Numerical Modelling of Mechanical Properties of C-Pd Film by Homogenization Technique and Finite Element Method

NASA Astrophysics Data System (ADS)

Rymarczyk, Joanna; Kowalczyk, Piotr; Czerwosz, Elzbieta; Bielski, Włodzimierz

2011-09-01

The nanomechanical properties of nanostructural carbonaceous-palladium films are studied. The nanoindentation experiments are numerically using the Finite Element Method. The homogenization theory is applied to compute the properties of the composite material used as the input data for nanoindentation calculations.

Numerical and Experimental Investigations of the Flow in a Stationary Pelton Bucket

NASA Astrophysics Data System (ADS)

Nakanishi, Yuji; Fujii, Tsuneaki; Kawaguchi, Sho

A numerical code based on one of mesh-free particle methods, a Moving-Particle Semi-implicit (MPS) Method has been used for the simulation of free surface flows in a bucket of Pelton turbines so far. In this study, the flow in a stationary bucket is investigated by MPS simulation and experiment to validate the numerical code. The free surface flow dependent on the angular position of the bucket and the corresponding pressure distribution on the bucket computed by the numerical code are compared with that obtained experimentally. The comparison shows that numerical code based on MPS method is useful as a tool to gain an insight into the free surface flows in Pelton turbines.

Localization of a variational particle smoother

NASA Astrophysics Data System (ADS)

Morzfeld, M.; Hodyss, D.; Poterjoy, J.

2017-12-01

Given the success of 4D-variational methods (4D-Var) in numerical weather prediction,and recent efforts to merge ensemble Kalman filters with 4D-Var,we consider a method to merge particle methods and 4D-Var.This leads us to revisit variational particle smoothers (varPS).We study the collapse of varPS in high-dimensional problemsand show how it can be prevented by weight-localization.We test varPS on the Lorenz'96 model of dimensionsn=40, n=400, and n=2000.In our numerical experiments, weight localization prevents the collapse of the varPS,and we note that the varPS yields results comparable to ensemble formulations of 4D-variational methods,while it outperforms EnKF with tuned localization and inflation,and the localized standard particle filter.Additional numerical experiments suggest that using localized weights in varPS may not yield significant advantages over unweighted or linearizedsolutions in near-Gaussian problems.

Numerical simulation of the hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor

NASA Astrophysics Data System (ADS)

Fortova, S. V.; Shepelev, V. V.; Troshkin, O. V.; Kozlov, S. A.

2017-09-01

The paper presents the results of numerical simulation of the development of hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor encountered in experiments [1-3]. For the numerical solution used the TPS software package (Turbulence Problem Solver) that implements a generalized approach to constructing computer programs for a wide range of problems of hydrodynamics, described by the system of equations of hyperbolic type. As numerical methods are used the method of large particles and ENO-scheme of the second order with Roe solver for the approximate solution of the Riemann problem.

Numerical simulation study on rolling-chemical milling process of aluminum-lithium alloy skin panel

NASA Astrophysics Data System (ADS)

Huang, Z. B.; Sun, Z. G.; Sun, X. F.; Li, X. Q.

2017-09-01

Single curvature parts such as aircraft fuselage skin panels are usually manufactured by rolling-chemical milling process, which is usually faced with the problem of geometric accuracy caused by springback. In most cases, the methods of manual adjustment and multiple roll bending are used to control or eliminate the springback. However, these methods can cause the increase of product cost and cycle, and lead to material performance degradation. Therefore, it is of significance to precisely control the springback of rolling-chemical milling process. In this paper, using the method of experiment and numerical simulation on rolling-chemical milling process, the simulation model for rolling-chemical milling process of 2060-T8 aluminum-lithium alloy skin was established and testified by the comparison between numerical simulation and experiment results for the validity. Then, based on the numerical simulation model, the relative technological parameters which influence on the curvature of the skin panel were analyzed. Finally, the prediction of springback and the compensation can be realized by controlling the process parameters.

Numerical study of the vortex tube reconnection using vortex particle method on many graphics cards

NASA Astrophysics Data System (ADS)

Kudela, Henryk; Kosior, Andrzej

2014-08-01

Vortex Particle Methods are one of the most convenient ways of tracking the vorticity evolution. In the article we presented numerical recreation of the real life experiment concerning head-on collision of two vortex rings. In the experiment the evolution and reconnection of the vortex structures is tracked with passive markers (paint particles) which in viscous fluid does not follow the evolution of vorticity field. In numerical computations we showed the difference between vorticity evolution and movement of passive markers. The agreement with the experiment was very good. Due to problems with very long time of computations on a single processor the Vortex-in-Cell method was implemented on the multicore architecture of the graphics cards (GPUs). Vortex Particle Methods are very well suited for parallel computations. As there are myriads of particles in the flow and for each of them the same equations of motion have to be solved the SIMD architecture used in GPUs seems to be perfect. The main disadvantage in this case is the small amount of the RAM memory. To overcome this problem we created a multiGPU implementation of the VIC method. Some remarks on parallel computing are given in the article.

Viscosity Measurement of Highly Viscous Liquids Using Drop Coalescence in Low Gravity

NASA Technical Reports Server (NTRS)

Antar, Basil N.; Ethridge, Edwin; Maxwell, Daniel

1999-01-01

The method of drop coalescence is being investigated for use as a method for determining the viscosity of highly viscous undercooled liquids. Low gravity environment is necessary in this case to minimize the undesirable effects of body forces and liquid motion in levitated drops. Also, the low gravity environment will allow for investigating large liquid volumes which can lead to much higher accuracy for the viscosity calculations than possible under 1 - g conditions. The drop coalescence method is preferred over the drop oscillation technique since the latter method can only be applied for liquids with vanishingly small viscosities. The technique developed relies on both the highly accurate solution of the Navier-Stokes equations as well as on data from experiments conducted in near zero gravity environment. In the analytical aspect of the method two liquid volumes are brought into contact which will coalesce under the action of surface tension alone. The free surface geometry development as well as its velocity during coalescence which are obtained from numerical computations are compared with an analogous experimental model. The viscosity in the numerical computations is then adjusted to bring into agreement of the experimental results with the calculations. The true liquid viscosity is the one which brings the experiment closest to the calculations. Results are presented for method validation experiments performed recently on board the NASA/KC-135 aircraft. The numerical solution for this validation case was produced using the Boundary Element Method. In these tests the viscosity of a highly viscous liquid, in this case glycerine at room temperature, was determined to high degree of accuracy using the liquid coalescence method. These experiments gave very encouraging results which will be discussed together with plans for implementing the method in a shuttle flight experiment.

25 Years of Self-organized Criticality: Numerical Detection Methods

NASA Astrophysics Data System (ADS)

McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna

2016-01-01

The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.

A study of various methods for calculating locations of lightning events

NASA Technical Reports Server (NTRS)

Cannon, John R.

1995-01-01

This article reports on the results of numerical experiments on finding the location of lightning events using different numerical methods. The methods include linear least squares, nonlinear least squares, statistical estimations, cluster analysis and angular filters and combinations of such techniques. The experiments involved investigations of methods for excluding fake solutions which are solutions that appear to be reasonable but are in fact several kilometers distant from the actual location. Some of the conclusions derived from the study are that bad data produces fakes, that no fool-proof method of excluding fakes was found, that a short base-line interferometer under development at Kennedy Space Center to measure the direction cosines of an event shows promise as a filter for excluding fakes. The experiments generated a number of open questions, some of which are discussed at the end of the report.

Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

NASA Astrophysics Data System (ADS)

Burnett, S. C.; Rojas, R.; Perevalov, A.; Lathrop, D. P.

2017-12-01

The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108. In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere [Schaeffer, N. G3 (2013)]. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

NASA Astrophysics Data System (ADS)

Burnett, Sarah; Rojas, Ruben; Perevalov, Artur; Lathrop, Daniel; Ide, Kayo; Schaeffer, Nathanael

2017-11-01

The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108 . In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

NASA Astrophysics Data System (ADS)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

NASA Astrophysics Data System (ADS)

Dudley Ward, N. F.; Lähivaara, T.; Eveson, S.

2017-12-01

In this paper, we consider a high-order discontinuous Galerkin (DG) method for modelling wave propagation in coupled poroelastic-elastic media. The upwind numerical flux is derived as an exact solution for the Riemann problem including the poroelastic-elastic interface. Attenuation mechanisms in both Biot's low- and high-frequency regimes are considered. The current implementation supports non-uniform basis orders which can be used to control the numerical accuracy element by element. In the numerical examples, we study the convergence properties of the proposed DG scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions.

New method of processing heat treatment experiments with numerical simulation support

NASA Astrophysics Data System (ADS)

Kik, T.; Moravec, J.; Novakova, I.

2017-08-01

In this work, benefits of combining modern software for numerical simulations of welding processes with laboratory research was described. Proposed new method of processing heat treatment experiments leading to obtaining relevant input data for numerical simulations of heat treatment of large parts was presented. It is now possible, by using experiments on small tested samples, to simulate cooling conditions comparable with cooling of bigger parts. Results from this method of testing makes current boundary conditions during real cooling process more accurate, but also can be used for improvement of software databases and optimization of a computational models. The point is to precise the computation of temperature fields for large scale hardening parts based on new method of temperature dependence determination of the heat transfer coefficient into hardening media for the particular material, defined maximal thickness of processed part and cooling conditions. In the paper we will also present an example of the comparison standard and modified (according to newly suggested methodology) heat transfer coefficient data’s and theirs influence on the simulation results. It shows how even the small changes influence mainly on distribution of temperature, metallurgical phases, hardness and stresses distribution. By this experiment it is also possible to obtain not only input data and data enabling optimization of computational model but at the same time also verification data. The greatest advantage of described method is independence of used cooling media type.

Four-Dimensional Data Assimilation Using the Adjoint Method

NASA Astrophysics Data System (ADS)

Bao, Jian-Wen

The calculus of variations is used to confirm that variational four-dimensional data assimilation (FDDA) using the adjoint method can be implemented when the numerical model equations have a finite number of first-order discontinuous points. These points represent the on/off switches associated with physical processes, for which the Jacobian matrix of the model equation does not exist. Numerical evidence suggests that, in some situations when the adjoint method is used for FDDA, the temperature field retrieved using horizontal wind data is numerically not unique. A physical interpretation of this type of non-uniqueness of the retrieval is proposed in terms of energetics. The adjoint equations of a numerical model can also be used for model-parameter estimation. A general computational procedure is developed to determine the size and distribution of any internal model parameter. The procedure is then applied to a one-dimensional shallow -fluid model in the context of analysis-nudging FDDA: the weighting coefficients used by the Newtonian nudging technique are determined. The sensitivity of these nudging coefficients to the optimal objectives and constraints is investigated. Experiments of FDDA using the adjoint method are conducted using the dry version of the hydrostatic Penn State/NCAR mesoscale model (MM4) and its adjoint. The minimization procedure converges and the initialization experiment is successful. Temperature-retrieval experiments involving an assimilation of the horizontal wind are also carried out using the adjoint of MM4.

Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

NASA Astrophysics Data System (ADS)

Figueroa, Aldo; Meunier, Patrice; Cuevas, Sergio; Villermaux, Emmanuel; Ramos, Eduardo

2014-01-01

We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, "The diffusive strip method for scalar mixing in two-dimensions," J. Fluid Mech. 662, 134-172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement with quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors.

Plasma Jet Simulations Using a Generalized Ohm's Law

NASA Technical Reports Server (NTRS)

Ebersohn, Frans; Shebalin, John V.; Girimaji, Sharath S.

2012-01-01

Plasma jets are important physical phenomena in astrophysics and plasma propulsion devices. A currently proposed dual jet plasma propulsion device to be used for ISS experiments strongly resembles a coronal loop and further draws a parallel between these physical systems [1]. To study plasma jets we use numerical methods that solve the compressible MHD equations using the generalized Ohm s law [2]. Here, we will discuss the crucial underlying physics of these systems along with the numerical procedures we utilize to study them. Recent results from our numerical experiments will be presented and discussed.

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

NASA Astrophysics Data System (ADS)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

Effect of seabed roughness on tidal current turbines

NASA Astrophysics Data System (ADS)

Gupta, Vikrant; Wan, Minping

2017-11-01

Tidal current turbines are shown to have potential to generate clean energy for a negligible environmental impact. These devices, however, operate in high to moderate current regions where the flow is highly turbulent. It has been shown in flume tank experiments at IFREMER in Boulogne-Sur-Mer (France) and NAFL in the University of Minnesota (US) that the level of turbulence and boundary layer profile affect a turbine's power output and wake characteristics. A major factor that determines these marine flow characteristics is the seabed roughness. Experiments, however, cannot simulate the high Reynolds number conditions of real marine flows. For that, we rely on numerical simulations. High accuracy numerical methods, such as DNS, of wall-bounded flows are very expensive, where the number of grid-points needed to resolve the flow varies as (Re) 9 / 4 (where Re is the flow Reynolds number). While numerically affordable RANS methods compromise on accuracy. Wall-modelled LES methods, which provide both accuracy and affordability, have been improved tremendously in the recent years. We discuss the application of such numerical methods for studying the effect of seabed roughness on marine flow features and their impact on turbine power output and wake characteristics. NSFC, Project Number 11672123.

Influence of the light propagation models on a linearized photoacoustic image reconstruction of the light absorption coefficient

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya

2015-03-01

Quantification of the optical properties of the tissues and blood by noninvasive photoacoustic (PA) imaging may provide useful information for screening and early diagnosis of diseases. Linearized 2D image reconstruction algorithm based on PA wave equation and the photon diffusion equation (PDE) can reconstruct the image with computational cost smaller than a method based on 3D radiative transfer equation. However, the reconstructed image is affected by the differences between the actual and assumed light propagations. A quantitative capability of a linearized 2D image reconstruction was investigated and discussed by the numerical simulations and the phantom experiment in this study. The numerical simulations with the 3D Monte Carlo (MC) simulation and the 2D finite element calculation of the PDE were carried out. The phantom experiment was also conducted. In the phantom experiment, the PA pressures were acquired by a probe which had an optical fiber for illumination and the ring shaped P(VDF-TrFE) ultrasound transducer. The measured object was made of Intralipid and Indocyanine green. In the numerical simulations, it was shown that the linearized image reconstruction method recovered the absorption coefficients with alleviating the dependency of the PA amplitude on the depth of the photon absorber. The linearized image reconstruction method worked effectively under the light propagation calculated by 3D MC simulation, although some errors occurred. The phantom experiments validated the result of the numerical simulations.

Observation of the development of secondary features in a Richtmyer–Meshkov instability driven flow

DOE PAGES

Bernard, Tennille; Truman, C. Randall; Vorobieff, Peter; ...

2014-09-10

Richtmyer–Meshkov instability (RMI) has long been the subject of interest for analytical, numerical, and experimental studies. In comparing results of experiment with numerics, it is important to understand the limitations of experimental techniques inherent in the chosen method(s) of data acquisition. We discuss results of an experiment where a laminar, gravity-driven column of heavy gas is injected into surrounding light gas and accelerated by a planar shock. A popular and well-studied method of flow visualization (using glycol droplet tracers) does not produce a flow pattern that matches the numerical model of the same conditions, while revealing the primary feature ofmore » the flow developing after shock acceleration: the pair of counter-rotating vortex columns. However, visualization using fluorescent gaseous tracer confirms the presence of features suggested by the numerics; in particular, a central spike formed due to shock focusing in the heavy-gas column. Furthermore, the streamwise growth rate of the spike appears to exhibit the same scaling with Mach number as that of the counter-rotating vortex pair (CRVP).« less

Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications. Volume 24. Note on Numerical Fluid Mechanics

DTIC Science & Technology

1989-01-01

Calculations and Experiments (B.van den Berg/ D.A. Humphreysl E. Krause /J.P. F. Lindhout) Volume 20 Proceedings of the Seventh GAMM-Conference on...GRID METHODS FOR HYPERBOLIC PROBLEMS Wolfgang Hackbusch Sigrid Hagemann Institut fUr Informatik und Praktische Mathematik Christian-Albrechts...Euler Equations. Proceedings of the 8th Inter- national Conference on Numerical Methods in Fluid Dynamics (E. Krause , ed.), Aachen, 1988. Springer

Singular boundary method for global gravity field modelling

NASA Astrophysics Data System (ADS)

Cunderlik, Robert

2014-05-01

The singular boundary method (SBM) and method of fundamental solutions (MFS) are meshless boundary collocation techniques that use the fundamental solution of a governing partial differential equation (e.g. the Laplace equation) as their basis functions. They have been developed to avoid singular numerical integration as well as mesh generation in the traditional boundary element method (BEM). SBM have been proposed to overcome a main drawback of MFS - its controversial fictitious boundary outside the domain. The key idea of SBM is to introduce a concept of the origin intensity factors that isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques. Consequently, the source points can be placed directly on the real boundary and coincide with the collocation nodes. In this study we deal with SBM applied for high-resolution global gravity field modelling. The first numerical experiment presents a numerical solution to the fixed gravimetric boundary value problem. The achieved results are compared with the numerical solutions obtained by MFS or the direct BEM indicating efficiency of all methods. In the second numerical experiments, SBM is used to derive the geopotential and its first derivatives from the Tzz components of the gravity disturbing tensor observed by the GOCE satellite mission. A determination of the origin intensity factors allows to evaluate the disturbing potential and gravity disturbances directly on the Earth's surface where the source points are located. To achieve high-resolution numerical solutions, the large-scale parallel computations are performed on the cluster with 1TB of the distributed memory and an iterative elimination of far zones' contributions is applied.

Numerical simulations of the flow with the prescribed displacement of the airfoil and comparison with experiment

NASA Astrophysics Data System (ADS)

Řidký, V.; Šidlof, P.; Vlček, V.

2013-04-01

The work is devoted to comparing measured data with the results of numerical simulations. As mathematical model was used mathematical model whitout turbulence for incompressible flow In the experiment was observed the behavior of designed NACA0015 airfoil in airflow. For the numerical solution was used OpenFOAM computational package, this is open-source software based on finite volume method. In the numerical solution is prescribed displacement of the airfoil, which corresponds to the experiment. The velocity at a point close to the airfoil surface is compared with the experimental data obtained from interferographic measurements of the velocity field. Numerical solution is computed on a 3D mesh composed of about 1 million ortogonal hexahedron elements. The time step is limited by the Courant number. Parallel computations are run on supercomputers of the CIV at Technical University in Prague (HAL and FOX) and on a computer cluster of the Faculty of Mechatronics of Liberec (HYDRA). Run time is fixed at five periods, the results from the fifth periods and average value for all periods are then be compared with experiment.

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1980-01-01

A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

NASA Astrophysics Data System (ADS)

He, Yang; Sun, Yajuan; Zhang, Ruili; Wang, Yulei; Liu, Jian; Qin, Hong

2016-09-01

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracy-enhancing processing technique, the explicit methods obtain high-order accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations.

Evaluation of the tripolar electrode stimulation method by numerical analysis and animal experiments for cochlear implants.

PubMed

Miyoshi, S; Sakajiri, M; Ifukube, T; Matsushima, J

1997-01-01

We have proposed the Tripolar Electrode Stimulation Method (TESM) which may enable us to narrow the stimulation region and to move continuously the stimulation site for the cochlear implants. We evaluated whether or not TESM works according to a theory based on numerical analysis using the auditory nerve fiber model. In this simulation, the sum of the excited model fibers were compared with the compound actions potentials obtained from animal experiments. As a result, this experiment showed that TESM could narrow a stimulation region by controlling the sum of the currents emitted from the electrodes on both sides, and continuously move a stimulation site by changing the ratio of the currents emitted from the electrodes on both sides.

Three-Dimensional Numerical Simulation to Mud Turbine for LWD

NASA Astrophysics Data System (ADS)

Yao, Xiaojiang; Dong, Jingxin; Shang, Jie; Zhang, Guanqi

Hydraulic performance analysis was discussed for a type of turbine on generator used for LWD. The simulation models were built by CFD analysis software FINE/Turbo, and full three-dimensional numerical simulation was carried out for impeller group. The hydraulic parameter such as power, speed and pressure drop, were calculated in two kinds of medium water and mud. Experiment was built in water environment. The error of numerical simulation was less than 6%, verified by experiment. Based on this rationalization proposals would be given to choice appropriate impellers, and the rationalization of methods would be explored.

Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

2017-07-01

The paper considers a generalized functional and algorithmic construction of direct computational experiments in fluid dynamics. Notation of tensor mathematics is naturally embedded in the finite - element operation in the construction of numerical schemes. Large fluid particle, which have a finite size, its own weight, internal displacement and deformation is considered as an elementary computing object. Tensor representation of computational objects becomes strait linear and uniquely approximation of elementary volumes and fluid particles inside them. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. It is shown that advantages of the proposed approach are achieved among them by considering representation of large particles of a continuous medium motion in dual coordinate systems and computing operations in the projections of these two coordinate systems with direct and inverse transformations. So new method for mathematical representation and synthesis of computational experiment based on large particle method is proposed.

Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

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

Figueroa, Aldo; Meunier, Patrice; Villermaux, Emmanuel

2014-01-15

We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, “The diffusive strip method for scalar mixing in two-dimensions,” J. Fluid Mech. 662, 134–172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement withmore » quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors.« less

Numerical Investigation of the Performance of a Supersonic Combustion Chamber and Comparison with Experiments

NASA Astrophysics Data System (ADS)

Banica, M. C.; Chun, J.; Scheuermann, T.; Weigand, B.; Wolfersdorf, J. v.

2009-01-01

Scramjet powered vehicles can decrease costs for access to space but substantial obstacles still exist in their realization. For example, experiments in the relevant Mach number regime are difficult to perform and flight testing is expensive. Therefore, numerical methods are often employed for system layout but they require validation against experimental data. Here, we validate the commercial code CFD++ against experimental results for hydrogen combustion in the supersonic combustion facility of the Institute of Aerospace Thermodynamics (ITLR) at the Universität Stuttgart. Fuel is injected through a lobed a strut injector, which provides rapid mixing. Our numerical data shows reasonable agreement with experiments. We further investigate effects of varying equivalence ratios on several important performance parameters.

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Numerical and experimental studies of hydrodynamics of flapping foils

NASA Astrophysics Data System (ADS)

Zhou, Kai; Liu, Jun-kao; Chen, Wei-shan

2018-04-01

The flapping foil based on bionics is a sort of simplified models which imitate the motion of wings or fins of fish or birds. In this paper, a universal kinematic model with three degrees of freedom is adopted and the motion parallel to the flow direction is considered. The force coefficients, the torque coefficient, and the flow field characteristics are extracted and analyzed. Then the propulsive efficiency is calculated. The influence of the motion parameters on the hydrodynamic performance of the bionic foil is studied. The results show that the motion parameters play important roles in the hydrodynamic performance of the flapping foil. To validate the reliability of the numerical method used in this paper, an experiment platform is designed and verification experiments are carried out. Through the comparison, it is found that the numerical results compare well with the experimental results, to show that the adopted numerical method is reliable. The results of this paper provide a theoretical reference for the design of underwater vehicles based on the flapping propulsion.

Estimation of state and material properties during heat-curing molding of composite materials using data assimilation: A numerical study.

PubMed

Matsuzaki, Ryosuke; Tachikawa, Takeshi; Ishizuka, Junya

2018-03-01

Accurate simulations of carbon fiber-reinforced plastic (CFRP) molding are vital for the development of high-quality products. However, such simulations are challenging and previous attempts to improve the accuracy of simulations by incorporating the data acquired from mold monitoring have not been completely successful. Therefore, in the present study, we developed a method to accurately predict various CFRP thermoset molding characteristics based on data assimilation, a process that combines theoretical and experimental values. The degree of cure as well as temperature and thermal conductivity distributions during the molding process were estimated using both temperature data and numerical simulations. An initial numerical experiment demonstrated that the internal mold state could be determined solely from the surface temperature values. A subsequent numerical experiment to validate this method showed that estimations based on surface temperatures were highly accurate in the case of degree of cure and internal temperature, although predictions of thermal conductivity were more difficult.

Numerical Simulation of Creep Characteristic for Composite Rock Mass with Weak Interlayer

NASA Astrophysics Data System (ADS)

Li, Jian-guang; Zhang, Zuo-liang; Zhang, Yu-biao; Shi, Xiu-wen; Wei, Jian

2017-06-01

The composite rock mass with weak interlayer is widely exist in engineering, and it’s essential to research the creep behavior which could cause stability problems of rock engineering and production accidents. However, due to it is difficult to take samples, the losses and damages in delivery and machining process, we always cannot get enough natural layered composite rock mass samples, so the indirect test method has been widely used. In this paper, we used ANSYS software (a General Finite Element software produced by American ANSYS, Inc) to carry out the numerical simulation based on the uniaxial compression creep experiments of artificial composite rock mass with weak interlayer, after experimental data fitted. The results show that the laws obtained by numerical simulations and experiments are consistent. Thus confirmed that carry out numerical simulation for the creep characteristics of rock mass with ANSYS software is feasible, and this method can also be extended to other underground engineering of simulate the weak intercalations.

Simulation of two-dimensional turbulent flows in a rotating annulus

NASA Astrophysics Data System (ADS)

Storey, Brian D.

2004-05-01

Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments.

Study of detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance model.

PubMed

Jingyi, Zhu

2015-01-01

The detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance (MSR) model was studied in this paper. A numerically stimulating model based on MSR was established. And gas-ionizing experiment by adding electronic white noise to induce 1.65 MHz periodic component in the carbon nanotubes gas sensor was performed. It was found that the signal-to-noise ratio (SNR) spectrum displayed 2 maximal values, which accorded to the change of the broken-line potential function. The experimental results of gas-ionizing experiment demonstrated that periodic component of 1.65 MHz had multiple MSR phenomena, which was in accordance with the numerical stimulation results. In this way, the numerical stimulation method provides an innovative method for the detecting mechanism research of carbon nanotubes gas sensor.

Numerical modeling of the acoustic wave propagation across a homogenized rigid microstructure in the time domain

NASA Astrophysics Data System (ADS)

Lombard, Bruno; Maurel, Agnès; Marigo, Jean-Jacques

2017-04-01

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt the Explicit Simplified Interface Method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in a homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem.

The numerical simulation of heat transfer during a hybrid laser-MIG welding using equivalent heat source approach

NASA Astrophysics Data System (ADS)

Bendaoud, Issam; Matteï, Simone; Cicala, Eugen; Tomashchuk, Iryna; Andrzejewski, Henri; Sallamand, Pierre; Mathieu, Alexandre; Bouchaud, Fréderic

2014-03-01

The present study is dedicated to the numerical simulation of an industrial case of hybrid laser-MIG welding of high thickness duplex steel UR2507Cu with Y-shaped chamfer geometry. It consists in simulation of heat transfer phenomena using heat equivalent source approach and implementing in finite element software COMSOL Multiphysics. A numerical exploratory designs method is used to identify the heat sources parameters in order to obtain a minimal required difference between the numerical results and the experiment which are the shape of the welded zone and the temperature evolution in different locations. The obtained results were found in good correspondence with experiment, both for melted zone shape and thermal history.

Unsteady Computations of a Jet in a Crossflow with Ground Effect

NASA Technical Reports Server (NTRS)

Pandya, Shishir; Murman, Scott; Venkateswaran, Sankaran; Kwak, Dochan (Technical Monitor)

2002-01-01

A numerical study of a jet in crossflow with ground effect is conducted using OVERFLOW with dual time-stepping and low Mach number preconditioning. The results of the numerical study are compared to an experiment to show that the numerical methods are capable of capturing the dominant features of the flow field as well as the unsteadiness associated with the ground vortex.

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Numerical Study on Focusing of Ultrasounds in Microbubble-enhanced HIFU

NASA Astrophysics Data System (ADS)

Matsumoto, Yoichiro; Okita, Kohei; Takagi, Shu

2011-11-01

The injection of microbubbles into the target tissue enhances tissue heating in High-Intensity Focused Ultrasound therapy, via inertial cavitation. The control of the inertial cavitation is required to achieve the efficient tissue ablation. Microbubbles between a transducer and a target disturb the ultrasound propagation depending on the conditions. A method to clear such microbubbles has been proposed by Kajiyama et al. [Physics Procedia 3 (2010) 305-314]. In the method, the irradiation of intense ultrasounds with a burst waveform fragmentize microbubbles in the pathways before the irradiation of ultrasounds for tissue heating. The vitro experiment using a gel containing microbubbles has showed that the method enables to heat the target correctly by controlling the microbubble distribution. Following the experiment, we simulate the focusing of ultrasounds through a mixture containing microbubbles with considering the size and number density distributions in space. The numerical simulation shows that the movement of the heating region from the transducer side to the target by controlling the microbubble distributions. The numerical results elucidate well the experimental ones.

Implicit Large Eddy Simulation of a wingtip vortex at Rec =1.2x106

NASA Astrophysics Data System (ADS)

Lombard, Jean-Eloi; Moxey, Dave; Sherwin, Spencer; SherwinLab Team

2015-11-01

We present recent developments in numerical methods for performing a Large Eddy Simulation (LES) of the formation and evolution of a wingtip vortex. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, make these types of test cases particularly challenging to investigate numerically. To demonstrate the method's viability, we present results from numerical simulations of flow over a NACA 0012 profile wingtip at Rec = 1.2 x106 and compare them against experimental data, which is to date the highest Reynolds number achieved for a LES that has been correlated with experiments for this test case. Our model correlates favorably with experiment, both for the characteristic jetting in the primary vortex and pressure distribution on the wing surface. The proposed method is of general interest for the modeling of transitioning vortex dominated flows over complex geometries. McLaren Racing/Royal Academy of Engineering Research Chair.

A weak Galerkin generalized multiscale finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-03-31

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.

A weak Galerkin generalized multiscale finite element method

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

Mu, Lin; Wang, Junping; Ye, Xiu

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.

Analysis of stability for stochastic delay integro-differential equations.

PubMed

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.

2017-02-01

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.

