on multiple wall systems: a thin steel plate, a polymethyl methacrylate panel, a thick brick wall, a sandwich panel, a double-leaf wall with poro-elastic material in the cavity, and a double glazing. The predictions are compared with experimental data and with results obtained using alternative prediction methods such as the transfer matrix method with spatial windowing, the hybrid wave based-transfer matrix method, and the hybrid finite element-statistical energy analysis method. These comparisons confirm the prediction accuracy of the proposed method and the computational efficiency against the conventional hybrid finite element-statistical energy analysis method.

Numerical Simulation of Plume Transport in Channel Bend with Different Sediment Diameters

NASA Astrophysics Data System (ADS)

Kim, H. S.; Chen, H. C.

2017-12-01

The flow and transport of suspended sediment particles, in the form of plume, were simulated using an in-house Computational Fluid Dynamics (CFD) solver FANS3D (Finite Analytic Navier-Stokes code for 3D flow). The motivation for this investigation is to provide a means to simulate and visualize dispersal systems in a complex flow environment. The physical domain considered is a 90-degrees channel bend with wingwall abutments, which induces complex, three-dimensional flow characteristics. At the inlet of the channel, a sediment plume with the volumetric concentration of 1,000 parts per million (ppm) was constantly supplied. For simplicity, it was assumed that neither deposition nor erosion takes place inside the channel and settling sediment was made to pass through the bed surface. The effect of the sediment particle size was also analyzed using two different median diameters: 0.10 mm and 0.20 mm. It was shown that flow acceleration and vortices cause strong mixing inside the channel. The three-dimensional time series from the simulation captured increasing suspended sediment concentration downstream of the abutments, along the outer bank. When the median diameter was varied, the sediment concentration at certain locations differed by orders of magnitude, indicating that the settling velocity dominates the transport process for larger diameters.

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.

Combustion chamber analysis code

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Lai, Y. G.; Krishnan, A.; Avva, R. K.; Giridharan, M. G.

1993-01-01

A three-dimensional, time dependent, Favre averaged, finite volume Navier-Stokes code has been developed to model compressible and incompressible flows (with and without chemical reactions) in liquid rocket engines. The code has a non-staggered formulation with generalized body-fitted-coordinates (BFC) capability. Higher order differencing methodologies such as MUSCL and Osher-Chakravarthy schemes are available. Turbulent flows can be modeled using any of the five turbulent models present in the code. A two-phase, two-liquid, Lagrangian spray model has been incorporated into the code. Chemical equilibrium and finite rate reaction models are available to model chemically reacting flows. The discrete ordinate method is used to model effects of thermal radiation. The code has been validated extensively against benchmark experimental data and has been applied to model flows in several propulsion system components of the SSME and the STME.

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

Exchange-driven growth.

PubMed

Ben-Naim, E; Krapivsky, P L

2003-09-01

We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: (I) Growth-clusters grow indefinitely, (II) gelation-all mass is transformed into an infinite gel in a finite time, and (III) instant gelation. In regimes I and II, the cluster size distribution attains a self-similar form. The large size tail of the scaling distribution is Phi(x) approximately exp(-x(2-nu)), where nu is a homogeneity degree of the rate of exchange. At the borderline case nu=2, the distribution exhibits a generic algebraic tail, Phi(x) approximately x(-5). In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T approximately [lnN](-(nu-2)), in the large system size limit N--> infinity. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.

A hybrid incremental projection method for thermal-hydraulics applications

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; Berndt, Markus; Francois, Marianne M.; Stagg, Alan K.; Xia, Yidong; Luo, Hong

2016-07-01

A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuška-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

A hybrid incremental projection method for thermal-hydraulics applications

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

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

A hybrid incremental projection method for thermal-hydraulics applications

DOE PAGES

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; ...

2016-07-01

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

Some aspects of the stability of the plane deformation mode of filaments of finite stiffness beyond the elasticity limits

NASA Astrophysics Data System (ADS)

Shimanovskii, A. V.

A method for calculating the plane bending of elastic-plastic filaments of finite stiffness is proposed on the basis of plastic flow theory. The problem considered is shown to reduce to relations similar to Kirchhoff equations for elastic work. Expressions are obtained for determining the normalized stiffness characteristics for the cross section of a filament with plastic regions containing beam theory equations as a particular case. A study is made of the effect of the plastic region size on the position of the elastic deformation-unloading interface and on the normalized stiffness of the filament cross section. Calculation results are presented in graphic form.

Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Singh, Rajiv R. P.

2015-10-01

We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.

Finite-Size Effects on the Behavior of the Susceptibility in van der Waals Films Bounded by Strongly Absorbing Substrates

NASA Technical Reports Server (NTRS)

Dantchev, Daniel; Rudnick, Joseph; Barmatz, M.

2007-01-01

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of 3He and 4He films in the vicinity of their respective liquid-vapor critical points.

Minimal measures for Euler-Lagrange flows on finite covering spaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Xia, Zhihong

2016-12-01

In this paper we study the minimal measures for positive definite Lagrangian systems on compact manifolds. We are particularly interested in manifolds with more complicated fundamental groups. Mather’s theory classifies the minimal or action-minimizing measures according to the first (co-)homology group of a given manifold. We extend Mather’s notion of minimal measures to a larger class for compact manifolds with non-commutative fundamental groups, and use finite coverings to study the structure of these extended minimal measures. We also define action-minimizers and minimal measures in the homotopical sense. Our program is to study the structure of homotopical minimal measures by considering Mather’s minimal measures on finite covering spaces. Our goal is to show that, in general, manifolds with a non-commutative fundamental group have a richer set of minimal measures, hence a richer dynamical structure. As an example, we study the geodesic flow on surfaces of higher genus. Indeed, by going to the finite covering spaces, the set of minimal measures is much larger and more interesting.

Atmospheric effect on classification of finite fields. [satellite-imaged agricultural areas

NASA Technical Reports Server (NTRS)

Kaufman, Y. J.; Fraser, R. S.

1984-01-01

The atmospheric effect on the upward radiance of sunlight scattered from the earth-atmosphere system is strongly influenced by the contrasts between fields and their sizes. In this paper, the radiances above finite fields are computed to simulate radiances measured by a satellite. A simulation case including 11 agricultural fields and four natural fields (water, soil, savanah, and forest) is used to test the effect of field size, background reflectance, and optical thickness of the atmosphere on the classification accuracy. For a given atmospheric turbidity, the atmospheric effect on classification of surface features may be much stronger for nonuniform surfaces than for uniform surfaces. Therefore, the classification accuracy of agricultural fields and urban areas is dependent not only on the optical characteristics of the atmosphere, but also on the size of the surface elements to be classified and their contrasts. It is concluded that new atmospheric correction methods, which take into account the finite size of the fields, are needed.

Simulation of cylindrical flow to a well using the U.S. Geological Survey Modular Finite-Difference Ground-Water Flow Model

USGS Publications Warehouse

Reilly, Thomas E.; Harbaugh, Arlen W.

1993-01-01

Cylindrical (axisymmetric) flow to a well is an important specialized topic of ground-water hydraulics and has been applied by many investigators to determine aquifer properties and determine heads and flows in the vicinity of the well. A recent modification to the U.S. Geological Survey Modular Three-Dimensional Finite-Difference Ground-Water Flow Model provides the opportunity to simulate axisymmetric flow to a well. The theory involves the conceptualization of a system of concentric shells that are capable of reproducing the large variations in gradient in the vicinity of the well by decreasing their area in the direction of the well. The computer program presented serves as a preprocessor to the U.S. Geological Survey model by creating the input data file needed to implement the axisymmetric conceptualization. Data input requirements to this preprocessor are described, and a comparison with a known analytical solution indicates that the model functions appropriately.

A comparative study of computational solutions to flow over a backward-facing step

NASA Technical Reports Server (NTRS)

Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.

1993-01-01

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

A combined volume-of-fluid method and low-Mach-number approach for DNS of evaporating droplets in turbulence

NASA Astrophysics Data System (ADS)

Dodd, Michael; Ferrante, Antonino

2017-11-01

Our objective is to perform DNS of finite-size droplets that are evaporating in isotropic turbulence. This requires fully resolving the process of momentum, heat, and mass transfer between the droplets and surrounding gas. We developed a combined volume-of-fluid (VOF) method and low-Mach-number approach to simulate this flow. The two main novelties of the method are: (i) the VOF algorithm captures the motion of the liquid gas interface in the presence of mass transfer due to evaporation and condensation without requiring a projection step for the liquid velocity, and (ii) the low-Mach-number approach allows for local volume changes caused by phase change while the total volume of the liquid-gas system is constant. The method is verified against an analytical solution for a Stefan flow problem, and the D2 law is verified for a single droplet in quiescent gas. We also demonstrate the schemes robustness when performing DNS of an evaporating droplet in forced isotropic turbulence.

Electrokinetic mixing at high zeta potentials: ionic size effects on cross stream diffusion.

PubMed

Ahmadian Yazdi, Alireza; Sadeghi, Arman; Saidi, Mohammad Hassan

2015-03-15

The electrokinetic phenomena at high zeta potentials may show several unique features which are not normally observed. One of these features is the ionic size (steric) effect associated with the solutions of high ionic concentration. In the present work, attention is given to the influences of finite ionic size on the cross stream diffusion process in an electrokinetically actuated Y-shaped micromixer. The method consists of a finite difference based numerical approach for non-uniform grid which is applied to the dimensionless form of the governing equations, including the modified Poisson-Boltzmann equation. The results reveal that, neglecting the ionic size at high zeta potentials gives rise to the overestimation of the mixing length, because the steric effects retard liquid flow, thereby enhancing the mixing efficiency. The importance of steric effects is found to be more intense for channels of smaller width to height ratio. It is also observed that, in sharp contrast to the conditions that the ions are treated as point charges, increasing the zeta potential improves the cross stream diffusion when incorporating the ionic size. Moreover, increasing the EDL thickness decreases the mixing length, whereas the opposite is true for the channel aspect ratio. Copyright © 2014 Elsevier Inc. All rights reserved.

Energetics of Vortex Ring Formation.

DTIC Science & Technology

1983-11-01

Sorohia, V., "An Experimental Investigation of Thrust Augmenting Ejector Flows", Proceedings of the Ejector Workshop for Aerospace Applications, AFWAL-TR...induction thrust augmentrs, su’h comparing thr mass and energy content of fully formed as the ejector , the migration of finite sized eddie, laminar vortex...Intermittent Jet to a Secondary Fluid in an Ejector Type Thrust Augmentor", Hiller Aircraft Company, Interim Report ARD-305, June 1962. 3. Bernal, L. and

Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter

NASA Astrophysics Data System (ADS)

Ghose, Somdeb; Adhikari, R.

2014-03-01

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

An extended algebraic variational multiscale-multigrid-multifractal method (XAVM4) for large-eddy simulation of turbulent two-phase flow

NASA Astrophysics Data System (ADS)

Rasthofer, U.; Wall, W. A.; Gravemeier, V.

2018-04-01

A novel and comprehensive computational method, referred to as the eXtended Algebraic Variational Multiscale-Multigrid-Multifractal Method (XAVM4), is proposed for large-eddy simulation of the particularly challenging problem of turbulent two-phase flow. The XAVM4 involves multifractal subgrid-scale modeling as well as a Nitsche-type extended finite element method as an approach for two-phase flow. The application of an advanced structural subgrid-scale modeling approach in conjunction with a sharp representation of the discontinuities at the interface between two bulk fluids promise high-fidelity large-eddy simulation of turbulent two-phase flow. The high potential of the XAVM4 is demonstrated for large-eddy simulation of turbulent two-phase bubbly channel flow, that is, turbulent channel flow carrying a single large bubble of the size of the channel half-width in this particular application.

75 FR 48815 - Medicaid Program and Children's Health Insurance Program (CHIP); Revisions to the Medicaid...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-11

... size may be reduced by the finite population correction factor. The finite population correction is a statistical formula utilized to determine sample size where the population is considered finite rather than... program may notify us and the annual sample size will be reduced by the finite population correction...

The effect of finite field size on classification and atmospheric correction

NASA Technical Reports Server (NTRS)

Kaufman, Y. J.; Fraser, R. S.

1981-01-01

The atmospheric effect on the upward radiance of sunlight scattered from the Earth-atmosphere system is strongly influenced by the contrasts between fields and their sizes. For a given atmospheric turbidity, the atmospheric effect on classification of surface features is much stronger for nonuniform surfaces than for uniform surfaces. Therefore, the classification accuracy of agricultural fields and urban areas is dependent not only on the optical characteristics of the atmosphere, but also on the size of the surface do not account for the nonuniformity of the surface have only a slight effect on the classification accuracy; in other cases the classification accuracy descreases. The radiances above finite fields were computed to simulate radiances measured by a satellite. A simulation case including 11 agricultural fields and four natural fields (water, soil, savanah, and forest) was used to test the effect of the size of the background reflectance and the optical thickness of the atmosphere on classification accuracy. It is concluded that new atmospheric correction methods, which take into account the finite size of the fields, have to be developed to improve significantly the classification accuracy.

Quantum state discrimination bounds for finite sample size

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

Audenaert, Koenraad M. R.; Mosonyi, Milan; Mathematical Institute, Budapest University of Technology and Economics, Egry Jozsef u 1., Budapest 1111

2012-12-15

In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of the two given and completely known states, {rho} or {sigma}. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking {rho} for {sigma}, or the other way around) are treated as of equal importance or not. Results on the quantum Chernoff and Hoeffding bounds and the quantum Stein'smore » lemma show that, if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies, and the decay rate is given by a certain statistical distance between {rho} and {sigma} (the Chernoff distance, the Hoeffding distances, and the relative entropy, respectively). While these results provide a complete solution to the asymptotic problem, they are not completely satisfying from a practical point of view. Indeed, in realistic scenarios one has access only to finitely many copies of a system, and therefore it is desirable to have bounds on the error probabilities for finite sample size. In this paper we provide finite-size bounds on the so-called Stein errors, the Chernoff errors, the Hoeffding errors, and the mixed error probabilities related to the Chernoff and the Hoeffding errors.« less

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.

Finite element analysis of inviscid subsonic boattail flow

NASA Technical Reports Server (NTRS)

Chima, R. V.; Gerhart, P. M.

1981-01-01

A finite element code for analysis of inviscid subsonic flows over arbitrary nonlifting planar or axisymmetric bodies is described. The code solves a novel primitive variable formulation of the coupled irrotationality and compressible continuity equations. Results for flow over a cylinder, a sphere, and a NACA 0012 airfoil verify the code. Computed subcritical flows over an axisymmetric boattailed afterbody compare well with finite difference results and experimental data. Interative coupling with an integral turbulent boundary layer code shows strong viscous effects on the inviscid flow. Improvements in code efficiency and extensions to transonic flows are discussed.

Sensitivity Analysis for Multidisciplinary Systems (SAMS)

DTIC Science & Technology

2016-12-01

support both mode-based structural representations and time-dependent, nonlinear finite element structural dynamics. This interim report describes...Adaptation, & Sensitivity Toolkit • Elasticity, heat transfer, & compressible flow • Adjoint solver for sensitivity analysis • High-order finite elements ...PROGRAM ELEMENT NUMBER 62201F 6. AUTHOR(S) Richard D. Snyder 5d. PROJECT NUMBER 2401 5e. TASK NUMBER N/A 5f. WORK UNIT NUMBER Q1FS 7

Excitations in the Yang–Gaudin Bose gas

DOE PAGES

Robinson, Neil J.; Konik, Robert M.

2017-06-01

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

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

Robinson, Neil J.; Konik, Robert M.

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats

NASA Astrophysics Data System (ADS)

Stalter, S.; Yelash, L.; Emamy, N.; Statt, A.; Hanke, M.; Lukáčová-Medvid'ová, M.; Virnau, P.

2018-03-01

Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation boxes. We also argue that if colloidal systems are considered as opposed to atomistic systems, the gap between microscopic and macroscopic simulations regarding time and length scales is significantly smaller. We propose a novel reduced-order technique for the coupling to the macroscopic solver, which allows us to approximate a non-linear stress-strain relation efficiently and thus further reduce computational effort of microscopic simulations.

The MV model of the color glass condensate for a finite number of sources including Coulomb interactions

DOE PAGES

McLerran, Larry; Skokov, Vladimir V.

2016-09-19

We modify the McLerran–Venugopalan model to include only a finite number of sources of color charge. In the effective action for such a system of a finite number of sources, there is a point-like interaction and a Coulombic interaction. The point interaction generates the standard fluctuation term in the McLerran–Venugopalan model. The Coulomb interaction generates the charge screening originating from well known evolution in x. Such a model may be useful for computing angular harmonics of flow measured in high energy hadron collisions for small systems. In this study we provide a basic formulation of the problem on a lattice.

A new class of finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2014-02-01

This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.

Numerical investigation of flow parameters for solid rigid spheroidal particle in a pulsatile pipe flow

NASA Astrophysics Data System (ADS)

Varghese, Joffin; Jayakumar, J. S.

2017-09-01

Quantifying, forecasting and analysing the displacement rates of suspended particles are essential while discussing about blood flow analysis. Because blood is one of the major organs in the body, which enables transport phenomena, comprising of numerous blood cells. In order to model the blood flow, a flow domain was created and numerically simulated. Flow field velocity in the stream is solved utilizing Finite Volume Method utilizing FVM unstructured solver. In pulsatile flow, the effect of parameters such as average Reynolds number, tube radius, particle size and Womersley number are taken into account. In this study spheroidal particle trajectory in axial direction is simulated at different values of pulsating frequency including 1.2 Hz, 3.33 Hz and 4.00 Hz and various densities including 1005 kg/m3 and 1025 kg/m3 for the flow domain. The analysis accomplishes the interaction study of blood constituents for different flow situations which have applications in diagnosis and treatment of cardio vascular related diseases.

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

USGS Publications Warehouse

Umari, A.M.; Szeliga, T.L.

1989-01-01

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Reentry heat transfer analysis of the space shuttle orbiter

NASA Technical Reports Server (NTRS)

Ko, W. L.; Quinn, R. D.; Gong, L.

1982-01-01

A structural performance and resizing finite element thermal analysis computer program was used in the reentry heat transfer analysis of the space shuttle. Two typical wing cross sections and a midfuselage cross section were selected for the analysis. The surface heat inputs to the thermal models were obtained from aerodynamic heating analyses, which assumed a purely turbulent boundary layer, a purely laminar boundary layer, separated flow, and transition from laminar to turbulent flow. The effect of internal radiation was found to be quite significant. With the effect of the internal radiation considered, the wing lower skin temperature became about 39 C (70 F) lower. The results were compared with fight data for space transportation system, trajectory 1. The calculated and measured temperatures compared well for the wing if laminar flow was assumed for the lower surface and bay one upper surface and if separated flow was assumed for the upper surfaces of bays other than bay one. For the fuselage, good agreement between the calculated and measured data was obtained if laminar flow was assumed for the bottom surface. The structural temperatures were found to reach their peak values shortly before touchdown. In addition, the finite element solutions were compared with those obtained from the conventional finite difference solutions.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

A Navier-Stokes phase-field crystal model for colloidal suspensions

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

Praetorius, Simon, E-mail: simon.praetorius@tu-dresden.de; Voigt, Axel, E-mail: axel.voigt@tu-dresden.de

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

A Navier-Stokes phase-field crystal model for colloidal suspensions.

PubMed

Praetorius, Simon; Voigt, Axel

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

The study on deformation characterization in micro rolling for ultra-thin strip

NASA Astrophysics Data System (ADS)

Xie, H. B.; Manabe, K.; Furushima, T.; Jiang, Z. Y.

2013-12-01

The demand for miniaturized parts and miniaturized semi-finished products is increasing. Metal forming processes cannot be simply scaled down to produce miniaturized micro parts and microforming processes have the capability of improving mass production and minimizing material waste. In this study, experimental and theoretical investigations on the micro rolling process have proven that the micro rolling deformation of thin strip is influenced by size effects from specimen sizeon flow stress and friction coefficient. The analytical and finite element (FE) models for describing the size effect related phenomena for SUS 304 stainless steel, such as the change of flow stress, friction and deformation behaviour, are proposed. The material surface constraint and the material deformation mode are critical in determination of material flow stress curve. The identified deformation and mechanics behaviours provide a basis for further exploration of the material deformation behaviour in plastic deformation of micro scale and the development of micro scale products via micro rolling.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback. Results indicate: (1) The new method exhibits quadratic convergence for homogeneous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. ?? 2002 Elsevier Science Ltd. All rights reserved.

Intrinsic particle-induced lateral transport in microchannels

PubMed Central

Amini, Hamed; Sollier, Elodie; Weaver, Westbrook M.; Di Carlo, Dino

2012-01-01

In microfluidic systems at low Reynolds number, the flow field around a particle is assumed to maintain fore-aft symmetry, with fluid diverted by the presence of a particle, returning to its original streamline downstream. This current model considers particles as passive components of the system. However, we demonstrate that at finite Reynolds number, when inertia is taken into consideration, particles are not passive elements in the flow but significantly disturb and modify it. In response to the flow field, particles translate downstream while rotating. The combined effect of the flow of fluid around particles, particle rotation, channel confinement (i.e., particle dimensions approaching those of the channel), and finite fluid inertia creates a net recirculating flow perpendicular to the primary flow direction within straight channels that resembles the well-known Dean flow in curved channels. Significantly, the particle generating this flow remains laterally fixed as it translates downstream and only the fluid is laterally transferred. Therefore, as the particles remain inertially focused, operations can be performed around the particles in a way that is compatible with downstream assays such as flow cytometry. We apply this particle-induced transfer to perform fluid switching and mixing around rigid microparticles as well as deformable cells. This transport phenomenon, requiring only a simple channel geometry with no external forces to operate, offers a practical approach for fluid transfer at high flow rates with a wide range of applications, including sample preparation, flow reaction, and heat transfer. PMID:22761309

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

NASA Astrophysics Data System (ADS)

Zhang, Xueying; Zhang, Yichen; Zhao, Yijia; Wang, Xiangyu; Yu, Song; Guo, Hong

2017-10-01

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

FINITE-ELEMENT ANALYSIS OF MULTIPHASE IMMISCIBLE FLOW THROUGH SOILS

EPA Science Inventory

A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equation...

Transient queue-size distribution in a finite-capacity queueing system with server breakdowns and Bernoulli feedback

NASA Astrophysics Data System (ADS)

Kempa, Wojciech M.

2017-12-01

A finite-capacity queueing system with server breakdowns is investigated, in which successive exponentially distributed failure-free times are followed by repair periods. After the processing a customer may either rejoin the queue (feedback) with probability q, or definitely leave the system with probability 1 - q. The system of integral equations for transient queue-size distribution, conditioned by the initial level of buffer saturation, is build. The solution of the corresponding system written for Laplace transforms is found using the linear algebraic approach. The considered queueing system can be successfully used in modelling production lines with machine failures, in which the parameter q may be considered as a typical fraction of items demanding corrections. Morever, this queueing model can be applied in the analysis of real TCP/IP performance, where q stands for the fraction of packets requiring retransmission.

Finite-Size Effects in Single Chain Magnets: An Experimental and Theoretical Study

NASA Astrophysics Data System (ADS)

Bogani, L.; Caneschi, A.; Fedi, M.; Gatteschi, D.; Massi, M.; Novak, M. A.; Pini, M. G.; Rettori, A.; Sessoli, R.; Vindigni, A.

2004-05-01

The problem of finite-size effects in s=1/2 Ising systems showing slow dynamics of the magnetization is investigated introducing diamagnetic impurities in a Co2+-radical chain. The static magnetic properties have been measured and analyzed considering the peculiarities induced by the ferrimagnetic character of the compound. The dynamic susceptibility shows that an Arrhenius law is observed with the same energy barrier for the pure and the doped compounds while the prefactor decreases, as theoretically predicted. Multiple spin reversal has also been investigated.

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Small, Des; Wiggins, Stephen

2006-12-01

In the past 15 years the framework and ideas from dynamical systems theory have been applied to a variety of transport and mixing problems in oceanic flows. The motivation for this approach comes directly from advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.) which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. In this tutorial, we motivate this approach by showing the relationship between fluid transport in two-dimensional time-periodic incompressible flows and the geometrical structures that exist for two-dimensional area-preserving maps, such as hyperbolic periodic orbits, their stable and unstable manifolds and KAM (Kolmogorov-Arnold-Moser) tori. This serves to set the stage for the attempt to “transfer” this approach to more realistic flows modelling the ocean. However, in order to accomplish this several difficulties must be overcome. The first difficulty that confronts us that any attempt to carry out a dynamical systems approach to transport requires us to obtain the appropriate “dynamical system”, which is the velocity field describing the fluid flow. In general, adequate model velocity fields are obtained by numerical solution of appropriate partial differential equations describing the dynamical evolution of the velocity field. Numerical solution of the partial differential equations can only be done for a finite time interval, and since the ocean is generally not time-periodic, this leads to a new type of dynamical system: a finite-time, aperiodically time-dependent velocity field defined as a data set on a space-time grid. The global, geometrical analysis of transport in such dynamical systems requires both new concepts and new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. The purpose of this tutorial is to describe these new concepts and analytical tools first using simple dynamical systems where quantities can be computed exactly. We then discuss their computational implications and implementation in the context of a model geophysical flow: a turbulent wind-driven double-gyre in the quasigeostrophic approximation.

MODFLOW-2005 : the U.S. Geological Survey modular ground-water model--the ground-water flow process

USGS Publications Warehouse

Harbaugh, Arlen W.

2005-01-01

This report presents MODFLOW-2005, which is a new version of the finite-difference ground-water model commonly called MODFLOW. Ground-water flow is simulated using a block-centered finite-difference approach. Layers can be simulated as confined or unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and rivers, also can be simulated. The report includes detailed explanations of physical and mathematical concepts on which the model is based, an explanation of how those concepts are incorporated in the modular structure of the computer program, instructions for using the model, and details of the computer code. The modular structure consists of a MAIN Program and a series of highly independent subroutines. The subroutines are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system that is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving the set of simultaneous equations resulting from the finite-difference method. Several solution methods are incorporated, including the Preconditioned Conjugate-Gradient method. The division of the program into packages permits the user to examine specific hydrologic features of the model independently. This also facilitates development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program also are designed to permit maximum flexibility. The program is designed to allow other capabilities, such as transport and optimization, to be incorporated, but this report is limited to describing the ground-water flow capability. The program is written in Fortran 90 and will run without modification on most computers that have a Fortran 90 compiler.

Scale-invariant cascades in turbulence and evolution

NASA Astrophysics Data System (ADS)

Guttenberg, Nicholas Ryan

In this dissertation, I present work addressing three systems which are traditionally considered to be unrelated: turbulence, evolution, and social organization. The commonality between these systems is that in each case, microscopic interaction rules give rise to an emergent behavior that in some way makes contact with the macroscopic scale of the problem. The open-ended evolution of complexity in evolving systems is analogous to the scale-free structure established in turbulent flows through local transportation of energy. In both cases, an invariance is required for the cascading behavior to occur, and in both cases the scale-free structure is built up from some initial scale from which the behavior is fed. In turbulence, I examine the case of two-dimensional turbulence in order to support the hypothesis that the friction factor and velocity profile of turbulent pipe flows depend on the turbulent energy spectrum in a way unpredicted by the classic Prandtl theory. By simulating two-dimensional flows in controlled geometries, either an inverse energy cascade or forward enstrophy cascade can be produced. The friction factor scaling of the flow changes depending on which cascade is present, in a way consistent with momentum transfer theory and roughness-induced criticality. In the problem of evolution, I show that open-ended growth of complexity can be obtained by ensuring that the evolutionary dynamics are invariant with respect to changes in complexity. Finite system size, finite point mutation rate, and fixed points in the fitness landscape can all interrupt this cascade behavior, producing an analogue to the integral scale of turbulence. This complexity cascade can exist both for competing and for symbiotic sets of organisms. Extending this picture to the qualitatively-different levels of organization of real lifeforms (viruses, unicellular, biofilms, multicellular) requires an understanding of how the processes of evolution themselves evolve. I show that a separation of spatial or temporal scales can enhance selection pressure on parameters that only matter several generations down the line. Because of this, I conclude that the prime candidates for the emergence of novel evolutionary mechanisms are biofilms and things living in oscillating environments. Finally, in the problem of social organization, I show that different types of control hierarchies - leaders or communal decision making - can emerge depending on the relationship between the environment in which members of the social group act and the development and exchange of information.

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; da Silva, Elton C.; Caldas, Iberê L.

2004-12-01

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincaré recurrence time statistics.

A two-dimensional numerical simulation of a supersonic, chemically reacting mixing layer

NASA Technical Reports Server (NTRS)

Drummond, J. Philip

1988-01-01

Research has been undertaken to achieve an improved understanding of physical phenomena present when a supersonic flow undergoes chemical reaction. A detailed understanding of supersonic reacting flows is necessary to successfully develop advanced propulsion systems now planned for use late in this century and beyond. In order to explore such flows, a study was begun to create appropriate physical models for describing supersonic combustion, and to develop accurate and efficient numerical techniques for solving the governing equations that result from these models. From this work, two computer programs were written to study reacting flows. Both programs were constructed to consider the multicomponent diffusion and convection of important chemical species, the finite rate reaction of these species, and the resulting interaction of the fluid mechanics and the chemistry. The first program employed a finite difference scheme for integrating the governing equations, whereas the second used a hybrid Chebyshev pseudospectral technique for improved accuracy.

Impact of tip-gap size and periodicity on turbulent transition

NASA Astrophysics Data System (ADS)

Pogorelov, Alexej; Meinke, Matthias; Schroeder, Wolfgang

2015-11-01

Large-Eddy Simulations of the flow field in an axial fan are performed at a Reynolds number of 936.000 based on the diameter and the rotational speed of the casing wall. A finite-volume flow solver based on a conservative Cartesian cut-cell method is used to solve the unsteady compressible Navier-Stokes equations. Computations are performed at a flow rate coefficient of 0.165 and a tip-gap size of s/D =0.01, for a 72 degrees fan section resolving only one out of five blades and a full fan resolving all five blades to investigate the impact of the periodic boundary condition. Furthermore, a grid convergence study is performed using four computational grids. Results of the flow field are analyzed for the computational grid with 1 billion cells. An interaction of the turbulent wake, generated by the tip-gap vortex, with the downstream blade, is observed, which leads to a cyclic transition with high pressure fluctuations on the suction side of the blade. Two dominant frequencies are identified which perfectly match with the characteristic frequencies in the experimental sound power level such that their physical origin is explained. A variation of the tip-gap size alters the transition on the suction side, i.e., no cyclic transition is observed.

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

NASA Astrophysics Data System (ADS)

Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu

2014-11-01

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.

Radiation Modeling in Shock-Tubes and Entry Flows

DTIC Science & Technology

2009-09-01

the MSRO surface , the local spherical coordinate system with a normal n is entered. Radiation Modeling in Shock-Tubes and Entry Flows 10 - 30 RTO...for each simulated photon group. Radiation Modeling in Shock-Tubes and Entry Flows 10 - 52 RTO-EN-AVT-162 There are two algorithms. In the first...Tubes and Entry Flows RTO-EN-AVT-162 10 - 57 all surfaces of the spatial finite-difference mesh should be calculated. This is illustrated in Figure

Fatigue response of perforated titanium for application in laminar flow control

NASA Technical Reports Server (NTRS)

Johnson, W. Steven; Miller, Jennifer L.; Newman, Jr., James

1996-01-01

The room temperature tensile and fatigue response of non-perforated and perforated titanium for laminar flow control application was investigated both experimentally and analytically. Results showed that multiple perforations did not affect the tensile response, but did reduce the fatigue life. A two dimensional finite element stress analysis was used to determine that the stress fields from adjacent perforations did not influence one another. The stress fields around the holes did not overlap one another, allowing the materials to be modeled as a plate with a center hole. Fatigue life was predicted using an equivalent MW flow size approach to relate the experimental results to microstructural features of the titanium. Predictions using flaw sizes ranging from 1 to 15 microns correlated within a factor of 2 with the experimental results by using a flow stress of 260 MPa. By using two different flow stresses in the crack closure model and correcting for plasticity, the experimental results were bounded by the predictions for high applied stresses. Further analysis of the complex geometry of the perforations and the local material chemistry is needed to further understand the fatigue behavior of the perforated titanium.

An efficient, explicit finite-rate algorithm to compute flows in chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

An explicit finite-rate code was developed to compute hypersonic viscous chemically reacting flows about three-dimensional bodies. Equations describing the finite-rate chemical reactions were fully coupled to the gas dynamic equations using a new coupling technique. The new technique maintains stability in the explicit finite-rate formulation while permitting relatively large global time steps.

Lagrangian motion, coherent structures, and lines of persistent material strain.

PubMed

Samelson, R M

2013-01-01

Lagrangian motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.

Control Theory based Shape Design for the Incompressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Cowles, G.; Martinelli, L.

2003-12-01

A design method for shape optimization in incompressible turbulent viscous flow has been developed and validated for inverse design. The gradient information is determined using a control theory based algorithm. With such an approach, the cost of computing the gradient is negligible. An additional adjoint system must be solved which requires the cost of a single steady state flow solution. Thus, this method has an enormous advantage over traditional finite-difference based algorithms. The method of artificial compressibility is utilized to solve both the flow and adjoint systems. An algebraic turbulence model is used to compute the eddy viscosity. The method is validated using several inverse wing design test cases. In each case, the program must modify the shape of the initial wing such that its pressure distribution matches that of the target wing. Results are shown for the inversion of both finite thickness wings as well as zero thickness wings which can be considered a model of yacht sails.