Numerical investigation of flow on NACA4412 aerofoil with different aspect ratios

NASA Astrophysics Data System (ADS)

Demir, Hacımurat; Özden, Mustafa; Genç, Mustafa Serdar; Çağdaş, Mücahit

2016-03-01

In this study, the flow over NACA4412 was investigated both numerically and experimentally at a different Reynolds numbers. The experiments were carried out in a low speed wind tunnel with various angles of attack and different Reynolds numbers (25000 and 50000). Airfoil was manufactured using 3D printer with a various aspect ratios (AR = 1 and AR = 3). Smoke-wire and oil flow visualization methods were used to visualize the surface flow patterns. NACA4412 aerofoil was designed by using SOLIDWORKS. The structural grid of numerical model was constructed by ANSYS ICEM CFD meshing software. Furthermore, ANSYS FLUENT™ software was used to perform numerical calculations. The numerical results were compared with experimental results. Bubble formation was shown in CFD streamlines and smoke-wire experiments at z / c = 0.4. Furthermore, bubble shrunk at z / c = 0.2 by reason of the effects of tip vortices in both numerical and experimental studies. Consequently, it was seen that there was a good agreement between numerical and experimental results.

An Accurate and Stable FFT-based Method for Pricing Options under Exp-Lévy Processes

NASA Astrophysics Data System (ADS)

Ding, Deng; Chong U, Sio

2010-05-01

An accurate and stable method for pricing European options in exp-Lévy models is presented. The main idea of this new method is combining the quadrature technique and the Carr-Madan Fast Fourier Transform methods. The theoretical analysis shows that the overall complexity of this new method is still O(N log N) with N grid points as the fast Fourier transform methods. Numerical experiments for different exp-Lévy processes also show that the numerical algorithm proposed by this new method has an accuracy and stability for the small strike prices K. That develops and improves the Carr-Madan method.

A Model for Engaging Students in a Research Experience Involving Variational Techniques, Mathematica, and Descent Methods.

ERIC Educational Resources Information Center

Mahavier, W. Ted

2002-01-01

Describes a two-semester numerical methods course that serves as a research experience for undergraduate students without requiring external funding or the modification of current curriculum. Uses an engineering problem to introduce students to constrained optimization via a variation of the traditional isoperimetric problem of finding the curve…

Wave propagation simulation in the upper core of sodium-cooled fast reactors using a spectral-element method for heterogeneous media

NASA Astrophysics Data System (ADS)

Nagaso, Masaru; Komatitsch, Dimitri; Moysan, Joseph; Lhuillier, Christian

2018-01-01

ASTRID project, French sodium cooled nuclear reactor of 4th generation, is under development at the moment by Alternative Energies and Atomic Energy Commission (CEA). In this project, development of monitoring techniques for a nuclear reactor during operation are identified as a measure issue for enlarging the plant safety. Use of ultrasonic measurement techniques (e.g. thermometry, visualization of internal objects) are regarded as powerful inspection tools of sodium cooled fast reactors (SFR) including ASTRID due to opacity of liquid sodium. In side of a sodium cooling circuit, heterogeneity of medium occurs because of complex flow state especially in its operation and then the effects of this heterogeneity on an acoustic propagation is not negligible. Thus, it is necessary to carry out verification experiments for developments of component technologies, while such kind of experiments using liquid sodium may be relatively large-scale experiments. This is why numerical simulation methods are essential for preceding real experiments or filling up the limited number of experimental results. Though various numerical methods have been applied for a wave propagation in liquid sodium, we still do not have a method for verifying on three-dimensional heterogeneity. Moreover, in side of a reactor core being a complex acousto-elastic coupled region, it has also been difficult to simulate such problems with conventional methods. The objective of this study is to solve these 2 points by applying three-dimensional spectral element method. In this paper, our initial results on three-dimensional simulation study on heterogeneous medium (the first point) are shown. For heterogeneity of liquid sodium to be considered, four-dimensional temperature field (three spatial and one temporal dimension) calculated by computational fluid dynamics (CFD) with Large-Eddy Simulation was applied instead of using conventional method (i.e. Gaussian Random field). This three-dimensional numerical experiment yields that we could verify the effects of heterogeneity of propagation medium on waves in Liquid sodium.

Prestressing force monitoring method for a box girder through distributed long-gauge FBG sensors

NASA Astrophysics Data System (ADS)

Chen, Shi-Zhi; Wu, Gang; Xing, Tuo; Feng, De-Cheng

2018-01-01

Monitoring prestressing forces is essential for prestressed concrete box girder bridges. However, the current monitoring methods used for prestressing force were not applicable for a box girder neither because of the sensor’s setup being constrained or shear lag effect not being properly considered. Through combining with the previous analysis model of shear lag effect in the box girder, this paper proposed an indirect monitoring method for on-site determination of prestressing force in a concrete box girder utilizing the distributed long-gauge fiber Bragg grating sensor. The performance of this method was initially verified using numerical simulation for three different distribution forms of prestressing tendons. Then, an experiment involving two concrete box girders was conducted to study the feasibility of this method under different prestressing levels preliminarily. The results of both numerical simulation and lab experiment validated this method’s practicability in a box girder.

Representing ductile damage with the dual domain material point method

DOE PAGES

Long, C. C.; Zhang, D. Z.; Bronkhorst, C. A.; ...

2015-12-14

In this study, we incorporate a ductile damage material model into a computational framework based on the Dual Domain Material Point (DDMP) method. As an example, simulations of a flyer plate experiment involving ductile void growth and material failure are performed. The results are compared with experiments performed on high purity tantalum. We also compare the numerical results obtained from the DDMP method with those obtained from the traditional Material Point Method (MPM). Effects of an overstress model, artificial viscosity, and physical viscosity are investigated. Our results show that a physical bulk viscosity and overstress model are important in thismore » impact and failure problem, while physical shear viscosity and artificial shock viscosity have negligible effects. A simple numerical procedure with guaranteed convergence is introduced to solve for the equilibrium plastic state from the ductile damage model.« less

Determination of Global Stability of the Slosh Motion in a Spacecraft via Num Erical Experiment

NASA Astrophysics Data System (ADS)

Kang, Ja-Young

2003-12-01

The global stability of the attitude motion of a spin-stabilized space vehicle is investigated by performing numerical experiment. In the previous study, a stationary solution and a particular resonant condition for a given model were found by using analytical method but failed to represent the system stability over parameter values near and off the stationary points. Accordingly, as an extension of the previous work, this study performs numerical experiment to investigate the stability of the system across the parameter space and determines stable and unstable regions of the design parameters of the system.

A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.

PubMed

Ling, Hong; Luo, Ercang; Dai, Wei

2006-12-22

Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.

Hybrid Particle-Element Simulation of Impact on Composite Orbital Debris Shields

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2004-01-01

This report describes the development of new numerical methods and new constitutive models for the simulation of hypervelocity impact effects on spacecraft. The research has included parallel implementation of the numerical methods and material models developed under the project. Validation work has included both one dimensional simulations, for comparison with exact solutions, and three dimensional simulations of published hypervelocity impact experiments. The validated formulations have been applied to simulate impact effects in a velocity and kinetic energy regime outside the capabilities of current experimental methods. The research results presented here allow for the expanded use of numerical simulation, as a complement to experimental work, in future design of spacecraft for hypervelocity impact effects.

A numeric investigation of co-flowing liquid streams using the Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Somogyi, Andy; Tagg, Randall

2007-11-01

We present a numerical investigation of co-flowing immiscible liquid streams using the Lattice Boltzmann Method (LBM) for multi component, dissimilar viscosity, immiscible fluid flow. When a liquid is injected into another immiscible liquid, the flow will eventually transition from jetting to dripping due to interfacial tension. Our implementation of LBM models the interfacial tension through a variety of techniques. Parallelization is also straightforward for both single and multi component models as only near local interaction is required. We compare the results of our numerical investigation using LBM to several recent physical experiments.

The challenges of numerically simulating analogue brittle thrust wedges

NASA Astrophysics Data System (ADS)

Buiter, Susanne; Ellis, Susan

2017-04-01

Fold-and-thrust belts and accretionary wedges form when sedimentary and crustal rocks are compressed into thrusts and folds in the foreland of an orogen or at a subduction trench. For over a century, analogue models have been used to investigate the deformation characteristics of such brittle wedges. These models predict wedge shapes that agree with analytical critical taper theory and internal deformation structures that well resemble natural observations. In a series of comparison experiments for thrust wedges, called the GeoMod2004 (1,2) and GeoMod2008 (3,4) experiments, it was shown that different numerical solution methods successfully reproduce sandbox thrust wedges. However, the GeoMod2008 benchmark also pointed to the difficulties of representing frictional boundary conditions and sharp velocity discontinuities with continuum numerical methods, in addition to the well-known challenges of numerical plasticity. Here we show how details in the numerical implementation of boundary conditions can substantially impact numerical wedge deformation. We consider experiment 1 of the GeoMod2008 brittle thrust wedge benchmarks. This experiment examines a triangular thrust wedge in the stable field of critical taper theory that should remain stable, that is, without internal deformation, when sliding over a basal frictional surface. The thrust wedge is translated by lateral displacement of a rigid mobile wall. The corner between the mobile wall and the subsurface is a velocity discontinuity. Using our finite-element code SULEC, we show how different approaches to implementing boundary friction (boundary layer or contact elements) and the velocity discontinuity (various smoothing schemes) can cause the wedge to indeed translate in a stable manner or to undergo internal deformation (which is a fail). We recommend that numerical studies of sandbox setups not only report the details of their implementation of boundary conditions, but also document the modelling attempts that failed. References 1. Buiter and the GeoMod2004 Team, 2006. The numerical sandbox: comparison of model results for a shortening and an extension experiment. Geol. Soc. Lond. Spec. Publ. 253, 29-64 2. Schreurs and the GeoMod2004 Team, 2006. Analogue benchmarks of shortening and extension experiments. Geol. Soc. Lond. Spec. Publ. 253, 1-27 3. Buiter, Schreurs and the GeoMod2008 Team, 2016. Benchmarking numerical models of brittle thrust wedges, J. Struct. Geol. 92, 140-177 4. Schreurs, Buiter and the GeoMod2008 Team, 2016. Benchmarking analogue models of brittle thrust wedges, J. Struct. Geol. 92, 116-13

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

USGS Publications Warehouse

Schaffranek, R.W.; Lai, C.

1996-01-01

The friction-slope term in the unsteady open-channel flow equations is examined using two numerical models based on different formulations of the governing equations and employing different solution methods. The purposes of the study are to analyze, evaluate, and demonstrate the behavior of the term in a set of controlled numerical experiments using varied types and combinations of boundary conditions. Results of numerical experiments illustrate that a given model can respond inconsistently for the identical resistance-coefficient value under different types and combinations of boundary conditions. Findings also demonstrate that two models employing different dependent variables and solution methods can respond similarly for the identical resistance-coefficient value under similar types and combinations of boundary conditions. Discussion of qualitative considerations and quantitative experimental results provides insight into the proper treatment, evaluation, and significance of the friction-slope term, thereby offering practical guidelines for model implementation and calibration.

Earth-moon system: Dynamics and parameter estimation; numerical considerations and program documentation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1976-01-01

Major activities included coding and verifying equations of motion for the earth-moon system. Some attention was also given to numerical integration methods and parameter estimation methods. Existing analytical theories such as Brown's lunar theory, Eckhardt's theory for lunar rotation, and Newcomb's theory for the rotation of the earth were coded and verified. These theories serve as checks for the numerical integration. Laser ranging data for the period January 1969 - December 1975 was collected and stored on tape. The main goal of this research is the development of software to enable physical parameters of the earth-moon system to be estimated making use of data available from the Lunar Laser Ranging Experiment and the Very Long Base Interferometry experiment of project Apollo. A more specific goal is to develop software for the estimation of certain physical parameters of the moon such as inertia ratios, and the third and fourth harmonic gravity coefficients.

Measurements and simulation of liquid films during drainage displacements and snap-off in constricted capillary tubes.

PubMed

Roman, Sophie; Abu-Al-Saud, Moataz O; Tokunaga, Tetsu; Wan, Jiamin; Kovscek, Anthony R; Tchelepi, Hamdi A

2017-12-01

When a wetting liquid is displaced by air in a capillary tube, a wetting film develops between the tube wall and the air that is responsible for the snap-off mechanism of the gas phase. By dissolving a dye in the wetting phase it is possible to relate a measure of the absorbance in the capillary to the thickness of liquid films. These data could be used to compare with cutting edge numerical simulations of the dynamics of snap-off for which experimental and numerical data are lacking. Drainage experiments in constricted capillary tubes were performed where a dyed wetting liquid is displaced by air for varying flow rates. We developed an optical method to measure liquid film thicknesses that range from 3 to 1000μm. The optical measures are validated by comparison with both theory and direct numerical simulations. In a constricted capillary tube we observed, both experimentally and numerically, a phenomenon of snap-off coalescence events in the vicinity of the constriction that bring new insights into our understanding and modeling of two-phase flows. In addition, the good agreement between experiments and numerical simulations gives confidence to use the numerical method for more complex geometries in the future. Copyright © 2017 Elsevier Inc. All rights reserved.

The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

NASA Astrophysics Data System (ADS)

Divakov, Dmitriy; Malykh, Mikhail; Sevastianov, Leonid; Sevastianov, Anton; Tiutiunnik, Anastasiia

2017-04-01

In the paper we construct a method for approximate solution of the waveguide problem for guided modes of an open irregular waveguide transition. The method is based on straightening of the curved waveguide boundaries by introducing new variables and applying the Kantorovich method to the problem formulated in the new variables to get a system of ordinary second-order differential equations. In the method, the boundary conditions are formulated by analogy with the partial radiation conditions in the similar problem for closed waveguide transitions. The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.

Numerical modeling of zero-offset laboratory data in a strong topographic environment: results for a spectral-element method and a discretized Kirchhoff integral method

NASA Astrophysics Data System (ADS)

Favretto-Cristini, Nathalie; Tantsereva, Anastasiya; Cristini, Paul; Ursin, Bjørn; Komatitsch, Dimitri; Aizenberg, Arkady M.

2014-08-01

Accurate simulation of seismic wave propagation in complex geological structures is of particular interest nowadays. However conventional methods may fail to simulate realistic wavefields in environments with great and rapid structural changes, due for instance to the presence of shadow zones, diffractions and/or edge effects. Different methods, developed to improve seismic modeling, are typically tested on synthetic configurations against analytical solutions for simple canonical problems or reference methods, or via direct comparison with real data acquired in situ. Such approaches have limitations, especially if the propagation occurs in a complex environment with strong-contrast reflectors and surface irregularities, as it can be difficult to determine the method which gives the best approximation of the "real" solution, or to interpret the results obtained without an a priori knowledge of the geologic environment. An alternative approach for seismics consists in comparing the synthetic data with high-quality data collected in laboratory experiments under controlled conditions for a known configuration. In contrast with numerical experiments, laboratory data possess many of the characteristics of field data, as real waves propagate through models with no numerical approximations. We thus present a comparison of laboratory-scaled measurements of 3D zero-offset wave reflection of broadband pulses from a strong topographic environment immersed in a water tank with numerical data simulated by means of a spectral-element method and a discretized Kirchhoff integral method. The results indicate a good quantitative fit in terms of time arrivals and acceptable fit in amplitudes for all datasets.

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

NASA Astrophysics Data System (ADS)

Khait, A.; Shemer, L.

2018-05-01

The evolution of unidirectional wave trains containing a wave that gradually becomes steep is evaluated experimentally and numerically using the Boundary Element Method (BEM). The boundary conditions for the nonlinear numerical simulations corresponded to the actual movements of the wavemaker paddle as recorded in the physical experiments, allowing direct comparison between the measured in experiments' characteristics of the wave train and the numerical predictions. The high level of qualitative and quantitative agreement between the measurements and simulations validated the kinematic criterion for the inception of breaking and the location of the spilling breaker, on the basis of the BEM computations and associated experiments. The breaking inception is associated with the fluid particle at the crest of the steep wave that has been accelerated to match and surpass the crest velocity. The previously observed significant slow-down of the crest while approaching breaking is verified numerically; both narrow-/broad-banded wave trains are considered. Finally, the relative importance of linear and nonlinear contributions is analyzed.

Constraints on the rheology of the partially molten mantle from numerical models of laboratory experiments

NASA Astrophysics Data System (ADS)

Rudge, J. F.; Alisic Jewell, L.; Rhebergen, S.; Katz, R. F.; Wells, G. N.

2015-12-01

One of the fundamental components in any dynamical model of melt transport is the rheology of partially molten rock. This rheology is poorly understood, and one way in which a better understanding can be obtained is by comparing the results of laboratory deformation experiments to numerical models. Here we present a comparison between numerical models and the laboratory setup of Qi et al. 2013 (EPSL), where a cylinder of partially molten rock containing rigid spherical inclusions was placed under torsion. We have replicated this setup in a finite element model which solves the partial differential equations describing the mechanical process of compaction. These computationally-demanding 3D simulations are only possible due to the recent development of a new preconditioning method for the equations of magma dynamics. The experiments show a distinct pattern of melt-rich and melt-depleted regions around the inclusions. In our numerical models, the pattern of melt varies with key rheological parameters, such as the ratio of bulk to shear viscosity, and the porosity- and strain-rate-dependence of the shear viscosity. These observed melt patterns therefore have the potential to constrain rheological properties. While there are many similarities between the experiments and the numerical models, there are also important differences, which highlight the need for better models of the physics of two-phase mantle/magma dynamics. In particular, the laboratory experiments display more pervasive melt-rich bands than is seen in our numerics.

On the remote sensing of cloud properties from satellite infrared sounder data

NASA Technical Reports Server (NTRS)

Yeh, H. Y. M.

1984-01-01

A method for remote sensing of cloud parameters by using infrared sounder data has been developed on the basis of the parameterized infrared transfer equation applicable to cloudy atmospheres. The method is utilized for the retrieval of the cloud height, amount, and emissivity in 11 micro m region. Numerical analyses and retrieval experiments have been carried out by utilizing the synthetic sounder data for the theoretical study. The sensitivity of the numerical procedures to the measurement and instrument errors are also examined. The retrieved results are physically discussed and numerically compared with the model atmospheres. Comparisons reveal that the recovered cloud parameters agree reasonably well with the pre-assumed values. However, for cases when relatively thin clouds and/or small cloud fractional cover within a field of view are present, the recovered cloud parameters show considerable fluctuations. Experiments on the proposed algorithm are carried out utilizing High Resolution Infrared Sounder (HIRS/2) data of NOAA 6 and TIROS-N. Results of experiments show reasonably good comparisons with the surface reports and GOES satellite images.

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Du, Jian; Glimm, James; Xu, Zhiliang

2007-10-01

We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic-elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic solvers, and the embedded boundary method for the elliptic problem in complex domains. The numerical algorithm has been implemented as an MHD extension of FronTier, a hydrodynamic code with free interface support. The code is applicable for numerical simulations of free surface flows of conductive liquids or weakly ionized plasmas. The code has been validated through the comparison of numerical simulations of a liquid metal jet in a non-uniform magnetic field with experiments and theory. Simulations of the Muon Collider/Neutrino Factory target have also been discussed.

Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1995-01-01

We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.

Piecewise parabolic method for simulating one-dimensional shear shock wave propagation in tissue-mimicking phantoms

NASA Astrophysics Data System (ADS)

Tripathi, B. B.; Espíndola, D.; Pinton, G. F.

2017-11-01

The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.

Effects of Numeric Representation of Women on Interest in Engineering as a Career

ERIC Educational Resources Information Center

Creamer, Elizabeth G.

2012-01-01

Little is known about how the presence of women influences undergraduates' experiences in engineering. This paper presents results from a mixed methods, multivariate, and multi-institutional study to determine the impact of the numeric representation of women on the intent to be employed in engineering following graduation. Results from the…

Experiment on Chinese Postgraduates' Recognizing 100 Everyday English Adopting "MMOASAPMI"

ERIC Educational Resources Information Center

Wang, Hongli; Li, Jinghua; Luo, Jing; Liu, Hong

2008-01-01

The purpose of this study was to investigate the memory effects of the postgraduates' memorizing Everyday English from 30 to 100 using the Natural Numeral Imagery Memory (Method by memorizing the concrete objects associated with the shapes of Arabic numeral to produce marvelous imagination, MMOASAPMI). The results indicated as follows: Firstly,…

Conforming and nonconforming virtual element methods for elliptic problems

DOE PAGES

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

2016-08-03

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1- and L 2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

NASA Technical Reports Server (NTRS)

Buell, Jeffrey C.

1988-01-01

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

A projection method for low speed flows

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

Colella, P.; Pao, K.

The authors propose a decomposition applicable to low speed, inviscid flows of all Mach numbers less than 1. By using the Hodge decomposition, they may write the velocity field as the sum of a divergence-free vector field and a gradient of a scalar function. Evolution equations for these parts are presented. A numerical procedure based on this decomposition is designed, using projection methods for solving the incompressible variables and a backward-Euler method for solving the potential variables. Numerical experiments are included to illustrate various aspects of the algorithm.

Conforming and nonconforming virtual element methods for elliptic problems

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

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1- and L 2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Putting Biology Students Out to Grass: the Nettlecombe Experiment After Thirteen Years.

ERIC Educational Resources Information Center

Crothers, J. H.; Lucas, A. M.

1982-01-01

The importance of examining both the natural history of organisms being investigated and numerical data from long-term field experiments is illustrated by describing a long-running field experiment at an English Field Study Council Centre. Sample results are discussed and alternative methods of using field studies in biology instruction are…

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

JDiffraction: A GPGPU-accelerated JAVA library for numerical propagation of scalar wave fields

NASA Astrophysics Data System (ADS)

Piedrahita-Quintero, Pablo; Trujillo, Carlos; Garcia-Sucerquia, Jorge

2017-05-01

JDiffraction, a GPGPU-accelerated JAVA library for numerical propagation of scalar wave fields, is presented. Angular spectrum, Fresnel transform, and Fresnel-Bluestein transform are the numerical algorithms implemented in the methods and functions of the library to compute the scalar propagation of the complex wavefield. The functionality of the library is tested with the modeling of easy to forecast numerical experiments and also with the numerical reconstruction of a digitally recorded hologram. The performance of JDiffraction is contrasted with a library written for C++, showing great competitiveness in the apparently less complex environment of JAVA language. JDiffraction also includes JAVA easy-to-use methods and functions that take advantage of the computation power of the graphic processing units to accelerate the processing times of 2048×2048 pixel images up to 74 frames per second.

Image analysis method for the measurement of water saturation in a two-dimensional experimental flow tank

NASA Astrophysics Data System (ADS)

Belfort, Benjamin; Weill, Sylvain; Lehmann, François

2017-07-01

A novel, non-invasive imaging technique is proposed that determines 2D maps of water content in unsaturated porous media. This method directly relates digitally measured intensities to the water content of the porous medium. This method requires the classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The main advantages of this approach are that no calibration experiment is needed, because calibration curve relating water content and reflected light intensities is established during the main monitoring phase of each experiment and that no tracer or dye is injected into the flow tank. The procedure enables effective processing of a large number of photographs and thus produces 2D water content maps at high temporal resolution. A drainage/imbibition experiment in a 2D flow tank with inner dimensions of 40 cm × 14 cm × 6 cm (L × W × D) is carried out to validate the methodology. The accuracy of the proposed approach is assessed using a statistical framework to perform an error analysis and numerical simulations with a state-of-the-art computational code that solves the Richards' equation. Comparison of the cumulative mass leaving and entering the flow tank and water content maps produced by the photographic measurement technique and the numerical simulations demonstrate the efficiency and high accuracy of the proposed method for investigating vadose zone flow processes. Finally, the photometric procedure has been developed expressly for its extension to heterogeneous media. Other processes may be investigated through different laboratory experiments which will serve as benchmark for numerical codes validation.

High-Order Numerical Simulations of Wind Turbine Wakes

NASA Astrophysics Data System (ADS)

Kleusberg, E.; Mikkelsen, R. F.; Schlatter, P.; Ivanell, S.; Henningson, D. S.

2017-05-01

Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite-volume solvers. We employ the higher-order spectral-element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral-element method enables an accurate representation of the vortical structures, with lower numerical dissipation than the more commonly used finite-volume codes. The wind-turbine blades are modeled as body forces using the actuator-line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates homogeneous isotropic turbulence of wind-tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology (NTNU Blind Tests), investigate parametric influences and compare computational aspects with existing numerical simulations. In general the results show good agreement between the experiments and the numerical simulations both for a single-turbine setup as well as a two-turbine setup where the turbines are offset in the spanwise direction. A shift in the wake center caused by the tower wake is detected similar to experiments. The additional velocity deficit caused by the tower agrees well with the experimental data. The wake is captured well by Nek5000 in comparison with experiments both for the single wind turbine and in the two-turbine setup. The blade loading however shows large discrepancies for the high-turbulence, two-turbine case. While the experiments predicted higher thrust for the downstream turbine than for the upstream turbine, the opposite case was observed in Nek5000.

Analysis of real-time numerical integration methods applied to dynamic clamp experiments.

PubMed

Butera, Robert J; McCarthy, Maeve L

2004-12-01

Real-time systems are frequently used as an experimental tool, whereby simulated models interact in real time with neurophysiological experiments. The most demanding of these techniques is known as the dynamic clamp, where simulated ion channel conductances are artificially injected into a neuron via intracellular electrodes for measurement and stimulation. Methodologies for implementing the numerical integration of the gating variables in real time typically employ first-order numerical methods, either Euler or exponential Euler (EE). EE is often used for rapidly integrating ion channel gating variables. We find via simulation studies that for small time steps, both methods are comparable, but at larger time steps, EE performs worse than Euler. We derive error bounds for both methods, and find that the error can be characterized in terms of two ratios: time step over time constant, and voltage measurement error over the slope factor of the steady-state activation curve of the voltage-dependent gating variable. These ratios reliably bound the simulation error and yield results consistent with the simulation analysis. Our bounds quantitatively illustrate how measurement error restricts the accuracy that can be obtained by using smaller step sizes. Finally, we demonstrate that Euler can be computed with identical computational efficiency as EE.

Accurate Projection Methods for the Incompressible Navier–Stokes Equations

DOE PAGES

Brown, David L.; Cortez, Ricardo; Minion, Michael L.

2001-04-10

This paper considers the accuracy of projection method approximations to the initial–boundary-value problem for the incompressible Navier–Stokes equations. The issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second-order methodology a decade and a half ago. It has been observed that while the velocity can be reliably computed to second-order accuracy in time and space, the pressure is typically only first-order accurate in the L ∞-norm. Here, we identify the source of this problem in the interplay of the global pressure-update formula with the numerical boundary conditions and presentsmore » an improved projection algorithm which is fully second-order accurate, as demonstrated by a normal mode analysis and numerical experiments. In addition, a numerical method based on a gauge variable formulation of the incompressible Navier–Stokes equations, which provides another option for obtaining fully second-order convergence in both velocity and pressure, is discussed. The connection between the boundary conditions for projection methods and the gauge method is explained in detail.« less

A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system

NASA Astrophysics Data System (ADS)

Lee, Hyun Geun; Choi, Jeong-Whan; Kim, Junseok

2012-02-01

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn-Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component Cahn-Hilliard system into a system of N-1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

An advanced three-phase physical, experimental and numerical method for tsunami induced boulder transport

NASA Astrophysics Data System (ADS)

Oetjen, Jan; Engel, Max; Prasad Pudasaini, Shiva; Schüttrumpf, Holger; Brückner, Helmut

2017-04-01

Coasts around the world are affected by high-energy wave events like storm surges or tsunamis depending on their regional climatological and geological settings. By focusing on tsunami impacts, we combine the abilities and experiences of different scientific fields aiming at improved insights of near- and onshore tsunami hydrodynamics. We investigate the transport of coarse clasts - so called boulders - due to tsunami impacts by a multi-methodology approach of numerical modelling, laboratory experiments, and sedimentary field records. Coupled numerical hydrodynamic and boulder transport models (BTM) are widely applied for analysing the impact characteristics of the transport by tsunami, such as wave height and flow velocity. Numerical models able to simulate past tsunami events and the corresponding boulder transport patterns with high accuracy and acceptable computational effort can be utilized as powerful forecasting models predicting the impact of a coast approaching tsunami. We have conducted small-scale physical experiments in the tilting flume with real shaped boulder models. Utilizing the structure from motion technique (Westoby et al., 2012) we reconstructed real boulders from a field study on the Island of Bonaire (Lesser Antilles, Caribbean Sea, Engel & May, 2012). The obtained three-dimensional boulder meshes are utilized for creating downscaled replica of the real boulder for physical experiments. The results of the irregular shaped boulder are compared to experiments with regular shaped boulder models to achieve a better insight about the shape related influence on transport patterns. The numerical model is based on the general two-phase mass flow model by Pudasaini (2012) enhanced for boulder transport simulations. The boulder is implemented using the immersed boundary technique (Peskin, 2002) and the direct forcing approach. In this method Cartesian grids (fluid and particle phase) and Lagrangian meshes (boulder) are combined. By applying the immersed boundary method we can compute the interactions between fluid, particles and arbitrary boulder shape. We are able to reproduce the exact physical experiment for calibration and verification of the tsunami boulder transport phenomena. First results of the study will be presented. Engel, M.; May, S.M.: Bonaire's boulder fields revisited: evidence for Holocene tsunami impact on the Leeward, Antilles. Quaternary Science Reviews 54, 126-141, 2012. Peskin, C.S.: The immersed boundary method. Acta Numerica, 479 - 517, 2002. Pudasaini, S. P.: A general two-phase debris flow model. J. Geophys. Res. Earth Surf., 117, F03010, 2012. Westoby, M.J.; Brasington, J.; Glasser, N.F.; Hambrey, M.J.; Reynolds, J.M.: 'Structure-from-Motion' photogrammetry - a low-cost, effective tool for geoscience applications. Geomorphology 179, 300-314, 2012.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

Five-Junction Solar Cell Optimization Using Silvaco Atlas

DTIC Science & Technology

2017-09-01

experimental sources [1], [4], [6]. f. Numerical Method The method selected for solving the non -linear equations that make up the simulation can be...and maximize efficiency. Optimization of solar cell efficiency is carried out via nearly orthogonal balanced design of experiments methodology . Silvaco...Optimization of solar cell efficiency is carried out via nearly orthogonal balanced design of experiments methodology . Silvaco ATLAS is utilized to

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

PubMed Central

Ribeiro, Haroldo V.; Zunino, Luciano; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.