Buyer-vendor coordination for fixed lifetime product with quantity discount under finite production rate

NASA Astrophysics Data System (ADS)

Zhang, Qinghong; Luo, Jianwen; Duan, Yongrui

2016-03-01

Buyer-vendor coordination has been widely addressed; however, the fixed lifetime of the product is seldom considered. In this paper, we study the coordination of an integrated production-inventory system with quantity discount for a fixed lifetime product under finite production rate and deterministic demand. We first derive the buyer's ordering policy and the vendor's production batch size in decentralised and centralised systems. We then compare the two systems and show the non-coordination of the ordering policies and the production batch sizes. To improve the supply chain efficiency, we propose quantity discount contract and prove that the contract can coordinate the buyer-vendor supply chain. Finally, we present analytically tractable solutions and give a numerical example to illustrate the benefits of the proposed quantity discount strategy.

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

Saha, Sourabh K.

Although geometric imperfections have a detrimental effect on buckling, imperfection sensitivity has not been well studied in the past during design of sinusoidal micro and nano-scale structures via wrinkling of supported thin films. This is likely because one is more interested in predicting the shape/size of the resultant patterns than the buckling bifurcation onset strain during fabrication of such wrinkled structures. Herein, I have demonstrated that even modest geometric imperfections alter the final wrinkled mode shapes via the mode locking phenomenon wherein the imperfection mode grows in exclusion to the natural mode of the system. To study the effect ofmore » imperfections on mode locking, I have (i) developed a finite element mesh perturbation scheme to generate arbitrary geometric imperfections in the system and (ii) performed a parametric study via finite element methods to link the amplitude and period of the sinusoidal imperfections to the observed wrinkle mode shape and size. Based on this, a non-dimensional geometric parameter has been identified that characterizes the effect of imperfection on the mode locking phenomenon – the equivalent imperfection size. An upper limit for this equivalent imperfection size has been identified via a combination of analytical and finite element modeling. During compression of supported thin films, the system gets “locked” into the imperfection mode if its equivalent imperfection size is above this critical limit. For the polydimethylsiloxane/glass bilayer with a wrinkle period of 2 µm, this mode lock-in limit corresponds to an imperfection amplitude of 32 nm for an imperfection period of 5 µm and 8 nm for an imperfection period of 0.8 µm. Interestingly, when the non-dimensional critical imperfection size is scaled by the bifurcation onset strain, the scaled critical size depends solely on the ratio of the imperfection to natural periods. Furthermore, the computational data generated here can be generalized beyond the specific natural periods and bilayer systems studied to enable deterministic design of a variety of wrinkled micro and nano-scale structures.« less

Investigation of Micro- and Nanosized Particle Erosion in a 90° Pipe Bend Using a Two-Phase Discrete Phase Model

PubMed Central

Safaei, M. R.; Mahian, O.; Garoosi, F.; Hooman, K.; Karimipour, A.; Kazi, S. N.; Gharehkhani, S.

2014-01-01

This paper addresses erosion prediction in 3-D, 90° elbow for two-phase (solid and liquid) turbulent flow with low volume fraction of copper. For a range of particle sizes from 10 nm to 100 microns and particle volume fractions from 0.00 to 0.04, the simulations were performed for the velocity range of 5–20 m/s. The 3-D governing differential equations were discretized using finite volume method. The influences of size and concentration of micro- and nanoparticles, shear forces, and turbulence on erosion behavior of fluid flow were studied. The model predictions are compared with the earlier studies and a good agreement is found. The results indicate that the erosion rate is directly dependent on particles' size and volume fraction as well as flow velocity. It has been observed that the maximum pressure has direct relationship with the particle volume fraction and velocity but has a reverse relationship with the particle diameter. It also has been noted that there is a threshold velocity as well as a threshold particle size, beyond which significant erosion effects kick in. The average friction factor is independent of the particle size and volume fraction at a given fluid velocity but increases with the increase of inlet velocities. PMID:25379542

CFD propels NASP propulsion progress

NASA Technical Reports Server (NTRS)

Povinelli, Louis A.; Dwoyer, Douglas L.; Green, Michael J.

1990-01-01

The most complex aerothermodynamics encountered in the National Aerospace Plane (NASP) propulsion system are associated with the fuel-mixing and combustion-reaction flows of its combustor section; adequate CFD tools must be developed to model shock-wave systems, turbulent hydrogen/air mixing, flow separation, and combustion. Improvements to existing CFD codes have involved extension from two dimensions to three, as well as the addition of finite-rate hydrogen-air chemistry. A novel CFD code for the treatment of reacting flows throughout the NASP, designated GASP, uses the most advanced upwind-differencing technology.

CFD propels NASP propulsion progress

NASA Astrophysics Data System (ADS)

Povinelli, Louis A.; Dwoyer, Douglas L.; Green, Michael J.

1990-07-01

The most complex aerothermodynamics encountered in the National Aerospace Plane (NASP) propulsion system are associated with the fuel-mixing and combustion-reaction flows of its combustor section; adequate CFD tools must be developed to model shock-wave systems, turbulent hydrogen/air mixing, flow separation, and combustion. Improvements to existing CFD codes have involved extension from two dimensions to three, as well as the addition of finite-rate hydrogen-air chemistry. A novel CFD code for the treatment of reacting flows throughout the NASP, designated GASP, uses the most advanced upwind-differencing technology.

Simulation of a Canard in Fluid Flow Driven by a Piezoelectric Beam with a Software Control Loop

DTIC Science & Technology

2014-04-01

The canard is actuated by a piezoelectric beam that bends as voltage is applied. The voltage is controlled by a software subroutine that measures...Dynamic system Modeling Co-simulation Simulation Abaqus Finite element analysis (FEA) Finite element method (FEM) Computational...is unlimited. i CONTENTS Page Introduction 1 Model Description 1 Fluid Model 2 Structural Model 3 Control Subroutine 4 Results 4

Entanglement entropy in a boundary impurity model.

PubMed

Levine, G C

2004-12-31

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

Thermal and hydrodynamic studies for micro-channel cooling for large area silicon sensors in high energy physics experiments

NASA Astrophysics Data System (ADS)

Flaschel, Nils; Ariza, Dario; Díez, Sergio; Gerboles, Marta; Gregor, Ingrid-Maria; Jorda, Xavier; Mas, Roser; Quirion, David; Tackmann, Kerstin; Ullan, Miguel

2017-08-01

Micro-channel cooling initially aiming at small-sized high-power integrated circuits is being transferred to the field of high energy physics. Today's prospects of micro-fabricating silicon opens a door to a more direct cooling of detector modules. The challenge in high energy physics is to save material in the detector construction and to cool large areas. In this paper, we are investigating micro-channel cooling as a candidate for a future cooling system for silicon detectors in a generic research and development approach. The work presented in this paper includes the production and the hydrodynamic and thermal testing of a micro-channel equipped prototype optimized to achieve a homogeneous flow distribution. Furthermore, the device was simulated using finite element methods.

Finite-size anomalies of the Drude weight: Role of symmetries and ensembles

NASA Astrophysics Data System (ADS)

Sánchez, R. J.; Varma, V. K.

2017-12-01

We revisit the numerical problem of computing the high temperature spin stiffness, or Drude weight, D of the spin-1 /2 X X Z chain using exact diagonalization to systematically analyze its dependence on system symmetries and ensemble. Within the canonical ensemble and for states with zero total magnetization, we find D vanishes exactly due to spin-inversion symmetry for all but the anisotropies Δ˜M N=cos(π M /N ) with N ,M ∈Z+ coprimes and N >M , provided system sizes L ≥2 N , for which states with different spin-inversion signature become degenerate due to the underlying s l2 loop algebra symmetry. All these loop-algebra degenerate states carry finite currents which we conjecture [based on data from the system sizes and anisotropies Δ˜M N (with N

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Collective Surfing of Chemically Active Particles

NASA Astrophysics Data System (ADS)

Masoud, Hassan; Shelley, Michael J.

2014-03-01

We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.

A Moving Discontinuous Galerkin Finite Element Method for Flows with Interfaces

DTIC Science & Technology

2017-12-07

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6040--17-9765 A Moving Discontinuous Galerkin Finite Element Method for Flows with...guidance to revise the method to ensure such properties. Acknowledgements This work was sponsored by the Office of Naval Research through the Naval...18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT A Moving Discontinuous Galerkin Finite Element Method for Flows with Interfaces Andrew Corrigan, Andrew

Transport and fate of engineered silver nanoparticles in aquifer media

NASA Astrophysics Data System (ADS)

Adrian, Y.; Schneidewind, U.; Azzam, R.

2016-12-01

Engineered silver nanoparticles (AgNPs) are used in various consumer and medical products due to their antimicrobial properties. Their transport behavior in the environment is still under investigation. Previous studies have been focusing on the transport of AgNPs in test systems with pure quartz sand or top soil materials, but studies investigating aquifer material are rare. However, the protection of groundwater resources is an important part in the protection of human health and the assurance of future economic activities. Therefore, expert knowledge regarding the transport, behavior and fate of engineered nanoparticles as potential contaminants in aquifers is essential. The transport and retention behavior of two commercially available engineered AgNPs (one stabilized with a polymere and one with a surfactant) in natural silicate-dominated aquifer material was investigated in saturated laboratory columns. For the experiments a mean grain size diameter of 0.7 mm was chosen with varying silt and clay contents to investigate their effect on the transport behavior of the AgNPs. Typical flow velocities were chosen to represent natural conditions. Particle concentration in the effluent was measured using ICP-MS and the finite element code HYDRUS-1D was used to model the transport and retention processes. The size of the silver nanoparticles in the effluent was analyzed using Flow Field-Flow Fractionation. The obtained results show that silt and clay contents as well as the stabilization of the AgNPs control the transport and retention of AgNPs. Increasing breakthrough was observed with decreasing clay and silt content.

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

Numerical study of heat transfer and fluid flow for steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Pohlman, Matthew Michael

The study of heat transfer and fluid flow in a vertical Bridgman device is motivated by current industrial difficulties in growing crystals with as few defects as possible. For example, Gallium Arsenide (GaAs) is of great interest to the semiconductor industry but remains an uneconomical alternative to silicon because of the manufacturing problems. This dissertation is a two dimensional study of the fluid in an idealized Bridgman device. The model nonlinear PDEs are discretized using second order finite differencing. Newton's method solves the resulting nonlinear discrete equations. The large sparse linear systems involving the Jacobian are solved iteratively using the Generalized Minimum Residual method (GMRES). By adapting fast direct solvers for elliptic equations with simple boundary conditions, a good preconditioner is developed which is essential for GMRES to converge quickly. Trends of the fluid flow and heat transfer for typical ranges of the physical parameters are determined. Also, the size of the terms in the mathematical model are found by numerical investigation, in order to find what terms are in balance as the physical parameters vary. The results suggest the plausibility of simpler asymptotic solutions.

Cavitation Inside High-Pressure Optically Transparent Fuel Injector Nozzles

NASA Astrophysics Data System (ADS)

Falgout, Z.; Linne, M.

2015-12-01

Nozzle-orifice flow and cavitation have an important effect on primary breakup of sprays. For this reason, a number of studies in recent years have used injectors with optically transparent nozzles so that orifice flow cavitation can be examined directly. Many of these studies use injection pressures scaled down from realistic injection pressures used in modern fuel injectors, and so the geometry must be scaled up so that the Reynolds number can be matched with the industrial applications of interest. A relatively small number of studies have shown results at or near the injection pressures used in real systems. Unfortunately, neither the specifics of the design of the optical nozzle nor the design methodology used is explained in detail in these papers. Here, a methodology demonstrating how to prevent failure of a finished design made from commonly used optically transparent materials will be explained in detail, and a description of a new design for transparent nozzles which minimizes size and cost will be shown. The design methodology combines Finite Element Analysis with relevant materials science to evaluate the potential for failure of the finished assembly. Finally, test results imaging a cavitating flow at elevated pressures are presented.

Simulating effects of highway embankments on estuarine circulation

USGS Publications Warehouse

Lee, Jonathan K.; Schaffranek, Raymond W.; Baltzer, Robert A.

1994-01-01

A two-dimensional depth-averaged, finite-difference, numerical model was used to simulate tidal circulation and mass transport in the Port Royal Sound. South Carolina, estuarine system. The purpose of the study was to demonstrate the utility of the Surface-Water. Integrated. Flow and Transport model (SWIFT2D) for evaluating changes in circulation patterns and mass transport caused by highway-crossing embankments. A model of subregion of Port Royal Sound including the highway crossings and having a grid size of 61 m (200ft) was derived from a 183-m (600-ft) model of the entire Port Royal Sound estuarine system. The 183-m model was used to compute boundary-value data for the 61-m submodel, which was then used to simulate flow conditions with and without the highway embankments in place. The numerical simulations show that, with the highway embankment in place, mass transport between the Broad River and Battery Creek is reduced and mass transport between the Beaufort River and Battery Creek is increased. The net result is that mass transport into and out of upper Battery Creek is reduced. The presence of the embankments also alters circulation patterns within Battery Creek.

Jamming and condensation in one-dimensional driven flow

NASA Astrophysics Data System (ADS)

Soh, Hyungjoon; Ha, Meesoon; Jeong, Hawoong

2018-03-01

We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially condensed phase is the most interesting, compared to that in the original SB problem.

Jamming and condensation in one-dimensional driven flow.

PubMed

Soh, Hyungjoon; Ha, Meesoon; Jeong, Hawoong

2018-03-01

We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially condensed phase is the most interesting, compared to that in the original SB problem.

Polyelectrolyte Bundles: Finite size at thermodynamic equilibrium?

NASA Astrophysics Data System (ADS)

Sayar, Mehmet

2005-03-01

Experimental observation of finite size aggregates formed by polyelectrolytes such as DNA and F-actin, as well as synthetic polymers like poly(p-phenylene), has created a lot of attention in recent years. Here, bundle formation in rigid rod-like polyelectrolytes is studied via computer simulations. For the case of hydrophobically modified polyelectrolytes finite size bundles are observed even in the presence of only monovalent counterions. Furthermore, in the absence of a hydrophobic backbone, we have also observed formation of finite size aggregates via multivalent counterion condensation. The size distribution of such aggregates and the stability is analyzed in this study.

Solidification Microstructure, Segregation, and Shrinkage of Fe-Mn-C Twinning-Induced Plasticity Steel by Simulation and Experiment

NASA Astrophysics Data System (ADS)

Lan, Peng; Tang, Haiyan; Zhang, Jiaquan

2016-06-01

A 3D cellular automaton finite element model with full coupling of heat, flow, and solute transfer incorporating solidification grain nucleation and growth was developed for a multicomponent system. The predicted solidification process, shrinkage porosity, macrosegregation, grain orientation, and microstructure evolution of Fe-22Mn-0.7C twinning-induced plasticity (TWIP) steel match well with the experimental observation and measurement. Based on a new solute microsegregation model using the finite difference method, the thermophysical parameters including solid fraction, thermal conductivity, density, and enthalpy were predicted and compared with the results from thermodynamics and experiment. The effects of flow and solute transfer in the liquid phase on the solidification microstructure of Fe-22Mn-0.7C TWIP steel were compared numerically. Thermal convection decreases the temperature gradient in the liquid steel, leading to the enlargement of the equiaxed zone. Solute enrichment in front of the solid/liquid interface weakens the thermal convection, resulting in a little postponement of columnar-to-equiaxed transition (CET). The CET behavior of Fe-Mn-C TWIP steel during solidification was fully described and mathematically quantized by grain morphology statistics for the first time. A new methodology to figure out the CET location by linear regression of grain mean size with least-squares arithmetic was established, by which a composition design strategy for Fe-Mn-C TWIP steel according to solidification microstructure, matrix compactness, and homogeneity was developed.

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

Local Modelling of Groundwater Flow Using Analytic Element Method Three-dimensional Transient Unconfined Groundwater Flow With Partially Penetrating Wells and Ellipsoidal Inhomogeneites

NASA Astrophysics Data System (ADS)

Jankovic, I.; Barnes, R. J.; Soule, R.