2012-01-01

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable. PMID:22916097

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

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

Kaurov, Alexander A., E-mail: kaurov@uchicago.edu

The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emergedmore » from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large-scale statistical properties. These mock catalogs are particularly useful for cosmic microwave background polarization and 21 cm experiments, where large volumes are required to simulate the observed signal.« less

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Spinon confinement in a quasi-one-dimensional XXZ Heisenberg antiferromagnet

NASA Astrophysics Data System (ADS)

Lake, Bella; Bera, Anup K.; Essler, Fabian H. L.; Vanderstraeten, Laurens; Hubig, Claudius; Schollwock, Ulrich; Islam, A. T. M. Nazmul; Schneidewind, Astrid; Quintero-Castro, Diana L.

Half-integer spin Heisenberg chains constitute a key paradigm for quantum number fractionalization: flipping a spin creates a minimum of two elementary spinon excitations. These have been observed in numerous experiments. We report on inelastic neutron scattering experiments on the quasi-one-dimensional anisotropic spin-1/2 Heisenberg antiferromagnet SrCo2V2O8. These reveal a mechanism for temperature-induced spinon confinement, manifesting itself in the formation of sequences of spinon bound states. A theoretical description of this effect is achieved by a combination of analytical and numerical methods.

A fast numerical method for the valuation of American lookback put options

NASA Astrophysics Data System (ADS)

Song, Haiming; Zhang, Qi; Zhang, Ran

2015-10-01

A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.

Computation of transonic viscous-inviscid interacting flow

NASA Technical Reports Server (NTRS)

Whitfield, D. L.; Thomas, J. L.; Jameson, A.; Schmidt, W.

1983-01-01

Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829

A critical evaluation of various methods for the analysis of flow-solid interaction in a nest of thin cylinders subjected to cross flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1987-01-01

Various experimental, analytical, and numerical analysis methods for flow-solid interaction of a nest of cylinders subjected to cross flows are reviewed. A nest of cylinders subjected to cross flows can be found in numerous engineering applications including the Space Shuttle Maine Engine-Main Injector Assembly (SSME-MIA) and nuclear reactor heat exchangers. Despite its extreme importance in engineering applications, understanding of the flow-solid interaction process is quite limited and design of the tube banks are mostly dependent on experiments and/or experimental correlation equations. For future development of major numerical analysis methods for the flow-solid interaction of a nest of cylinders subjected to cross flow, various turbulence models, nonlinear structural dynamics, and existing laminar flow-solid interaction analysis methods are included.

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Simulation of Plasma Jet Merger and Liner Formation within the PLX- α Project

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Chen, Hsin-Chiang; Shih, Wen; Hsu, Scott

2015-11-01

Detailed numerical studies of the propagation and merger of high Mach number argon plasma jets and the formation of plasma liners have been performed using the newly developed method of Lagrangian particles (LP). The LP method significantly improves accuracy and mathematical rigor of common particle-based numerical methods such as smooth particle hydrodynamics while preserving their main advantages compared to grid-based methods. A brief overview of the LP method will be presented. The Lagrangian particle code implements main relevant physics models such as an equation of state for argon undergoing atomic physics transformation, radiation losses in thin optical limit, and heat conduction. Simulations of the merger of two plasma jets are compared with experimental data from past PLX experiments. Simulations quantify the effect of oblique shock waves, ionization, and radiation processes on the jet merger process. Results of preliminary simulations of future PLX- alpha experiments involving the ~ π / 2 -solid-angle plasma-liner configuration with 9 guns will also be presented. Partially supported by ARPA-E's ALPHA program.

The Capillary Flow Experiments Aboard the International Space Station: Increments 9-15

NASA Technical Reports Server (NTRS)

Jenson, Ryan M.; Weislogel, Mark M.; Tavan, Noel T.; Chen, Yongkang; Semerjian, Ben; Bunnell, Charles T.; Collicott, Steven H.; Klatte, Jorg; dreyer, Michael E.

2009-01-01

This report provides a summary of the experimental, analytical, and numerical results of the Capillary Flow Experiment (CFE) performed aboard the International Space Station (ISS). The experiments were conducted in space beginning with Increment 9 through Increment 16, beginning August 2004 and ending December 2007. Both primary and extra science experiments were conducted during 19 operations performed by 7 astronauts including: M. Fincke, W. McArthur, J. Williams, S. Williams, M. Lopez-Alegria, C. Anderson, and P. Whitson. CFE consists of 6 approximately 1 to 2 kg handheld experiment units designed to investigate a selection of capillary phenomena of fundamental and applied importance, such as large length scale contact line dynamics (CFE-Contact Line), critical wetting in discontinuous structures (CFE-Vane Gap), and capillary flows and passive phase separations in complex containers (CFE-Interior Corner Flow). Highly quantitative video from the simply performed flight experiments provide data helpful in benchmarking numerical methods, confirming theoretical models, and guiding new model development. In an extensive executive summary, a brief history of the experiment is reviewed before introducing the science investigated. A selection of experimental results and comparisons with both analytic and numerical predictions is given. The subsequent chapters provide additional details of the experimental and analytical methods developed and employed. These include current presentations of the state of the data reduction which we anticipate will continue throughout the year and culminate in several more publications. An extensive appendix is used to provide support material such as an experiment history, dissemination items to date (CFE publication, etc.), detailed design drawings, and crew procedures. Despite the simple nature of the experiments and procedures, many of the experimental results may be practically employed to enhance the design of spacecraft engineering systems involving capillary interface dynamics.

NSR&D FY17 Report: CartaBlanca Capability Enhancements

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

Long, Christopher Curtis; Dhakal, Tilak Raj; Zhang, Duan Zhong

Over the last several years, particle technology in the CartaBlanca code has been matured and has been successfully applied to a wide variety of physical problems. It has been shown that the particle methods, especially Los Alamos's dual domain material point method, is capable of computing many problems involves complex physics, chemistries accompanied by large material deformations, where the traditional finite element or Eulerian method encounter significant difficulties. In FY17, the CartaBlanca code has been enhanced with physical models and numerical algorithms. We started out to compute penetration and HE safety problems. Most of the year we focused on themore » TEPLA model improvement testing against the sweeping wave experiment by Gray et al., because it was found that pore growth and material failure are essentially important for our tasks and needed to be understood for modeling the penetration and the can experiments efficiently. We extended the TEPLA mode from the point view of ensemble phase average to include the effects of nite deformation. It is shown that the assumed pore growth model in TEPLA is actually an exact result from the theory. Alone this line, we then generalized the model to include finite deformations to consider nonlinear dynamics of large deformation. The interaction between the HE product gas and the solid metal is based on the multi-velocity formation. Our preliminary numerical results suggest good agreement between the experiment and the numerical results, pending further verification. To improve the parallel processing capabilities of the CartaBlanca code, we are actively working with the Next Generation Code (NGC) project to rewrite selected packages using C++. This work is expected to continue in the following years. This effort also makes the particle technology developed with CartaBlanca project available to other part of the laboratory. Working with the NGC project and rewriting some parts of the code also given us an opportunity to improve our numerical implementations of the method and to take advantage of recently advances in the numerical methods, such as multiscale algorithms.« less

Optics simulations: a Python workshop

NASA Astrophysics Data System (ADS)

Ghalila, H.; Ammar, A.; Varadharajan, S.; Majdi, Y.; Zghal, M.; Lahmar, S.; Lakshminarayanan, V.

2017-08-01

Numerical simulations allow teachers and students to indirectly perform sophisticated experiments that cannot be realizable otherwise due to cost and other constraints. During the past few decades there has been an explosion in the development of numerical tools concurrently with open source environments such as Python software. This availability of open source software offers an incredible opportunity for advancing teaching methodologies as well as in research. More specifically it is possible to correlate theoretical knowledge with experimental measurements using "virtual" experiments. We have been working on the development of numerical simulation tools using the Python program package and we have concentrated on geometric and physical optics simulations. The advantage of doing hands-on numerical experiments is that it allows the student learner to be an active participant in the pedagogical/learning process rather than playing a passive role as in the traditional lecture format. Even in laboratory classes because of constraints of space, lack of equipment and often-large numbers of students, many students play a passive role since they work in groups of 3 or more students. Furthermore these new tools help students get a handle on numerical methods as well simulations and impart a "feel" for the physics under investigation.

Numerical modeling and characterization of blast waves for application in blast-induced mild traumatic brain injury research

NASA Astrophysics Data System (ADS)

Phillips, Michael G.

Human exposure to blast waves, including blast-induced traumatic brain injury, is a developing field in medical research. Experiments with explosives have many disadvantages including safety, cost, and required area for trials. Shock tubes provide an alternative method to produce free field blast wave profiles. A compressed nitrogen shock tube experiment instrumented with static and reflective pressure taps is modeled using a numerical simulation. The geometry of the numerical model is simplified and blast wave characteristics are derived based upon static and pressure profiles. The pressure profiles are analyzed along the shock tube centerline and radially away from the tube axis. The blast wave parameters found from the pressure profiles provide guidelines for spatial location of a specimen. The location could be based on multiple parameters and provides a distribution of anticipated pressure profiles experience by the specimen.

Numerical simulation of the wave-induced non-linear bending moment of ships

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

Xia, J.; Wang, Z.; Gu, X.

1995-12-31

Ships traveling in moderate or rough seas may experience non-linear bending moments due to flare effect and slamming loads. The numerical simulation of the total wave-induced bending moment contributed from both the wave frequency component induced by wave forces and the high frequency whipping component induced by slamming actions is very important in predicting the responses and ensuring the safety of the ship in rough seas. The time simulation is also useful for the reliability analysis of ship girder strength. The present paper discusses four different methods of the numerical simulation of wave-induced non-linear vertical bending moment of ships recentlymore » developed in CSSRC, including the hydroelastic integral-differential method (HID), the hydroelastic differential analysis method (HDA), the combined seakeeping and structural forced vibration method (CSFV), and the modified CSFV method (MCSFV). Numerical predictions are compared with the experimental results obtained from the elastic ship model test of S-175 container ship in regular and irregular waves presented by Watanabe Ueno and Sawada (1989).« less

Numerical verification of three point bending experiment of magnetorheological elastomer (MRE) in magnetic field

NASA Astrophysics Data System (ADS)

Miedzinska, Danuta; Boczkowska, Anna; Zubko, Konrad

2010-07-01

In the article a method of numerical verification of experimental results for magnetorheological elastomer samples (MRE) is presented. The samples were shaped into cylinders with diameter of 8 mm and height of 20 mm with various carbonyl iron volume shares (1,5%, 11,5% and 33%). The diameter of soft ferromagnetic substance particles ranged from 6 to 9 μm. During the experiment, initially bended samples were exposed to the magnetic field with intensity levels at 0,1T, 0,3T, 0,5T, 0,7 and 1T. The reaction of the sample to the field action was measured as a displacement of a specimen. Numerical calculation was carried out with the MSC Patran/Marc computer code. For the purpose of numerical analysis the orthotropic material model with the material properties of magnetorheological elastomer along the iron chains, and of the pure elastomer along other directions, was applied. The material properties were obtained from the experimental tests. During the numerical analysis, the initial mechanical load resulting from cylinder deflection was set. Then, the equivalent external force, that was set on the basis of analytical calculations of intermolecular reaction within iron chains in the specific magnetic field, was put on the bended sample. Correspondence of such numerical model with results of the experiment was verified. Similar results of the experiments and both theoretical and FEM analysis indicates that macroscopic modeling of magnetorheological elastomer mechanical properties as orthotropic material delivers accurate enough description of the material's behavior.

Generation of dense plume fingers in saturated-unsaturated homogeneous porous media

NASA Astrophysics Data System (ADS)

Cremer, Clemens J. M.; Graf, Thomas

2015-02-01

Flow under variable-density conditions is widespread, occurring in geothermal reservoirs, at waste disposal sites or due to saltwater intrusion. The migration of dense plumes typically results in the formation of vertical plume fingers which are known to be triggered by material heterogeneity or by variations in source concentration that causes the density variation. Using a numerical groundwater model, six perturbation methods are tested under saturated and unsaturated flow conditions to mimic heterogeneity and concentration variations on the pore scale in order to realistically generate dense fingers. A laboratory-scale sand tank experiment is numerically simulated, and the perturbation methods are evaluated by comparing plume fingers obtained from the laboratory experiment with numerically simulated fingers. Dense plume fingering for saturated flow can best be reproduced with a spatially random, time-constant perturbation of the solute source. For unsaturated flow, a spatially and temporally random noise of solute concentration or a random conductivity field adequately simulate plume fingering.

Efficient Permeability Measurement and Numerical Simulation of the Resin Flow in Low Permeability Preform Fabricated by Automated Dry Fiber Placement

NASA Astrophysics Data System (ADS)

Agogue, Romain; Chebil, Naziha; Deleglise-Lagardere, Mylène; Beauchene, Pierre; Park, Chung Hae

2017-10-01

We propose a new experimental method using a Hassler cell and air injection to measure the permeability of fiber preform while avoiding a race tracking effect. This method was proven to be particularly efficient to measure very low through-thickness permeability of preform fabricated by automated dry fiber placement. To validate the reliability of the permeability measurement, the experiments of viscous liquid infusion into the preform with or without a distribution medium were performed. The experimental data of flow front advancement was compared with the numerical simulation result using the permeability values obtained by the Hassler cell permeability measurement set-up as well as by the liquid infusion experiments. To address the computational cost issue, the model for the equivalent permeability of distribution medium was employed in the numerical simulation of liquid flow. The new concept using air injection and Hassler cell for the fiber preform permeability measurement was shown to be reliable and efficient.

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

Jing Yanfei, E-mail: yanfeijing@uestc.edu.c; Huang Tingzhu, E-mail: tzhuang@uestc.edu.c; Duan Yong, E-mail: duanyong@yahoo.c

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

Numerical Investigation of Different Radial Inlet Forms for Centrifugal Compressor and Influence of the Deflectors Number by Means of Computational Fluid Dynamics Methods with Computational Model Validation

NASA Astrophysics Data System (ADS)

Kozhukhov, Y. V.; Yun, V. K.; Reshetnikova, L. V.; Prokopovich, M. V.

2015-08-01

The goal of this work is numerical experiments for five different types of the centrifugal compressor's inlet chambers with the help of CFD-methods and comparison of the computational results with the results of the real experiment which was held in the Nevskiy Lenin Plant in Saint-Petersburg. In the context of one of the chambers the influence of deflectors on its characteristics was investigated. The objects of investigation are 5 inlet chambers of different types which differ from each other by deflectors’ existence and by its number. The comparative analyze of the results of numerical and real experiments was held by means of comparison of relative velocity and static pressure coefficient distribution on hub and shroud region, and also by means of loss coefficient values change for all five chambers. As a result of the numerical calculation the quantitative and qualitative departure of CFD- calculations results and real experiment were found out. The investigation of the influence of the number of deflectors on flow parameters was carried out. The results of the study prove that the presence of the deflectors on flow path significantly increases the probability of the flow separations and reversed flows appearance on them. At the same time, the complete absence of the deflectors in the chamber significantly increases circumferential distortion of the flow; however the loss coefficient decreases anyway, the high values of which are caused by the shock flow existence. Thus, the profiling of the deflectors of the inlet chamber should be given a special attention.

Validation of the enthalpy method by means of analytical solution

NASA Astrophysics Data System (ADS)

Kleiner, Thomas; Rückamp, Martin; Bondzio, Johannes; Humbert, Angelika

2014-05-01

Numerical simulations moved in the recent year(s) from describing the cold-temperate transition surface (CTS) towards an enthalpy description, which allows avoiding incorporating a singular surface inside the model (Aschwanden et al., 2012). In Enthalpy methods the CTS is represented as a level set of the enthalpy state variable. This method has several numerical and practical advantages (e.g. representation of the full energy by one scalar field, no restriction to topology and shape of the CTS). The proposed method is rather new in glaciology and to our knowledge not verified and validated against analytical solutions. Unfortunately we are still lacking analytical solutions for sufficiently complex thermo-mechanically coupled polythermal ice flow. However, we present two experiments to test the implementation of the enthalpy equation and corresponding boundary conditions. The first experiment tests particularly the functionality of the boundary condition scheme and the corresponding basal melt rate calculation. Dependent on the different thermal situations that occur at the base, the numerical code may have to switch to another boundary type (from Neuman to Dirichlet or vice versa). The main idea of this set-up is to test the reversibility during transients. A former cold ice body that run through a warmer period with an associated built up of a liquid water layer at the base must be able to return to its initial steady state. Since we impose several assumptions on the experiment design analytical solutions can be formulated for different quantities during distinct stages of the simulation. The second experiment tests the positioning of the internal CTS in a parallel-sided polythermal slab. We compare our simulation results to the analytical solution proposed by Greve and Blatter (2009). Results from three different ice flow-models (COMIce, ISSM, TIMFD3) are presented.

On the superposition principle in interference experiments.

PubMed

Sinha, Aninda; H Vijay, Aravind; Sinha, Urbasi

2015-05-14

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrödinger equation.

Increasing the computational efficient of digital cross correlation by a vectorization method

NASA Astrophysics Data System (ADS)

Chang, Ching-Yuan; Ma, Chien-Ching

2017-08-01

This study presents a vectorization method for use in MATLAB programming aimed at increasing the computational efficiency of digital cross correlation in sound and images, resulting in a speedup of 6.387 and 36.044 times compared with performance values obtained from looped expression. This work bridges the gap between matrix operations and loop iteration, preserving flexibility and efficiency in program testing. This paper uses numerical simulation to verify the speedup of the proposed vectorization method as well as experiments to measure the quantitative transient displacement response subjected to dynamic impact loading. The experiment involved the use of a high speed camera as well as a fiber optic system to measure the transient displacement in a cantilever beam under impact from a steel ball. Experimental measurement data obtained from the two methods are in excellent agreement in both the time and frequency domain, with discrepancies of only 0.68%. Numerical and experiment results demonstrate the efficacy of the proposed vectorization method with regard to computational speed in signal processing and high precision in the correlation algorithm. We also present the source code with which to build MATLAB-executable functions on Windows as well as Linux platforms, and provide a series of examples to demonstrate the application of the proposed vectorization method.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

Dynamics of anchor last deployment of submersible buoy system

NASA Astrophysics Data System (ADS)

Zheng, Zhongqiang; Xu, Jianpeng; Huang, Peng; Wang, Lei; Yang, Xiaoguang; Chang, Zongyu

2016-02-01

Submersible buoy systems are widely used for oceanographic research, ocean engineering and coastal defense. Severe sea environment has obvious effects on the dynamics of submersible buoy systems. Huge tension can occur and may cause the snap of cables, especially during the deployment period. This paper studies the deployment dynamics of submersible buoy systems with numerical and experimental methods. By applying the lumped mass approach, a three-dimensional multi-body model of submersible buoy system is developed considering the hydrodynamic force, tension force and impact force between components of submersible buoy system and seabed. Numerical integration method is used to solve the differential equations. The simulation output includes tension force, trajectory, profile and dropping location and impact force of submersible buoys. In addition, the deployment experiment of a simplified submersible buoy model was carried out. The profile and different nodes' velocities of the submersible buoy are obtained. By comparing the results of the two methods, it is found that the numerical model well simulates the actual process and conditions of the experiment. The simulation results agree well with the results of the experiment such as gravity anchor's location and velocities of different nodes of the submersible buoy. The study results will help to understand the conditions of submersible buoy's deployment, operation and recovery, and can be used to guide the design and optimization of the system.

Lexical Link Analysis Application: Improving Web Service to Acquisition Visibility Portal

DTIC Science & Technology

2013-09-30

during the Empire Challenge 2008 and 2009 (EC08/09) field experiments and for numerous other field experiments of new technologies during Trident Warrior...Empirical Methods in Natural Language Processing and Very Large Corpora (EMNLP/ VLC -2000) (pp. 63–70). Retrieved from http://nlp.stanford.edu/manning

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators

NASA Astrophysics Data System (ADS)

You, Xiong; Zhang, Yonghui; Zhao, Jinxi

2011-07-01

In this paper, a new family of trigonometrically-fitted Scheifele two-step (TFSTS) methods for the numerical integration of perturbed oscillators is proposed and investigated. An essential feature of TFSTS methods is that they are exact in both the internal stages and the updates when solving the unperturbed harmonic oscillator y″ = -ω2 y for known frequency ω. Based on the linear operator theory, the necessary and sufficient conditions for TFSTS methods of up to order five are derived. Two specific TFSTS methods of orders four and five respectively are constructed and their stability and phase properties are examined. In the five numerical experiments carried out the new integrators are shown to be more efficient and competent than some well-known methods in the literature.

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Numerical study on anaerobic digestion of fruit and vegetable waste: Biogas generation

NASA Astrophysics Data System (ADS)

Wardhani, Puteri Kusuma; Watanabe, Masaji

2016-02-01

The study provides experimental results and numerical results concerning anaerobic digestion of fruit and vegetable waste. Experiments were carried out by using batch floating drum type digester without mixing and temperature setting. The retention time was 30 days. Numerical results based on Monod type model with influence of temperature is introduced. Initial value problems were analyzed numerically, while kinetic parameters were analyzed by using trial error methods. The numerical results for the first five days seems appropriate in comparison with the experimental outcomes. However, numerical results shows that the model is inappropriate for 30 days of fermentation. This leads to the conclusion that Monod type model is not suitable for describe the mixture degradation of fruit and vegetable waste and horse dung.

Numerical simulation and analysis for low-frequency rock physics measurements

NASA Astrophysics Data System (ADS)

Dong, Chunhui; Tang, Genyang; Wang, Shangxu; He, Yanxiao

2017-10-01

In recent years, several experimental methods have been introduced to measure the elastic parameters of rocks in the relatively low-frequency range, such as differential acoustic resonance spectroscopy (DARS) and stress-strain measurement. It is necessary to verify the validity and feasibility of the applied measurement method and to quantify the sources and levels of measurement error. Relying solely on the laboratory measurements, however, we cannot evaluate the complete wavefield variation in the apparatus. Numerical simulations of elastic wave propagation, on the other hand, are used to model the wavefield distribution and physical processes in the measurement systems, and to verify the measurement theory and analyze the measurement results. In this paper we provide a numerical simulation method to investigate the acoustic waveform response of the DARS system and the quasi-static responses of the stress-strain system, both of which use axisymmetric apparatus. We applied this method to parameterize the properties of the rock samples, the sample locations and the sensor (hydrophone and strain gauges) locations and simulate the measurement results, i.e. resonance frequencies and axial and radial strains on the sample surface, from the modeled wavefield following the physical experiments. Rock physical parameters were estimated by inversion or direct processing of these data, and showed a perfect match with the true values, thus verifying the validity of the experimental measurements. Error analysis was also conducted for the DARS system with 18 numerical samples, and the sources and levels of error are discussed. In particular, we propose an inversion method for estimating both density and compressibility of these samples. The modeled results also showed fairly good agreement with the real experiment results, justifying the effectiveness and feasibility of our modeling method.

Novel X-ray Communication Based XNAV Augmentation Method Using X-ray Detectors

PubMed Central

Song, Shibin; Xu, Luping; Zhang, Hua; Bai, Yuanjie

2015-01-01

The further development of X-ray pulsar-based NAVigation (XNAV) is hindered by its lack of accuracy, so accuracy improvement has become a critical issue for XNAV. In this paper, an XNAV augmentation method which utilizes both pulsar observation and X-ray ranging observation for navigation filtering is proposed to deal with this issue. As a newly emerged concept, X-ray communication (XCOM) shows great potential in space exploration. X-ray ranging, derived from XCOM, could achieve high accuracy in range measurement, which could provide accurate information for XNAV. For the proposed method, the measurement models of pulsar observation and range measurement observation are established, and a Kalman filtering algorithm based on the observations and orbit dynamics is proposed to estimate the position and velocity of a spacecraft. A performance comparison of the proposed method with the traditional pulsar observation method is conducted by numerical experiments. Besides, the parameters that influence the performance of the proposed method, such as the pulsar observation time, the SNR of the ranging signal, etc., are analyzed and evaluated by numerical experiments. PMID:26404295

Experiments study on attitude coupling control method for flexible spacecraft

NASA Astrophysics Data System (ADS)

Wang, Jie; Li, Dongxu

2018-06-01

High pointing accuracy and stabilization are significant for spacecrafts to carry out Earth observing, laser communication and space exploration missions. However, when a spacecraft undergoes large angle maneuver, the excited elastic oscillation of flexible appendages, for instance, solar wing and onboard antenna, would downgrade the performance of the spacecraft platform. This paper proposes a coupling control method, which synthesizes the adaptive sliding mode controller and the positive position feedback (PPF) controller, to control the attitude and suppress the elastic vibration simultaneously. Because of its prominent performance for attitude tracking and stabilization, the proposed method is capable of slewing the flexible spacecraft with a large angle. Also, the method is robust to parametric uncertainties of the spacecraft model. Numerical simulations are carried out with a hub-plate system which undergoes a single-axis attitude maneuver. An attitude control testbed for the flexible spacecraft is established and experiments are conducted to validate the coupling control method. Both numerical and experimental results demonstrate that the method discussed above can effectively decrease the stabilization time and improve the attitude accuracy of the flexible spacecraft.

Art for the Ages.

ERIC Educational Resources Information Center

Casazza, Ornella; Franchi, Paolo

1985-01-01

Description of encoding of art works and digitization of paintings to preserve and restore them reviews experiments which used chromatic selection and abstraction as a painting restoration method. This method utilizes the numeric processing resulting from digitization to restore a painting and computer simulation to shorten the restoration…

Penalty methods for the numerical solution of American multi-asset option problems

NASA Astrophysics Data System (ADS)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

Online machining error estimation method of numerical control gear grinding machine tool based on data analysis of internal sensors

NASA Astrophysics Data System (ADS)

Zhao, Fei; Zhang, Chi; Yang, Guilin; Chen, Chinyin

2016-12-01

This paper presents an online estimation method of cutting error by analyzing of internal sensor readings. The internal sensors of numerical control (NC) machine tool are selected to avoid installation problem. The estimation mathematic model of cutting error was proposed to compute the relative position of cutting point and tool center point (TCP) from internal sensor readings based on cutting theory of gear. In order to verify the effectiveness of the proposed model, it was simulated and experimented in gear generating grinding process. The cutting error of gear was estimated and the factors which induce cutting error were analyzed. The simulation and experiments verify that the proposed approach is an efficient way to estimate the cutting error of work-piece during machining process.

Experiments and Dynamic Finite Element Analysis of a Wire-Rope Rockfall Protective Fence

NASA Astrophysics Data System (ADS)

Tran, Phuc Van; Maegawa, Koji; Fukada, Saiji

2013-09-01

The imperative need to protect structures in mountainous areas against rockfall has led to the development of various protection methods. This study introduces a new type of rockfall protection fence made of posts, wire ropes, wire netting and energy absorbers. The performance of this rock fence was verified in both experiments and dynamic finite element analysis. In collision tests, a reinforced-concrete block rolled down a natural slope and struck the rock fence at the end of the slope. A specialized system of measuring instruments was employed to accurately measure the acceleration of the block without cable connection. In particular, the performance of two energy absorbers, which contribute also to preventing wire ropes from breaking, was investigated to determine the best energy absorber. In numerical simulation, a commercial finite element code having explicit dynamic capabilities was employed to create models of the two full-scale tests. To facilitate simulation, certain simplifying assumptions for mechanical data of each individual component of the rock fence and geometrical data of the model were adopted. Good agreement between numerical simulation and experimental data validated the numerical simulation. Furthermore, the results of numerical simulation helped highlight limitations of the testing method. The results of numerical simulation thus provide a deeper understanding of the structural behavior of individual components of the rock fence during rockfall impact. More importantly, numerical simulations can be used not only as supplements to or substitutes for full-scale tests but also in parametric study and design.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

Numerical prediction of wall temperatures for near-critical para-hydrogen in turbulent upflow inside vertical tubes

NASA Technical Reports Server (NTRS)

Bellmore, C. P.; Reid, R. L.

1980-01-01

Presented herein is a method of including density fluctuations in the equations of turbulent transport. Results of a numerical analysis indicate that the method may be used to predict heat transfer for the case of near-critical para-hydrogen in turbulent upflow inside vertical tubes. Wall temperatures, heat transfer coefficients, and velocities obtained by coupling the equations of turbulent momentum and heat transfer with a perturbed equation of state show good agreement with experiment for inlet reduced pressures of 1.28-5.83.

Dense velocity reconstruction from tomographic PTV with material derivatives

NASA Astrophysics Data System (ADS)

Schneiders, Jan F. G.; Scarano, Fulvio

2016-09-01

A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e.g., 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. The constraint to the measured temporal derivative of the PTV particle tracks improves the consistency of the reconstructed velocity field. The method is christened as pouring time into space, as it leverages temporal information to increase the spatial resolution of volumetric PTV measurements. This approach becomes relevant in cases where the spatial resolution is limited by the seeding concentration. The method solves an optimization problem to find the vorticity and velocity fields that minimize a cost function, which includes next to instantaneous velocity, also the velocity material derivative. The velocity and its material derivative are related through the vorticity transport equation, and the cost function is minimized using the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. The procedure is assessed numerically with a simulated PTV experiment in a turbulent boundary layer from a direct numerical simulation (DNS). The experimental validation considers a tomographic particle image velocimetry (PIV) experiment in a similar turbulent boundary layer and the additional case of a jet flow. The proposed technique (`vortex-in-cell plus', VIC+) is compared to tomographic PIV analysis (3D iterative cross-correlation), PTV interpolation methods (linear and adaptive Gaussian windowing) and to vortex-in-cell (VIC) interpolation without the material derivative. A visible increase in resolved details in the turbulent structures is obtained with the VIC+ approach, both in numerical simulations and experiments. This results in a more accurate determination of the turbulent stresses distribution in turbulent boundary layer investigations. Data from a jet experiment, where the vortex topology is retrieved with a small number of tracers indicate the potential utilization of VIC+ in low-concentration experiments as for instance occurring in large-scale volumetric PTV measurements.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

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

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution ofmore » dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.« less

Numerical investigation for formability of aluminum 6016 alloy under non-isothermal warm forming process

NASA Astrophysics Data System (ADS)

Hu, P.; Dai, M. H.; Ying, L.; Shi, D. Y.; Zhao, K. M.; Lu, J. D.