2001-12-01

The analytic element method is used to model local three-dimensional flow in the vicinity of partially penetrating wells. The flow domain is bounded by an impermeable horizontal base, a phreatic surface with recharge and a cylindrical lateral boundary. The analytic element solution for this problem contains (1) a fictitious source technique to satisfy the head and the discharge conditions along the phreatic surface, (2) a fictitious source technique to satisfy specified head conditions along the cylindrical boundary, (3) a method of imaging to satisfy the no-flow condition across the impermeable base, (4) the classical analytic solution for a well and (5) spheroidal harmonics to account for the influence of the inhomogeneities in hydraulic conductivity. Temporal variations of the flow system due to time-dependent recharge and pumping are represented by combining the analytic element method with a finite difference method: analytic element method is used to represent spatial changes in head and discharge, while the finite difference method represents temporal variations. The solution provides a very detailed description of local groundwater flow with an arbitrary number of wells of any orientation and an arbitrary number of ellipsoidal inhomogeneities of any size and conductivity. These inhomogeneities may be used to model local hydrogeologic features (such as gravel packs and clay lenses) that significantly influence the flow in the vicinity of partially penetrating wells. Several options for specifying head values along the lateral domain boundary are available. These options allow for inclusion of the model into steady and transient regional groundwater models. The head values along the lateral domain boundary may be specified directly (as time series). The head values along the lateral boundary may also be assigned by specifying the water-table gradient and a head value at a single point (as time series). A case study is included to demonstrate the application of the model in local modeling of the groundwater flow. Transient three-dimensional capture zones are delineated for a site on Prairie Island, MN. Prairie Island is located on the Mississippi River 40 miles south of the Twin Cities metropolitan area. The case study focuses on a well that has been known to contain viral DNA. The objective of the study was to assess the potential for pathogen migration toward the well.

Characteristics of the Shuttle Orbiter Leeside Flow During A Reentry Condition

NASA Technical Reports Server (NTRS)

Kleb, William L.; Weilmuenster, K. James

1992-01-01

A study of the leeside flow characteristics of the Shuttle Orbiter is presented for a reentry flight condition. The flow is computed using a point-implicit, finite-volume scheme known as the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). LAURA is a second-order accurate, laminar Navier-Stokes solver, incorporating finite-rate chemistry with a radiative equilibrium wall temperature distribution and finite-rate wall catalysis. The resulting computational solution is analyzed in terms of salient flow features and the surface quantities are compared with flight data.

Stochastic Oscillation in Self-Organized Critical States of Small Systems: Sensitive Resting State in Neural Systems

NASA Astrophysics Data System (ADS)

Wang, Sheng-Jun; Ouyang, Guang; Guang, Jing; Zhang, Mingsha; Wong, K. Y. Michael; Zhou, Changsong

2016-01-01

Self-organized critical states (SOCs) and stochastic oscillations (SOs) are simultaneously observed in neural systems, which appears to be theoretically contradictory since SOCs are characterized by scale-free avalanche sizes but oscillations indicate typical scales. Here, we show that SOs can emerge in SOCs of small size systems due to temporal correlation between large avalanches at the finite-size cutoff, resulting from the accumulation-release process in SOCs. In contrast, the critical branching process without accumulation-release dynamics cannot exhibit oscillations. The reconciliation of SOCs and SOs is demonstrated both in the sandpile model and robustly in biologically plausible neuronal networks. The oscillations can be suppressed if external inputs eliminate the prominent slow accumulation process, providing a potential explanation of the widely studied Berger effect or event-related desynchronization in neural response. The features of neural oscillations and suppression are confirmed during task processing in monkey eye-movement experiments. Our results suggest that finite-size, columnar neural circuits may play an important role in generating neural oscillations around the critical states, potentially enabling functional advantages of both SOCs and oscillations for sensitive response to transient stimuli.

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Random-field-induced disordering mechanism in a disordered ferromagnet: Between the Imry-Ma and the standard disordering mechanism

NASA Astrophysics Data System (ADS)

Andresen, Juan Carlos; Katzgraber, Helmut G.; Schechter, Moshe

2017-12-01

Random fields disorder Ising ferromagnets by aligning single spins in the direction of the random field in three space dimensions, or by flipping large ferromagnetic domains at dimensions two and below. While the former requires random fields of typical magnitude similar to the interaction strength, the latter Imry-Ma mechanism only requires infinitesimal random fields. Recently, it has been shown that for dilute anisotropic dipolar systems a third mechanism exists, where the ferromagnetic phase is disordered by finite-size glassy domains at a random field of finite magnitude that is considerably smaller than the typical interaction strength. Using large-scale Monte Carlo simulations and zero-temperature numerical approaches, we show that this mechanism applies to disordered ferromagnets with competing short-range ferromagnetic and antiferromagnetic interactions, suggesting its generality in ferromagnetic systems with competing interactions and an underlying spin-glass phase. A finite-size-scaling analysis of the magnetization distribution suggests that the transition might be first order.

Computational study of generic hypersonic vehicle flow fields

NASA Technical Reports Server (NTRS)

Narayan, Johnny R.

1994-01-01

The geometric data of the generic hypersonic vehicle configuration included body definitions and preliminary grids for the forebody (nose cone excluded), midsection (propulsion system excluded), and afterbody sections. This data was to be augmented by the nose section geometry (blunt conical section mated with the noncircular cross section of the forebody initial plane) along with a grid and a detailed supersonic combustion ramjet (scramjet) geometry (inlet and combustor) which should be merged with the nozzle portion of the afterbody geometry. The solutions were to be obtained by using a Navier-Stokes (NS) code such as TUFF for the nose portion, a parabolized Navier-Stokes (PNS) solver such as the UPS and STUFF codes for the forebody, a NS solver with finite rate hydrogen-air chemistry capability such as TUFF and SPARK for the scramjet and a suitable solver (NS or PNS) for the afterbody and external nozzle flows. The numerical simulation of the hypersonic propulsion system for the generic hypersonic vehicle is the major focus of this entire work. Supersonic combustion ramjet is such a propulsion system, hence the main thrust of the present task has been to establish a solution procedure for the scramjet flow. The scramjet flow is compressible, turbulent, and reacting. The fuel used is hydrogen and the combustion process proceeds at a finite rate. As a result, the solution procedure must be capable of addressing such flows.

Practical performance of real-time shot-noise measurement in continuous-variable quantum key distribution

NASA Astrophysics Data System (ADS)

Wang, Tao; Huang, Peng; Zhou, Yingming; Liu, Weiqi; Zeng, Guihua

2018-01-01

In a practical continuous-variable quantum key distribution (CVQKD) system, real-time shot-noise measurement (RTSNM) is an essential procedure for preventing the eavesdropper exploiting the practical security loopholes. However, the performance of this procedure itself is not analyzed under the real-world condition. Therefore, we indicate the RTSNM practical performance and investigate its effects on the CVQKD system. In particular, due to the finite-size effect, the shot-noise measurement at the receiver's side may decrease the precision of parameter estimation and consequently result in a tight security bound. To mitigate that, we optimize the block size for RTSNM under the ensemble size limitation to maximize the secure key rate. Moreover, the effect of finite dynamics of amplitude modulator in this scheme is studied and its mitigation method is also proposed. Our work indicates the practical performance of RTSNM and provides the real secret key rate under it.

Finite size effects in epidemic spreading: the problem of overpopulated systems

NASA Astrophysics Data System (ADS)

Ganczarek, Wojciech

2013-12-01

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.

Role of relaxation and time-dependent formation of x-ray spectra

NASA Astrophysics Data System (ADS)

Privalov, Timofei; Gel'mukhanov, Faris; Ågren, Hans

2001-10-01

A fundamental problem of x-ray spectroscopy is the role of relaxation of the electronic subsystem in the field of the transient core hole. The main intention of the present study is to explore the dynamics due to core-hole relaxation in the whole time domain, and to find out how it is manifested in finite molecular systems in comparison with solids. A technique is developed based on a reduction of the Noziéres-De Dominicis equation to a set of linear algebraic equations. The developed time-dependent formalism is applied to a numerical investigation of a one-dimensional tight-binding model. The formation of the x-ray profiles is explored on the real time scale, and the role of interaction with the core hole, band filling, and the final-state rule are investigated for systems of different size. The formation of spectra of the infinite translational invariant system is studied by extensions of the finite systems. We found that the dynamics of finite systems, like molecules, differs qualitatively from solids: Contrary to the latter the time lapse of the Noziéres-De Dominicis domain for finite systems is squeezed between the inverse bandwidth and the revival time, which is proportional to the system size. For small molecules this means that there is no time for a ``Mahan-Noziéres-De Dominicis singularity'' to develop. Comparison with the strict solution of the Noziéres-De Dominicis equation shows that the adiabatic approximation describes x-ray absorption and emission considerably better than the fast approximation. This explains the suppression of the relaxation effects in x-ray emission of, e.g., gas phase and surface adsorbed molecules, but also that these effects are essential for the absorption case. There is still a quantitative distinction between the adiabatic approximation and the strict approach, which becomes more important for larger systems. Adopting the so-called finite state rule by von Barth and Grossman also for molecules, an almost complete numerical agreement between this rule and the strict x-ray-absorption and emission profiles for systems of different sizes is obtained. The simulations indicate that the final-state rule correction is important mainly near the absorption edge and at the top of the emission band.

Development of an Unstructured Mesh Code for Flows About Complete Vehicles

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Gupta, K. K. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology, under NASA Research Grant NAG4-157. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of flow simulations about complete vehicle configurations. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms, flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the code which incorporates real gas effects, has been produced. The FELISA system is also a component of the STARS aeroservoelastic system developed at NASA Dryden. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. We show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although this initial results were encouraging it became apparent that in order to develop a fully functional capability for viscous flows, several advances in solution accuracy, robustness and efficiency were required. In this grant we set out to investigate some novel methodologies that could lead to the required improvements. In particular we focused on two fronts: (1) finite element methods and (2) iterative algebraic multigrid solution techniques.

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

USGS Publications Warehouse

Voss, Clifford I.; Provost, A.M.

2002-01-01

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

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.

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

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

Lin, Guang; Liu, Jiangguo; Mu, Lin

2014-11-01

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors.more » We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.« less

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

Prince, K.R.; Schneider, B.J.

This study obtained estimates of the hydraulic properties of the upper glacial and Magothy aquifers in the East Meadow area for use in analyzing the movement of reclaimed waste water through the aquifer system. This report presents drawdown and recovery data form the two aquifer tests of 1978 and 1985, describes the six methods of analysis used, and summarizes the results of the analyses in tables and graphs. The drawdown and recovery data were analyzed through three simple analytical equations, two curve-matching techniques, and a finite-element radial-flow model. The resulting estimates of hydraulic conductivity, anisotropy, and storage characteristics were usedmore » as initial input values to the finite-element radial-flow model (Reilly, 1984). The flow model was then used to refine the estimates of the aquifer properties by more accurately representing the aquifer geometry and field conditions of the pumping tests.« less

A multidimensional finite element method for CFD

NASA Technical Reports Server (NTRS)

Pepper, Darrell W.; Humphrey, Joseph W.

1991-01-01

A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.

Magnetic Shear Damped Polar Convective Fluid Instabilities

NASA Astrophysics Data System (ADS)

Atul, Jyoti K.; Singh, Rameswar; Sarkar, Sanjib; Kravchenko, Oleg V.; Singh, Sushil K.; Chattopadhyaya, Prabal K.; Kaw, Predhiman K.

2018-01-01

The influence of the magnetic field shear is studied on the E × B (and/or gravitational) and the Current Convective Instabilities (CCI) occurring in the high-latitude F layer ionosphere. It is shown that magnetic shear reduces the growth rate of these instabilities. The magnetic shear-induced stabilization is more effective at the larger-scale sizes (≥ tens of kilometers) while at the scintillation causing intermediate scale sizes (˜ a few kilometers), the growth rate remains largely unaffected. The eigenmode structure gets localized about a rational surface due to finite magnetic shear and has broken reflectional symmetry due to centroid shift of the mode by equilibrium parallel flow or current.

Finite area method for nonlinear conical flows

NASA Technical Reports Server (NTRS)

Sritharan, S. S.; Seebass, A. R.

1982-01-01

A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Sonnad, Vijay

1991-01-01

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

Generalized epidemic process on modular networks.

PubMed

Chung, Kihong; Baek, Yongjoo; Kim, Daniel; Ha, Meesoon; Jeong, Hawoong

2014-05-01

Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process on modular networks with equal-sized finite communities and adjustable modularity. Using the analytical approach originally applied to clique-based random networks, we show that the system exhibits a bond-percolation type continuous phase transition for weak social reinforcement, whereas a discontinuous phase transition occurs for sufficiently strong social reinforcement. Our findings are numerically verified using the finite-size scaling analysis and the crossings of the bimodality coefficient.

Natural convection in melt crystal growth - The influence of flow pattern on solute segregation

NASA Technical Reports Server (NTRS)

Brown, R. A.; Yamaguchi, Y.; Chang, C. J.

1982-01-01

The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.

Numerical investigation of electron localization in polymer chains

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Stafström, Sven

1998-01-01

Using finite-size scaling, we have calculated the localization-delocalization phase diagrams for electronic wave functions in different disordered polymeric systems. The disorder considered here simulates finite polymer chain lengths, breaks in the conjugation, and disorder in an external potential. It is shown that a system of interacting chains, even at rather weak interchain interactions, allows for enough flexibility for the scattered waves to avoid dephasing and localization. Localization and the metal-insulator transition in highly conducting polymers are discussed in view of these results.

Coherent structures and dynamical systems

NASA Technical Reports Server (NTRS)

Jimenez, Javier

1987-01-01

Any flow of a viscous fluid has a finite number of degrees of freedom, and can therefore be seen as a dynamical system. A coherent structure can be thought of as a lower dimensional manifold in whose neighborhood the dynamical system spends a substantial fraction of its time. If such a manifold exists, and if its dimensionality is substantially lower that that of the full flow, it is conceivable that the flow could be described in terms of the reduced set of degrees of freedom, and that such a description would be simpler than one in which the existence of structure was not recognized. Several examples are briefly summarized.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

NASA Astrophysics Data System (ADS)

Zhao, Hanqing; Wang, Wen-ge

2018-01-01

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

A Streamline-Upwind Petrov-Galerkin Finite Element Scheme for Non-Ionized Hypersonic Flows in Thermochemical Nonequilibrium

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.; Bova, Stephen W.; Bond, Ryan B.

2011-01-01

Presentation topics include background and motivation; physical modeling including governing equations and thermochemistry; finite element formulation; results of inviscid thermal nonequilibrium chemically reacting flow and viscous thermal equilibrium chemical reacting flow; and near-term effort.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Effect of a crystal-melt interface on Taylor-vortex flow

NASA Technical Reports Server (NTRS)

Mcfadden, G. B.; Coriell, S. R.; Murray, B. T.; Glicksman, M. E.; Selleck, M. E.

1990-01-01

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.

Dynamic properties of epidemic spreading on finite size complex networks

NASA Astrophysics Data System (ADS)

Li, Ying; Liu, Yang; Shan, Xiu-Ming; Ren, Yong; Jiao, Jian; Qiu, Ben

2005-11-01

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS (susceptible-infected-susceptible) model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.

Overcoming time scale and finite size limitations to compute nucleation rates from small scale well tempered metadynamics simulations.

PubMed

Salvalaglio, Matteo; Tiwary, Pratyush; Maggioni, Giovanni Maria; Mazzotti, Marco; Parrinello, Michele

2016-12-07

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated. Nucleation rates spanning a range of 10 orders of magnitude are computed at moderate supersaturation levels, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres.

PubMed

Dreyfus, Remi; Xu, Ye; Still, Tim; Hough, L A; Yodh, A G; Torquato, Salvatore

2015-01-01

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Overcoming time scale and finite size limitations to compute nucleation rates from small scale well tempered metadynamics simulations

NASA Astrophysics Data System (ADS)

Salvalaglio, Matteo; Tiwary, Pratyush; Maggioni, Giovanni Maria; Mazzotti, Marco; Parrinello, Michele

2016-12-01

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated. Nucleation rates spanning a range of 10 orders of magnitude are computed at moderate supersaturation levels, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres

NASA Astrophysics Data System (ADS)

Dreyfus, Remi; Xu, Ye; Still, Tim; Hough, L. A.; Yodh, A. G.; Torquato, Salvatore

2015-01-01

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Numerical Large Deviation Analysis of the Eigenstate Thermalization Hypothesis

NASA Astrophysics Data System (ADS)

Yoshizawa, Toru; Iyoda, Eiki; Sagawa, Takahiro

2018-05-01

A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have thermal properties. We numerically investigate the ETH by focusing on the large deviation property, which directly evaluates the ratio of athermal energy eigenstates in the energy shell. As a consequence, we have systematically confirmed that the strong ETH is indeed true even for near-integrable systems. Furthermore, we found that the finite-size scaling of the ratio of athermal eigenstates is a double exponential for nonintegrable systems. Our result illuminates the universal behavior of quantum chaos, and suggests that a large deviation analysis would serve as a powerful method to investigate thermalization in the presence of the large finite-size effect.

The application of an atomistic J-integral to a ductile crack.

PubMed

Zimmerman, Jonathan A; Jones, Reese E

2013-04-17

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data to estimate the J-integral for the emission dislocations from a crack tip. Face-centered cubic (fcc) gold and body-centered cubic (bcc) iron modeled with embedded atom method (EAM) potentials are used as example systems. The results of a single crack with a K-loading compare well to an analytical solution from anisotropic linear elastic fracture mechanics. We also discovered that in the post-emission of dislocations from the crack tip there is a loop size-dependent contribution to the J-integral. For a system with a finite width crack loaded in simple tension, the finite size effects for the systems that were feasible to compute prevented precise agreement with theory. However, our results indicate that there is a trend towards convergence.