2013-05-01

The warm forming technology of aluminum alloy has attracted attention from worldwide automotive engineering sector in recent years, with which the complex geometry parts can be realized at elevated temperature. A non-isothermal warm forming process for the heat treatable aluminum can quickly carry out its application on traditional production line by adding a furnace to heat up the aluminum alloy sheet. The 6000 aluminum alloy was investigated by numerical simulation and experiment using the Nakajima test model in this paper. A modified Fields-Backofen model was introduced into numerical simulation process to describe the thermo-mechanical flow behavior of a 6000 series aluminum alloy. The experimental data was obtained by conducting thermal-mechanical uniaxial tensile experiment in temperatures range of 25˜400°C to guarantee the numerical simulation more accurate. The numerical simulation was implemented with LS_DYNA software in terms of coupled dynamic explicit method for investigating the effect of initial forming temperature and the Binder Holder Force (BHF), which are critical process parameters in non-isothermal warm forming. The results showed that the optimal initial forming temperature range was 300°C˜350°C. By means of conducting numerical simulation in deep drawing box model, the forming window of BHF and temperature around the optimal initial forming temperature (275°, 300° and 325°) are investigated, which can provide guidance to actual experiment.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

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

Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.

2015-12-01

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated atmore » various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Numerical study of rotating detonation engine with an array of injection holes

NASA Astrophysics Data System (ADS)

Yao, S.; Han, X.; Liu, Y.; Wang, J.

2017-05-01

This paper aims to adopt the method of injection via an array of holes in three-dimensional numerical simulations of a rotating detonation engine (RDE). The calculation is based on the Euler equations coupled with a one-step Arrhenius chemistry model. A pre-mixed stoichiometric hydrogen-air mixture is used. The present study uses a more practical fuel injection method in RDE simulations, injection via an array of holes, which is different from the previous conventional simulations where a relatively simple full injection method is usually adopted. The computational results capture some important experimental observations and a transient period after initiation. These phenomena are usually absent in conventional RDE simulations due to the use of an idealistic injection approximation. The results are compared with those obtained from other numerical studies and experiments with RDEs.

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

DOE PAGES

Chen, Zheng; Liu, Liu; Mu, Lin

2017-05-03

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof ofmore » the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.« less

A new smoothing modified three-term conjugate gradient method for [Formula: see text]-norm minimization problem.

PubMed

Du, Shouqiang; Chen, Miao

2018-01-01

We consider a kind of nonsmooth optimization problems with [Formula: see text]-norm minimization, which has many applications in compressed sensing, signal reconstruction, and the related engineering problems. Using smoothing approximate techniques, this kind of nonsmooth optimization problem can be transformed into a general unconstrained optimization problem, which can be solved by the proposed smoothing modified three-term conjugate gradient method. The smoothing modified three-term conjugate gradient method is based on Polak-Ribière-Polyak conjugate gradient method. For the Polak-Ribière-Polyak conjugate gradient method has good numerical properties, the proposed method possesses the sufficient descent property without any line searches, and it is also proved to be globally convergent. Finally, the numerical experiments show the efficiency of the proposed method.

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

Rhinefrank, Kenneth E.; Lenee-Bluhm, Pukha; Prudell, Joseph H.

The most prudent path to a full-scale design, build and deployment of a wave energy conversion (WEC) system involves establishment of validated numerical models using physical experiments in a methodical scaling program. This Project provides essential additional rounds of wave tank testing at 1:33 scale and ocean/bay testing at a 1:7 scale, necessary to validate numerical modeling that is essential to a utility-scale WEC design and associated certification.

Experimental Validation of Numerical Simulations for an Acoustic Liner in Grazing Flow

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Pastouchenko, Nikolai N.; Jones, Michael G.; Watson, Willie R.

2013-01-01

A coordinated experimental and numerical simulation effort is carried out to improve our understanding of the physics of acoustic liners in a grazing flow as well our computational aeroacoustics (CAA) method prediction capability. A numerical simulation code based on advanced CAA methods is developed. In a parallel effort, experiments are performed using the Grazing Flow Impedance Tube at the NASA Langley Research Center. In the experiment, a liner is installed in the upper wall of a rectangular flow duct with a 2 inch by 2.5 inch cross section. Spatial distribution of sound pressure levels and relative phases are measured on the wall opposite the liner in the presence of a Mach 0.3 grazing flow. The computer code is validated by comparing computed results with experimental measurements. Good agreements are found. The numerical simulation code is then used to investigate the physical properties of the acoustic liner. It is shown that an acoustic liner can produce self-noise in the presence of a grazing flow and that a feedback acoustic resonance mechanism is responsible for the generation of this liner self-noise. In addition, the same mechanism also creates additional liner drag. An estimate, based on numerical simulation data, indicates that for a resonant liner with a 10% open area ratio, the drag increase would be about 4% of the turbulent boundary layer drag over a flat wall.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

NASA Astrophysics Data System (ADS)

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-05-01

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach's feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

A multi-level solution algorithm for steady-state Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham; Leutenegger, Scott T.

1993-01-01

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Rotordynamic Instability Problems in High-Performance Turbomachinery, 1993

NASA Technical Reports Server (NTRS)

1994-01-01

Numerical, theoretical, and experimental results and control methods for seals, bearings, and dampers with some attention given to variable thermospherical properties and turbulence measurements are reported along with field experiences.

Simple Criteria to Determine the Set of Key Parameters of the DRPE Method by a Brute-force Attack

NASA Astrophysics Data System (ADS)

Nalegaev, S. S.; Petrov, N. V.

Known techniques of breaking Double Random Phase Encoding (DRPE), which bypass the resource-intensive brute-force method, require at least two conditions: the attacker knows the encryption algorithm; there is an access to the pairs of source and encoded images. Our numerical results show that for the accurate recovery by numerical brute-force attack, someone needs only some a priori information about the source images, which can be quite general. From the results of our numerical experiments with optical data encryption DRPE with digital holography, we have proposed four simple criteria for guaranteed and accurate data recovery. These criteria can be applied, if the grayscale, binary (including QR-codes) or color images are used as a source.

Three-dimensional Diffusive Strip Method

NASA Astrophysics Data System (ADS)

Martinez-Ruiz, Daniel; Meunier, Patrice; Duchemin, Laurent; Villermaux, Emmanuel

2016-11-01

The Diffusive Strip Method (DSM) is a near-exact numerical method developed for mixing computations at large Péclet number in two-dimensions. The method consists in following stretched material lines to compute a-posteriori the resulting scalar field is extended here to three-dimensional flows, following surfaces. We describe its 3D peculiarities, and show how it applies to a simple Taylor-Couette configuration with non-rotating boundary conditions at the top end, bottom and outer cylinder. This flow produces an elaborate, although controlled, steady 3D flow which relies on the Ekman pumping arising from the rotation of the inner cylinder is both studied experimentally, and numerically modeled. A recurrent two-cells structure appears formed by stream tubes shaped as nested tori. A scalar blob in the flow experiences a Lagrangian oscillating dynamics with stretchings and compressions, driving the mixing process, and yielding both rapidly-mixed and nearly pure-diffusive regions. A triangulated-surface method is developed to calculate the blob elongation and scalar concentration PDFs through a single variable computation along the advected blob surface, capturing the rich evolution observed in the experiments.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Assessment of sub-grid scale dispersion closure with regularized deconvolution method in a particle-laden turbulent jet

NASA Astrophysics Data System (ADS)

Wang, Qing; Zhao, Xinyu; Ihme, Matthias

2017-11-01

Particle-laden turbulent flows are important in numerous industrial applications, such as spray combustion engines, solar energy collectors etc. It is of interests to study this type of flows numerically, especially using large-eddy simulations (LES). However, capturing the turbulence-particle interaction in LES remains challenging due to the insufficient representation of the effect of sub-grid scale (SGS) dispersion. In the present work, a closure technique for the SGS dispersion using regularized deconvolution method (RDM) is assessed. RDM was proposed as the closure for the SGS dispersion in a counterflow spray that is studied numerically using finite difference method on a structured mesh. A presumed form of LES filter is used in the simulations. In the present study, this technique has been extended to finite volume method with an unstructured mesh, where no presumption on the filter form is required. The method is applied to a series of particle-laden turbulent jets. Parametric analyses of the model performance are conducted for flows with different Stokes numbers and Reynolds numbers. The results from LES will be compared against experiments and direct numerical simulations (DNS).

A simplified parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.

Optimization of Selective Laser Melting by Evaluation Method of Multiple Quality Characteristics

NASA Astrophysics Data System (ADS)

Khaimovich, A. I.; Stepanenko, I. S.; Smelov, V. G.

2018-01-01

Article describes the adoption of the Taguchi method in selective laser melting process of sector of combustion chamber by numerical and natural experiments for achieving minimum temperature deformation. The aim was to produce a quality part with minimum amount of numeric experiments. For the study, the following optimization parameters (independent factors) were chosen: the laser beam power and velocity; two factors for compensating the effect of the residual thermal stresses: the scale factor of the preliminary correction of the part geometry and the number of additional reinforcing elements. We used an orthogonal plan of 9 experiments with a factor variation at three levels (L9). As quality criterias, the values of distortions for 9 zones of the combustion chamber and the maximum strength of the material of the chamber were chosen. Since the quality parameters are multidirectional, a grey relational analysis was used to solve the optimization problem for multiple quality parameters. As a result, according to the parameters obtained, the combustion chamber segments of the gas turbine engine were manufactured.

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

Evaluation of methods for measuring relative permeability of anhydride from the Salado Formation: Sensitivity analysis and data reduction

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

Christiansen, R.L.; Kalbus, J.S.; Howarth, S.M.

This report documents, demonstrates, evaluates, and provides theoretical justification for methods used to convert experimental data into relative permeability relationships. The report facilities accurate determination of relative permeabilities of anhydride rock samples from the Salado Formation at the Waste Isolation Pilot Plant (WIPP). Relative permeability characteristic curves are necessary for WIPP Performance Assessment (PA) predictions of the potential for flow of waste-generated gas from the repository and brine flow into repository. This report follows Christiansen and Howarth (1995), a comprehensive literature review of methods for measuring relative permeability. It focuses on unsteady-state experiments and describes five methods for obtaining relativemore » permeability relationships from unsteady-state experiments. Unsteady-state experimental methods were recommended for relative permeability measurements of low-permeability anhydrite rock samples form the Salado Formation because these tests produce accurate relative permeability information and take significantly less time to complete than steady-state tests. Five methods for obtaining relative permeability relationships from unsteady-state experiments are described: the Welge method, the Johnson-Bossler-Naumann method, the Jones-Roszelle method, the Ramakrishnan-Cappiello method, and the Hagoort method. A summary, an example of the calculations, and a theoretical justification are provided for each of the five methods. Displacements in porous media are numerically simulated for the calculation examples. The simulated product data were processed using the methods, and the relative permeabilities obtained were compared with those input to the numerical model. A variety of operating conditions were simulated to show sensitivity of production behavior to rock-fluid properties.« less

From three-dimensional long-term tectonic numerical models to synthetic structural data: semi-automatic extraction of instantaneous & finite strain quantities

NASA Astrophysics Data System (ADS)

Duclaux, Guillaume; May, Dave

2017-04-01

Over the past three decades thermo-mechanical numerical modelling has transformed the way we look at deformation in the lithosphere. More than just generating aesthetically pleasing pictures, the output from a numerical models contains a rich source of quantitative information that can be used to measure deformation quantities in plan view or three-dimensions. Adding value to any numerical experiment requires a thorough post-processing of the modelling results. Such work aims to produce visual information that will resonate to seasoned structural geologists and assist with comparing experimental and observational data. Here we introduce two methods to generate synthetic structural data from numerical model outputs. We first present an image processing and shape recognition workflow developed to extract the active faults orientation from surface velocity gradients. In order to measure the active faults lengths and directions along with their distribution at the surface of the model we implemented an automated sequential mapping technique based on the second invariant of the strain rate tensor and using a suite a python functions. Active fault direction measurements are achieved using a probabilistic method for extracting linear features orientation from any surface. This method has the undeniable advantage to avoid interpretation bias. Strike measurements for individual segments are weighted according to their length and orientation distribution data are presented in an equal-area moving average rose diagrams produced using a weighted method. Finally, we discuss a method for mapping finite strain in three-dimensions. A high-resolution Lagrangian regular grid which advects during the numerical experiment is used to track the progressive deformation within the model. Thanks to this data we can measure the finite strain ellipsoids for any region of interest in the model. This method assumes that the finite strain is homogenous within one unit cell of the grid. We can compute individual ellipsoid's parameters (orientation, shape, etc.) and represent the finite deformation for any region of interest in a Flinn diagram. In addition, we can use the finite strain ellipsoids to estimate the prevailing foliation and/or lineation directions anywhere in the model. These two methods are applied to measure the instantaneous and finite deformation patterns within an oblique rift zone ongoing constant extension in the absence of surface processes.

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

NASA Astrophysics Data System (ADS)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

Computation of rare transitions in the barotropic quasi-geostrophic equations

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bouchet, Freddy

2015-01-01

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager-Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

A tridiagonal parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.

Temporal and spatial temperature measurement in insulator-based dielectrophoretic devices.

PubMed

Nakano, Asuka; Luo, Jinghui; Ros, Alexandra

2014-07-01

Insulator-based dielectrophoresis is a relatively new analytical technique with a large potential for a number of applications, such as sorting, separation, purification, fractionation, and preconcentration. The application of insulator-based dielectrophoresis (iDEP) for biological samples, however, requires the precise control of the microenvironment with temporal and spatial resolution. Temperature variations during an iDEP experiment are a critical aspect in iDEP since Joule heating could lead to various detrimental effects hampering reproducibility. Additionally, Joule heating can potentially induce thermal flow and more importantly can degrade biomolecules and other biological species. Here, we investigate temperature variations in iDEP devices experimentally employing the thermosensitive dye Rhodamin B (RhB) and compare the measured results with numerical simulations. We performed the temperature measurement experiments at a relevant buffer conductivity range commonly used for iDEP applications under applied electric potentials. To this aim, we employed an in-channel measurement method and an alternative method employing a thin film located slightly below the iDEP channel. We found that the temperature does not deviate significantly from room temperature at 100 μS/cm up to 3000 V applied such as in protein iDEP experiments. At a conductivity of 300 μS/cm, such as previously used for mitochondria iDEP experiments at 3000 V, the temperature never exceeds 34 °C. This observation suggests that temperature effects for iDEP of proteins and mitochondria under these conditions are marginal. However, at larger conductivities (1 mS/cm) and only at 3000 V applied, temperature increases were significant, reaching a regime in which degradation is likely to occur. Moreover, the thin layer method resulted in lower temperature enhancement which was also confirmed with numerical simulations. We thus conclude that the thin film method is preferable providing closer agreement with numerical simulations and further since it does not depend on the iDEP channel material. Overall, our study provides a thorough comparison of two experimental techniques for direct temperature measurement, which can be adapted to a variety of iDEP applications in the future. The good agreement between simulation and experiment will also allow one to assess temperature variations for iDEP devices prior to experiments.

Study on the wind field and pollutant dispersion in street canyons using a stable numerical method.

PubMed

Xia, Ji-Yang; Leung, Dennis Y C

2005-01-01

A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the velocity field and the pressure field separately from the governing equations. The Streamline Upwind Petrov-Galerkin (SUPG) method was used to get stable numerical results. Numerical oscillation was minimized and satisfactory results can be obtained for flows at high Reynolds numbers. Simulating the flow over a square cylinder within a wide range of Reynolds numbers validates the wind field model. The Strouhal numbers obtained from the numerical simulation had a good agreement with those obtained from experiment. The wind field model developed in the present study is applied to simulate more complex flow phenomena in street canyons with two different building configurations. The results indicated that the flow at rooftop of buildings might not be assumed parallel to the ground as some numerical modelers did. A counter-clockwise rotating vortex may be found in street canyons with an inflow from the left to right. In addition, increasing building height can increase velocity fluctuations in the street canyon under certain circumstances, which facilitate pollutant dispersion. At high Reynolds numbers, the flow regimes in street canyons do not change with inflow velocity.

Scilab software as an alternative low-cost computing in solving the linear equations problem

NASA Astrophysics Data System (ADS)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

Some results on numerical methods for hyperbolic conservation laws

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

Yang Huanan.

1989-01-01

This dissertation contains some results on the numerical solutions of hyperbolic conservation laws. (1) The author introduced an artificial compression method as a correction to the basic ENO schemes. The method successfully prevents contact discontinuities from being smeared. This is achieved by increasing the slopes of the ENO reconstructions in such a way that the essentially non-oscillatory property of the schemes is kept. He analyzes the non-oscillatory property of the new artificial compression method by applying it to the UNO scheme which is a second order accurate ENO scheme, and proves that the resulting scheme is indeed non-oscillatory. Extensive 1-Dmore » numerical results and some preliminary 2-D ones are provided to show the strong performance of the method. (2) He combines the ENO schemes and the centered difference schemes into self-adjusting hybrid schemes which will be called the localized ENO schemes. At or near the jumps, he uses the ENO schemes with the field by field decompositions, otherwise he simply uses the centered difference schemes without the field by field decompositions. The method involves a new interpolation analysis. In the numerical experiments on several standard test problems, the quality of the numerical results of this method is close to that of the pure ENO results. The localized ENO schemes can be equipped with the above artificial compression method. In this way, he dramatically improves the resolutions of the contact discontinuities at very little additional costs. (3) He introduces a space-time mesh refinement method for time dependent problems.« less

Modeling of Convective-Stratiform Precipitation Processes: Sensitivity to Partitioning Methods and Numerical Advection Schemes

NASA Technical Reports Server (NTRS)

Lang, Steve; Tao, W.-K.; Simpson, J.; Ferrier, B.; Einaudi, Franco (Technical Monitor)

2001-01-01

Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional numerical simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different numerical advection schemes: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced numerous shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.

A wall interference assessment/correction system

NASA Technical Reports Server (NTRS)

Lo, Ching F.; Ulbrich, N.; Sickles, W. L.; Qian, Cathy X.

1992-01-01

A Wall Signature method, the Hackett method, has been selected to be adapted for the 12-ft Wind Tunnel wall interference assessment/correction (WIAC) system in the present phase. This method uses limited measurements of the static pressure at the wall, in conjunction with the solid wall boundary condition, to determine the strength and distribution of singularities representing the test article. The singularities are used in turn for estimating wall interferences at the model location. The Wall Signature method will be formulated for application to the unique geometry of the 12-ft Tunnel. The development and implementation of a working prototype will be completed, delivered and documented with a software manual. The WIAC code will be validated by conducting numerically simulated experiments rather than actual wind tunnel experiments. The simulations will be used to generate both free-air and confined wind-tunnel flow fields for each of the test articles over a range of test configurations. Specifically, the pressure signature at the test section wall will be computed for the tunnel case to provide the simulated 'measured' data. These data will serve as the input for the WIAC method-Wall Signature method. The performance of the WIAC method then may be evaluated by comparing the corrected parameters with those for the free-air simulation. Each set of wind tunnel/test article numerical simulations provides data to validate the WIAC method. A numerical wind tunnel test simulation is initiated to validate the WIAC methods developed in the project. In the present reported period, the blockage correction has been developed and implemented for a rectangular tunnel as well as the 12-ft Pressure Tunnel. An improved wall interference assessment and correction method for three-dimensional wind tunnel testing is presented in the appendix.

[Correlation of substrate structure and hydraulic characteristics in subsurface flow constructed wetlands].

PubMed

Bai, Shao-Yuan; Song, Zhi-Xin; Ding, Yan-Li; You, Shao-Hong; He, Shan

2014-02-01

The correlation of substrate structure and hydraulic characteristics was studied by numerical simulation combined with experimental method. The numerical simulation results showed that the permeability coefficient of matrix had a great influence on hydraulic efficiency in subsurface flow constructed wetlands. The filler with a high permeability coefficient had a worse flow field distribution in the constructed wetland with single layer structure. The layered substrate structure with the filler permeability coefficient increased from surface to bottom could avoid the short-circuited flow and dead-zones, and thus, increased the hydraulic efficiency. Two parallel pilot-scale constructed wetlands were built according to the numerical simulation results, and tracer experiments were conducted to validate the simulation results. The tracer experiment result showed that hydraulic characteristics in the layered constructed wetland were obviously better than that in the single layer system, and the substrate effective utilization rates were 0.87 and 0.49, respectively. It was appeared that numerical simulation would be favorable for substrate structure optimization in subsurface flow constructed wetlands.

Numerical calculation of primary slot leakage inductance of a Single-sided HTS linear induction motor used for linear metro

NASA Astrophysics Data System (ADS)

Li, Dong; Wen, Yinghong; Li, Weili; Fang, Jin; Cao, Junci; Zhang, Xiaochen; Lv, Gang

2017-03-01

In the paper, the numerical method calculating asymmetric primary slot leakage inductances of Single-sided High-Temperature Superconducting (HTS) Linear Induction Motor (HTS LIM) is presented. The mathematical and geometric models of three-dimensional nonlinear transient electromagnetic field are established and the boundary conditions are also given. The established model is solved by time-stepping Finite Element Method (FEM). Then, the three-phase asymmetric primary slot leakage inductances under different operation conditions are calculated by using the obtained electromagnetic field distribution. The influences of the special effects such as longitudinal end effects, transversal edge effects, etc. on the primary slot leakage inductance are investigated. The presented numerical method is validated by experiments carried out on a 3.5 kW prototype with copper wires which has the same structures with the HTS LIM.

Numerical tilting compensation in microscopy based on wavefront sensing using transport of intensity equation method

NASA Astrophysics Data System (ADS)

Hu, Junbao; Meng, Xin; Wei, Qi; Kong, Yan; Jiang, Zhilong; Xue, Liang; Liu, Fei; Liu, Cheng; Wang, Shouyu

2018-03-01

Wide-field microscopy is commonly used for sample observations in biological research and medical diagnosis. However, the tilting error induced by the oblique location of the image recorder or the sample, as well as the inclination of the optical path often deteriorates the imaging quality. In order to eliminate the tilting in microscopy, a numerical tilting compensation technique based on wavefront sensing using transport of intensity equation method is proposed in this paper. Both the provided numerical simulations and practical experiments prove that the proposed technique not only accurately determines the tilting angle with simple setup and procedures, but also compensates the tilting error for imaging quality improvement even in the large tilting cases. Considering its simple systems and operations, as well as image quality improvement capability, it is believed the proposed method can be applied for tilting compensation in the optical microscopy.

Evaluation of the Faraday angle by numerical methods and comparison with the Tore Supra and JET polarimeter electronics.

PubMed

Brault, C; Gil, C; Boboc, A; Spuig, P

2011-04-01

On the Tore Supra tokamak, a far infrared polarimeter diagnostic has been routinely used for diagnosing the current density by measuring the Faraday rotation angle. A high precision of measurement is needed to correctly reconstruct the current profile. To reach this precision, electronics used to compute the phase and the amplitude of the detected signals must have a good resilience to the noise in the measurement. In this article, the analogue card's response to the noise coming from the detectors and their impact on the Faraday angle measurements are analyzed, and we present numerical methods to calculate the phase and the amplitude. These validations have been done using real signals acquired by Tore Supra and JET experiments. These methods have been developed to be used in real-time in the future numerical cards that will replace the Tore Supra present analogue ones. © 2011 American Institute of Physics

Direct numerical simulation of transitional and turbulent flow over a heated flat plate using finite-difference schemes

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.

1995-01-01

This report deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux, were shown to compare well with experiment. The results indicate that the essential features of the transition process have been captured. The numerical method used here can be applied to complex geometries in a straightforward manner.

Infrared thermography applied to the study of heated and solar pavement: from numerical modeling to small scale laboratory experiments

NASA Astrophysics Data System (ADS)

Le Touz, N.; Toullier, T.; Dumoulin, J.

2017-05-01

The present study addresses the thermal behaviour of a modified pavement structure to prevent icing at its surface in adverse winter time conditions or overheating in hot summer conditions. First a multi-physic model based on infinite elements method was built to predict the evolution of the surface temperature. In a second time, laboratory experiments on small specimen were carried out and the surface temperature was monitored by infrared thermography. Results obtained are analyzed and performances of the numerical model for real scale outdoor application are discussed. Finally conclusion and perspectives are proposed.

User Experience in Digital Games: Differences between Laboratory and Home

ERIC Educational Resources Information Center

Takatalo, Jari; Hakkinen, Jukka; Kaistinen, Jyrki; Nyman, Gote

2011-01-01

Playing entertainment computer, video, and portable games, namely, digital games, is receiving more and more attention in academic research. Games are studied in different situations with numerous methods, but little is known about if and how the playing situation affects the user experience (UX) in games. In addition, it is hard to understand and…

A High Order Discontinuous Galerkin Method for 2D Incompressible Flows

NASA Technical Reports Server (NTRS)

Liu, Jia-Guo; Shu, Chi-Wang

1999-01-01

In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.

Improving designer productivity

NASA Technical Reports Server (NTRS)

Hill, Gary C.

1992-01-01

Designer and design team productivity improves with skill, experience, and the tools available. The design process involves numerous trials and errors, analyses, refinements, and addition of details. Computerized tools have greatly speeded the analysis, and now new theories and methods, emerging under the label Artificial Intelligence (AI), are being used to automate skill and experience. These tools improve designer productivity by capturing experience, emulating recognized skillful designers, and making the essence of complex programs easier to grasp. This paper outlines the aircraft design process in today's technology and business climate, presenting some of the challenges ahead and some of the promising AI methods for meeting those challenges.

A characteristics-based method for solving the transport equation and its application to the process of mantle differentiation and continental root growth

NASA Astrophysics Data System (ADS)

de Smet, Jeroen H.; van den Berg, Arie P.; Vlaar, Nico J.; Yuen, David A.

2000-03-01

Purely advective transport of composition is of major importance in the Geosciences, and efficient and accurate solution methods are needed. A characteristics-based method is used to solve the transport equation. We employ a new hybrid interpolation scheme, which allows for the tuning of stability and accuracy through a threshold parameter ɛth. Stability is established by bilinear interpolations, and bicubic splines are used to maintain accuracy. With this scheme, numerical instabilities can be suppressed by allowing numerical diffusion to work in time and locally in space. The scheme can be applied efficiently for preliminary modelling purposes. This can be followed by detailed high-resolution experiments. First, the principal effects of this hybrid interpolation method are illustrated and some tests are presented for numerical solutions of the transport equation. Second, we illustrate that this approach works successfully for a previously developed continental evolution model for the convecting upper mantle. In this model the transport equation contains a source term, which describes the melt production in pressure-released partial melting. In this model, a characteristic phenomenon of small-scale melting diapirs is observed (De Smet et al.1998; De Smet et al. 1999). High-resolution experiments with grid cells down to 700m horizontally and 515m vertically result in highly detailed observations of the diapiric melting phenomenon.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

An Laudau-Lifschitz theory based algorithm on calculating post-buckling configuration of a rod buckling in elastic media

NASA Astrophysics Data System (ADS)

Huang, Shicheng; Tan, Likun; Hu, Nan; Grover, Hannah; Chu, Kevin; Chen, Zi

This reserach introduces a new numerical approach of calculating the post-buckling configuration of a thin rod embedded in elastic media. The theoretical base is the governing ODEs describing the balance of forces and moments, the length conservation, and the physics of bending and twisting by Laudau and Lifschitz. The numerical methods applied in the calculation are continuation method and Newton's method of iteration in combination with spectrum method. To the authors' knowledge, it is the first trial of directly applying the L-L theory to numerically studying the phenomenon of rod buckling in elastic medium. This method accounts for nonlinearity of geometry, thus is capable of calculating large deformation. The stability of this method is another advantage achieved by expressing the governing equations in a set of first-order derivative form. The wave length, amplitude, and decay effect all agree with the experiment without any further assumptions. This program can be applied to different occasions with varying stiffness of the elastic medai and rigidity of the rod.

A methodology for designing aircraft to low sonic boom constraints

NASA Technical Reports Server (NTRS)

Mack, Robert J.; Needleman, Kathy E.

1991-01-01

A method for designing conceptual supersonic cruise aircraft to meet low sonic boom requirements is outlined and described. The aircraft design is guided through a systematic evolution from initial three view drawing to a final numerical model description, while the designer using the method controls the integration of low sonic boom, high supersonic aerodynamic efficiency, adequate low speed handling, and reasonable structure and materials technologies. Some experience in preliminary aircraft design and in the use of various analytical and numerical codes is required for integrating the volume and lift requirements throughout the design process.

A numerical model for simulation of bioremediation of hydrocarbons in aquifers

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

Munoz, J.F.; Irarrazaval, M.J.

1998-03-01

A numerical model was developed to describe the bioremediation of hydrocarbons in ground water aquifers considering aerobic degradation. The model solves the independent transport of three solutes (oxygen, hydrocarbons, and microorganisms) in ground water flow using the method of characteristics. Interactions between the three solutes, in which oxygen and hydrocarbons are consumed by microorganisms, are represented by Monod kinetics, solved using a Runge-Kutta method. Model simulations showed good correlation as compared with results of soil column experiments. The model was used to estimate the time needed to remediate the columns, which varied from one to two years.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

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

Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Meshfree and efficient modeling of swimming cells

NASA Astrophysics Data System (ADS)

Gallagher, Meurig T.; Smith, David J.