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles.

PubMed

Rajesh, R; Krishnamurthy, Supriya

2002-10-01

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation, and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady state, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite-size system, however, continues to show a signature of the original transition, and we characterize the finite-size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.

A model to study finite-size and magnetic effects on the phase transition of a fermion interacting system

NASA Astrophysics Data System (ADS)

Corrêa, Emerson B. S.; Linhares, César A.; Malbouisson, Adolfo P. C.

2018-03-01

We present a model to study the effects from external magnetic field, chemical potential and finite size on the phase structures of a massive four- and six-fermion interacting systems. These effects are introduced by a method of compactification of coordinates, a generalization of the standard Matsubara prescription. Through the compactification of the z-coordinate and of imaginary time, we describe a heated system with the shape of a film of thickness L, at temperature β-1 undergoing first- or second-order phase transition. We have found a strong dependence of the temperature transition on the coupling constants λ and η. Besides inverse magnetic catalysis and symmetry breaking for both kinds of transition, we have found an inverse symmetry breaking phenomenon with respect to first-order phase transition.

Progress Toward an Efficient and General CFD Tool for Propulsion Design/Analysis

NASA Technical Reports Server (NTRS)

Cox, C. F.; Cinnella, P.; Westmoreland, S.

1996-01-01

The simulation of propulsive flows inherently involves chemical activity. Recent years have seen substantial strides made in the development of numerical schemes for reacting flowfields, in particular those involving finite-rate chemistry. However, finite-rate calculations are computationally intensive and require knowledge of the actual kinetics, which are not always known with sufficient accuracy. Alternatively, flow simulations based on the assumption of local chemical equilibrium are capable of obtaining physically reasonable results at far less computational cost. The present study summarizes the development of efficient numerical techniques for the simulation of flows in local chemical equilibrium, whereby a 'Black Box' chemical equilibrium solver is coupled to the usual gasdynamic equations. The generalization of the methods enables the modelling of any arbitrary mixture of thermally perfect gases, including air, combustion mixtures and plasmas. As demonstration of the potential of the methodologies, several solutions, involving reacting and perfect gas flows, will be presented. Included is a preliminary simulation of the SSME startup transient. Future enhancements to the proposed techniques will be discussed, including more efficient finite-rate and hybrid (partial equilibrium) schemes. The algorithms that have been developed and are being optimized provide for an efficient and general tool for the design and analysis of propulsion systems.

Predicting Rediated Noise With Power Flow Finite Element Analysis

DTIC Science & Technology

2007-02-01

Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow Finite Element Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW FINITE ELEMENT ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated

Adaptive mixed finite element methods for Darcy flow in fractured porous media

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

Numerical Modeling of Fluid Flow in Solid Tumors

PubMed Central

Soltani, M.; Chen, P.

2011-01-01

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges. PMID:21673952

An Improved Treatment of External Boundary for Three-Dimensional Flow Computations

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.; Vatsa, Veer N.

1997-01-01

We present an innovative numerical approach for setting highly accurate nonlocal boundary conditions at the external computational boundaries when calculating three-dimensional compressible viscous flows over finite bodies. The approach is based on application of the difference potentials method by V. S. Ryaben'kii and extends our previous technique developed for the two-dimensional case. The new boundary conditions methodology has been successfully combined with the NASA-developed code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments, the improved external boundary conditions allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of convergence of the multigrid iterations.

Determining Aqueous Fullerene Particle Size Distributions by Asymmetric Flow Field-Flow Fractionation (AF4) without Surfactants

EPA Science Inventory

To determine the behavior of nanoparticles in environmental systems, methods must be developed to measure nanoparticle size. Asymmetric Flow Field Flow Fractionation (AF4) is an aqueous compatible size separation technique which is able to separate particles from 1 nm to 10 µm in...

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.

A simple finite element method for non-divergence form elliptic equation

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-01

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for non-divergence form elliptic equation

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

Mu, Lin; Ye, Xiu

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

Finite Size Effects in Submonolayer Catalysts Investigated by CO Electrosorption on PtsML/Pd(100).

PubMed

Yuan, Qiuyi; Doan, Hieu A; Grabow, Lars C; Brankovic, Stanko R

2017-10-04

A combination of scanning tunneling microscopy, subtractively normalized interfacial Fourier transform infrared spectroscopy (SNIFTIRS), and density functional theory (DFT) is used to quantify the local strain in 2D Pt clusters on the 100 facet of Pd and its effect on CO chemisorption. Good agreement between SNIFTIRS experiments and DFT simulations provide strong evidence that, in the absence of coherent strain between Pt and Pd, finite size effects introduce local compressive strain, which alters the chemisorption properties of the surface. Though this effect has been widely neglected in prior studies, our results suggest that accurate control over cluster sizes in submonolayer catalyst systems can be an effective approach to fine-tune their catalytic properties.

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

Critical Nucleation Length for Accelerating Frictional Slip

NASA Astrophysics Data System (ADS)

Aldam, Michael; Weikamp, Marc; Spatschek, Robert; Brener, Efim A.; Bouchbinder, Eran

2017-11-01

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically deformable bodies using model-dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half-spaces and rate-and-state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite-size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite-Element-Method calculations for a finite-size two-dimensional elastically deformable body in rate-and-state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite-size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.

Finite-size scaling and integer-spin Heisenberg chains

NASA Astrophysics Data System (ADS)

Bonner, Jill C.; Müller, Gerhard

1984-03-01

Finite-size scaling (phenomenological renormalization) techniques are trusted and widely applied in low-dimensional magnetism and, particularly, in lattice gauge field theory. Recently, investigations have begun which subject the theoretical basis to systematic and intensive scrutiny to determine the validity of finite-size scaling in a variety of situations. The 2D ANNNI model is an example of a situation where finite-size scaling methods encounter difficulty, related to the occurrence of a disorder line (one-dimensional line). A second example concerns the behavior of the spin-1/2 antiferromagnetic XXZ model where the T=0 critical behavior is exactly known and features an essential singularity at the isotropic Heisenberg point. Standard finite-size scaling techniques do not convincingly reproduce the exact phase behavior and this is attributable to the essential singularity. The point is relevant in connection with a finite-size scaling analysis of a spin-one antiferromagnetic XXZ model, which claims to support a conjecture by Haldane that the T=0 phase behavior of integer-spin Heisenberg chains is significantly different from that of half-integer-spin Heisenberg chains.

SAFSIM theory manual: A computer program for the engineering simulation of flow systems

NASA Astrophysics Data System (ADS)

Dobranich, Dean

1993-12-01

SAFSIM (System Analysis Flow SIMulator) is a FORTRAN computer program for simulating the integrated performance of complex flow systems. SAFSIM provides sufficient versatility to allow the engineering simulation of almost any system, from a backyard sprinkler system to a clustered nuclear reactor propulsion system. In addition to versatility, speed and robustness are primary SAFSIM development goals. SAFSIM contains three basic physics modules: (1) a fluid mechanics module with flow network capability; (2) a structure heat transfer module with multiple convection and radiation exchange surface capability; and (3) a point reactor dynamics module with reactivity feedback and decay heat capability. Any or all of the physics modules can be implemented, as the problem dictates. SAFSIM can be used for compressible and incompressible, single-phase, multicomponent flow systems. Both the fluid mechanics and structure heat transfer modules employ a one-dimensional finite element modeling approach. This document contains a description of the theory incorporated in SAFSIM, including the governing equations, the numerical methods, and the overall system solution strategies.

Finite-sized gas bubble motion in a blood vessel: Non-Newtonian effects

PubMed Central

Mukundakrishnan, Karthik; Ayyaswamy, Portonovo S.; Eckmann, David M.

2009-01-01

We have numerically investigated the axisymmetric motion of a finite-sized nearly occluding air bubble through a shear-thinning Casson fluid flowing in blood vessels of circular cross section. The numerical solution entails solving a two-layer fluid model—a cell-free layer and a non-Newtonian core together with the gas bubble. This problem is of interest to the field of rheology and for gas embolism studies in health sciences. The numerical method is based on a modified front-tracking method. The viscosity expression in the Casson model for blood (bulk fluid) includes the hematocrit [the volume fraction of red blood cells (RBCs)] as an explicit parameter. Three different flow Reynolds numbers, Reapp=ρlUmaxd/μapp, in the neighborhood of 0.2, 2, and 200 are investigated. Here, ρl is the density of blood, Umax is the centerline velocity of the inlet Casson profile, d is the diameter of the vessel, and μapp is the apparent viscosity of whole blood. Three different hematocrits have also been considered: 0.45, 0.4, and 0.335. The vessel sizes considered correspond to small arteries, and small and large arterioles in normal humans. The degree of bubble occlusion is characterized by the ratio of bubble to vessel radius (aspect ratio), λ, in the range 0.9≤λ≤1.05. For arteriolar flow, where relevant, the Fahraeus-Lindqvist effects are taken into account. Both horizontal and vertical vessel geometries have been investigated. Many significant insights are revealed by our study: (i) bubble motion causes large temporal and spatial gradients of shear stress at the “endothelial cell” (EC) surface lining the blood vessel wall as the bubble approaches the cell, moves over it, and passes it by; (ii) rapid reversals occur in the sign of the shear stress (+ → − → +) imparted to the cell surface during bubble motion; (iii) large shear stress gradients together with sign reversals are ascribable to the development of a recirculation vortex at the rear of the bubble; (iv) computed magnitudes of shear stress gradients coupled with their sign reversals may correspond to levels that cause injury to the cell by membrane disruption through impulsive compression and stretching; and (v) for the vessel sizes and flow rates investigated, gravitational effects are negligible. PMID:18851139

An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows.

PubMed

Oettinger, David; Haller, George

2016-10-01

Lagrangian coherent structures (LCSs) are material surfaces that shape the finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from different variational principles, solving different equations. Here we observe that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ 2 (x 0 ), of the Cauchy-Green strain tensor. This ξ 2 -system allows for the detection of LCSs in any unsteady flow by classical methods, such as Poincaré maps, developed for autonomous dynamical systems. As examples, we consider both steady and time-aperiodic flows, and use their dual ξ 2 -system to uncover both hyperbolic and elliptic LCSs from a single computation.

Principles of Considering the Effect of the Limited Volume of a System on Its Thermodynamic State

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-01-01

The features of a system with a finite volume that affect its thermodynamic state are considered in comparison to describing small bodies in macroscopic phases. Equations for unary and pair distribution functions are obtained using difference derivatives of a discrete statistical sum. The structure of the equation for the free energy of a system consisting of an ensemble of volume-limited regions with different sizes and a full set of equations describing a macroscopic polydisperse system are discussed. It is found that the equations can be applied to molecular adsorption on small faces of microcrystals, to bound and isolated pores of a polydisperse material, and to describe the spinodal decomposition of a fluid in brief periods of time and high supersaturations of the bulk phase when each local region functions the same on average. It is shown that as the size of a system diminishes, corrections must be introduced for the finiteness of the system volume and fluctuations of the unary and pair distribution functions.

Absence of thermalization in finite isolated interacting Floquet systems

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

Seetharam, Karthik; Titum, Paraj; Kolodrubetz, Michael

Conventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even withmore » no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have non-thermal average doublon densities. Finally, we show that this non-thermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.« less

Exact combinatorial approach to finite coagulating systems

NASA Astrophysics Data System (ADS)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Absence of thermalization in finite isolated interacting Floquet systems

NASA Astrophysics Data System (ADS)

Seetharam, Karthik; Titum, Paraj; Kolodrubetz, Michael; Refael, Gil

2018-01-01

Conventional wisdom suggests that the long-time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal-entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy nonthermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit nonthermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have nonthermal average doublon densities. We show that this nonthermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.

Absence of thermalization in finite isolated interacting Floquet systems

DOE PAGES

Seetharam, Karthik; Titum, Paraj; Kolodrubetz, Michael; ...

2018-01-29

Conventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even withmore » no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have non-thermal average doublon densities. Finally, we show that this non-thermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.« less

Numerical Simulation of Blood Flow in Human Artery Using (A, Q) and (A, u) Systems

NASA Astrophysics Data System (ADS)

Mungkasi, Sudi; Wijayanti Budiawan, Inge

2018-03-01

In this paper, we model blood flow in human artery in the form of (𝐴, 𝑄) and (𝐴, 𝑢) systems, then we use the Lax-Friedrichs finite volume method to find the numerical solution of each model. Here 𝐴 represents the cross sectional area of the artery, 𝑄 denotes the discharge of the blood flow, and 𝑢 is the velocity of the blood flow. We simulate the numerical scheme of each model and investigate how the blood pressure pulse propagates in human artery. Particularly, we use the residual of 𝐴 to determine which system is better numerically. We obtain that the (𝐴, 𝑄) system is better numerically than the (𝐴, 𝑢) system, because the absolute of the residual of 𝐴 using the (𝐴, 𝑄) system is smaller than the absolute of the residual of 𝐴 using the (𝐴, 𝑢) system.

Content analysis in information flows

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

Grusho, Alexander A.; Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow; Grusho, Nick A.

The paper deals with architecture of content recognition system. To analyze the problem the stochastic model of content recognition in information flows was built. We proved that under certain conditions it is possible to solve correctly a part of the problem with probability 1, viewing a finite section of the information flow. That means that good architecture consists of two steps. The first step determines correctly certain subsets of contents, while the second step may demand much more time for true decision.

Multi-scale modeling of multi-component reactive transport in geothermal aquifers

NASA Astrophysics Data System (ADS)

Nick, Hamidreza M.; Raoof, Amir; Wolf, Karl-Heinz; Bruhn, David

2014-05-01

In deep geothermal systems heat and chemical stresses can cause physical alterations, which may have a significant effect on flow and reaction rates. As a consequence it will lead to changes in permeability and porosity of the formations due to mineral precipitation and dissolution. Large-scale modeling of reactive transport in such systems is still challenging. A large area of uncertainty is the way in which the pore-scale information controlling the flow and reaction will behave at a larger scale. A possible choice is to use constitutive relationships relating, for example the permeability and porosity evolutions to the change in the pore geometry. While determining such relationships through laboratory experiments may be limited, pore-network modeling provides an alternative solution. In this work, we introduce a new workflow in which a hybrid Finite-Element Finite-Volume method [1,2] and a pore network modeling approach [3] are employed. Using the pore-scale model, relevant constitutive relations are developed. These relations are then embedded in the continuum-scale model. This approach enables us to study non-isothermal reactive transport in porous media while accounting for micro-scale features under realistic conditions. The performance and applicability of the proposed model is explored for different flow and reaction regimes. References: 1. Matthäi, S.K., et al.: Simulation of solute transport through fractured rock: a higher-order accurate finite-element finite-volume method permitting large time steps. Transport in porous media 83.2 (2010): 289-318. 2. Nick, H.M., et al.: Reactive dispersive contaminant transport in coastal aquifers: Numerical simulation of a reactive Henry problem. Journal of contaminant hydrology 145 (2012), 90-104. 3. Raoof A., et al.: PoreFlow: A Complex pore-network model for simulation of reactive transport in variably saturated porous media, Computers & Geosciences, 61, (2013), 160-174.

Supercomputer implementation of finite element algorithms for high speed compressible flows

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.

1986-01-01

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Cyclic Symmetry Finite Element Forced Response Analysis of a Distortion-Tolerant Fan with Boundary Layer Ingestion

NASA Technical Reports Server (NTRS)

Min, J. B.; Reddy, T. S. R.; Bakhle, M. A.; Coroneos, R. M.; Stefko, G. L.; Provenza, A. J.; Duffy, K. P.

2018-01-01

Accurate prediction of the blade vibration stress is required to determine overall durability of fan blade design under Boundary Layer Ingestion (BLI) distorted flow environments. Traditional single blade modeling technique is incapable of representing accurate modeling for the entire rotor blade system subject to complex dynamic loading behaviors and vibrations in distorted flow conditions. A particular objective of our work was to develop a high-fidelity full-rotor aeromechanics analysis capability for a system subjected to a distorted inlet flow by applying cyclic symmetry finite element modeling methodology. This reduction modeling method allows computationally very efficient analysis using a small periodic section of the full rotor blade system. Experimental testing by the use of the 8-foot by 6-foot Supersonic Wind Tunnel Test facility at NASA Glenn Research Center was also carried out for the system designated as the Boundary Layer Ingesting Inlet/Distortion-Tolerant Fan (BLI2DTF) technology development. The results obtained from the present numerical modeling technique were evaluated with those of the wind tunnel experimental test, toward establishing a computationally efficient aeromechanics analysis modeling tool facilitating for analyses of the full rotor blade systems subjected to a distorted inlet flow conditions. Fairly good correlations were achieved hence our computational modeling techniques were fully demonstrated. The analysis result showed that the safety margin requirement set in the BLI2DTF fan blade design provided a sufficient margin with respect to the operating speed range.

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.

Numerical Modeling of Self-Pressurization and Pressure Control by Thermodynamic Vent System in a Cryogenic Tank

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Valenzuela, Juan; LeClair, Andre; Moder, Jeff

2015-01-01

This paper presents a numerical model of a system-level test bed - the multipurpose hydrogen test bed (MHTB) using Generalized Fluid System Simulation Program (GFSSP). MHTB is representative in size and shape of a fully integrated space transportation vehicle liquid hydrogen (LH2) propellant tank and was tested at Marshall Space Flight Center (MSFC) to generate data for cryogenic storage. GFSSP is a finite volume based network flow analysis software developed at MSFC and used for thermo-fluid analysis of propulsion systems. GFSSP has been used to model the self-pressurization and ullage pressure control by Thermodynamic Vent System (TVS). A TVS typically includes a Joule-Thompson (J-T) expansion device, a two-phase heat exchanger, and a mixing pump and spray to extract thermal energy from the tank without significant loss of liquid propellant. Two GFSSP models (Self-Pressurization & TVS) were separately developed and tested and then integrated to simulate the entire system. Self-Pressurization model consists of multiple ullage nodes, propellant node and solid nodes; it computes the heat transfer through Multi-Layer Insulation blankets and calculates heat and mass transfer between ullage and liquid propellant and ullage and tank wall. TVS model calculates the flow through J-T valve, heat exchanger and spray and vent systems. Two models are integrated by exchanging data through User Subroutines of both models. The integrated models results have been compared with MHTB test data of 50% fill level. Satisfactory comparison was observed between test and numerical predictions.

Molecular Sieve Bench Testing and Computer Modeling

NASA Technical Reports Server (NTRS)

Mohamadinejad, Habib; DaLee, Robert C.; Blackmon, James B.

1995-01-01

The design of an efficient four-bed molecular sieve (4BMS) CO2 removal system for the International Space Station depends on many mission parameters, such as duration, crew size, cost of power, volume, fluid interface properties, etc. A need for space vehicle CO2 removal system models capable of accurately performing extrapolated hardware predictions is inevitable due to the change of the parameters which influences the CO2 removal system capacity. The purpose is to investigate the mathematical techniques required for a model capable of accurate extrapolated performance predictions and to obtain test data required to estimate mass transfer coefficients and verify the computer model. Models have been developed to demonstrate that the finite difference technique can be successfully applied to sorbents and conditions used in spacecraft CO2 removal systems. The nonisothermal, axially dispersed, plug flow model with linear driving force for 5X sorbent and pore diffusion for silica gel are then applied to test data. A more complex model, a non-darcian model (two dimensional), has also been developed for simulation of the test data. This model takes into account the channeling effect on column breakthrough. Four FORTRAN computer programs are presented: a two-dimensional model of flow adsorption/desorption in a packed bed; a one-dimensional model of flow adsorption/desorption in a packed bed; a model of thermal vacuum desorption; and a model of a tri-sectional packed bed with two different sorbent materials. The programs are capable of simulating up to four gas constituents for each process, which can be increased with a few minor changes.

Three dimensional finite element methods: Their role in the design of DC accelerator systems

NASA Astrophysics Data System (ADS)

Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.

2013-04-01

High Voltage Engineering has designed, built and tested a 2 MV dual irradiation system that will be applied for radiation damage studies and ion beam material modification. The system consists of two independent accelerators which support simultaneous proton and electron irradiation (energy range 100 keV - 2 MeV) of target sizes of up to 300 × 300 mm2. Three dimensional finite element methods were used in the design of various parts of the system. The electrostatic solver was used to quantify essential parameters of the solid-state power supply generating the DC high voltage. The magnetostatic solver and ray tracing were used to optimize the electron/ion beam transport. Close agreement between design and measurements of the accelerator characteristics as well as beam performance indicate the usefulness of three dimensional finite element methods during accelerator system design.

The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius

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

Gallagher, S.; Hnat, B.; Rowlands, G.

2012-12-15

The effects of the finite Larmor radius on the generation of zonal flows by the four-wave modulational instability are investigated using an extended form of the Hasegawa-Mima equation. Growth rates of the zonal mode are quantified using analytical predictions from a four-mode truncated model, as well as from direct numerical simulation of the nonlinear extended Hasegawa-Mima equation. We not only consider purely zonal flows but also examine the generic oblique case and show that, for small Larmor radii, off-axis modes may become dominant. We find a key parameter M{sub {rho}} which characterises the behaviour of the system due to changesmore » in the Larmor radius. We find that, similarly to previous results obtained by changing the driving wave amplitude, two separate dynamical regimes can be accessed. These correspond to oscillatory energy transfer between zonal flows and a driving wave and the fully saturated zonal flow.« less

Finite-block-length analysis in classical and quantum information theory.

PubMed

Hayashi, Masahito

2017-01-01

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.

Finite-block-length analysis in classical and quantum information theory

PubMed Central

HAYASHI, Masahito

2017-01-01

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects. PMID:28302962

Finite Element Analysis of Plastic Deformation During Impression Creep

NASA Astrophysics Data System (ADS)

Naveena; Ganesh Kumar, J.; Mathew, M. D.

2015-04-01

Finite element (FE) analysis of plastic deformation associated with impression creep deformation of 316LN stainless steel was carried out. An axisymmetric FE model of 10 × 10 × 10 mm specimen with 1-mm-diameter rigid cylindrical flat punch was developed. FE simulation of impression creep deformation was performed by assuming elastic-plastic-power-law creep deformation behavior. Evolution of the stress with time under the punch during elastic, plastic, and creep processes was analyzed. The onset of plastic deformation was found to occur at a nominal stress about 1.12 times the yield stress of the material. The size of the developed plastic zone was predicted to be about three times the radius of the punch. The material flow behavior and the pile-up on specimen surface have been modeled.

MISSISSIPPI EMBAYMENT AQUIFER SYSTEM IN MISSISSIPPI: GEOHYDROLOGIC DATA COMPILATION FOR FLOW MODEL SIMULATION.

USGS Publications Warehouse

Arthur, J.K.; Taylor, R.E.

1986-01-01

As part of the Gulf Coast Regional Aquifer System Analysis (GC RASA) study, data from 184 geophysical well logs were used to define the geohydrologic framework of the Mississippi embayment aquifer system in Mississippi for flow model simulation. Five major aquifers of Eocene and Paleocene age were defined within this aquifer system in Mississippi. A computer data storage system was established to assimilate the information obtained from the geophysical logs. Computer programs were developed to manipulate the data to construct geologic sections and structure maps. Data from the storage system will be input to a five-layer, three-dimensional, finite-difference digital computer model that is used to simulate the flow dynamics in the five major aquifers of the Mississippi embayment aquifer system.

Influence of numerical dissipation in computing supersonic vortex-dominated flows

NASA Technical Reports Server (NTRS)

Kandil, O. A.; Chuang, A.

1986-01-01

Steady supersonic vortex-dominated flows are solved using the unsteady Euler equations for conical and three-dimensional flows around sharp- and round-edged delta wings. The computational method is a finite-volume scheme which uses a four-stage Runge-Kutta time stepping with explicit second- and fourth-order dissipation terms. The grid is generated by a modified Joukowski transformation. The steady flow solution is obtained through time-stepping with initial conditions corresponding to the freestream conditions, and the bow shock is captured as a part of the solution. The scheme is applied to flat-plate and elliptic-section wings with a leading edge sweep of 70 deg at an angle of attack of 10 deg and a freestream Mach number of 2.0. Three grid sizes of 29 x 39, 65 x 65 and 100 x 100 have been used. The results for sharp-edged wings show that they are consistent with all grid sizes and variation of the artificial viscosity coefficients. The results for round-edged wings show that separated and attached flow solutions can be obtained by varying the artificial viscosity coefficients. They also show that the solutions are independent of the way time stepping is done. Local time-stepping and global minimum time-steeping produce same solutions.

Zonal Flows and Long-lived Axisymmetric Pressure Bumps in Magnetorotational Turbulence

NASA Astrophysics Data System (ADS)

Johansen, A.; Youdin, A.; Klahr, H.

2009-06-01

We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to 10 scale heights. Maxwell and Reynolds stresses are found to increase by more than a factor of 2 when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This, in turn, generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short timescales creates zonal flow structures with lifetimes of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.

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

Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

NASA Astrophysics Data System (ADS)

Shamshuddin, MD.; Anwar Bég, O.; Sunder Ram, M.; Kadir, A.

2018-02-01

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic, incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Analysis of Adsorbed Natural Gas Tank Technology

NASA Astrophysics Data System (ADS)

Knight, Ernest; Schultz, Conrad; Rash, Tyler; Dohnke, Elmar; Stalla, David; Gillespie, Andrew; Sweany, Mark; Seydel, Florian; Pfeifer, Peter

With gasoline being an ever decreasing finite resource and with the desire to reduce humanity's carbon footprint, there has been an increasing focus on innovation of alternative fuel sources. Natural gas burns cleaner, is more abundant, and conforms to modern engines. However, storing compressed natural gas (CNG) requires large, heavy gas cylinders, which limits space and fuel efficiency. Adsorbed natural gas (ANG) technology allows for much greater fuel storage capacity and the ability to store the gas at a much lower pressure. Thus, ANG tanks are much more flexible in terms of their size, shape, and weight. Our ANG tank employs monolithic nanoporous activated carbon as its adsorbent material. Several different configurations of this Flat Panel Tank Assembly (FPTA) along with a Fuel Extraction System (FES) were examined to compare with the mass flow rate demands of an engine.

Numerical investigation of a heat transfer characteristics of an impingement cooling system with non-uniform temperature on a cooled surface

NASA Astrophysics Data System (ADS)

Marzec, K.; Kucaba-Pietal, A.

2016-09-01

A series of numerical analysis have been performed to investigate heat transfer characteristics of an impingement cooling array of ten jets directed to the flat surface with different heat flux qw(x). A three-dimensional finite element model was used to solve equations of heat and mass transfer. The study focused on thermal stresses reduction on a cooled surface and aims at answering the question how the Nusselt number distribution on the cooled surface is affected by various inlet flow parameters for different heat flux distributions. The setup consists of a cylindrical plenum with an inline array of ten impingement jets. Simulation has been performed using the Computational Fluid Dynamics (CFD) code Ansys CFX. The k - ω shear stress transport (SST) turbulence model is used in calculations. The numerical analysis of the different mesh density results in good convergence of the GCI index, what excluded mesh size dependency. The physical model is simplified by using the steady state analysis and the incompressible and viscous flow of the fluid.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping.

PubMed

Tripathi, Dharmendra; Bég, O Anwar

2012-08-01

Magnetohydrodynamic peristaltic flows arise in controlled magnetic drug targeting, hybrid haemodynamic pumps and biomagnetic phenomena interacting with the human digestive system. Motivated by the objective of improving an understanding of the complex fluid dynamics in such flows, we consider in the present article the transient magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for temperature field, axial velocity, transverse velocity, pressure gradient, local wall shear stress, volume flowrate and averaged volume flowrate are obtained. The effects of the transverse magnetic field, Grashof number and thermal conductivity on the flow patterns induced by peristaltic waves (sinusoidal propagation along the length of channel) are studied using graphical plots. The present study identifies that greater pressure is required to propel the magneto-fluid by peristaltic pumping in comparison to a non-conducting Newtonian fluid, whereas, a lower pressure is required if heat transfer is effective. The analytical solutions further provide an important benchmark for future numerical simulations.

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Modeling and Simulation of A Microchannel Cooling System for Vitrification of Cells and Tissues.

PubMed

Wang, Y; Zhou, X M; Jiang, C J; Yu, Y T

The microchannel heat exchange system has several advantages and can be used to enhance heat transfer for vitrification. To evaluate the microchannel cooling method and to analyze the effects of key parameters such as channel structure, flow rate and sample size. A computational flow dynamics model is applied to study the two-phase flow in microchannels and its related heat transfer process. The fluid-solid coupling problem is solved with a whole field solution method (i.e., flow profile in channels and temperature distribution in the system being simulated simultaneously). Simulation indicates that a cooling rate >10 4 C/min is easily achievable using the microchannel method with the high flow rate for a board range of sample sizes. Channel size and material used have significant impact on cooling performance. Computational flow dynamics is useful for optimizing the design and operation of the microchannel system.

A reduced-order integral formulation to account for the finite size effect of isotropic square panels using the transfer matrix method.

PubMed

Bonfiglio, Paolo; Pompoli, Francesco; Lionti, Riccardo

2016-04-01

The transfer matrix method is a well-established prediction tool for the simulation of sound transmission loss and the sound absorption coefficient of flat multilayer systems. Much research has been dedicated to enhancing the accuracy of the method by introducing a finite size effect of the structure to be simulated. The aim of this paper is to present a reduced-order integral formulation to predict radiation efficiency and radiation impedance for a panel with equal lateral dimensions. The results are presented and discussed for different materials in terms of radiation efficiency, sound transmission loss, and the sound absorption coefficient. Finally, the application of the proposed methodology for rectangular multilayer systems is also investigated and validated against experimental data.

Thermalization without eigenstate thermalization hypothesis after a quantum quench.

PubMed

Mori, Takashi; Shiraishi, Naoto

2017-08-01

Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature, although it does not satisfy the eigenstate thermalization hypothesis. In contrast, when the system size is finite and the temperature is low enough, the system may not thermalize. In this case, the steady state is well described by the generalized Gibbs ensemble constructed by using highly nonlocal conserved quantities. We also show that this model exhibits prethermalization, in which the prethermalized state is characterized by nonthermal energy eigenstates.

Finite-element simulation of ground-water flow in the vicinity of Yucca Mountain, Nevada-California

USGS Publications Warehouse

Czarnecki, J.B.; Waddell, R.K.

1984-01-01

A finite-element model of the groundwater flow system in the vicinity of Yucca Mountain at the Nevada Test Site was developed using parameter estimation techniques. The model simulated steady-state ground-water flow occurring in tuffaceous, volcanic , and carbonate rocks, and alluvial aquifers. Hydraulic gradients in the modeled area range from 0.00001 for carbonate aquifers to 0.19 for barriers in tuffaceous rocks. Three model parameters were used in estimating transmissivity in six zones. Simulated hydraulic-head values range from about 1,200 m near Timber Mountain to about 300 m near Furnace Creek Ranch. Model residuals for simulated versus measured hydraulic heads range from -28.6 to 21.4 m; most are less than +/-7 m, indicating an acceptable representation of the hydrologic system by the model. Sensitivity analyses of the model 's flux boundary condition variables were performed to assess the effect of varying boundary fluxes on the calculation of estimated model transmissivities. Varying the flux variables representing discharge at Franklin Lake and Furnace Creek Ranch has greater effect than varying other flux variables. (Author 's abstract)

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Liu, C. H.; Wong, Tin-Chee; Kandil, Osama A.

1992-01-01

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, thin-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption have been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5-deg semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers have been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5-deg circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.

NASCRIN - NUMERICAL ANALYSIS OF SCRAMJET INLET

NASA Technical Reports Server (NTRS)

Kumar, A.

1994-01-01

The NASCRIN program was developed for analyzing two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. NASCRIN solves the two-dimensional Euler or Navier-Stokes equations in conservative form by an unsplit, explicit, two-step finite-difference method. A more recent explicit-implicit, two-step scheme has also been incorporated in the code for viscous flow analysis. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow calculations. NASCRIN can analyze both inviscid and viscous flows with no struts, one strut, or multiple struts embedded in the flow field. NASCRIN can be used in a quasi-three-dimensional sense for some scramjet inlets under certain simplifying assumptions. Although developed for supersonic internal flow, NASCRIN may be adapted to a variety of other flow problems. In particular, it should be readily adaptable to subsonic inflow with supersonic outflow, supersonic inflow with subsonic outflow, or fully subsonic flow. The NASCRIN program is available for batch execution on the CDC CYBER 203. The vectorized FORTRAN version was developed in 1983. NASCRIN has a central memory requirement of approximately 300K words for a grid size of about 3,000 points.