2018-05-01

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab® or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

Fast calculation of low altitude disturbing gravity for ballistics

NASA Astrophysics Data System (ADS)

Wang, Jianqiang; Wang, Fanghao; Tian, Shasha

2018-03-01

Fast calculation of disturbing gravity is a key technology in ballistics while spherical cap harmonic(SCH) theory can be used to solve this problem. By using adjusted spherical cap harmonic(ASCH) methods, the spherical cap coordinates are projected into a global coordinates, then the non-integer associated Legendre functions(ALF) of SCH are replaced by integer ALF of spherical harmonics(SH). This new method is called virtual spherical harmonics(VSH) and some numerical experiment were done to test the effect of VSH. The results of earth's gravity model were set as the theoretical observation, and the model of regional gravity field was constructed by the new method. Simulation results show that the approximated errors are less than 5mGal in the low altitude range of the central region. In addition, numerical experiments were conducted to compare the calculation speed of SH model, SCH model and VSH model, and the results show that the calculation speed of the VSH model is raised one order magnitude in a small scope.

A new fictitious domain approach for Stokes equation

NASA Astrophysics Data System (ADS)

Yang, Min

2017-10-01

The purpose of this paper is to present a new fictitious domain approach based on the Nietzsche’s method combining with a penalty method for the Stokes equation. This method allows for an easy and flexible handling of the geometrical aspects. Stability and a priori error estimate are proved. Finally, a numerical experiment is provided to verify the theoretical findings.

Encouraging Teacher Change within the Realities of School-Based Agricultural Education: Lessons from Teachers' Initial Use of Socioscientific Issues-Based Instruction

ERIC Educational Resources Information Center

Wilcox, Amie K.; Shoulders, Catherine W.; Myers, Brian E.

2014-01-01

Calls for increased interdisciplinary education have led to the development of numerous teaching methods designed to help teachers provide meaningful experiences for their students. However, methods of guiding teachers in the successful adoption of innovative teaching methods are not firmly set. This qualitative study sought to better understand…

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

NASA Astrophysics Data System (ADS)

Mier-Torrecilla, Monica; Geyer, Adelina; Phillips, Jeremy C.; Idelsohn, Sergio R.; Oñate, Eugenio

2010-05-01

In this work we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method (PFEM), a newly developed tool that combines the flexibility of particle-based methods with the accuracy of the finite element discretization. In order to test the applicability of PFEM to the study of negatively buoyant jets, we have compared the two-dimensional numerical results with experiments investigating the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter were varied to cover a wide range of Reynolds Re and Froude numbers Fr, such that 0.1 < Fr < 30, reproducing both weak and strong fountains in a laminar regime (8 < Re < 1350). Numerical results, together with the experimental observations, allow us to describe three different fountain behaviors that have not been previously reported. Based on the Re and Fr values for the numerical and experimental simulations, we have built a regime map to define how these values may control the occurrence of each of the observed flow types. Whereas the Fr number itself provides a prediction of the maximum penetration height of the jet, its combination with the Re number provides a prediction of the flow behavior for a specific nozzle diameter and injection velocity. Conclusive remarks concerning the dynamics of negatively buoyant jets may be applied later on to several geological situations, e.g. the flow structure of a fully submerged subaqueous eruptive vent discharging magma or the replenishment of magma chambers in the Earth's crust.

The computation of thermo-chemical nonequilibrium hypersonic flows

NASA Technical Reports Server (NTRS)

Candler, Graham

1989-01-01

Several conceptual designs for vehicles that would fly in the atmosphere at hypersonic speeds have been developed recently. For the proposed flight conditions the air in the shock layer that envelops the body is at a sufficiently high temperature to cause chemical reaction, vibrational excitation, and ionization. However, these processes occur at finite rates which, when coupled with large convection speeds, cause the gas to be removed from thermo-chemical equilibrium. This non-ideal behavior affects the aerothermal loading on the vehicle and has ramifications in its design. A numerical method to solve the equations that describe these types of flows in 2-D was developed. The state of the gas is represented with seven chemical species, a separate vibrational temperature for each diatomic species, an electron translational temperature, and a mass-average translational-rotational temperature for the heavy particles. The equations for this gas model are solved numerically in a fully coupled fashion using an implicit finite volume time-marching technique. Gauss-Seidel line-relaxation is used to reduce the cost of the solution and flux-dependent differencing is employed to maintain stability. The numerical method was tested against several experiments. The calculated bow shock wave detachment on a sphere and two cones was compared to those measured in ground testing facilities. The computed peak electron number density on a sphere-cone was compared to that measured in a flight test. In each case the results from the numerical method were in excellent agreement with experiment. The technique was used to predict the aerothermal loads on an Aeroassisted Orbital Transfer Vehicle including radiative heating. These results indicate that the current physical model of high temperature air is appropriate and that the numerical algorithm is capable of treating this class of flows.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

Transonic Symposium: Theory, Application, and Experiment, volume 1, part 2

NASA Technical Reports Server (NTRS)

Foughner, Jerome T., Jr. (Compiler)

1989-01-01

In order to assess the state of the art in transonic flow disciplines and to glimpse at future directions, NASA-Langley held a Transonic Symposium. Emphasis was placed on steady, three dimensional external, transonic flow and its simulation, both numerically and experimentally. The symposium included technical sessions on wind tunnel and flight experiments; computational fluid dynamic applications; inviscid methods and grid generation; viscous methods and boundary layer stability; and wind tunnel techniques and wall interference. This, being volume 1, is unclassified.

GPU accelerated manifold correction method for spinning compact binaries

NASA Astrophysics Data System (ADS)

Ran, Chong-xi; Liu, Song; Zhong, Shuang-ying

2018-04-01

The graphics processing unit (GPU) acceleration of the manifold correction algorithm based on the compute unified device architecture (CUDA) technology is designed to simulate the dynamic evolution of the Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries. The feasibility and the efficiency of parallel computation on GPU have been confirmed by various numerical experiments. The numerical comparisons show that the accuracy on GPU execution of manifold corrections method has a good agreement with the execution of codes on merely central processing unit (CPU-based) method. The acceleration ability when the codes are implemented on GPU can increase enormously through the use of shared memory and register optimization techniques without additional hardware costs, implying that the speedup is nearly 13 times as compared with the codes executed on CPU for phase space scan (including 314 × 314 orbits). In addition, GPU-accelerated manifold correction method is used to numerically study how dynamics are affected by the spin-induced quadrupole-monopole interaction for black hole binary system.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Computational method for exact frequency-dependent rays on the basis of the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Protasov, M.; Gadylshin, K.

2017-07-01

A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analysed and compared with classical ray theory and with the method of finite-difference modelling for the first time. In this paper, we study the dependence of these rays on the frequency of signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones that are impenetrable for classical rays.

Numerical experiment for ultrasonic-measurement-integrated simulation of three-dimensional unsteady blood flow.

PubMed

Funamoto, Kenichi; Hayase, Toshiyuki; Saijo, Yoshifumi; Yambe, Tomoyuki

2008-08-01

Integration of ultrasonic measurement and numerical simulation is a possible way to break through limitations of existing methods for obtaining complete information on hemodynamics. We herein propose Ultrasonic-Measurement-Integrated (UMI) simulation, in which feedback signals based on the optimal estimation of errors in the velocity vector determined by measured and computed Doppler velocities at feedback points are added to the governing equations. With an eye towards practical implementation of UMI simulation with real measurement data, its efficiency for three-dimensional unsteady blood flow analysis and a method for treating low time resolution of ultrasonic measurement were investigated by a numerical experiment dealing with complicated blood flow in an aneurysm. Even when simplified boundary conditions were applied, the UMI simulation reduced the errors of velocity and pressure to 31% and 53% in the feedback domain which covered the aneurysm, respectively. Local maximum wall shear stress was estimated, showing both the proper position and the value with 1% deviance. A properly designed intermittent feedback applied only at the time when measurement data were obtained had the same computational accuracy as feedback applied at every computational time step. Hence, this feedback method is a possible solution to overcome the insufficient time resolution of ultrasonic measurement.

Study on launch scheme of space-net capturing system.

PubMed

Gao, Qingyu; Zhang, Qingbin; Feng, Zhiwei; Tang, Qiangang

2017-01-01

With the continuous progress in active debris-removal technology, scientists are increasingly concerned about the concept of space-net capturing system. The space-net capturing system is a long-range-launch flexible capture system, which has great potential to capture non-cooperative targets such as inactive satellites and upper stages. In this work, the launch scheme is studied by experiment and simulation, including two-step ejection and multi-point-traction analyses. The numerical model of the tether/net is based on finite element method and is verified by full-scale ground experiment. The results of the ground experiment and numerical simulation show that the two-step ejection and six-point traction scheme of the space-net system is superior to the traditional one-step ejection and four-point traction launch scheme.

Study on launch scheme of space-net capturing system

PubMed Central

Zhang, Qingbin; Feng, Zhiwei; Tang, Qiangang

2017-01-01

With the continuous progress in active debris-removal technology, scientists are increasingly concerned about the concept of space-net capturing system. The space-net capturing system is a long-range-launch flexible capture system, which has great potential to capture non-cooperative targets such as inactive satellites and upper stages. In this work, the launch scheme is studied by experiment and simulation, including two-step ejection and multi-point-traction analyses. The numerical model of the tether/net is based on finite element method and is verified by full-scale ground experiment. The results of the ground experiment and numerical simulation show that the two-step ejection and six-point traction scheme of the space-net system is superior to the traditional one-step ejection and four-point traction launch scheme. PMID:28877187

Study on magnetic circuit of moving magnet linear compressor

NASA Astrophysics Data System (ADS)

Xia, Ming; Chen, Xiaoping; Chen, Jun

2015-05-01

The moving magnet linear compressors are very popular in the tactical miniature stirling cryocoolers. The magnetic circuit of LFC3600 moving magnet linear compressor, manufactured by Kunming institute of Physics, was studied in this study. Three methods of the analysis theory, numerical calculation and experiment study were applied in the analysis process. The calculated formula of magnetic reluctance and magnetomotive force were given in theoretical analysis model. The magnetic flux density and magnetic flux line were analyzed in numerical analysis model. A testing method was designed to test the magnetic flux density of the linear compressor. When the piston of the motor was in the equilibrium position, the value of the magnetic flux density was at the maximum of 0.27T. The results were almost equal to the ones from numerical analysis.

Experimental and numerical characterization of expanded glass granules

NASA Astrophysics Data System (ADS)

Chaudry, Mohsin Ali; Woitzik, Christian; Düster, Alexander; Wriggers, Peter

2018-07-01

In this paper, the material response of expanded glass granules at different scales and under different boundary conditions is investigated. At grain scale, single particle tests can be used to determine properties like Young's modulus or crushing strength. With experiments like triaxial and oedometer tests, it is possible to examine the bulk mechanical behaviour of the granular material. Our experimental investigation is complemented by a numerical simulation where the discrete element method is used to compute the mechanical behaviour of such materials. In order to improve the simulation quality, effects such as rolling resistance, inelastic behaviour, damage, and crushing are also included in the discrete element method. Furthermore, the variation of the material properties of granules is modelled by a statistical distribution and included in our numerical simulation.

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

Bogdanov, Yu. I., E-mail: bogdanov-yurii@inbox.ru; Avosopyants, G. V.; Belinskii, L. V.

We describe a new method for reconstructing the quantum state of the electromagnetic field from the results of mutually complementary optical quadrature measurements. This method is based on the root approach and displaces squeezed Fock states are used as the basis. Theoretical analysis and numerical experiments demonstrate the considerable advantage of the developed tools over those described in the literature.

Bayesian-based estimation of acoustic surface impedance: Finite difference frequency domain approach.

PubMed

Bockman, Alexander; Fackler, Cameron; Xiang, Ning

2015-04-01

Acoustic performance for an interior requires an accurate description of the boundary materials' surface acoustic impedance. Analytical methods may be applied to a small class of test geometries, but inverse numerical methods provide greater flexibility. The parameter estimation problem requires minimizing prediction vice observed acoustic field pressure. The Bayesian-network sampling approach presented here mitigates other methods' susceptibility to noise inherent to the experiment, model, and numerics. A geometry agnostic method is developed here and its parameter estimation performance is demonstrated for an air-backed micro-perforated panel in an impedance tube. Good agreement is found with predictions from the ISO standard two-microphone, impedance-tube method, and a theoretical model for the material. Data by-products exclusive to a Bayesian approach are analyzed to assess sensitivity of the method to nuisance parameters.

Resolved-particle simulation by the Physalis method: Enhancements and new capabilities

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

Sierakowski, Adam J., E-mail: sierakowski@jhu.edu; Prosperetti, Andrea; Faculty of Science and Technology and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede

2016-03-15

We present enhancements and new capabilities of the Physalis method for simulating disperse multiphase flows using particle-resolved simulation. The current work enhances the previous method by incorporating a new type of pressure-Poisson solver that couples with a new Physalis particle pressure boundary condition scheme and a new particle interior treatment to significantly improve overall numerical efficiency. Further, we implement a more efficient method of calculating the Physalis scalar products and incorporate short-range particle interaction models. We provide validation and benchmarking for the Physalis method against experiments of a sedimenting particle and of normal wall collisions. We conclude with an illustrativemore » simulation of 2048 particles sedimenting in a duct. In the appendix, we present a complete and self-consistent description of the analytical development and numerical methods.« less

Investigation of Multiphase Flow in a Packed Bed Reactor Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Lian, Yongsheng; Motil, Brian; Rame, Enrique

2016-01-01

In this paper we study the two-phase flow phenomena in a packed bed reactor using an integrated experimental and numerical method. The cylindrical bed is filled with uniformly sized spheres. In the experiment water and air are injected into the bed simultaneously. The pressure distribution along the bed will be measured. The numerical simulation is based on a two-phase flow solver which solves the Navier-Stokes equations on Cartesian grids. A novel coupled level set and moment of fluid method is used to construct the interface. A sequential method is used to position spheres in the cylinder. Preliminary experimental results showed that the tested flow rates resulted in pulse flow. The numerical simulation revealed that air bubbles could merge into larger bubbles and also could break up into smaller bubbles to pass through the pores in the bed. Preliminary results showed that flow passed through regions where the porosity is high. Comparison between the experimental and numerical results in terms of pressure distributions at different flow injection rates will be conducted. Comparison of flow phenomena under terrestrial gravity and microgravity will be made.

Towards an Airframe Noise Prediction Methodology: Survey of Current Approaches

NASA Technical Reports Server (NTRS)

Farassat, Fereidoun; Casper, Jay H.

2006-01-01

In this paper, we present a critical survey of the current airframe noise (AFN) prediction methodologies. Four methodologies are recognized. These are the fully analytic method, CFD combined with the acoustic analogy, the semi-empirical method and fully numerical method. It is argued that for the immediate need of the aircraft industry, the semi-empirical method based on recent high quality acoustic database is the best available method. The method based on CFD and the Ffowcs William- Hawkings (FW-H) equation with penetrable data surface (FW-Hpds ) has advanced considerably and much experience has been gained in its use. However, more research is needed in the near future particularly in the area of turbulence simulation. The fully numerical method will take longer to reach maturity. Based on the current trends, it is predicted that this method will eventually develop into the method of choice. Both the turbulence simulation and propagation methods need to develop more for this method to become useful. Nonetheless, the authors propose that the method based on a combination of numerical and analytical techniques, e.g., CFD combined with FW-H equation, should also be worked on. In this effort, the current symbolic algebra software will allow more analytical approaches to be incorporated into AFN prediction methods.

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

Forward-facing cavity and opposing jet combined thermal protection system

NASA Astrophysics Data System (ADS)

Lu, H. B.; Liu, W. Q.

2012-12-01

This paper focuses on the design of a forward-facing cavity and opposing jet combined configuration for thermal protection system (TPS) of hypersonic vehicles. The cooling efficiency of the combined TPS was investigated numerically, and the numerical method was validated by the related experiment in the open literature. The flow field parameters, aerodynamic force, and surface heat flux distribution were obtained. The detailed numerical results show that this kind of combined TPS has an excellent impact on cooling the nose-tip, and it is suitable for the thermal protection of hypersonic vehicles which require long-range and time to cruise.

Hot forming of composite prepreg: Numerical analyses

NASA Astrophysics Data System (ADS)

Guzman-Maldonado, Eduardo; Hamila, Nahiène; Boisse, Philippe; El Azzouzi, Khalid; Tardif, Xavier; Moro, Tanguy; Chatel, Sylvain; Fideu, Paulin

2017-10-01

The work presented here is part of the "FORBANS" project about the Hot Drape Forming (HDF) process consisting of unidirectional prepregs laminates. To ensure a fine comprehension of this process a combination strategy between experiment and numerical analysis is adopted. This paper is focused on the numerical analysis using the finite element method (FEM) with a hyperelastic constitutive law. Each prepreg layer is modelled by shell elements. These elements consider the tension, in-plane shear and bending behaviour of the ply at different temperatures. The contact/friction during the forming process is taken into account using forward increment Lagrange multipliers.

A novel hybrid scattering order-dependent variance reduction method for Monte Carlo simulations of radiative transfer in cloudy atmosphere

NASA Astrophysics Data System (ADS)

Wang, Zhen; Cui, Shengcheng; Yang, Jun; Gao, Haiyang; Liu, Chao; Zhang, Zhibo

2017-03-01

We present a novel hybrid scattering order-dependent variance reduction method to accelerate the convergence rate in both forward and backward Monte Carlo radiative transfer simulations involving highly forward-peaked scattering phase function. This method is built upon a newly developed theoretical framework that not only unifies both forward and backward radiative transfer in scattering-order-dependent integral equation, but also generalizes the variance reduction formalism in a wide range of simulation scenarios. In previous studies, variance reduction is achieved either by using the scattering phase function forward truncation technique or the target directional importance sampling technique. Our method combines both of them. A novel feature of our method is that all the tuning parameters used for phase function truncation and importance sampling techniques at each order of scattering are automatically optimized by the scattering order-dependent numerical evaluation experiments. To make such experiments feasible, we present a new scattering order sampling algorithm by remodeling integral radiative transfer kernel for the phase function truncation method. The presented method has been implemented in our Multiple-Scaling-based Cloudy Atmospheric Radiative Transfer (MSCART) model for validation and evaluation. The main advantage of the method is that it greatly improves the trade-off between numerical efficiency and accuracy order by order.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

PubMed Central

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-01-01

Abstract. Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method. PMID:28464120

A hybrid method combining the surface integral equation method and ray tracing for the numerical simulation of high frequency diffraction involved in ultrasonic NDT

NASA Astrophysics Data System (ADS)

Bonnet, M.; Collino, F.; Demaldent, E.; Imperiale, A.; Pesudo, L.

2018-05-01

Ultrasonic Non-Destructive Testing (US NDT) has become widely used in various fields of applications to probe media. Exploiting the surface measurements of the ultrasonic incident waves echoes after their propagation through the medium, it allows to detect potential defects (cracks and inhomogeneities) and characterize the medium. The understanding and interpretation of those experimental measurements is performed with the help of numerical modeling and simulations. However, classical numerical methods can become computationally very expensive for the simulation of wave propagation in the high frequency regime. On the other hand, asymptotic techniques are better suited to model high frequency scattering over large distances but nevertheless do not allow accurate simulation of complex diffraction phenomena. Thus, neither numerical nor asymptotic methods can individually solve high frequency diffraction problems in large media, as those involved in UNDT controls, both quickly and accurately, but their advantages and limitations are complementary. Here we propose a hybrid strategy coupling the surface integral equation method and the ray tracing method to simulate high frequency diffraction under speed and accuracy constraints. This strategy is general and applicable to simulate diffraction phenomena in acoustic or elastodynamic media. We provide its implementation and investigate its performances for the 2D acoustic diffraction problem. The main features of this hybrid method are described and results of 2D computational experiments discussed.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

Isentropic Compression up to 200 KBars for LX 04, Numerical Simulations and Comparison with Experiments

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

Lefrancois, A.; Hare, D.; L'Eplattenier, P.

2006-02-13

Isentropic compression experiments and numerical simulations on LX-04 (HMX / Viton 85/15) were performed respectively at Z accelerator facility from Sandia National Laboratory and at Lawrence Livermore National Laboratory in order to study the isentrope and associated Hugoniot of this HE. 2D and 3D configurations have been calculated here to test the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the ICE Z shot 1067 on LX 04. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. Themore » Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

Mode I Fracture Toughness of Rock - Intrinsic Property or Pressure-Dependent?

NASA Astrophysics Data System (ADS)

Stoeckhert, F.; Brenne, S.; Molenda, M.; Alber, M.

2016-12-01

The mode I fracture toughness of rock is usually regarded as an intrinsic material parameter independent of pressure. However, most fracture toughness laboratory tests are conducted only at ambient pressure. To investigate fracture toughness of rock under elevated pressures, sleeve fracturing laboratory experiments were conducted with various rock types and a new numerical method was developed for the evaluation of these experiments. The sleeve fracturing experiments involve rock cores with central axial boreholes that are placed in a Hoek triaxial pressure cell to apply an isostatic confining pressure. A polymere tube is pressurized inside these hollow rock cylinders until they fail by tensile fracturing. Numerical simulations incorporating fracture mechanical models are used to obtain a relation between tensile fracture propagation and injection pressure. These simulations indicate that the magnitude of the injection pressure at specimen failure is only depending on the fracture toughness of the tested material, the specimen dimensions and the magnitude of external loading. The latter two are known parameters in the experiments. Thus, the fracture toughness can be calculated from the injection pressure recorded at specimen breakdown. All specimens had a borehole diameter to outer diameter ratio of about 1:10 with outer diameters of 40 and 62 mm. The length of the specimens was about two times the diameter. Maximum external loading was 7.5 MPa corresponding to maximum injection pressures at specimen breakdown of about 100 MPa. The sample set tested in this work includes Permian and Carboniferous sandstones, Jurassic limestones, Triassic marble, Permian volcanic rocks and Devonian slate from Central Europe. The fracture toughness values determined from the sleeve fracturing experiments without confinement using the new numerical method were found to be in good agreement with those from Chevron bend testing according to the ISRM suggested methods. At elevated confining pressures, the results indicate a significant positive correlation between fracture toughness and confining pressure for most tested rock types.

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere

NASA Astrophysics Data System (ADS)

Blakely, Christopher D.

This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Daily, Michael; Baker, Nathan A.

2015-05-07

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates. Results: The numerical method is first verified in simple systems and thenmore » applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

A New Runge-Kutta Discontinuous Galerkin Method with Conservation Constraint to Improve CFL Condition for Solving Conservation Laws

PubMed Central

Xu, Zhiliang; Chen, Xu-Yan; Liu, Yingjie

2014-01-01

We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [17, 33] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method. PMID:25414520

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

NASA Astrophysics Data System (ADS)

Medl'a, Matej; Mikula, Karol; Čunderlík, Róbert; Macák, Marek

2018-01-01

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth's topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth's surface. It is based on an evolution of a surface, which approximates the Earth's topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth's surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth's topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows

NASA Astrophysics Data System (ADS)

Suzuki, Yukihito

2018-03-01

A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn-Hilliard and Allen-Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.

Steepest descent method implementation on unconstrained optimization problem using C++ program

NASA Astrophysics Data System (ADS)

Napitupulu, H.; Sukono; Mohd, I. Bin; Hidayat, Y.; Supian, S.

2018-03-01

Steepest Descent is known as the simplest gradient method. Recently, many researches are done to obtain the appropriate step size in order to reduce the objective function value progressively. In this paper, the properties of steepest descent method from literatures are reviewed together with advantages and disadvantages of each step size procedure. The development of steepest descent method due to its step size procedure is discussed. In order to test the performance of each step size, we run a steepest descent procedure in C++ program. We implemented it to unconstrained optimization test problem with two variables, then we compare the numerical results of each step size procedure. Based on the numerical experiment, we conclude the general computational features and weaknesses of each procedure in each case of problem.

Detection of Orbital Debris Collision Risks for the Automated Transfer Vehicle

NASA Technical Reports Server (NTRS)

Peret, L.; Legendre, P.; Delavault, S.; Martin, T.

2007-01-01

In this paper, we present a general collision risk assessment method, which has been applied through numerical simulations to the Automated Transfer Vehicle (ATV) case. During ATV ascent towards the International Space Station, close approaches between the ATV and objects of the USSTRACOM catalog will be monitored through collision rosk assessment. Usually, collision risk assessment relies on an exclusion volume or a probability threshold method. Probability methods are more effective than exclusion volumes but require accurate covariance data. In this work, we propose to use a criterion defined by an adaptive exclusion area. This criterion does not require any probability calculation but is more effective than exclusion volume methods as demonstrated by our numerical experiments. The results of these studies, when confirmed and finalized, will be used for the ATV operations.

A multilevel finite element method for Fredholm integral eigenvalue problems

NASA Astrophysics Data System (ADS)

Xie, Hehu; Zhou, Tao

2015-12-01

In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.

Unconstrained handwritten numeral recognition based on radial basis competitive and cooperative networks with spatio-temporal feature representation.

PubMed

Lee, S; Pan, J J

1996-01-01

This paper presents a new approach to representation and recognition of handwritten numerals. The approach first transforms a two-dimensional (2-D) spatial representation of a numeral into a three-dimensional (3-D) spatio-temporal representation by identifying the tracing sequence based on a set of heuristic rules acting as transformation operators. A multiresolution critical-point segmentation method is then proposed to extract local feature points, at varying degrees of scale and coarseness. A new neural network architecture, referred to as radial-basis competitive and cooperative network (RCCN), is presented especially for handwritten numeral recognition. RCCN is a globally competitive and locally cooperative network with the capability of self-organizing hidden units to progressively achieve desired network performance, and functions as a universal approximator of arbitrary input-output mappings. Three types of RCCNs are explored: input-space RCCN (IRCCN), output-space RCCN (ORCCN), and bidirectional RCCN (BRCCN). Experiments against handwritten zip code numerals acquired by the U.S. Postal Service indicated that the proposed method is robust in terms of variations, deformations, transformations, and corruption, achieving about 97% recognition rate.

Climate Prediction for Brazil's Nordeste: Performance of Empirical and Numerical Modeling Methods.

NASA Astrophysics Data System (ADS)

Moura, Antonio Divino; Hastenrath, Stefan

2004-07-01

Comparisons of performance of climate forecast methods require consistency in the predictand and a long common reference period. For Brazil's Nordeste, empirical methods developed at the University of Wisconsin use preseason (October January) rainfall and January indices of the fields of meridional wind component and sea surface temperature (SST) in the tropical Atlantic and the equatorial Pacific as input to stepwise multiple regression and neural networking. These are used to predict the March June rainfall at a network of 27 stations. An experiment at the International Research Institute for Climate Prediction, Columbia University, with a numerical model (ECHAM4.5) used global SST information through February to predict the March June rainfall at three grid points in the Nordeste. The predictands for the empirical and numerical model forecasts are correlated at +0.96, and the period common to the independent portion of record of the empirical prediction and the numerical modeling is 1968 99. Over this period, predicted versus observed rainfall are evaluated in terms of correlation, root-mean-square error, absolute error, and bias. Performance is high for both approaches. Numerical modeling produces a correlation of +0.68, moderate errors, and strong negative bias. For the empirical methods, errors and bias are small, and correlations of +0.73 and +0.82 are reached between predicted and observed rainfall.

The potential impact of scatterometry on oceanography - A wave forecasting case

NASA Technical Reports Server (NTRS)

Cane, M. A.; Cardone, V. J.

1981-01-01

A series of observing system simulation experiments have been performed in order to assess the potential impact of marine surface wind data on numerical weather prediction. In addition to conventional data, the experiments simulated the time-continuous assimilation of remotely sensed marine surface wind or temperature sounding data. The wind data were fabricated directly for model grid points intercepted by a Seasat-1 scatterometer swath and were assimilated into the lowest active level (945 mb) of the model using a localized successive correction method. It is shown that Seasat wind data can greatly improve numerical weather forecasts due to better definition of specific features. The case of the QE II storm is examined.

Dynamical spin structure factors of α-RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-03-01

Honeycomb-lattice magnet α-RuCl3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.

Utilization of Low Gravity Environment for Measuring Liquid Viscosity

NASA Technical Reports Server (NTRS)

Antar, Basil N.; Ethridge, Edwin

1998-01-01

The method of drop coalescence is used for determining the viscosity of highly viscous undercooled liquids. Low gravity environment is necessary in order to allow for examining large volumes affording much higher accuracy for the viscosity calculations than possible for smaller volumes available under 1 - g conditions. The drop coalescence method is preferred over the drop oscillation technique since the latter method can only be applied for liquids with vanishingly small viscosities. The technique developed relies on both the highly accurate solution of the Navier-Stokes equations as well as on data from experiments conducted in near zero gravity environment. Results are presented for method validation experiments recently performed on board the NASA/KC-135 aircraft. While the numerical solution was produced using the Boundary Element Method. In these tests the viscosity of a highly viscous liquid, glycerine at room temperature, was determined using the liquid coalescence method. The results from these experiments will be discussed.

Study of Wind Effects on Unique Buildings

NASA Astrophysics Data System (ADS)

Olenkov, V.; Puzyrev, P.

2017-11-01

The article deals with a numerical simulation of wind effects on the building of the Church of the Intercession of the Holy Virgin in the village Bulzi of the Chelyabinsk region. We presented a calculation algorithm and obtained pressure fields, velocity fields and the fields of kinetic energy of a wind stream, as well as streamlines. Computational fluid dynamic (CFD) evolved three decades ago at the interfaces of calculus mathematics and theoretical hydromechanics and has become a separate branch of science the subject of which is a numerical simulation of different fluid and gas flows as well as the solution of arising problems with the help of methods that involve computer systems. This scientific field which is of a great practical value is intensively developing. The increase in CFD-calculations is caused by the improvement of computer technologies, creation of multipurpose easy-to-use CFD-packagers that are available to a wide group of researchers and cope with various tasks. Such programs are not only competitive in comparison with physical experiments but sometimes they provide the only opportunity to answer the research questions. The following advantages of computer simulation can be pointed out: a) Reduction in time spent on design and development of a model in comparison with a real experiment (variation of boundary conditions). b) Numerical experiment allows for the simulation of conditions that are not reproducible with environmental tests (use of ideal gas as environment). c) Use of computational gas dynamics methods provides a researcher with a complete and ample information that is necessary to fully describe different processes of the experiment. d) Economic efficiency of computer calculations is more attractive than an experiment. e) Possibility to modify a computational model which ensures efficient timing (change of the sizes of wall layer cells in accordance with the chosen turbulence model).