Transient well flow in layered aquifer systems: the uniform well-face drawdown solution

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

Previously a hybrid analytical-numerical solution for the general problem of computing transient well flow in vertically heterogeneous aquifers was proposed by the author. The radial component of flow was treated analytically, while the finite-difference technique was used for the vertical flow component only. In the present work the hybrid solution has been modified by replacing the previously assumed uniform well-face gradient (UWG) boundary condition in such a way that the drawdown remains uniform along the well screen. The resulting uniform well-face drawdown (UWD) solution also includes the effects of a finite diameter well, wellbore storage and a thin skin, while partial penetration and vertical heterogeneity are accommodated by the one-dimensional discretization. Solutions are proposed for well flow caused by constant, variable and slug discharges. The model was verified by comparing wellbore drawdowns and well-face flux distributions with published numerical solutions. Differences between UWG and UWD well flow will occur in all situations with vertical flow components near the well, which is demonstrated by considering: (1) partially penetrating wells in confined aquifers, (2) fully penetrating wells in unconfined aquifers with delayed response and (3) layered aquifers and leaky multiaquifer systems. The presented solution can be a powerful tool for solving many well-hydraulic problems, including well tests, flowmeter tests, slug tests and pumping tests. A computer program for the analysis of pumping tests, based on the hybrid analytical-numerical technique and UWG or UWD conditions, is available from the author.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

Simulation of controllable permeation in PNIPAAm coated membranes

NASA Astrophysics Data System (ADS)

Ehrenhofer, Adrian; Wallmersperger, Thomas; Richter, Andreas

2016-04-01

Membranes separate fluid compartments and can comprise transport structures for selective permeation. In biology, channel proteins are specialized in their atomic structure to allow transport of specific compounds (selectivity). Conformational changes in protein structure allow the control of the permeation abilities by outer stimuli (gating). In polymeric membranes, the selectivity is due to electrostatic or size-exclusion. It can thus be controlled by size variation or electric charges. Controllable permeation can be useful to determine particle-size distributions in continuous flow, e.g. in microfluidics and biomedicine to gain cell diameter profiles in blood. The present approach uses patterned polyethylene terephthalate (PET) membranes with hydrogel surface coating for permeation control by size-exclusion. The thermosensitive hydrogel poly(N-isopropylacrylamide) (PNIPAAm) is structured with a cross-shaped pore geometry. A change in the temperature of the water flow through the membrane leads to a pore shape variation. The temperature dependent behavior of PNIPAAm can be numerically modeled with a temperature expansion model, where the swelling and deswelling is depicted by temperature dependent expansion coefficients. In the present study, the free swelling behavior was implemented to the Finite Element tool ABAQUS for the complex composite structure of the permeation control membrane. Experimental values of the geometry characteristics were derived from microscopy images with the tool Image J and compared to simulation results. Numerical simulations using the derived thermo-mechanical model for different pore geometries (circular, rectangle, cross and triangle) were performed. With this study, we show that the temperature expansion model with values from the free swelling behavior can be used to adequately predict the deformation behavior of the complex membrane system. The predictions can be used to optimize the behavior of the membrane pores and the overall performance of the smart membrane.

Phase equilibria in polymer-blend thin films

NASA Astrophysics Data System (ADS)

Clarke, Nigel; Souche, Mireille

2010-03-01

To describe equilibrium concentration profiles in thin films of polymer mixtures, we propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We first focus on the case of 50:50 polymer blends confined between anti-symmetric walls. The different phases of the system and the transitions between them, including finite size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films. The addition of a further degree of freedom in the system, namely a solvent, may result in a chaotic behavior of the system, characterized by the existence of solutions with exponential sensitivity to initial conditions. Such solutions and there subsequent contribution to the out-of-equilibrium dynamics of the system are well described in Hamiltonian formalism. A fully consistent treatment of the Flory-Huggins-de Gennes theory of thin film polymer blend solutions, in the spirit of the Hamiltonian approach will be presented. 1. M. Souche and N. Clarke, J. Chem. Phys., submitted.

Stochastic gain in finite populations

NASA Astrophysics Data System (ADS)

Röhl, Torsten; Traulsen, Arne; Claussen, Jens Christian; Schuster, Heinz Georg

2008-08-01

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen , Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

Rashba and Dresselhaus spin-orbit interactions effects on electronic features of a two dimensional elliptic quantum dot

NASA Astrophysics Data System (ADS)

Mokhtari, P.; Rezaei, G.; Zamani, A.

2017-06-01

In this paper, electronic structure of a two dimensional elliptic quantum dot under the influence of external electric and magnetic fields are studied in the presence of Rashba and Dresselhaus spin-orbit interactions. This investigation is done computationally and to do this, at first, the effective Hamiltonian of the system by considering the spin-orbit coupling is demonstrated in the presence of applied electric and magnetic fields and afterwards the Schrödinger equation is solved using the finite difference approach. Utilizing finite element method, eigenvalues and eigenstates of the system are calculated and the effect of the external fields, the size of the dot as well as the strength of Rashba spin-orbit interaction are studied. Our results indicate that, Spin-orbit interactions, external fields and the dot size have a great influence on the electronic structure of the system.

Finite-size effects on current correlation functions

NASA Astrophysics Data System (ADS)

Chen, Shunda; Zhang, Yong; Wang, Jiao; Zhao, Hong

2014-02-01

We study why the calculation of current correlation functions (CCFs) still suffers from finite-size effects even when the periodic boundary condition is taken. Two important one-dimensional, momentum-conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as ˜t-2/3 in the diatomic hard-core gas model and in a manner close to ˜t-1/2 in the Fermi-Pasta-Ulam-β model.

Parallel Three-Dimensional Computation of Fluid Dynamics and Fluid-Structure Interactions of Ram-Air Parachutes

NASA Technical Reports Server (NTRS)

Tezduyar, Tayfun E.

1998-01-01

This is a final report as far as our work at University of Minnesota is concerned. The report describes our research progress and accomplishments in development of high performance computing methods and tools for 3D finite element computation of aerodynamic characteristics and fluid-structure interactions (FSI) arising in airdrop systems, namely ram-air parachutes and round parachutes. This class of simulations involves complex geometries, flexible structural components, deforming fluid domains, and unsteady flow patterns. The key components of our simulation toolkit are a stabilized finite element flow solver, a nonlinear structural dynamics solver, an automatic mesh moving scheme, and an interface between the fluid and structural solvers; all of these have been developed within a parallel message-passing paradigm.

Finite-Difference Solutions for Compressible Laminar Boundary-Layer Flows of a Dusty Gas over a Semi-Infinite Flat Plate.

DTIC Science & Technology

1986-08-01

AD-A174 952 FINITE - DIFFERENCE SOLUTIONS FOR CONPRESSIBLE LANINAR 1/2 BOUNDARY-LAYER FLOUS (U) TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE...dilute dusty gas over a semi-infinite flat plate. Details are given of the impliit finite , difference schemes as well as the boundary conditions... FINITE - DIFFERENCE SOLUTIONS FOR COMPRESSIBLE LAMINAR BOUNDARY-LAYER FLOWS OF A DUSTY GAS OVER A SEMI-INFINITE FLAT PLATE by B. Y. Wang and I. I

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien; Volin, Dmytro

2015-09-01

We give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system — a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

JacketSE: An Offshore Wind Turbine Jacket Sizing Tool; Theory Manual and Sample Usage with Preliminary Validation

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

Damiani, Rick

This manual summarizes the theory and preliminary verifications of the JacketSE module, which is an offshore jacket sizing tool that is part of the Wind-Plant Integrated System Design & Engineering Model toolbox. JacketSE is based on a finite-element formulation and on user-prescribed inputs and design standards' criteria (constraints). The physics are highly simplified, with a primary focus on satisfying ultimate limit states and modal performance requirements. Preliminary validation work included comparing industry data and verification against ANSYS, a commercial finite-element analysis package. The results are encouraging, and future improvements to the code are recommended in this manual.

A combined molecular dynamics/micromechanics/finite element approach for multiscale constitutive modeling of nanocomposites with interface effects

NASA Astrophysics Data System (ADS)

Yang, B. J.; Shin, H.; Lee, H. K.; Kim, H.

2013-12-01

We introduce a multiscale framework based on molecular dynamic (MD) simulation, micromechanics, and finite element method (FEM). A micromechanical model, which considers influences of the interface properties, nanoparticle (NP) size, and microcracks, is developed. Then, we perform MD simulations to characterize the mechanical properties of the nanocomposite system (silica/nylon 6) with varying volume fraction and size of NPs. By comparing the MD with micromechanics results, intrinsic physical properties at interfacial region are derived. Finally, we implement the developed model in the FEM code with the derived interfacial parameters, and predict the mechanical behavior of the nanocomposite at the macroscopic scale.

Institute for Aviation Research and Development Research Project

DTIC Science & Technology

1989-01-01

Symbolics Artificial Intelligence * Vision Systems * Finite Element Modeling ( NASTRAN ) * Aerodynamic Paneling (VSAERO) Projects: * Software...34Wall Functions for k and epsilon for Turbulent Flow Through Rough and Smooth Pipes," Eleventh International Symposium on Turbulence, October 17-19, 1988

Sensitivity of the mode locking phenomenon to geometric imperfections during wrinkling of supported thin films

DOE PAGES

Saha, Sourabh K.

2017-01-11

Although geometric imperfections have a detrimental effect on buckling, imperfection sensitivity has not been well studied in the past during design of sinusoidal micro and nano-scale structures via wrinkling of supported thin films. This is likely because one is more interested in predicting the shape/size of the resultant patterns than the buckling bifurcation onset strain during fabrication of such wrinkled structures. Herein, I have demonstrated that even modest geometric imperfections alter the final wrinkled mode shapes via the mode locking phenomenon wherein the imperfection mode grows in exclusion to the natural mode of the system. To study the effect ofmore » imperfections on mode locking, I have (i) developed a finite element mesh perturbation scheme to generate arbitrary geometric imperfections in the system and (ii) performed a parametric study via finite element methods to link the amplitude and period of the sinusoidal imperfections to the observed wrinkle mode shape and size. Based on this, a non-dimensional geometric parameter has been identified that characterizes the effect of imperfection on the mode locking phenomenon – the equivalent imperfection size. An upper limit for this equivalent imperfection size has been identified via a combination of analytical and finite element modeling. During compression of supported thin films, the system gets “locked” into the imperfection mode if its equivalent imperfection size is above this critical limit. For the polydimethylsiloxane/glass bilayer with a wrinkle period of 2 µm, this mode lock-in limit corresponds to an imperfection amplitude of 32 nm for an imperfection period of 5 µm and 8 nm for an imperfection period of 0.8 µm. Interestingly, when the non-dimensional critical imperfection size is scaled by the bifurcation onset strain, the scaled critical size depends solely on the ratio of the imperfection to natural periods. Furthermore, the computational data generated here can be generalized beyond the specific natural periods and bilayer systems studied to enable deterministic design of a variety of wrinkled micro and nano-scale structures.« less

Charging and hybridization in the finite cluster model

NASA Technical Reports Server (NTRS)

Bauschlicher, C. W., Jr.; Bagus, P. S.; Nelin, C. J.

1984-01-01

Cluster wavefunctions which have appropriate hybridization and polarization lead to reasonable properties for the interaction of an adsorbate with a solid surface. However, for Al clusters, it was found that the atomic change distribution is not uniform. The finite cluster size leads to changes not representative for an extended system. This effect appears to be dependent on the particular materials being studied; it does not occur in all cases.

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

A critical evaluation of an asymmetrical flow field-flow fractionation system for colloidal size characterization of natural organic matter.

PubMed

Zhou, Zhengzhen; Guo, Laodong

2015-06-19

Colloidal retention characteristics, recovery and size distribution of model macromolecules and natural dissolved organic matter (DOM) were systematically examined using an asymmetrical flow field-flow fractionation (AFlFFF) system under various membrane size cutoffs and carrier solutions. Polystyrene sulfonate (PSS) standards with known molecular weights (MW) were used to determine their permeation and recovery rates by membranes with different nominal MW cutoffs (NMWCO) within the AFlFFF system. Based on a ≥90% recovery rate for PSS standards by the AFlFFF system, the actual NMWCOs were determined to be 1.9 kDa for the 0.3 kDa membrane, 2.7 kDa for the 1 kDa membrane, and 33 kDa for the 10 kDa membrane, respectively. After membrane calibration, natural DOM samples were analyzed with the AFlFFF system to determine their colloidal size distribution and the influence from membrane NMWCOs and carrier solutions. Size partitioning of DOM samples showed a predominant colloidal size fraction in the <5 nm or <10 kDa size range, consistent with the size characteristics of humic substances as the main terrestrial DOM component. Recovery of DOM by the AFlFFF system, as determined by UV-absorbance at 254 nm, decreased significantly with increasing membrane NMWCO, from 45% by the 0.3 kDa membrane to 2-3% by the 10 kDa membrane. Since natural DOM is mostly composed of lower MW substances (<10 kDa) and the actual membrane cutoffs are normally larger than their manufacturer ratings, a 0.3 kDa membrane (with an actual NMWCO of 1.9 kDa) is highly recommended for colloidal size characterization of natural DOM. Among the three carrier solutions, borate buffer seemed to provide the highest recovery and optimal separation of DOM. Rigorous calibration with macromolecular standards and optimization of system conditions are a prerequisite for quantifying colloidal size distribution using the flow field-flow fractionation technique. In addition, the coupling of AFlFFF with fluorescence EEMs could provide new insights into DOM heterogeneity in different colloidal size fractions. Copyright © 2015 Elsevier B.V. All rights reserved.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Unstructured Mesh Methods for the Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Bibb, K. L. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite element algorithm for the solution of the viscous compressible flow equations which can solve flows all the way down to the incompressible limit and that can use higher order (quadratic) approximations leading to highly accurate answers, and 3) and iterative algebraic multigrid solution techniques.

Emergence of jams in the generalized totally asymmetric simple exclusion process

NASA Astrophysics Data System (ADS)

Derbyshev, A. E.; Povolotsky, A. M.; Priezzhev, V. B.

2015-02-01

The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014, 10.1088/1742-5468/2012/05/P05014] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as an isolated particle. We are interested in the large time behavior of this process on a ring in the whole range of the parameter λ controlling the interaction. We study the stationary state correlations, the cluster size distribution, and the large-time fluctuations of integrated particle current. When λ is finite, we find the usual TASEP-like behavior: The correlation length is finite; there are only clusters of finite size in the stationary state and current fluctuations belong to the Kardar-Parisi-Zhang universality class. When λ grows with the system size, so does the correlation length. We find a nontrivial transition regime with clusters of all sizes on the lattice. We identify a crossover parameter and derive the large deviation function for particle current, which interpolates between the case considered by Derrida-Lebowitz and a single-particle diffusion.

Universality and tails of long-range interactions in one dimension

NASA Astrophysics Data System (ADS)

Valiente, Manuel; Öhberg, Patrik

2017-07-01

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional s -wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalization of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalization. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multichannel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

In this paper a finite Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame. From these solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. In addition we derive the drag force the finite sized impurity approximately experiences as it moves through the superfluid, which proves the existence of a superfluid phase for finite extensions of the impurities below the speed of sound. Finally we find that the force increases with velocity until an inflection point from which it decreases again in 2 and 3d.

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 velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Comparison of variational real-space representations of the kinetic energy operator

NASA Astrophysics Data System (ADS)

Skylaris, Chris-Kriton; Diéguez, Oswaldo; Haynes, Peter D.; Payne, Mike C.

2002-08-01

We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a real-space method that is not variational) and the reciprocal-space plane-wave method which is fully variational. We find that a definition of the finite-difference method [P. Maragakis, J. Soler, and E. Kaxiras, Phys. Rev. B 64, 193101 (2001)] satisfies one of the two properties of variational behavior at the cost of larger errors than the conventional finite-difference method. On the other hand, a technique which represents functions in a number of plane waves which is independent of system size closely follows the plane-wave method and therefore also the criteria for variational behavior. Its application is only limited by the requirement of having functions strictly localized in regions of real space, but this is a characteristic of an increasing number of modern real-space methods, as they are designed to have a computational cost that scales linearly with system size.

Natural Crack Sizing Based on Eddy Current Image and Electromagnetic Field Analyses

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

Endo, H.; Uchimoto, T.; Takagi, T.

2006-03-06

An eddy current testing (ECT) system with multi-coil type probes is applied to size up cracks fabricated on austenite stainless plates. We have developed muti-channel ECT system to produce data as digital images. The probes consist of transmit-receive type sensors as elements to classify crack directions, working as two scan direction modes simultaneously. Template matching applied to the ECT images determines regions of interest in sizing up cracks. Finite element based inversion sizes up the crack depth from the measured ECT signal. The present paper demonstrates this approach for fatigue crack and stress corrosion cracking.

Multiscale modeling of a Chemofilter device for filtering chemotherapy toxins from blood

NASA Astrophysics Data System (ADS)

Maani, Nazanin; Beyhaghi, Saman; Yee, Daryl; Nosonovsky, Micheal; Greer, Julia; Hetts, Steven; Rayz, Vitaliy

2016-11-01

Purpose: Chemotherapy drugs injected intra-arterially to treat cancer can cause systemic toxic effects. A catheter-based Chemofilter device, temporarily deployed in a vein during the procedure can filter excessive drug from the blood thus reducing chemotherapy side-effects. CFD modeling is used to design the membrane of the Chemofilter in order to optimize its hemodynamic performance. Methods: Multiscale approach is used to model blood flow through the Chemofilter. The toxins bind to the Chemofilter's membrane formed by a lattice of numerous micro cells deployed in a blood vessel of much larger size. A detailed model of the flow through a 2x2 microcell matrix with periodic boundary conditions is used to determine the permeability of the membrane. The results are used to simulate the flow through the whole device modeled as a uniform porous membrane. The finite-volume solver Fluent is used to obtain the numerical solution. Results: The micro cell matrix has a porosity of 0.92. The pressure drop across the resolved microcells was found to be 630 Pa, resulting in the permeability of 6.21 x10-11 m2 in the normal direction. These values were used to optimize the device geometry in order to increase the contact area of the membrane, while minimizing its obstruction to the flow. NIH NCI R01CA194533.

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

NASA Technical Reports Server (NTRS)

Hall, Philip; Balakumar, P.

1990-01-01

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.

1973-01-01

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

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.

A finite element study of the EIDI system. [Electro-Impulse De-Icing System

NASA Technical Reports Server (NTRS)

Khatkhate, A. A.; Scavuzzo, R. J.; Chu, M. L.

1988-01-01

This paper presents a method for modeling the structural dynamics of an Electro-Impulse De-Icing System, using finite element analyses procedures. A guideline for building a representative finite element model is discussed. Modeling was done initially using four noded cubic elements, four noded isoparametric plate elements and eight noded isoparametric shell elements. Due to the size of the problem and due to the underestimation of shear stress results when compared to previous analytical work an approximate model was created to predict possible areas of shedding of ice. There appears to be good agreement with the test data provided by The Boeing Commercial Airplane Company. Thus these initial results of this method were found to be encouraging. Additional analytical work and comparison with experiment is needed in order to completely evaluate this approach.

Size-scaling behaviour of the electronic polarizability of one-dimensional interacting systems

NASA Astrophysics Data System (ADS)

Chiappe, G.; Louis, E.; Vergés, J. A.

2018-05-01

Electronic polarizability of finite chains is accurately calculated from the total energy variation of the system produced by small but finite static electric fields applied along the chain direction. Normalized polarizability, that is, polarizability divided by chain length, diverges as the second power of length for metallic systems but approaches a constant value for insulating systems. This behaviour provides a very convenient way to characterize the wave-function malleability of finite systems as it avoids the need of attaching infinite contacts to the chain ends. Hubbard model calculations at half filling show that the method works for a small U  =  1 interaction value that corresponds to a really small spectral gap of 0.005 (hopping t  =  ‑1 is assumed). Once successfully checked, the method has been applied to the long-range hopping model of Gebhard and Ruckenstein showing 1/r hopping decay (Gebhard and Ruckenstein 1992 Phys. Rev. Lett. 68 244; Gebhard et al 1994 Phys. Rev. B 49 10926). Metallicity for U values below the reported metal-insulator transition is obtained but the surprise comes for U values larger than the critical one (when a gap appears in the spectral density of states) because a steady increase of the normalized polarizability with size is obtained. This critical size-scaling behaviour can be understood as corresponding to a molecule which polarizability is unbounded. We have checked that a real transfer of charge from one chain end to the opposite occurs as a response to very small electric fields in spite of the existence of a large gap of the order of U for one-particle excitations. Finally, ab initio quantum chemistry calculations of realistic poly-acetylene chains prove that the occurrence of such critical behaviour in real systems is unlikely.

A finite element solver for 3-D compressible viscous flows

NASA Technical Reports Server (NTRS)

Reddy, K. C.; Reddy, J. N.; Nayani, S.

1990-01-01

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

Mathematical modelling of the human cardiovascular system in the presence of stenosis

NASA Technical Reports Server (NTRS)

Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

1993-01-01

This paper reports a theoretical study on the distribution of blood flow in the human cardiovascular system when one or more blood vessels are affected by stenosis. The analysis employs a mathematical model of the entire system based on the finite element method. The arterial-venous network is represented by a large number of interconnected segments in the model. Values for the model parameters are based upon the published data on the physiological and rheological properties of blood. Computational results show how blood flow through various parts of the cardiovascular system is affected by stenosis in different blood vessels. No significant changes in the flow parameters of the cardiovascular system were found to occur when the reduction in the lumen diameter of the stenosed vessels was less than 65%.

(Finite) statistical size effects on compressive strength.

PubMed

Weiss, Jérôme; Girard, Lucas; Gimbert, Florent; Amitrano, David; Vandembroucq, Damien

2014-04-29

The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules.

Accuracy of topological entanglement entropy on finite cylinders.

PubMed

Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon

2013-09-06

Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

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

Teomy, Eial, E-mail: eialteom@post.tau.ac.il; Shokef, Yair, E-mail: shokef@tau.ac.il

2014-08-14

We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10{sup 7} ×more » 10{sup 7}, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.« less

Effect of zone size on the convergence of exact solutions for diffusion in single phase systems with planar, cylindrical or spherical geometry

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.

1981-01-01

Exact solutions for diffusion in single phase binary alloy systems with constant diffusion coefficient and zero-flux boundary condition have been evaluated to establish the optimum zone size of applicability. Planar, cylindrical and spherical interface geometry, and finite, singly infinite, and doubly infinite systems are treated. Two solutions are presented for each geometry, one well suited to short diffusion times, and one to long times. The effect of zone-size on the convergence of these solutions is discussed. A generalized form of the diffusion solution for doubly infinite systems is proposed.

The effect of external forces on discrete motion within holographic optical tweezers.

PubMed

Eriksson, E; Keen, S; Leach, J; Goksör, M; Padgett, M J

2007-12-24

Holographic optical tweezers is a widely used technique to manipulate the individual positions of optically trapped micron-sized particles in a sample. The trap positions are changed by updating the holographic image displayed on a spatial light modulator. The updating process takes a finite time, resulting in a temporary decrease of the intensity, and thus the stiffness, of the optical trap. We have investigated this change in trap stiffness during the updating process by studying the motion of an optically trapped particle in a fluid flow. We found a highly nonlinear behavior of the change in trap stiffness vs. changes in step size. For step sizes up to approximately 300 nm the trap stiffness is decreasing. Above 300 nm the change in trap stiffness remains constant for all step sizes up to one particle radius. This information is crucial for optical force measurements using holographic optical tweezers.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

NASA Astrophysics Data System (ADS)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

High cleanliness globe valve with sine mechanism drive

NASA Astrophysics Data System (ADS)

Luo, Hu

2018-06-01

This paper gives a new type of quick-opening globe valve for life support pneumatic control system of the safety cabin at underground coal mine. The valve adopts the sine mechanism to transmit the rotating of the handle in the range of 90° to the reciprocating motion of the spool. The mechanism implements the quick-opening function of the valve through controlling the contact and separation between the O-ring and the end face of the valve. Since there is no relative sliding between the sealing interfaces, the valve solute uncontrollable disadvantage wear particles which produced by package ball valve, to ensure high cleanliness in flow path. Traditional transmission mechanism has a reinforcement effect and reduce handle open torque. By the finite element method, the relationship between the contact force and the compression of O-ring is analyzed to provide the boundary condition for the calculation of the rotational torque. Meanwhile the velocity field and pressure field along the flow path are simulated. The caliber size of the valve and the flow resistance coefficient are obtained. There is higher cleanliness, more reliable sealing, smaller handle open torque advantage compared with existing packing ball valve. The above work presents a new technical approach for the design of pneumatic control valve of the safety cabin.

Thermodynamics of quasideterministic digital computers

NASA Astrophysics Data System (ADS)

Chu, Dominique

2018-02-01

A central result of stochastic thermodynamics is that irreversible state transitions of Markovian systems entail a cost in terms of an infinite entropy production. A corollary of this is that strictly deterministic computation is not possible. Using a thermodynamically consistent model, we show that quasideterministic computation can be achieved at finite, and indeed modest cost with accuracies that are indistinguishable from deterministic behavior for all practical purposes. Concretely, we consider the entropy production of stochastic (Markovian) systems that behave like and and a not gates. Combinations of these gates can implement any logical function. We require that these gates return the correct result with a probability that is very close to 1, and additionally, that they do so within finite time. The central component of the model is a machine that can read and write binary tapes. We find that the error probability of the computation of these gates falls with the power of the system size, whereas the cost only increases linearly with the system size.

A three-dimensional turbulent compressible flow model for ejector and fluted mixers

NASA Technical Reports Server (NTRS)

Rushmore, W. L.; Zelazny, S. W.

1978-01-01

A three dimensional finite element computer code was developed to analyze ejector and axisymmetric fluted mixer systems whose flow fields are not significantly influenced by streamwise diffusion effects. A two equation turbulence model was used to make comparisons between theory and data for various flow fields which are components of the ejector system, i.e., (1) turbulent boundary layer in a duct; (2) rectangular nozzle (free jet); (3) axisymmetric nozzle (free jet); (4) hypermixing nozzle (free jet); and (5) plane wall jet. Likewise, comparisons of the code with analytical results and/or other numerical solutions were made for components of the axisymmetric fluted mixer system. These included: (1) developing pipe flow; (2) developing flow in an annular pipe; (3) developing flow in an axisymmetric pipe with conical center body and no fluting and (4) developing fluted pipe flow. Finally, two demonstration cases are presented which show the code's ability to analyze both the ejector and axisymmetric fluted mixers.

Elastic contact mechanics: percolation of the contact area and fluid squeeze-out.

PubMed

Persson, B N J; Prodanov, N; Krick, B A; Rodriguez, N; Mulakaluri, N; Sawyer, W G; Mangiagalli, P

2012-01-01

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.

Modeling of Compressible Flow with Friction and Heat Transfer Using the Generalized Fluid System Simulation Program (GFSSP)

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Alak; Majumdar, Alok

2007-01-01

The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.

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.

The flow dynamics behind a flexible finite cylinder as a flexible agitator

NASA Astrophysics Data System (ADS)

Yong, T. H.; Chan, H. B.; Dol, S. S.; Wee, S. K.; Kumar, P.

2017-06-01

This paper investigates the flow dynamics behind a flexible finite cylinder in a single-phase flow using a water tunnel. The cylinder was individually submerged in water at ReD = 4000, 6000 and 8000. The cylinder investigated has a AR = 10 and 16 and is made of EVA in order to achieve the lower stiffness for flexibility. A same AR of its aluminium rigid cylinder was investigated to serve as a benchmark to the flow dynamics behind a flexible cylinder. The results the downwash that hinders the transportation of vortices to the downstream was diminished. As a direct consequence of this phenomenon, the turbulence production has seen significant improvement for flexible finite cylinder.

On the structure of viscous flow about the afterbody of hull

NASA Astrophysics Data System (ADS)

Yoshida, Osamu; Zhu, Ming; Miyata, Hideaki

1993-09-01

A finite-volume method is applied to a flow about full ship models in the curvilinear coordinate system. Simulations are carried out for SR196 frame-line series. The simulated results show the difference of the wake and the longitudinal vorticity between the different hull forms. The comparisons between simulated and measured results show qualitative agreements in the wake distributions near the propeller disk circumference.

A three-dimensional multiphase flow model for assessing NAPL contamination in porous and fractured media, 2. Porous medium simulation examples

NASA Astrophysics Data System (ADS)

Panday, S.; Wu, Y. S.; Huyakorn, P. S.; Springer, E. P.

1994-06-01

This paper discusses the verification and application of the three-dimensional (3-D) multiphase flow model presented by Huyakorn et al. (Part 1 in this issue) for assessing contamination due to subsurface releases of non-aqueous-phase liquids (NAPL's). Attention is focussed on situations involving one-, two- and three-dimensional flow through porous media. The model formulations and numerical schemes are tested for highly nonlinear field conditions. The utility and accuracy of various simplifications to certain simulation scenarios are assessed. Five simulation examples are included for demonstrative purposes. The first example verifies the model for vertical flow and compares the performance of the fully three-phase and the passive-air-phase formulations. Air-phase boundary conditions are noted to have considerable effects on simulation results. The second example verifies the model for cross-sectional analyses involving LNAPL and DNAPL migration. Finite-difference (5-point) and finite-element (9-point) spatial approximations are compared for different grid aspect ratios. Unless corrected, negative-transmissivity conditions were found to have undesirable impact on the finite-element solutions. The third example provides a model validation against laboratory experimental data on 5-spot water-flood treatment of oil reservoirs. The sensitivity to grid orientation is noted for the finite-difference schemes. The fourth example demonstrates model utility in characterizing the 3-D migration of LNAPL and DNAPL from surface sources. The final example present a modeling study of air sparging. Critical parameters affecting the performance of air-sparging system are examined. In general, the modeling results indicate sparging is more effective in water-retentive soils, and larger values of sparge influence radius may be achieved for certain anisotropic conditions.

Development of a nondestructive vibration technique for bond assessment of Space Shuttle tiles

NASA Technical Reports Server (NTRS)

Moslehy, Faissal A.

1994-01-01

This final report describes the achievements of the above titled project. The project is funded by NASA-KSC (Grant No. NAG 10-0117) for the period of 1 Jan. to 31 Dec. 1993. The purpose of this project was to develop a nondestructive, noncontact technique based on 'vibration signature' of tile systems to quantify the bond conditions of the thermal protection system) tiles of Space Shuttle orbiters. The technique uses a laser rapid scan system, modal measurements, and finite element modeling. Finite element models were developed for tiles bonded to both clamped and deformable integrated skin-stringer orbiter mid-fuselage. Results showed that the size and location of a disbonded tile can be determined from frequency and mode shape information. Moreover, a frequency response survey was used to quickly identify the disbonded tiles. The finite element results were compared with experimentally determined frequency responses of a 17-tile test panel, where a rapidscan laser system was employed. An excellent degree of correlation between the mathematical simulation and experimental results was realized. An inverse solution for single-tile assemblies was also derived and is being implemented into a computer program that can interact with the modal testing software. The output of the program displays the size and location of disbond. This program has been tested with simulated input (i.e., finite element data), and excellent agreement between predicted and simulated disbonds was shown. Finally, laser vibration imaging and acoustic emission techniques were shown to be well suited for detecting and monitoring the progressive damage in Graphite/Epoxy composite materials.

Phase order in superfluid helium films

NASA Astrophysics Data System (ADS)

Bramwell, Steven T.; Faulkner, Michael F.; Holdsworth, Peter C. W.; Taroni, Andrea

2015-12-01

Classic experimental data on helium films are transformed to estimate a finite-size phase order parameter that measures the thermal degradation of the condensate fraction in the two-dimensional superfluid. The order parameter is found to evolve thermally with the exponent β = 3 π^2/128 , a characteristic, in analogous magnetic systems, of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Universal scaling near the BKT fixed point generates a collapse of experimental data on helium and ferromagnetic films, and implies new experiments and theoretical protocols to explore the phase order. These results give a striking example of experimental finite-size scaling in a critical system that is broadly relevant to two-dimensional Bose fluids. This paper is dedicated to the memory of our friend and colleague Maxime Clusel, with whom we enjoyed many stimulating discussions on related topics.

Finite length Taylor Couette flow

NASA Technical Reports Server (NTRS)

Streett, C. L.; Hussaini, M. Y.

1987-01-01

Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.

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

Aleman, S.E.

This report documents a finite element code designed to model subsurface flow and contaminant transport, named FACT. FACT is a transient three-dimensional, finite element code designed to simulate isothermal groundwater flow, moisture movement, and solute transport in variably saturated and fully saturated subsurface porous media.

Patterns and rates of ground-water flow on Long Island, New York

USGS Publications Warehouse

Buxton, Herbert T.; Modica, Edward

1992-01-01

Increased ground-water contamination from human activities on Long Island has prompted studies to define the pattern and rate of ground-water movement. A two-dimensional, fine-mesh, finite-element model consisting of 11,969 nodes and 22,880 elements was constructed to represent ground-water flow along a north-south section through central Long Island. The model represents average hydrologic conditions within a corridor approximately 15 miles wide. The model solves discrete approximations of both the potential and stream functions. The resulting flownet depicts flow paths and defines the vertical distribution of flow within the section. Ground-water flow rates decrease with depth. Sixty-two percent of the water flows no deeper than the upper glacial (water-table) aquifer, 38 percent enters the underlying Magothy aquifer, and only 3.1 percent enters the Lloyd aquifer. The limiting streamlines for flow to the Magothy and Lloyd aquifers indicate that aquifer recharge areas are narrow east-west bands through the center of the island. The recharge area of the Magothy aquifer is only 5.4 miles wide; that of the Lloyd aquifer is less than 0.5 miles. The distribution of ground-water traveltime and a flownet are calculated from model results; both are useful in the investigation of contaminant transport or the chemical evolution of ground water within the flow system. A major discontinuity in traveltime occurs across the streamline which separates the flow subsystems of the two confined aquifers. Water that reaches the Lloyd aquifer attains traveltimes as high as 10,000 years, whereas water that has not penetrated deeper than the Magothy aquifer attains traveltimes of only 2,000 years. The finite-element approach used in this study is particularly suited to ground-water systems that have complex hydrostratigraphy and cross-sectional symmetry.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things

PubMed Central

Akan, Ozgur B.

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics. PMID:29415019

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

PubMed

Kuscu, Murat; Akan, Ozgur B

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.