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.

Effects of solid barriers on dispersion of roadway emissions

EPA Science Inventory

Several studies have found that exposure to traffic-generated air pollution is associated with several adverse health effects. Field studies, laboratory experiments, and numerical simulations indicate that roadside barriers represent a practical method of mitigating the impact of...

Numerically pricing American options under the generalized mixed fractional Brownian motion model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying

2016-06-01

In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.

The shallow water equations as a hybrid flow model for the numerical and experimental analysis of hydro power stations

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

Ostermann, Lars; Seidel, Christian

2015-03-10

The numerical analysis of hydro power stations is an important method of the hydraulic design and is used for the development and optimisation of hydro power stations in addition to the experiments with the physical submodel of a full model in the hydraulic laboratory. For the numerical analysis, 2D and 3D models are appropriate and commonly used.The 2D models refer mainly to the shallow water equations (SWE), since for this flow model a large experience on a wide field of applications for the flow analysis of numerous problems in hydraulic engineering already exists. Often, the flow model is verified bymore » in situ measurements. In order to consider 3D flow phenomena close to singularities like weirs, hydro power stations etc. the development of a hybrid fluid model is advantageous to improve the quality and significance of the global model. Here, an extended hybrid flow model based on the principle of the SWE is presented. The hybrid flow model directly links the numerical model with the experimental data, which may originate from physical full models, physical submodels and in-situ measurements. Hence a wide field of application of the hybrid model emerges including the improvement of numerical models and the strong coupling of numerical and experimental analysis.« less

Improving designer productivity. [artificial intelligence

NASA Technical Reports Server (NTRS)

Hill, Gary C.

1992-01-01

Designer and design team productivity improves with skill, experience, and the tools available. The design process involves numerous trials and errors, analyses, refinements, and addition of details. Computerized tools have greatly speeded the analysis, and now new theories and methods, emerging under the label Artificial Intelligence (AI), are being used to automate skill and experience. These tools improve designer productivity by capturing experience, emulating recognized skillful designers, and making the essence of complex programs easier to grasp. This paper outlines the aircraft design process in today's technology and business climate, presenting some of the challenges ahead and some of the promising AI methods for meeting these challenges.

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element method

PubMed Central

Bolis, A; Cantwell, C D; Kirby, R M; Sherwin, S J

2014-01-01

We investigate the relative performance of a second-order Adams–Bashforth scheme and second-order and fourth-order Runge–Kutta schemes when time stepping a 2D linear advection problem discretised using a spectral/hp element technique for a range of different mesh sizes and polynomial orders. Numerical experiments explore the effects of short (two wavelengths) and long (32 wavelengths) time integration for sets of uniform and non-uniform meshes. The choice of time-integration scheme and discretisation together fixes a CFL limit that imposes a restriction on the maximum time step, which can be taken to ensure numerical stability. The number of steps, together with the order of the scheme, affects not only the runtime but also the accuracy of the solution. Through numerical experiments, we systematically highlight the relative effects of spatial resolution and choice of time integration on performance and provide general guidelines on how best to achieve the minimal execution time in order to obtain a prescribed solution accuracy. The significant role played by higher polynomial orders in reducing CPU time while preserving accuracy becomes more evident, especially for uniform meshes, compared with what has been typically considered when studying this type of problem.© 2014. The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons, Ltd. PMID:25892840

Phospholipid dynamics in graphene of different topologies: predictive modeling

NASA Astrophysics Data System (ADS)

Glukhova, O. E.; Slepchenkov, M. M.

2017-02-01

The subject of our scientific interest is the dynamics of the phospholipid molecules into a corrugated graphene sheet. According to our assumption by changing the topology of graphene properly it is possible to find the ways for management of the selective localization of phospholipid molecules to form the desired configuration of these structures. We considered DPPC (dipalmitoylphosphatidylcholine) phospholipids, which are the part of cell membranes and lipoproteins. We investigated the behavior of the phospholipids on the graphene sheet consisting of 1710 atoms with the size of 6.9 nm along the zigzag edge and 6.25 nm along the armchair edge. The numerical experiment was carried out using the original AMBER/AIREBO hybrid method with Lennard-Jones potential to describe the interaction between unbound atoms of different structures. The temperature was maintained at 300 K during the numerical experiment. All numerical experiments were performed using KVAZAR software system. We considered several cases of corrugated graphene with different width and dept of the corrugation. Special attention in our work was paid to the orientation of the phospholipids in the plane of graphene sheet.

Probing numerical Laplace inversion methods for two and three-site molecular exchange between interconnected pore structures.

PubMed

Silletta, Emilia V; Franzoni, María B; Monti, Gustavo A; Acosta, Rodolfo H

2018-01-01

Two-dimension (2D) Nuclear Magnetic Resonance relaxometry experiments are a powerful tool extensively used to probe the interaction among different pore structures, mostly in inorganic systems. The analysis of the collected experimental data generally consists of a 2D numerical inversion of time-domain data where T 2 -T 2 maps are generated. Through the years, different algorithms for the numerical inversion have been proposed. In this paper, two different algorithms for numerical inversion are tested and compared under different conditions of exchange dynamics; the method based on Butler-Reeds-Dawson (BRD) algorithm and the fast-iterative shrinkage-thresholding algorithm (FISTA) method. By constructing a theoretical model, the algorithms were tested for a two- and three-site porous media, varying the exchange rates parameters, the pore sizes and the signal to noise ratio. In order to test the methods under realistic experimental conditions, a challenging organic system was chosen. The molecular exchange rates of water confined in hierarchical porous polymeric networks were obtained, for a two- and three-site porous media. Data processed with the BRD method was found to be accurate only under certain conditions of the exchange parameters, while data processed with the FISTA method is precise for all the studied parameters, except when SNR conditions are extreme. Copyright © 2017 Elsevier Inc. All rights reserved.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

Variational method for integrating radial gradient field

NASA Astrophysics Data System (ADS)

Legarda-Saenz, Ricardo; Brito-Loeza, Carlos; Rivera, Mariano; Espinosa-Romero, Arturo

2014-12-01

We propose a variational method for integrating information obtained from circular fringe pattern. The proposed method is a suitable choice for objects with radial symmetry. First, we analyze the information contained in the fringe pattern captured by the experimental setup and then move to formulate the problem of recovering the wavefront using techniques from calculus of variations. The performance of the method is demonstrated by numerical experiments with both synthetic and real data.

Morphodynamic Responses of a River-Floodplain System to a Chute Cutoff: Numerical Experiments to Investigate the Role of Multiple Active Factors

NASA Astrophysics Data System (ADS)

Li, Z.; Garcia, M. H.

2017-12-01

Unlike neck cutoffs, which are caused by meander migration to an over-mature stage, a chute cutoff is governed by many more factors. A chute cutoff always occurs when there is over-bank flow caused by floods. During this process, the river-floodplain system characteristics will determine the newly formed cutoff channel location and extent. Hence, a comprehensive study of the influence which different active factors have on a cutoff channel is necessary. Numerical experiments are well suited in this case because of the possibility of studying a large number of scenarios and also the practical and econocmical challenges of collecting high quality data during floods in the field. Numerical simulations were performed using the open TELEMAC-MASCARET modeling suite, which can solve the two-dimensional Shallow Water Equations, the three-dimensional, Reynolds-averaged Navier-Stokes equations (RANS). It can also be coupled with sediment transport equations. It is implemented on unstructured meshes using the Finite Element Method (FEM). The modeling results show the great detail the morphodynamic response attributed to each active factor (flow magnitude, sediment erosive properties, channel sinuosity, etc.), as well as paving the way and showing how to use the dimensionless relations obtained with the numerical experiments.

Modeling of Powder Bed Manufacturing Defects

NASA Astrophysics Data System (ADS)

Mindt, H.-W.; Desmaison, O.; Megahed, M.; Peralta, A.; Neumann, J.

2018-01-01

Powder bed additive manufacturing offers unmatched capabilities. The deposition resolution achieved is extremely high enabling the production of innovative functional products and materials. Achieving the desired final quality is, however, hampered by many potential defects that have to be managed in due course of the manufacturing process. Defects observed in products manufactured via powder bed fusion have been studied experimentally. In this effort we have relied on experiments reported in the literature and—when experimental data were not sufficient—we have performed additional experiments providing an extended foundation for defect analysis. There is large interest in reducing the effort and cost of additive manufacturing process qualification and certification using integrated computational material engineering. A prerequisite is, however, that numerical methods can indeed capture defects. A multiscale multiphysics platform is developed and applied to predict and explain the origin of several defects that have been observed experimentally during laser-based powder bed fusion processes. The models utilized are briefly introduced. The ability of the models to capture the observed defects is verified. The root cause of the defects is explained by analyzing the numerical results thus confirming the ability of numerical methods to provide a foundation for rapid process qualification.

Studies in astronomical time series analysis. I - Modeling random processes in the time domain

NASA Technical Reports Server (NTRS)

Scargle, J. D.

1981-01-01

Several random process models in the time domain are defined and discussed. Attention is given to the moving average model, the autoregressive model, and relationships between and combinations of these models. Consideration is then given to methods for investigating pulse structure, procedures of model construction, computational methods, and numerical experiments. A FORTRAN algorithm of time series analysis has been developed which is relatively stable numerically. Results of test cases are given to study the effect of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the light curve of the quasar 3C 272 is considered as an example.

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

PubMed Central

Sakamoto, Julia A.; Barrett, Harrison H.

2012-01-01

A method for determining the pupil phase distribution of an optical system is demonstrated. Coefficients in a wavefront expansion were estimated using likelihood methods, where the data consisted of multiple irradiance patterns near focus. Proof-of-principle results were obtained in both simulation and experiment. Large-aberration wavefronts were handled in the numerical study. Experimentally, we discuss the handling of nuisance parameters. Fisher information matrices, Cramér-Rao bounds, and likelihood surfaces are examined. ML estimates were obtained by simulated annealing to deal with numerous local extrema in the likelihood function. Rapid processing techniques were employed to reduce the computational time. PMID:22772282

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

NASA Astrophysics Data System (ADS)

Abert, Claas; Exl, Lukas; Bruckner, Florian; Drews, André; Suess, Dieter

2013-11-01

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Study of eigenfrequencies with the help of Prony's method

NASA Astrophysics Data System (ADS)

Drobakhin, O. O.; Olevskyi, O. V.; Olevskyi, V. I.

2017-10-01

Eigenfrequencies can be crucial in the design of a construction. They define many parameters that determine limit parameters of the structure. Exceeding these values can lead to the structural failure of an object. It is especially important in the design of structures which support heavy equipment or are subjected to the forces of airflow. One of the most effective ways to acquire the frequencies' values is a computer-based numerical simulation. The existing methods do not allow to acquire the whole range of needed parameters. It is well known that Prony's method, is highly effective for the investigation of dynamic processes. Thus, it is rational to adapt Prony's method for such investigation. The Prony method has advantage in comparison with other numerical schemes because it provides the possibility to process not only the results of numerical simulation, but also real experimental data. The research was carried out for a computer model of a steel plate. The input data was obtained by using the Dassault Systems SolidWorks computer package with the Simulation add-on. We investigated the acquired input data with the help of Prony's method. The result of the numerical experiment shows that Prony's method can be used to investigate the mechanical eigenfrequencies with good accuracy. The output of Prony's method not only contains the information about values of frequencies themselves, but also contains data regarding the amplitudes, initial phases and decaying factors of any given mode of oscillation, which can also be used in engineering.

Modal interactions due to friction in the nonlinear vibration response of the "Harmony" test structure: Experiments and simulations

NASA Astrophysics Data System (ADS)

Claeys, M.; Sinou, J.-J.; Lambelin, J.-P.; Todeschini, R.

2016-08-01

The nonlinear vibration response of an assembly with friction joints - named "Harmony" - is studied both experimentally and numerically. The experimental results exhibit a softening effect and an increase of dissipation with excitation level. Modal interactions due to friction are also evidenced. The numerical methodology proposed groups together well-known structural dynamic methods, including finite elements, substructuring, Harmonic Balance and continuation methods. On the one hand, the application of this methodology proves its capacity to treat a complex system where several friction movements occur at the same time. On the other hand, the main contribution of this paper is the experimental and numerical study of evidence of modal interactions due to friction. The simulation methodology succeeds in reproducing complex form of dynamic behavior such as these modal interactions.

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

Observations of experimental and numerical waveforms of piezoelectric signals generated in bovine cancellous bone by ultrasound waves

NASA Astrophysics Data System (ADS)

Hosokawa, Atsushi

2018-07-01

Experimental and numerical waveforms of piezoelectric signals generated in the bovine cancellous bone by ultrasound waves at 1.0 MHz were observed. The experimental observations were performed using a “piezoelectric cell (PE-cell)”, in which an air-saturated cancellous bone specimen was electrically shielded. The PE-cell was used to receive burst ultrasound waves. The numerical observations were performed using a piezoelectric finite-difference time-domain (PE-FDTD) method, which was an elastic FDTD method with piezoelectric constitutive equations. The cancellous bone model was reconstructed from the three-dimensional X-ray microcomputed tomographic image of the specimen used in the experiments. Both experimental and numerical results showed that the repetitive piezoelectric signals could be generated by the multireflected ultrasound waves within the cancellous bone specimen. Moreover, it was shown that the output piezoelectric signal in the PE-cell could be the overlap of the local signals in the trabecular elements at various depths (or thicknesses) in the cancellous bone specimen.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

Polarization-insensitive techniques for optical signal processing

NASA Astrophysics Data System (ADS)

Salem, Reza

2006-12-01

This thesis investigates polarization-insensitive methods for optical signal processing. Two signal processing techniques are studied: clock recovery based on two-photon absorption in silicon and demultiplexing based on cross-phase modulation in highly nonlinear fiber. The clock recovery system is tested at an 80 Gb/s data rate for both back-to-back and transmission experiments. The demultiplexer is tested at a 160 Gb/s data rate in a back-to-back experiment. We experimentally demonstrate methods for eliminating polarization dependence in both systems. Our experimental results are confirmed by theoretical and numerical analysis.

Development of Tsunami Numerical Model Considering the Disaster Debris such as Cars, Ships and Collapsed Buildings

NASA Astrophysics Data System (ADS)

Kozono, Y.; Takahashi, T.; Sakuraba, M.; Nojima, K.

2016-12-01

A lot of debris by tsunami, such as cars, ships and collapsed buildings were generated in the 2011 Tohoku tsunami. It is useful for rescue and recovery after tsunami disaster to predict the amount and final position of disaster debris. The transport form of disaster debris varies as drifting, rolling and sliding. These transport forms need to be considered comprehensively in tsunami simulation. In this study, we focused on the following three points. Firstly, the numerical model considering various transport forms of disaster debris was developed. The proposed numerical model was compared with the hydraulic experiment by Okubo et al. (2004) in order to verify transport on the bottom surface such as rolling and sliding. Secondly, a numerical experiment considering transporting on the bottom surface and drifting was studied. Finally, the numerical model was applied for Kesennuma city where serious damage occurred by the 2011 Tohoku tsunami. In this model, the influence of disaster debris was considered as tsunami flow energy loss. The hydraulic experiments conducted in a water tank which was 10 m long by 30 cm wide. The gate confined water in a storage tank, and acted as a wave generator. A slope was set at downstream section. The initial position of a block (width: 3.2 cm, density: 1.55 g/cm3) assuming the disaster debris was placed in front of the slope. The proposed numerical model simulated well the maximum transport distance and the final stop position of the block. In the second numerical experiment, the conditions were the same as the hydraulic experiment, except for the density of the block. The density was set to various values (from 0.30 to 4.20 g/cm3). This model was able to estimate various transport forms including drifting and sliding. In the numerical simulation of the 2011 Tohoku tsunami, the condition of buildings was modeled as follows: (i)the resistance on the bottom using Manning roughness coefficient (conventional method), and (ii)structure of buildings with collapsing and washing-away due to tsunami wave pressure. In this calculation, disaster debris of collapsed buildings, cars and ships was considered. As a result, the proposed model showed that it is necessary to take the disaster debris into account in order to predict tsunami inundation accurately.

An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data.

PubMed

Zhou, Yunyi; Tao, Chenyang; Lu, Wenlian; Feng, Jianfeng

2018-04-20

Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis. Copyright © 2018. Published by Elsevier B.V.

A flux splitting scheme with high-resolution and robustness for discontinuities

NASA Technical Reports Server (NTRS)

Wada, Yasuhiro; Liou, Meng-Sing

1994-01-01

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J. A.; Golberg, M. A.

1979-01-01

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

Numerical investigation of velocity slip and temperature jump effects on unsteady flow over a stretching permeable surface

NASA Astrophysics Data System (ADS)

Hosseini, E.; Loghmani, G. B.; Heydari, M.; Rashidi, M. M.

2017-02-01

In this paper, the boundary layer flow and heat transfer of unsteady flow over a porous accelerating stretching surface in the presence of the velocity slip and temperature jump effects are investigated numerically. A new effective collocation method based on rational Bernstein functions is applied to solve the governing system of nonlinear ordinary differential equations. This method solves the problem on the semi-infinite domain without truncating or transforming it to a finite domain. In addition, the presented method reduces the solution of the problem to the solution of a system of algebraic equations. Graphical and tabular results are presented to investigate the influence of the unsteadiness parameter A , Prandtl number Pr, suction parameter fw, velocity slip parameter γ and thermal slip parameter φ on the velocity and temperature profiles of the fluid. The numerical experiments are reported to show the accuracy and efficiency of the novel proposed computational procedure. Comparisons of present results are made with those obtained by previous works and show excellent agreement.

Numerical investigations of wake interactions of two wind turbines in tandem

NASA Astrophysics Data System (ADS)

Qian, Yaoru; Wang, Tongguang

2018-05-01

Aerodynamic performance and wake interactions between two wind turbine models under different layouts are investigated numerically using large eddy simulation in conjunction with actuator line method based on the “Blind Test” series wind tunnel experiments from Norwegian University of Science and Technology. Numerical results of the power and thrust coefficients of the two rotors and wake characteristics are in good agreement with the experimental measurements. Extended investigations emphasizing the influence of different layout arrangements on the downstream rotor performance and wake development are conducted. Results show that layout arrangements have great influence on the power and thrust prediction of the downstream turbine.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Experimental and numerical study on the strength of all-ceramic crowns

NASA Astrophysics Data System (ADS)

Lu, Chenglin; Zhang, Xiuyin; Zhang, Dongsheng

2008-11-01

Two types of sectioned tooth-like ceramic crowns (IPS Empress 2) were prepared along lingual-facial direction and the fracture process of crowns under contact load was directly monitored with the use of imaging system. The displacement filed resulted from digital image correlation indicate that the fracture mode of real crown is more complicated while the flat crown has the same rupture mode as described by other investigators. Meanwhile numerical simulation was also carried out to support the experiments. Stress distributions in individual layer and interface were presented. Results indicate that the presented experimental and numerical methods are efficient in studying the fracture mechanism of all-ceramic crowns.

A no-gold-standard technique for objective assessment of quantitative nuclear-medicine imaging methods

PubMed Central

Jha, Abhinav K; Caffo, Brian; Frey, Eric C

2016-01-01

The objective optimization and evaluation of nuclear-medicine quantitative imaging methods using patient data is highly desirable but often hindered by the lack of a gold standard. Previously, a regression-without-truth (RWT) approach has been proposed for evaluating quantitative imaging methods in the absence of a gold standard, but this approach implicitly assumes that bounds on the distribution of true values are known. Several quantitative imaging methods in nuclear-medicine imaging measure parameters where these bounds are not known, such as the activity concentration in an organ or the volume of a tumor. We extended upon the RWT approach to develop a no-gold-standard (NGS) technique for objectively evaluating such quantitative nuclear-medicine imaging methods with patient data in the absence of any ground truth. Using the parameters estimated with the NGS technique, a figure of merit, the noise-to-slope ratio (NSR), can be computed, which can rank the methods on the basis of precision. An issue with NGS evaluation techniques is the requirement of a large number of patient studies. To reduce this requirement, the proposed method explored the use of multiple quantitative measurements from the same patient, such as the activity concentration values from different organs in the same patient. The proposed technique was evaluated using rigorous numerical experiments and using data from realistic simulation studies. The numerical experiments demonstrated that the NSR was estimated accurately using the proposed NGS technique when the bounds on the distribution of true values were not precisely known, thus serving as a very reliable metric for ranking the methods on the basis of precision. In the realistic simulation study, the NGS technique was used to rank reconstruction methods for quantitative single-photon emission computed tomography (SPECT) based on their performance on the task of estimating the mean activity concentration within a known volume of interest. Results showed that the proposed technique provided accurate ranking of the reconstruction methods for 97.5% of the 50 noise realizations. Further, the technique was robust to the choice of evaluated reconstruction methods. The simulation study pointed to possible violations of the assumptions made in the NGS technique under clinical scenarios. However, numerical experiments indicated that the NGS technique was robust in ranking methods even when there was some degree of such violation. PMID:26982626

A no-gold-standard technique for objective assessment of quantitative nuclear-medicine imaging methods.

PubMed

Jha, Abhinav K; Caffo, Brian; Frey, Eric C

2016-04-07

The objective optimization and evaluation of nuclear-medicine quantitative imaging methods using patient data is highly desirable but often hindered by the lack of a gold standard. Previously, a regression-without-truth (RWT) approach has been proposed for evaluating quantitative imaging methods in the absence of a gold standard, but this approach implicitly assumes that bounds on the distribution of true values are known. Several quantitative imaging methods in nuclear-medicine imaging measure parameters where these bounds are not known, such as the activity concentration in an organ or the volume of a tumor. We extended upon the RWT approach to develop a no-gold-standard (NGS) technique for objectively evaluating such quantitative nuclear-medicine imaging methods with patient data in the absence of any ground truth. Using the parameters estimated with the NGS technique, a figure of merit, the noise-to-slope ratio (NSR), can be computed, which can rank the methods on the basis of precision. An issue with NGS evaluation techniques is the requirement of a large number of patient studies. To reduce this requirement, the proposed method explored the use of multiple quantitative measurements from the same patient, such as the activity concentration values from different organs in the same patient. The proposed technique was evaluated using rigorous numerical experiments and using data from realistic simulation studies. The numerical experiments demonstrated that the NSR was estimated accurately using the proposed NGS technique when the bounds on the distribution of true values were not precisely known, thus serving as a very reliable metric for ranking the methods on the basis of precision. In the realistic simulation study, the NGS technique was used to rank reconstruction methods for quantitative single-photon emission computed tomography (SPECT) based on their performance on the task of estimating the mean activity concentration within a known volume of interest. Results showed that the proposed technique provided accurate ranking of the reconstruction methods for 97.5% of the 50 noise realizations. Further, the technique was robust to the choice of evaluated reconstruction methods. The simulation study pointed to possible violations of the assumptions made in the NGS technique under clinical scenarios. However, numerical experiments indicated that the NGS technique was robust in ranking methods even when there was some degree of such violation.

Investigation of the Rock Fragmentation Process by a Single TBM Cutter Using a Voronoi Element-Based Numerical Manifold Method

NASA Astrophysics Data System (ADS)

Liu, Quansheng; Jiang, Yalong; Wu, Zhijun; Xu, Xiangyu; Liu, Qi

2018-04-01

In this study, a two-dimensional Voronoi element-based numerical manifold method (VE-NMM) is developed to analyze the granite fragmentation process by a single tunnel boring machine (TBM) cutter under different confining stresses. A Voronoi tessellation technique is adopted to generate the polygonal grain assemblage to approximate the microstructure of granite sample from the Gubei colliery of Huainan mining area in China. A modified interface contact model with cohesion and tensile strength is embedded into the numerical manifold method (NMM) to interpret the interactions between the rock grains. Numerical uniaxial compression and Brazilian splitting tests are first conducted to calibrate and validate the VE-NMM models based on the laboratory experiment results using a trial-and-error method. On this basis, numerical simulations of rock fragmentation by a single TBM cutter are conducted. The simulated crack initiation and propagation process as well as the indentation load-penetration depth behaviors in the numerical models accurately predict the laboratory indentation test results. The influence of confining stress on rock fragmentation is also investigated. Simulation results show that radial tensile cracks are more likely to be generated under a low confining stress, eventually coalescing into a major fracture along the loading axis. However, with the increase in confining stress, more side cracks initiate and coalesce, resulting in the formation of rock chips at the upper surface of the model. In addition, the peak indentation load also increases with the increasing confining stress, indicating that a higher thrust force is usually needed during the TBM boring process in deep tunnels.

Numerical simulation of mud erosion rate in sand-mud alternate layer and comparison with experiment

NASA Astrophysics Data System (ADS)

Yoshida, T.; Yamaguchi, T.; Oyama, H.; Sato, T.

2015-12-01

For gas production from methane hydrates in sand-mud alternate layers, depressurization method is expected as feasible. After methane hydrate is dissociated, gas and water flow in pore space. There is a concern about the erosion of mud surface and it may result in flow blockage that disturbs the gas production. As a part of a Japanese National hydrate research program (MH21, funded by METI), we developed a numerical simulation of water-induced mud erosion in pore-scale sand-mud domains to model such mud erosion. The size of which is of the order of 100 micro meter. Water flow is simulated using a lattice Boltzmann method (LBM) and mud surface is treated as solid boundary with arbitrary shape, which changes with time. Periodic boundary condition is adopted at the domain boundaries, except for the surface of mud layers and the upper side. Shear stress acting on the mud surface is calculated using a momentum-exchange method. Mud layer is eroded when the shear stress exceeds a threshold coined a critical shear stress. In this study, we compared the simulated mud erosion rate with experimental data acquired from an experiment using artificial sand-mud core. As a result, the simulated erosion rate agrees well with that of the experiment.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

Fully coupled methods for multiphase morphodynamics

NASA Astrophysics Data System (ADS)

Michoski, C.; Dawson, C.; Mirabito, C.; Kubatko, E. J.; Wirasaet, D.; Westerink, J. J.

2013-09-01

We present numerical methods for a system of equations consisting of the two dimensional Saint-Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge-Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge-Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments.

The meaning of vaguely quantified frequency response options on a quality of life scale depends on respondents’ medical status and age

PubMed Central

Schneider, Stefan; Stone, Arthur A.

2017-01-01

Purpose Self-report items in quality of life (QoL) scales commonly use vague quantifiers like “sometimes” or “often” to measure the frequency of health-related experiences. This study examined whether the meaning of such vaguely quantified response options differs depending on people’s medical status and age, which may undermine the validity of QoL group comparisons. Methods Respondents (n = 600) rated the frequency of positive and negative QoL experiences using vague quantifiers (never, rarely, sometimes, often, always) and provided open-ended numeric frequency counts for the same items. Negative binomial regression analyses examined whether the numeric frequencies associated with each vague quantifier differed between medical status (no vs. one or more medical conditions) and age (18–40 years vs. 60+ years) groups. Results Compared to respondents without a chronic condition, those with a medical condition assigned a higher numeric frequency to the same vague quantifiers for negative QoL experiences; this effect was not evident for positive QoL experiences. Older respondents’ numeric frequencies were more extreme (i.e., lower at the low end and somewhat higher at the high end of the response range) than those of younger respondents. After adjusting for these effects, differences in QoL became somewhat more pronounced between medical status groups, but not between age groups. Conclusions The results suggest that people with different medical backgrounds and age do not interpret vague frequency quantifiers on a QoL scale in the same way. Open-ended numeric frequency reports may be useful to detect and potentially correct for differences in the meaning of vague quantifiers. PMID:27071685

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

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

Kawaguchi, Tomoya; Liu, Yihua; Reiter, Anthony

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Modified Method of Adaptive Artificial Viscosity for Solution of Gas Dynamics Problems on Parallel Computer Systems

NASA Astrophysics Data System (ADS)

Popov, Igor; Sukov, Sergey

2018-02-01

A modification of the adaptive artificial viscosity (AAV) method is considered. This modification is based on one stage time approximation and is adopted to calculation of gasdynamics problems on unstructured grids with an arbitrary type of grid elements. The proposed numerical method has simplified logic, better performance and parallel efficiency compared to the implementation of the original AAV method. Computer experiments evidence the robustness and convergence of the method to difference solution.

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

DOE PAGES

Kawaguchi, Tomoya; Liu, Yihua; Reiter, Anthony; ...

2018-04-20

Here, a one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Numerical-graphical method for describing the creep of damaged highly filled polymer materials

NASA Astrophysics Data System (ADS)

Bykov, D. L.; Martynova, E. D.; Mel'nikov, V. P.

2015-09-01

A method for describing the creep behavior until fracture of a highly filled polymer material previously damaged in preliminary tests is proposed. The constitutive relations are the relations of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) [1]. The numerical-graphical method for identifying the functions occurring in NETAVEM, which was proposed in [2] for describing loading processes at a constant strain rate, is used here for the first time in creep theory. We use the results of experiments with undamaged and preliminary damaged specimens under the action of the same constant tensile loads. The creep kernel is determined in experiments with an undamaged specimen. The reduced time function contained in NETAVEM is determined from the position of points corresponding to the same values of strain on the creep curves of the damaged and undamaged specimens. An integral equation is solved to obtain the aging function, and then the viscosity function is determined. The knowledge of all functions contained in the constitutive relations permits solving the creep problem for products manufactured from a highly filled polymer material.

Surface electrical properties experiment. Part 2: Theory of radio-frequency interferometry in geophysical subsurface probing

NASA Technical Reports Server (NTRS)

Kong, J. A.; Tsang, L.

1974-01-01

The radiation fields due to a horizontal electric dipole laid on the surface of a stratified medium were calculated using a geometrical optics approximation, a modal approach, and direct numerical integration. The solutions were obtained from the reflection coefficient formulation and written in integral forms. The calculated interference patterns are compared in terms of the usefulness of the methods used to obtain them. Scattering effects are also discussed and all numerical results for anisotropic and isotropic cases are presented.

Thermal lattice BGK models for fluid dynamics

NASA Astrophysics Data System (ADS)

Huang, Jian

1998-11-01

As an alternative in modeling fluid dynamics, the Lattice Boltzmann method has attracted considerable attention. In this thesis, we shall present a general form of thermal Lattice BGK. This form can handle large differences in density, temperature, and high Mach number. This generalized method can easily model gases with different adiabatic index values. The numerical transport coefficients of this model are estimated both theoretically and numerically. Their dependency on the sizes of integration steps in time and space, and on the flow velocity and temperature, are studied and compared with other established CFD methods. This study shows that the numerical viscosity of the Lattice Boltzmann method depends linearly on the space interval, and on the flow velocity as well for supersonic flow. This indicates this method's limitation in modeling high Reynolds number compressible thermal flow. On the other hand, the Lattice Boltzmann method shows promise in modeling micro-flows, i.e., gas flows in micron-sized devices. A two-dimensional code has been developed based on the conventional thermal lattice BGK model, with some modifications and extensions for micro- flows and wall-fluid interactions. Pressure-driven micro- channel flow has been simulated. Results are compared with experiments and simulations using other methods, such as a spectral element code using slip boundary condition with Navier-Stokes equations and a Direct Simulation Monte Carlo (DSMC) method.

Rank-k modification methods for recursive least squares problems

NASA Astrophysics Data System (ADS)

Olszanskyj, Serge; Lebak, James; Bojanczyk, Adam

1994-09-01

In least squares problems, it is often desired to solve the same problem repeatedly but with several rows of the data either added, deleted, or both. Methods for quickly solving a problem after adding or deleting one row of data at a time are known. In this paper we introduce fundamental rank-k updating and downdating methods and show how extensions of rank-1 downdating methods based on LINPACK, Corrected Semi-Normal Equations (CSNE), and Gram-Schmidt factorizations, as well as new rank-k downdating methods, can all be derived from these fundamental results. We then analyze the cost of each new algorithm and make comparisons tok applications of the corresponding rank-1 algorithms. We provide experimental results comparing the numerical accuracy of the various algorithms, paying particular attention to the downdating methods, due to their potential numerical difficulties for ill-conditioned problems. We then discuss the computation involved for each downdating method, measured in terms of operation counts and BLAS calls. Finally, we provide serial execution timing results for these algorithms, noting preferable points for improvement and optimization. From our experiments we conclude that the Gram-Schmidt methods perform best in terms of numerical accuracy, but may be too costly for serial execution for large problems.

Error Analysis of p-Version Discontinuous Galerkin Method for Heat Transfer in Built-up Structures

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki; Bey, Kim S.

2004-01-01

The purpose of this paper is to provide an error analysis for the p-version of the discontinuous Galerkin finite element method for heat transfer in built-up structures. As a special case of the results in this paper, a theoretical error estimate for the numerical experiments recently conducted by James Tomey is obtained.

A new measurement method of coatings thickness based on lock-in thermography

NASA Astrophysics Data System (ADS)

Zhang, Jin-Yu; Meng, Xiang-bin; Ma, Yong-chao

2016-05-01

Coatings have been widely used in modern industry and it plays an important role. Coatings thickness is directly related to the performance of the functional coatings, therefore, rapid and accurate coatings thickness inspection has great significance. Existing coatings thickness measurement method is difficult to achieve fast and accurate on-site non-destructive coatings inspection due to cost, accuracy, destruction during inspection and other reasons. This paper starts from the introduction of the principle of lock-in thermography, and then performs an in-depth study on the application of lock-in thermography in coatings inspection through numerical modeling and analysis. The numerical analysis helps explore the relationship between coatings thickness and phase, and the relationship lays the foundation for accurate calculation of coatings thickness. The author sets up a lock-in thermography inspection system and uses thermal barrier coatings specimens to conduct an experiment. The specimen coatings thickness is measured and calibrated to verify the quantitative inspection. Experiment results show that the lock-in thermography method can perform fast coatings inspection and the inspection accuracy is about 95%. Therefore, the method can meet the field testing requirements for engineering projects.

Taylor bubbles at high viscosity ratios: experiments and numerical simulations

NASA Astrophysics Data System (ADS)

Hewakandamby, Buddhika; Hasan, Abbas; Azzopardi, Barry; Xie, Zhihua; Pain, Chris; Matar, Omar

2015-11-01

The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube, often occurring in gas-liquid slug flows in many industrial applications, particularly oil and gas production. The objective of this study is to investigate the fluid dynamics of three-dimensional Taylor bubble rising in highly viscous silicone oil in a vertical pipe. An adaptive unstructured mesh modelling framework is adopted here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rising and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a `volume of fluid'-type method for the interface-capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Experimental results for the Taylor bubble shape and rise velocity are presented, together with numerical results for the dynamics of the bubbles. A comparison of the simulation predictions with experimental data available in the literature is also presented to demonstrate the capabilities of our numerical method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Numerical study on flow over stepped spillway using Lagrangian method

NASA Astrophysics Data System (ADS)

Wang, Junmin; Fu, Lei; Xu, Haibo; Jin, Yeechung

2018-02-01

Flow over stepped spillway has been studied for centuries, due to its unstable and the characteristics of cavity, the simulation of this type of spillway flow is always difficult. Most of the early studies of flow over stepped spillway are based on experiment, while in the recent decades, numerical studies of flow over stepped spillway draw most of the researchers’ attentions due to its simplicity and efficiency. In this study, a new Lagrangian based particle method is introduced to reproduce the phenomenon of flow over stepped spillway, the inherent advantages of this particle based method provide a convincing free surface and velocity profiles compared with previous experimental data. The capacity of this new method is proved and it is anticipated to be an alternative tool of traditional mesh based method in environmental engineering field such as the simulation of flow over stepped spillway.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

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

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less

A parallel orbital-updating based plane-wave basis method for electronic structure calculations

NASA Astrophysics Data System (ADS)

Pan, Yan; Dai, Xiaoying; de Gironcoli, Stefano; Gong, Xin-Gao; Rignanese, Gian-Marco; Zhou, Aihui

2017-11-01

Motivated by the recently proposed parallel orbital-updating approach in real space method [1], we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

Path suppression of strongly collapsing bubbles at finite and low Reynolds numbers.

PubMed

Rechiman, Ludmila M; Dellavale, Damián; Bonetto, Fabián J

2013-06-01

We study, numerically and experimentally, three different methods to suppress the trajectories of strongly collapsing and sonoluminescent bubbles in a highly viscous sulfuric acid solution. A new numerical scheme based on the window method is proposed to account for the history force acting on a spherical bubble with variable radius. We could quantify the history force, which is not negligible in comparison with the primary Bjerknes force in this type of problem, and results are in agreement with the classical primary Bjerknes force trapping threshold analysis. Moreover, the present numerical implementation reproduces the spatial behavior associated with the positional and path instability of sonoluminescent argon bubbles in strongly gassed and highly degassed sulfuric acid solutions. Finally, the model allows us to demonstrate that spatially stationary bubbles driven by biharmonic excitation could be obtained with a different mode from the one used in previous reported experiments.

Numerical simulation of heat transfer and fluid flow in laser drilling of metals

NASA Astrophysics Data System (ADS)

Zhang, Tingzhong; Ni, Chenyin; Zhou, Jie; Zhang, Hongchao; Shen, Zhonghua; Ni, Xiaowu; Lu, Jian

2015-05-01

Laser processing as laser drilling, laser welding and laser cutting, etc. is rather important in modern manufacture, and the interaction of laser and matter is a complex phenomenon which should be detailed studied in order to increase the manufacture efficiency and quality. In this paper, a two-dimensional transient numerical model was developed to study the temperature field and molten pool size during pulsed laser keyhole drilling. The volume-of-fluid method was employed to track free surfaces, and melting and evaporation enthalpy, recoil pressure, surface tension, and energy loss due to evaporating materials were considered in this model. Besides, the enthalpy-porosity technique was also applied to account for the latent heat during melting and solidification. Temperature fields and melt pool size were numerically simulated via finite element method. Moreover, the effectiveness of the developed computational procedure had been confirmed by experiments.

Experiments and Simulations of Fully Hydro-Mechanically Coupled Response of Rough Fractures Exposed to High-Pressure Fluid Injection

NASA Astrophysics Data System (ADS)

Vogler, D.; Settgast, R. R.; Annavarapu, C.; Madonna, C.; Bayer, P.; Amann, F.

2018-02-01

In this work, we present the application of a fully coupled hydro-mechanical method to investigate the effect of fracture heterogeneity on fluid flow through fractures at the laboratory scale. Experimental and numerical studies of fracture closure behavior in the presence of heterogeneous mechanical and hydraulic properties are presented. We compare the results of two sets of laboratory experiments on granodiorite specimens against numerical simulations in order to investigate the mechanical fracture closure and the hydro-mechanical effects, respectively. The model captures fracture closure behavior and predicts a nonlinear increase in fluid injection pressure with loading. Results from this study indicate that the heterogeneous aperture distributions measured for experiment specimens can be used as model input for a local cubic law model in a heterogeneous fracture to capture fracture closure behavior and corresponding fluid pressure response.

Free-decay time-domain modal identification for large space structures

NASA Technical Reports Server (NTRS)

Kim, Hyoung M.; Vanhorn, David A.; Doiron, Harold H.

1992-01-01

Concept definition studies for the Modal Identification Experiment (MIE), a proposed space flight experiment for the Space Station Freedom (SSF), have demonstrated advantages and compatibility of free-decay time-domain modal identification techniques with the on-orbit operational constraints of large space structures. Since practical experience with modal identification using actual free-decay responses of large space structures is very limited, several numerical and test data reduction studies were conducted. Major issues and solutions were addressed, including closely-spaced modes, wide frequency range of interest, data acquisition errors, sampling delay, excitation limitations, nonlinearities, and unknown disturbances during free-decay data acquisition. The data processing strategies developed in these studies were applied to numerical simulations of the MIE, test data from a deployable truss, and launch vehicle flight data. Results of these studies indicate free-decay time-domain modal identification methods can provide accurate modal parameters necessary to characterize the structural dynamics of large space structures.

Practical witness for electronic coherences

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

Johnson, Allan S.; Department of Physics, Imperial College London, London; Yuen-Zhou, Joel

2014-12-28

The origin of the coherences in two-dimensional spectroscopy of photosynthetic complexes remains disputed. Recently, it has been shown that in the ultrashort-pulse limit, oscillations in a frequency-integrated pump-probe signal correspond exclusively to electronic coherences, and thus such experiments can be used to form a test for electronic vs. vibrational oscillations in such systems. Here, we demonstrate a method for practically implementing such a test, whereby pump-probe signals are taken at several different pulse durations and used to extrapolate to the ultrashort-pulse limit. We present analytic and numerical results determining requirements for pulse durations and the optimal choice of pulse centralmore » frequency, which can be determined from an absorption spectrum. Our results suggest that for numerous systems, the required experiment could be implemented by many ultrafast spectroscopy laboratories using pulses of tens of femtoseconds in duration. Such experiments could resolve the standing debate over the nature of coherences in photosynthetic complexes.« less

Similarity Theory of Withdrawn Water Temperature Experiment

PubMed Central

2015-01-01

Selective withdrawal from a thermal stratified reservoir has been widely utilized in managing reservoir water withdrawal. Besides theoretical analysis and numerical simulation, model test was also necessary in studying the temperature of withdrawn water. However, information on the similarity theory of the withdrawn water temperature model remains lacking. Considering flow features of selective withdrawal, the similarity theory of the withdrawn water temperature model was analyzed theoretically based on the modification of governing equations, the Boussinesq approximation, and some simplifications. The similarity conditions between the model and the prototype were suggested. The conversion of withdrawn water temperature between the model and the prototype was proposed. Meanwhile, the fundamental theory of temperature distribution conversion was firstly proposed, which could significantly improve the experiment efficiency when the basic temperature of the model was different from the prototype. Based on the similarity theory, an experiment was performed on the withdrawn water temperature which was verified by numerical method. PMID:26065020

The Mpemba effect: When can hot water freeze faster than cold?

NASA Astrophysics Data System (ADS)

Jeng, Monwhea

2006-06-01

We review the Mpemba effect, where initially hot water freezes faster than initially cold water. Although the effect might appear impossible, it has been observed in numerous experiments and was discussed by Aristotle, Francis Bacon, Roger Bacon, and Descartes. It has a rich and fascinating history, including the story of the secondary school student, Erasto Mpemba, who reintroduced the effect to the twentieth century scientific community. The phenomenon is simple to describe and illustrates numerous important issues about the scientific method: the role of skepticism in scientific inquiry, the influence of theory on experiment and observation, the need for precision in the statement of a scientific hypothesis, and the nature of falsifiability. Proposed theoretical mechanisms for the Mpemba effect and the results of contemporary experiments on the phenomenon are surveyed. The observation that hot water pipes are more likely to burst than cold water pipes is also discussed.

Practical witness for electronic coherences.

PubMed

Johnson, Allan S; Yuen-Zhou, Joel; Aspuru-Guzik, Alán; Krich, Jacob J

2014-12-28

The origin of the coherences in two-dimensional spectroscopy of photosynthetic complexes remains disputed. Recently, it has been shown that in the ultrashort-pulse limit, oscillations in a frequency-integrated pump-probe signal correspond exclusively to electronic coherences, and thus such experiments can be used to form a test for electronic vs. vibrational oscillations in such systems. Here, we demonstrate a method for practically implementing such a test, whereby pump-probe signals are taken at several different pulse durations and used to extrapolate to the ultrashort-pulse limit. We present analytic and numerical results determining requirements for pulse durations and the optimal choice of pulse central frequency, which can be determined from an absorption spectrum. Our results suggest that for numerous systems, the required experiment could be implemented by many ultrafast spectroscopy laboratories using pulses of tens of femtoseconds in duration. Such experiments could resolve the standing debate over the nature of coherences in photosynthetic complexes.

Effects of viscosity on shock-induced damping of an initial sinusoidal disturbance

NASA Astrophysics Data System (ADS)

Ma, Xiaojuan; Liu, Fusheng; Jing, Fuqian

2010-05-01

A lack of reliable data treatment method has been for several decades the bottleneck of viscosity measurement by disturbance amplitude damping method of shock waves. In this work the finite difference method is firstly applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in inviscid and viscous flow. When water shocked to 15 GPa is taken as an example, the main results are as follows: (1) For inviscid and lower viscous flows the numerical method gives results in good agreement with the analytic solutions under the condition of small disturbance ( a 0/ λ=0.02); (2) For the flow of viscosity beyond 200 Pa s ( η = κ) the analytic solution is found to overestimate obviously the effects of viscosity. It is attributed to the unreal pre-conditions of analytic solution by Miller and Ahrens; (3) The present numerical method provides an effective tool with more confidence to overcome the bottleneck of data treatment when the effects of higher viscosity in experiments of Sakharov and flyer impact are expected to be analyzed, because it can in principle simulate the development of shock waves in flows with larger disturbance amplitude, higher viscosity, and complicated initial flow.

Limited-memory trust-region methods for sparse relaxation

NASA Astrophysics Data System (ADS)

Adhikari, Lasith; DeGuchy, Omar; Erway, Jennifer B.; Lockhart, Shelby; Marcia, Roummel F.

2017-08-01

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and applying a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving computational time.

Errors incurred in profile reconstruction and methods for increasing inversion accuracies for occultation type measurements

NASA Technical Reports Server (NTRS)

Gross, S. H.; Pirraglia, J. A.

1972-01-01

A method for augmenting the occultation experiment is described for slightly refractive media. This method which permits separation of the components of the gradient of refractivity, appears applicable to most of the planets for a major portion of their atmospheres and ionospheres. The analytic theory is given, and the results of numerical tests with a radially and angularly varying model of an ionosphere are discussed.

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

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

Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

THz-waves channeling in a monolithic saddle-coil for Dynamic Nuclear Polarization enhanced NMR

NASA Astrophysics Data System (ADS)

Macor, A.; de Rijk, E.; Annino, G.; Alberti, S.; Ansermet, J.-Ph.

2011-10-01

A saddle coil manufactured by electric discharge machining (EDM) from a solid piece of copper has recently been realized at EPFL for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance experiments (DNP-NMR) at 9.4 T. The corresponding electromagnetic behavior of radio-frequency (400 MHz) and THz (263 GHz) waves were studied by numerical simulation in various measurement configurations. Moreover, we present an experimental method by which the results of the THz-wave numerical modeling are validated. On the basis of the good agreement between numerical and experimental results, we conducted by numerical simulation a systematic analysis on the influence of the coil geometry and of the sample properties on the THz-wave field, which is crucial in view of the optimization of DNP-NMR in solids.

Physical similarity or numerical representation counts in same-different, numerical comparison, physical comparison, and priming tasks?

PubMed

Zhang, Li; Xin, Ziqiang; Feng, Tingyong; Chen, Yinghe; Szűcs, Denes

2018-03-01

Recent studies have highlighted the fact that some tasks used to study symbolic number representations are confounded by judgments about physical similarity. Here, we investigated whether the contribution of physical similarity and numerical representation differed in the often-used symbolic same-different, numerical comparison, physical comparison, and priming tasks. Experiment 1 showed that subjective physical similarity was the best predictor of participants' performance in the same-different task, regardless of simultaneous or sequential presentation. Furthermore, the contribution of subjective physical similarity was larger in a simultaneous presentation than in a sequential presentation. Experiment 2 showed that only numerical representation was involved in numerical comparison. Experiment 3 showed that both subjective physical similarity and numerical representation contributed to participants' physical comparison performance. Finally, only numerical representation contributed to participants' performance in a priming task as revealed by Experiment 4. Taken together, the contribution of physical similarity and numerical representation depends on task demands. Performance primarily seems to rely on numerical properties in tasks that require explicit quantitative comparison judgments (physical or numerical), while physical stimulus properties exert an effect in the same-different task.

Advances in Optical Fiber-Based Faraday Rotation Diagnostics

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

White, A D; McHale, G B; Goerz, D A

2009-07-27

In the past two years, we have used optical fiber-based Faraday Rotation Diagnostics (FRDs) to measure pulsed currents on several dozen capacitively driven and explosively driven pulsed power experiments. We have made simplifications to the necessary hardware for quadrature-encoded polarization analysis, including development of an all-fiber analysis scheme. We have developed a numerical model that is useful for predicting and quantifying deviations from the ideal diagnostic response. We have developed a method of analyzing quadrature-encoded FRD data that is simple to perform and offers numerous advantages over several existing methods. When comparison has been possible, we have seen good agreementmore » with our FRDs and other current sensors.« less

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

Numerical experiments in homogeneous turbulence

NASA Technical Reports Server (NTRS)

Rogallo, R. S.

1981-01-01

The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.

A numerical study of mobility in thin films of fullerene derivatives.

PubMed

Mackenzie, Roderick C I; Frost, Jarvist M; Nelson, Jenny

2010-02-14

The effect of functional group size on the electron mobility in films of fullerene derivatives is investigated numerically. A series of four C(60) derivatives are formed by attaching saturated hydrocarbon chains to the C(60) cage via a methano bridge. For each of the derivatives investigated, molecular dynamics is used to generate a realistic material morphology. Quantum chemical methods are then used to calculate intermolecular charge transfer rates. Finally, Monte Carlo methods are used to simulate time-of-flight experiments and thus calculate the electron mobility. It is found that as the length of the aliphatic side chain increases, the configurational disorder increases and thus the mobility decreases.

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

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

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

2017-02-01

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

Modeling of Bulk Evaporation and Condensation

NASA Technical Reports Server (NTRS)

Anghaie, S.; Ding, Z.

1996-01-01

This report describes the modeling and mathematical formulation of the bulk evaporation and condensation involved in liquid-vapor phase change processes. An internal energy formulation, for these phase change processes that occur under the constraint of constant volume, was studied. Compared to the enthalpy formulation, the internal energy formulation has a more concise and compact form. The velocity and time scales of the interface movement were obtained through scaling analysis and verified by performing detailed numerical experiments. The convection effect induced by the density change was analyzed and found to be negligible compared to the conduction effect. Two iterative methods for updating the value of the vapor phase fraction, the energy based (E-based) and temperature based (T-based) methods, were investigated. Numerical experiments revealed that for the evaporation and condensation problems the E-based method is superior to the T-based method in terms of computational efficiency. The internal energy formulation and the E-based method were used to compute the bulk evaporation and condensation processes under different conditions. The evolution of the phase change processes was investigated. This work provided a basis for the modeling of thermal performance of multi-phase nuclear fuel elements under variable gravity conditions, in which the buoyancy convection due to gravity effects and internal heating are involved.

Immersed boundary lattice Boltzmann model based on multiple relaxation times

NASA Astrophysics Data System (ADS)

Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli

2012-01-01

As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.

Prediction of dynamic and aerodynamic characteristics of the centrifugal fan with forward curved blades

NASA Astrophysics Data System (ADS)

Polanský, Jiří; Kalmár, László; Gášpár, Roman

2013-12-01

The main aim of this paper is determine the centrifugal fan with forward curved blades aerodynamic characteristics based on numerical modeling. Three variants of geometry were investigated. The first, basic "A" variant contains 12 blades. The geometry of second "B" variant contains 12 blades and 12 semi-blades with optimal length [1]. The third, control variant "C" contains 24 blades without semi-blades. Numerical calculations were performed by CFD Ansys. Another aim of this paper is to compare results of the numerical simulation with results of approximate numerical procedure. Applied approximate numerical procedure [2] is designated to determine characteristics of the turbulent flow in the bladed space of a centrifugal-flow fan impeller. This numerical method is an extension of the hydro-dynamical cascade theory for incompressible and inviscid fluid flow. Paper also partially compares results from the numerical simulation and results from the experimental investigation. Acoustic phenomena observed during experiment, during numerical simulation manifested as deterioration of the calculation stability, residuals oscillation and thus also as a flow field oscillation. Pressure pulsations are evaluated by using frequency analysis for each variant and working condition.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

A simplified parsimonious higher order multivariate Markov chain model with new convergence condition

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a simplified parsimonious higher-order multivariate Markov chain model with new convergence condition. (TPHOMMCM-NCC). Moreover, estimation method of the parameters in TPHOMMCM-NCC is give. Numerical experiments illustrate the effectiveness of TPHOMMCM-NCC.

A Method for Large Eddy Simulation of Acoustic Combustion Instabilities

NASA Astrophysics Data System (ADS)

Wall, Clifton; Pierce, Charles; Moin, Parviz

2002-11-01

A method for performing Large Eddy Simulation of acoustic combustion instabilities is presented. By extending the low Mach number pressure correction method to the case of compressible flow, a numerical method is developed in which the Poisson equation for pressure is replaced by a Helmholtz equation. The method avoids the acoustic CFL condition by using implicit time advancement, leading to large efficiency gains at low Mach number. The method also avoids artificial damping of acoustic waves. The numerical method is attractive for the simulation of acoustic combustion instabilities, since these flows are typically at low Mach number, and the acoustic frequencies of interest are usually low. Both of these characteristics suggest the use of larger time steps than those allowed by an acoustic CFL condition. The turbulent combustion model used is the Combined Conserved Scalar/Level Set Flamelet model of Duchamp de Lageneste and Pitsch for partially premixed combustion. Comparison of LES results to the experiments of Besson et al will be presented.

The quasi-harmonic ultrasonic polar scan for material characterization: experiment and numerical modeling.

PubMed

Kersemans, Mathias; Martens, Arvid; Van Den Abeele, Koen; Degrieck, Joris; Pyl, Lincy; Zastavnik, Filip; Sol, Hugo; Van Paepegem, Wim

2015-04-01

Conventionally, the ultrasonic polar scan (UPS) records the amplitude or time-of-flight in transmission using short ultrasonic pulses for a wide range of incidence angles, resulting in a fingerprint of the critical bulk wave angles of the material at the insonified spot. Here, we investigate the use of quasi-harmonic ultrasound (bursts) in a polar scan experiment, both experimentally and numerically. It is shown that the nature of the fingerprint drastically changes, and reveals the positions of the leaky Lamb angles. To compare with experiments, both plane wave and bounded beam simulations have been performed based on the recursive stiffness matrix method. Whereas the plane wave computations yield a pure Lamb wave angle fingerprint, this is no longer valid for the more realistic case of a bounded beam. The experimental recordings are fully supported by the bounded beam simulations. To complement the traditional amplitude measurement, experimental and numerical investigations have been performed to record, predict and analyze the phase of the transmitted ultrasonic beam. This results in the conceptual introduction of the 'phase polar scan', exposing even more intriguing and detailed patterns. In fact, the combination of the amplitude and the phase polar scan provides the complete knowledge about the complex transmission coefficient for every possible angle of incidence. This comprehensive information will be very valuable for inverse modeling of the local elasticity tensor based on a single UPS experiment. Finally, the UPS method has been applied for the detection of an artificial delamination. Compared to the pulsed UPS, the quasi-harmonic UPS (both the amplitude and phase recording) shows a superior sensitivity to the presence of a delamination. Copyright © 2015 Elsevier B.V. All rights reserved.

Static behavior of the weld in the joint of the steel support element using experiment and numerical modeling

NASA Astrophysics Data System (ADS)

Krejsa, M.; Brozovsky, J.; Mikolasek, D.; Parenica, P.; Koubova, L.

2018-04-01

The paper is focused on the numerical modeling of welded steel bearing elements using commercial software system ANSYS, which is based on the finite element method - FEM. It is important to check and compare the results of FEM analysis with the results of physical verification test, in which the real behavior of the bearing element can be observed. The results of the comparison can be used for calibration of the computational model. The article deals with the physical test of steel supporting elements, whose main purpose is obtaining of material, geometry and strength characteristics of the fillet and butt welds including heat affected zone in the basic material of welded steel bearing element. The pressure test was performed during the experiment, wherein the total load value and the corresponding deformation of the specimens under the load was monitored. Obtained data were used for the calibration of numerical models of test samples and they are necessary for further stress and strain analysis of steel supporting elements.

Experiments and numerical simulations of nonlinear vibration responses of an assembly with friction joints - Application on a test structure named "Harmony"

NASA Astrophysics Data System (ADS)

Claeys, M.; Sinou, J.-J.; Lambelin, J.-P.; Todeschini, R.

2016-03-01

In presence of friction, the frequency response function of a metallic assembly is strongly dependent on the excitation level. The local stick-slip behavior at the friction interfaces induces energy dissipation and local stiffness softening. These phenomena are studied both experimentally and numerically on a test structure named "Harmony". Concerning the numerical part, a classical complete methodology from the finite element and friction modeling to the prediction of the nonlinear vibrational response is implemented. The well-known Harmonic Balance Method with a specific condensation process on the nonlinear frictional elements is achieved. Also, vibration experiments are performed to validate not only the finite element model of the test structure named "Harmony" at low excitation levels but also to investigate the nonlinear behavior of the system on several excitation levels. A scanning laser vibrometer is used to measure the nonlinear behavior and the local stick-slip movement near the contacts.

A Differential Scanning Calorimetry Method for Construction of Continuous Cooling Transformation Diagram of Blast Furnace Slag

NASA Astrophysics Data System (ADS)

Gan, Lei; Zhang, Chunxia; Shangguan, Fangqin; Li, Xiuping

2012-06-01

The continuous cooling crystallization of a blast furnace slag was studied by the application of the differential scanning calorimetry (DSC) method. A kinetic model describing the correlation between the evolution of the degree of crystallization with time was obtained. Bulk cooling experiments of the molten slag coupled with numerical simulation of heat transfer were conducted to validate the results of the DSC methods. The degrees of crystallization of the samples from the bulk cooling experiments were estimated by means of the X-ray diffraction (XRD) and the DSC method. It was found that the results from the DSC cooling and bulk cooling experiments are in good agreement. The continuous cooling transformation (CCT) diagram of the blast furnace slag was constructed according to crystallization kinetic model and experimental data. The obtained CCT diagram characterizes with two crystallization noses at different temperature ranges.

Analysis of Photothermal Characterization of Layered Materials: Design of Optimal Experiments

NASA Technical Reports Server (NTRS)

Cole, Kevin D.

2003-01-01

In this paper numerical calculations are presented for the steady-periodic temperature in layered materials and functionally-graded materials to simulate photothermal methods for the measurement of thermal properties. No laboratory experiments were performed. The temperature is found from a new Green s function formulation which is particularly well-suited to machine calculation. The simulation method is verified by comparison with literature data for a layered material. The method is applied to a class of two-component functionally-graded materials and results for temperature and sensitivity coefficients are presented. An optimality criterion, based on the sensitivity coefficients, is used for choosing what experimental conditions will be needed for photothermal measurements to determine the spatial distribution of thermal properties. This method for optimal experiment design is completely general and may be applied to any photothermal technique and to any functionally-graded material.

High mobility of large mass movements: a study by means of FEM/DEM simulations

NASA Astrophysics Data System (ADS)

Manzella, I.; Lisjak, A.; Grasselli, G.

2013-12-01

Large mass movements, such as rock avalanches and large volcanic debris avalanches are characterized by extremely long propagation, which cannot be modelled using normal sliding friction law. For this reason several studies and theories derived from field observation, physical theories and laboratory experiments, exist to try to explain their high mobility. In order to investigate more into deep some of the processes recalled by these theories, simulations have been run with a new numerical tool called Y-GUI based on the Finite Element-Discrete Element Method FEM/DEM. The FEM/DEM method is a numerical technique developed by Munjiza et al. (1995) where Discrete Element Method (DEM) algorithms are used to model the interaction between different solids, while Finite Element Method (FEM) principles are used to analyze their deformability being also able to explicitly simulate material sudden loss of cohesion (i.e. brittle failure). In particular numerical tests have been run, inspired by the small-scale experiments done by Manzella and Labiouse (2013). They consist of rectangular blocks released on a slope; each block is a rectangular discrete element made of a mesh of finite elements enabled to fragment. These simulations have highlighted the influence on the propagation of block packing, i.e. whether the elements are piled into geometrical ordinate structure before failure or they are chaotically disposed as a loose material, and of the topography, i.e. whether the slope break is smooth and regular or not. In addition the effect of fracturing, i.e. fragmentation, on the total runout have been studied and highlighted.

Quantum state estimation when qubits are lost: a no-data-left-behind approach

DOE PAGES

Williams, Brian P.; Lougovski, Pavel

2017-04-06

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.

Monotonicity-based electrical impedance tomography for lung imaging

NASA Astrophysics Data System (ADS)

Zhou, Liangdong; Harrach, Bastian; Seo, Jin Keun

2018-04-01

This paper presents a monotonicity-based spatiotemporal conductivity imaging method for continuous regional lung monitoring using electrical impedance tomography (EIT). The EIT data (i.e. the boundary current-voltage data) can be decomposed into pulmonary, cardiac and other parts using their different periodic natures. The time-differential current-voltage operator corresponding to the lung ventilation can be viewed as either semi-positive or semi-negative definite owing to monotonic conductivity changes within the lung regions. We used these monotonicity constraints to improve the quality of lung EIT imaging. We tested the proposed methods in numerical simulations, phantom experiments and human experiments.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

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

Fahimian, Benjamin P.; Zhao Yunzhe; Huang Zhifeng

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). Inmore » each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.« less

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

PubMed Central

Fahimian, Benjamin P.; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J.; Osher, Stanley J.; McNitt-Gray, Michael F.; Miao, Jianwei

2013-01-01

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method. PMID:23464329

Analytical treatment of gas flows through multilayer insulation, project 1

NASA Technical Reports Server (NTRS)

Lin, J. T.

1972-01-01

A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.

Numerical Leak Detection in a Pipeline Network of Complex Structure with Unsteady Flow

NASA Astrophysics Data System (ADS)

Aida-zade, K. R.; Ashrafova, E. R.

2017-12-01

An inverse problem for a pipeline network of complex loopback structure is solved numerically. The problem is to determine the locations and amounts of leaks from unsteady flow characteristics measured at some pipeline points. The features of the problem include impulse functions involved in a system of hyperbolic differential equations, the absence of classical initial conditions, and boundary conditions specified as nonseparated relations between the states at the endpoints of adjacent pipeline segments. The problem is reduced to a parametric optimal control problem without initial conditions, but with nonseparated boundary conditions. The latter problem is solved by applying first-order optimization methods. Results of numerical experiments are presented.

Faithful replication of grating patterns in polymer through electrohydrodynamic instabilities

NASA Astrophysics Data System (ADS)

Li, H.; Yu, W.; Wang, T.; Zhang, H.; Cao, Y.; Abraham, E.; Desmulliez, M. P. Y.

2014-07-01

Electrohydrodynamic instability patterning (EHDIP) as an alternative patterning method has attracted a great deal of attention over the past decade. This article demonstrates the faithful transfer of patterns with a high aspect ratio onto a polymer film via electrohydrodynamic instabilities for a given patterned grating mask. We perform a simple mathematical analysis to determine the influence of process parameters on the pressure difference ▵P. Through numerical simulation, it is demonstrated that thick films subject to large electric fields are essential to realize this faithful replication. In particular, the influence of the material properties of the polymer on pattern replication is discussed in detail. It is found that, to achieve the smaller periodic patterns with a higher resolution, film with a larger value of the dielectric constant and smaller value of the surface tension should be chosen. In addition, an ideal replication of the mask pattern with a short evolution time is possible by reducing the viscosity of the polymer liquid. Finally, the experiments of the pattern replication with and without defects are demonstrated to compare with the numerical simulation results. It is found that experiments are in good agreement with the simulation results and prove that the numerical simulation method provides an effective way to predict faithful replication.

The Impact of Current and Future Polar Orbiting Satellite Data on Numerical Weather Prediction at NASA/GSFC

NASA Technical Reports Server (NTRS)

Atlas, Robert

2004-01-01

The lack of adequate observational data continues to be recognized as a major factor limiting both atmospheric research and numerical prediction on a variety of temporal and spatial scales. Since the advent of meteorological satellites in the 1960's, a considerable research effort has been directed toward the design of space-borne meteorological sensors, the development of optimal methods for the utilization of these data, (and an assessment of the influence of existing satellite data and the potential influence of future satellite observations on numerical weather prediction. This has included both Observing System Experiments (OSEs) and Observing System Simulation Experiments (OSSEs). OSEs are conducted to evaluate the impact of specific observations or classes of observations on analyses and forecasts. While OSEs are performed with existing data, OSSEs are conducted to evaluate the potential for future observing systems to improve-NWP, as well as to evaluate trade-offs in observing system design, and to develop and test improved methods for data assimilation. At the conference, results from OSEs to evaluate satellite data sets that have recently become available to the global observing system, such as AIRS and Seawinds, and results from OSSEs to determine the potential impact of space-based lidar winds will be presented.

Numerical simulation of the processes in the normal incidence tube for high acoustic pressure levels

NASA Astrophysics Data System (ADS)

Fedotov, E. S.; Khramtsov, I. V.; Kustov, O. Yu.

2016-10-01

Numerical simulation of the acoustic processes in an impedance tube at high levels of acoustic pressure is a way to solve a problem of noise suppressing by liners. These studies used liner specimen that is one cylindrical Helmholtz resonator. The evaluation of the real and imaginary parts of the liner acoustic impedance and sound absorption coefficient was performed for sound pressure levels of 130, 140 and 150 dB. The numerical simulation used experimental data having been obtained on the impedance tube with normal incidence waves. At the first stage of the numerical simulation it was used the linearized Navier-Stokes equations, which describe well the imaginary part of the liner impedance whatever the sound pressure level. These equations were solved by finite element method in COMSOL Multiphysics program in axisymmetric formulation. At the second stage, the complete Navier-Stokes equations were solved by direct numerical simulation in ANSYS CFX in axisymmetric formulation. As the result, the acceptable agreement between numerical simulation and experiment was obtained.

Non-robust numerical simulations of analogue extension experiments

NASA Astrophysics Data System (ADS)

Naliboff, John; Buiter, Susanne

2016-04-01

Numerical and analogue models of lithospheric deformation provide significant insight into the tectonic processes that lead to specific structural and geophysical observations. As these two types of models contain distinct assumptions and tradeoffs, investigations drawing conclusions from both can reveal robust links between first-order processes and observations. Recent studies have focused on detailed comparisons between numerical and analogue experiments in both compressional and extensional tectonics, sometimes involving multiple lithospheric deformation codes and analogue setups. While such comparisons often show good agreement on first-order deformation styles, results frequently diverge on second-order structures, such as shear zone dip angles or spacing, and in certain cases even on first-order structures. Here, we present finite-element experiments that are designed to directly reproduce analogue "sandbox" extension experiments at the cm-scale. We use material properties and boundary conditions that are directly taken from analogue experiments and use a Drucker-Prager failure model to simulate shear zone formation in sand. We find that our numerical experiments are highly sensitive to numerous numerical parameters. For example, changes to the numerical resolution, velocity convergence parameters and elemental viscosity averaging commonly produce significant changes in first- and second-order structures accommodating deformation. The sensitivity of the numerical simulations to small parameter changes likely reflects a number of factors, including, but not limited to, high angles of internal friction assigned to sand, complex, unknown interactions between the brittle sand (used as an upper crust equivalent) and viscous silicone (lower crust), highly non-linear strain weakening processes and poor constraints on the cohesion of sand. Our numerical-analogue comparison is hampered by (a) an incomplete knowledge of the fine details of sand failure and sand properties, and (b) likely limitations to the use of a continuum Drucker-Prager model for representing shear zone formation in sand. In some cases our numerical experiments provide reasonable fits to first-order structures observed in the analogue experiments, but the numerical sensitivity to small parameter variations leads us to conclude that the numerical experiments are not robust.

State public policy issues involved with the Parkfield prediction experiment.

USGS Publications Warehouse

Andrews, R.; Goltz, J.

1988-01-01

The earthquake-prediction experiment at Parkfield may well be the most important such experiment currently underway worldwide. Its importance, however, extends beyond the scientific data that will be gathered and whether those data that will be gathered and whether those data can provide reliable prediction methods. Important public policy lessons are being learned (and are yet to be learned), and these lessons may be transferable to other parts of California and the nation. Indeed, the Parkfield experiment has captured the interest of numerous Californians, including State officials, emergency managers, the news media, and at least some of the public.

The Oceanographic Multipurpose Software Environment (OMUSE v1.0)

NASA Astrophysics Data System (ADS)

Pelupessy, Inti; van Werkhoven, Ben; van Elteren, Arjen; Viebahn, Jan; Candy, Adam; Portegies Zwart, Simon; Dijkstra, Henk

2017-08-01

In this paper we present the Oceanographic Multipurpose Software Environment (OMUSE). OMUSE aims to provide a homogeneous environment for existing or newly developed numerical ocean simulation codes, simplifying their use and deployment. In this way, numerical experiments that combine ocean models representing different physics or spanning different ranges of physical scales can be easily designed. Rapid development of simulation models is made possible through the creation of simple high-level scripts. The low-level core of the abstraction in OMUSE is designed to deploy these simulations efficiently on heterogeneous high-performance computing resources. Cross-verification of simulation models with different codes and numerical methods is facilitated by the unified interface that OMUSE provides. Reproducibility in numerical experiments is fostered by allowing complex numerical experiments to be expressed in portable scripts that conform to a common OMUSE interface. Here, we present the design of OMUSE as well as the modules and model components currently included, which range from a simple conceptual quasi-geostrophic solver to the global circulation model POP (Parallel Ocean Program). The uniform access to the codes' simulation state and the extensive automation of data transfer and conversion operations aids the implementation of model couplings. We discuss the types of couplings that can be implemented using OMUSE. We also present example applications that demonstrate the straightforward model initialization and the concurrent use of data analysis tools on a running model. We give examples of multiscale and multiphysics simulations by embedding a regional ocean model into a global ocean model and by coupling a surface wave propagation model with a coastal circulation model.

A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

NASA Astrophysics Data System (ADS)

Segal, Guus; Vuik, Kees; Vermolen, Fred

1998-03-01

The dissolution of a disk-likeAl2Cuparticle is considered. A characteristic property is that initially the particle has a nonsmooth boundary. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. It is impossible to obtain an analytical solution for a general two-dimensional Stefan problem, so we use the finite element method to solve this problem numerically. First, we apply a classical moving mesh method. Computations show that after some time steps the predicted particle interface becomes very unrealistic. Therefore, we derive a new method for the displacement of the free boundary based on the balance of atoms. This method leads to good results, also, for nonsmooth boundaries. Some numerical experiments are given for the dissolution of anAl2Cuparticle in anAl-Cualloy.

A method of measuring the effective thermal conductivity of thermoplastic foams

NASA Astrophysics Data System (ADS)

Asséko, André Chateau Akué; Cosson, Benoit; Chaki, Salim; Duborper, Clément; Lacrampe, Marie-France; Krawczak, Patricia

2017-10-01

An inverse method for determining the in-plane effective thermal conductivity of porous thermoplastics was implemented by coupling infrared thermography experiments and numerical solution of heat transfer in straight fins having temperature-dependent convective heat transfer coefficient. The obtained effective thermal conductivity values were compared with previous results obtained using a numerical solution based on periodic homogenization techniques (NSHT) in which the microstructure heterogeneity of extruded polymeric polyethylene (PE) foam in which pores are filled with air with different levels of open and closed porosity was taken into account and Transient Plane Source Technique (TPS) in order to verify the accuracy of the proposed method. The new method proposed in the present study is in good agreement with both NSHT and TPS. It is also applicable to structural materials such as composites, e.g. unidirectional fiber-reinforced plastics, where heat transfer is very different according to the fiber direction (parallel or transverse to the fibers).

Dynamic Responses of Flexible Cylinders with Low Mass Ratio

NASA Astrophysics Data System (ADS)

Olaoye, Abiodun; Wang, Zhicheng; Triantafyllou, Michael

2017-11-01

Flexible cylinders with low mass ratios such as composite risers are attractive in the offshore industry because they require lower top tension and are less likely to buckle under self-weight compared to steel risers. However, their relatively low stiffness characteristics make them more vulnerable to vortex induced vibrations. Additionally, numerical investigation of the dynamic responses of such structures based on realistic conditions is limited by high Reynolds number, complex sheared flow profile, large aspect ratio and low mass ratio challenges. In the framework of Fourier spectral/hp element method, the current technique employs entropy-viscosity method (EVM) based large-eddy simulation approach for flow solver and fictitious added mass method for structure solver. The combination of both methods can handle fluid-structure interaction problems at high Reynolds number with low mass ratio. A validation of the numerical approach is provided by comparison with experiments.

Optical Sensor/Actuator Locations for Active Structural Acoustic Control

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; Palumbo, Daniel L.; Kincaid, Rex K.

1998-01-01

Researchers at NASA Langley Research Center have extensive experience using active structural acoustic control (ASAC) for aircraft interior noise reduction. One aspect of ASAC involves the selection of optimum locations for microphone sensors and force actuators. This paper explains the importance of sensor/actuator selection, reviews optimization techniques, and summarizes experimental and numerical results. Three combinatorial optimization problems are described. Two involve the determination of the number and position of piezoelectric actuators, and the other involves the determination of the number and location of the sensors. For each case, a solution method is suggested, and typical results are examined. The first case, a simplified problem with simulated data, is used to illustrate the method. The second and third cases are more representative of the potential of the method and use measured data. The three case studies and laboratory test results establish the usefulness of the numerical methods.

A compensation controller based on a regional pole-assignment method for AMD control systems with a time-varying delay

NASA Astrophysics Data System (ADS)

Li, Zuohua; Chen, Chaojun; Teng, Jun; Wang, Ying

2018-04-01

Active mass damper/driver (AMD) control system has been proposed as an effective tool for high-rise buildings to resist strong dynamic loads. However, such disadvantage as time-varying delay in AMD control systems impedes their application in practices. Time-varying delay, which has an effect on the performance and stability of single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems, is considered in the paper. In addition, a new time-delay compensation controller based on regional pole-assignment method is presented. To verify its effectiveness, the proposed method is applied to a numerical example of a ten-storey frame and an experiment of a single span four-storey steel frame. Both numerical and experimental results demonstrate that the proposed method can enhance the performances of an AMD control system with time-varying delays.

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

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Computation of viscous flows over airfoils, including separation, with a coupling approach

NASA Technical Reports Server (NTRS)

Leballeur, J. C.

1983-01-01

Viscous incompressible flows over single or multiple airfoils, with or without separation, were computed using an inviscid flow calculation, with modified boundary conditions, and by a method providing calculation and coupling for boundary layers and wakes, within conditions of strong viscous interaction. The inviscid flow is calculated with a method of singularities, the numerics of which were improved by using both source and vortex distributions over profiles, associated with regularity conditions for the fictitious flows inside of the airfoils. The viscous calculation estimates the difference between viscous flow and inviscid interacting flow, with a direct or inverse integral method, laminar or turbulent, with or without reverse flow. The numerical method for coupling determines iteratively the boundary conditions for the inviscid flow. For attached viscous layers regions, an underrelaxation is locally calculated to insure stability. For separated or separating regions, a special semi-inverse algorithm is used. Comparisons with experiments are presented.

[Reduction of animal experiments in experimental drug testing].

PubMed

Behrensdorf-Nicol, H; Krämer, B

2014-10-01

In order to ensure the quality of biomedical products, an experimental test for every single manufactured batch is required for many products. Especially in vaccine testing, animal experiments are traditionally used for this purpose. For example, efficacy is often determined via challenge experiments in laboratory animals. Safety tests of vaccine batches are also mostly performed using laboratory animals. However, many animal experiments have clear inherent disadvantages (low accuracy, questionable transferability to humans, unclear significance). Furthermore, for ethical reasons and animal welfare aspects animal experiments are also seen very critical by the public. Therefore, there is a strong trend towards replacing animal experiments with methods in which no animals are used ("replacement"). If a replacement is not possible, the required animal experiments should be improved in order to minimize the number of animals necessary ("reduction") and to reduce pain and suffering caused by the experiment to a minimum ("refinement"). This "3R concept" is meanwhile firmly established in legislature. In recent years many mandatory animal experiments have been replaced by alternative in vitro methods or improved according to the 3R principles; numerous alternative methods are currently under development. Nevertheless, the process from the development of a new method to its legal implementation takes a long time. Therefore, supplementary regulatory measures to facilitate validation and acceptance of new alternative methods could contribute to a faster and more consequent implementation of the 3R concept in the testing of biomedical products.

Energy-Complexity Relations by Structural Complexity Methods

NASA Astrophysics Data System (ADS)

Ricca, Renzo L.

2011-09-01

In this paper we shall review some of the most recent developments and results on work on energy-complexity relations and, if time will allow it, we shall provide an analytical proof of eq. (3) below, a fundamental relation between energy and complexity established by numerical experiments.

3D Lagrangian VPM: simulations of the near-wake of an actuator disc and horizontal axis wind turbine

NASA Astrophysics Data System (ADS)

Berdowski, T.; Ferreira, C.; Walther, J.

2016-09-01

The application of a 3-dimensional Lagrangian vortex particle method has been assessed for modelling the near-wake of an axisymmetrical actuator disc and 3-bladed horizontal axis wind turbine with prescribed circulation from the MEXICO (Model EXperiments In COntrolled conditions) experiment. The method was developed in the framework of the open- source Parallel Particle-Mesh library for handling the efficient data-parallelism on a CPU (Central Processing Unit) cluster, and utilized a O(N log N)-type fast multipole method for computational acceleration. Simulations with the actuator disc resulted in a wake expansion, velocity deficit profile, and induction factor that showed a close agreement with theoretical, numerical, and experimental results from literature. Also the shear layer expansion was present; the Kelvin-Helmholtz instability in the shear layer was triggered due to the round-off limitations of a numerical method, but this instability was delayed to beyond 1 diameter downstream due to the particle smoothing. Simulations with the 3-bladed turbine demonstrated that a purely 3-dimensional flow representation is challenging to model with particles. The manifestation of local complex flow structures of highly stretched vortices made the simulation unstable, but this was successfully counteracted by the application of a particle strength exchange scheme. The axial and radial velocity profile over the near wake have been compared to that of the original MEXICO experiment, which showed close agreement between results.

Tensile Properties of Dyneema SK76 Single Fibers at Multiple Loading Rates Using a Direct Gripping Method

DTIC Science & Technology

2014-06-01

lower density compared with aramid fibers such as Kevlar and Twaron. Numerical modeling is used to design more effective fiber-based composite armor...in measuring fibers and doing experiments. vi INTENTIONALLY LEFT BLANK. 1 1. Introduction Aramid fibers such as Kevlar (DuPont) and Twaron...methyl methacrylate blocks. The efficacy of this method to grip Kevlar fibers has been rigorously studied using a variety of statistical methods at

Application of finite element method in mechanical design of automotive parts

NASA Astrophysics Data System (ADS)

Gu, Suohai

2017-09-01

As an effective numerical analysis method, finite element method (FEM) has been widely used in mechanical design and other fields. In this paper, the development of FEM is introduced firstly, then the specific steps of FEM applications are illustrated and the difficulties of FEM are summarized in detail. Finally, applications of FEM in automobile components such as automobile wheel, steel plate spring, body frame, shaft parts and so on are summarized, compared with related research experiments.

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems

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

Jia, Jun; Jingfang, Huang

2008-01-01

In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\\bf \\it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving amore » decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.« less

Eighth-order explicit two-step hybrid methods with symmetric nodes and weights for solving orbital and oscillatory IVPs

NASA Astrophysics Data System (ADS)

Franco, J. M.; Rández, L.

The construction of new two-step hybrid (TSH) methods of explicit type with symmetric nodes and weights for the numerical integration of orbital and oscillatory second-order initial value problems (IVPs) is analyzed. These methods attain algebraic order eight with a computational cost of six or eight function evaluations per step (it is one of the lowest costs that we know in the literature) and they are optimal among the TSH methods in the sense that they reach a certain order of accuracy with minimal cost per step. The new TSH schemes also have high dispersion and dissipation orders (greater than 8) in order to be adapted to the solution of IVPs with oscillatory solutions. The numerical experiments carried out with several orbital and oscillatory problems show that the new eighth-order explicit TSH methods are more efficient than other standard TSH or Numerov-type methods proposed in the scientific literature.

The propagation of sound in tunnels

NASA Astrophysics Data System (ADS)

Li, Kai Ming; Iu, King Kwong

2002-11-01

The sound propagation in tunnels is addressed theoretically and experimentally. In many previous studies, the image source method is frequently used. However, these early theoretical models are somewhat inadequate because the effect of multiple reflections in long enclosures is often modeled by the incoherent summation of contributions from all image sources. Ignoring the phase effect, these numerical models are unlikely to be satisfactory for predicting the intricate interference patterns due to contributions from each image source. In the present paper, the interference effect is incorporated by summing the contributions from the image sources coherently. To develop a simple numerical model, tunnels are represented by long rectangular enclosures with either geometrically reflecting or impedance boundaries. Scale model experiments are conducted for the validation of the numerical model. In some of the scale model experiments, the enclosure walls are lined with a carpet for simulating the impedance boundary condition. Large-scale outdoor measurements have also been conducted in two tunnels designed originally for road traffic use. It has been shown that the proposed numerical model agrees reasonably well with experimental data. [Work supported by the Research Grants Council, The Industry Department, NAP Acoustics (Far East) Ltd., and The Hong Kong Polytechnic University.

On numerical instabilities of Godunov-type schemes for strong shocks

NASA Astrophysics Data System (ADS)

Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha

2017-12-01

It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. Numerical results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed scheme.

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

Tuo, Rui; Jeff Wu, C. F.

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2-inconsistent calibration. This L 2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the Lmore » 2 calibration, is proposed and proven to be L 2-consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2-inconsistency problem.« less

Numerical modeling of NI-monitored 3D infiltration experiment

NASA Astrophysics Data System (ADS)

Dohnal, Michal; Dusek, Jaromir; Snehota, Michal; Sacha, Jan; Vogel, Tomas; Votrubova, Jana

2014-05-01

It is well known that the temporal changes of saturated hydraulic conductivity caused by the occurrence of air phase discontinuities often play an important role in water flow and solute transport experiments. In the present study, a series of infiltration-outflow experiments was conducted to test several working hypotheses about the mechanism of air phase trapping. The experiments were performed on a porous sample with artificial internal structure, using three sandy materials with contrasting hydraulic properties. The sample was axially symmetric with continuous preferential pathways and separate porous matrix blocks (the sample was 3.4 cm in diameter and 8.8 cm high). The infiltration experiments were monitored by neutron imaging (NI). The NI data were then used to quantify the water content of the selected sample regions. The flow regime in the sample was studied using a three-dimensional model based on Richards' equation. The equation was solved by the finite element method. The results of the numerical simulations of the infiltration experiments were compared with the measured outflow rates and with the spatial distribution of water content determined by NI. The research was supported by the Czech Science Foundation Project No. 14-03691S.

Well-conditioning global-local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felicio Bruzzi

2016-11-01

Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.

Polarisation in spin-echo experiments: Multi-point and lock-in measurements

NASA Astrophysics Data System (ADS)

Tamtögl, Anton; Davey, Benjamin; Ward, David J.; Jardine, Andrew P.; Ellis, John; Allison, William

2018-02-01

Spin-echo instruments are typically used to measure diffusive processes and the dynamics and motion in samples on ps and ns time scales. A key aspect of the spin-echo technique is to determine the polarisation of a particle beam. We present two methods for measuring the spin polarisation in spin-echo experiments. The current method in use is based on taking a number of discrete readings. The implementation of a new method involves continuously rotating the spin and measuring its polarisation after being scattered from the sample. A control system running on a microcontroller is used to perform the spin rotation and to calculate the polarisation of the scattered beam based on a lock-in amplifier. First experimental tests of the method on a helium spin-echo spectrometer show that it is clearly working and that it has advantages over the discrete approach, i.e., it can track changes of the beam properties throughout the experiment. Moreover, we show that real-time numerical simulations can perfectly describe a complex experiment and can be easily used to develop improved experimental methods prior to a first hardware implementation.

Flux control coefficients determined by inhibitor titration: the design and analysis of experiments to minimize errors.

PubMed Central

Small, J R

1993-01-01

This paper is a study into the effects of experimental error on the estimated values of flux control coefficients obtained using specific inhibitors. Two possible techniques for analysing the experimental data are compared: a simple extrapolation method (the so-called graph method) and a non-linear function fitting method. For these techniques, the sources of systematic errors are identified and the effects of systematic and random errors are quantified, using both statistical analysis and numerical computation. It is shown that the graph method is very sensitive to random errors and, under all conditions studied, that the fitting method, even under conditions where the assumptions underlying the fitted function do not hold, outperformed the graph method. Possible ways of designing experiments to minimize the effects of experimental errors are analysed and discussed. PMID:8257434

Advances in the computation of transonic separated flows over finite wings

NASA Technical Reports Server (NTRS)

Kaynak, Unver; Flores, Jolen

1989-01-01

Problems encountered in numerical simulations of transonic wind-tunnel experiments with low-aspect-ratio wings are surveyed and illustrated. The focus is on the zonal Euler/Navier-Stokes program developed by Holst et al. (1985) and its application to shock-induced separation. The physical basis and numerical implementation of the method are reviewed, and results are presented from studies of the effects of artificial dissipation, boundary conditions, grid refinement, the turbulence model, and geometry representation on the simulation accuracy. Extensive graphs and diagrams and typical flow visualizations are provided.

Manipulator trajectories during orbital servicing mission: numerical simulations and experiments on microgravity simulator

NASA Astrophysics Data System (ADS)

Rybus, T.; Seweryn, K.

2018-06-01

It is considered to use a manipulator-equipped satellite for performing On-Orbit Servicing (OOS) or Active Debris Removal (ADR) missions. In this paper, several possible approaches are reviewed for end-effector (EE) trajectory planning in the Cartesian space, such as application of the Bézier curves for singularity avoidance and method for trajectory optimization. The results of numerical simulations for a satellite equipped with a 7 degree-of-freedom (DoF) manipulator and results of experiments performed on a planar air-bearing microgravity simulator for a simplified two-dimensional (2D) case with a 2-DoF manipulator are presented. Differences between the free-floating case and the case where Attitude and Orbit Control Systems (AOCS) keep constant position and orientation of the satellite are also shown.

Simulation and experiment for depth sizing of cracks in anchor bolts by ultrasonic phased array technology

NASA Astrophysics Data System (ADS)

Lin, Shan

2018-04-01

There have been lots of reports about the occurrence of cracks in bolts in aging nuclear and thermal power plants. Sizing of such cracks is crucial for assessing the integrity of bolts. Currently, hammering and visual tests are used to detect cracks in bolts. However, they are not applicable for sizing cracks. Although the tip diffraction method is well known as a crack sizing technique, reflection echoes from threads make it difficult to apply this technique to bolts. This paper addresses a method for depth sizing of cracks in bolts by means of ultrasonic phased array technology. Numerical results of wave propagation in bolts by the finite element method (FEM) shows that a peak associated within the vicinity of a crack tip can be observed in the curve of echo intensity versus refraction angle for deep cracks. The refraction angle with respect to this peak decreases as crack depth increases. Such numerical results are verified by experiments on bolt specimens that have electrical discharge machining notches or fatigue cracks with different depths. In the experiment, a 10-MHz linear array probe is used. Depth of cracks in bolts using the refraction angle associated with the peak is determined and compared to actual depths. The comparison shows that accurately determining a crack depth from the inspection results is possible.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

PubMed

Fahimian, Benjamin P; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J; Osher, Stanley J; McNitt-Gray, Michael F; Miao, Jianwei

2013-03-01

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

NASA Astrophysics Data System (ADS)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

THz-waves channeling in a monolithic saddle-coil for Dynamic Nuclear Polarization enhanced NMR.

PubMed

Macor, A; de Rijk, E; Annino, G; Alberti, S; Ansermet, J-Ph

2011-10-01

A saddle coil manufactured by electric discharge machining (EDM) from a solid piece of copper has recently been realized at EPFL for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance experiments (DNP-NMR) at 9.4 T. The corresponding electromagnetic behavior of radio-frequency (400 MHz) and THz (263 GHz) waves were studied by numerical simulation in various measurement configurations. Moreover, we present an experimental method by which the results of the THz-wave numerical modeling are validated. On the basis of the good agreement between numerical and experimental results, we conducted by numerical simulation a systematic analysis on the influence of the coil geometry and of the sample properties on the THz-wave field, which is crucial in view of the optimization of DNP-NMR in solids. Copyright © 2011 Elsevier Inc. All rights reserved.

Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

NASA Astrophysics Data System (ADS)

Roubinet, D.; Linde, N.; Jougnot, D.; Irving, J.

2016-05-01

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse

NASA Astrophysics Data System (ADS)

Lusso, Christelle; Ern, Alexandre; Bouchut, François; Mangeney, Anne; Farin, Maxime; Roche, Olivier

2017-03-01

This work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. We consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2D setting with a free surface. We implement a regularization method to deal with the singularity of the rheological law, using a mixed finite element approximation of the momentum and incompressibility equations, and an arbitrary Lagrangian Eulerian (ALE) formulation for the displacement of the domain. The free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. Several tests are performed to assess the efficiency of our method. The first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. On this configuration we setup rules for the choice of the numerical parameters. The second test aims to compare the results of our numerical method to those predicted by an augmented Lagrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. Finally we show the reliability of our method by comparing numerical predictions to data from experiments of granular collapse of both trapezoidal and rectangular columns over horizontal rigid or erodible granular bed made of the same material. We compare the evolution of the free surface, the velocity profiles, and the static-flowing interface. The results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed.

Simplex-based optimization of numerical and categorical inputs in early bioprocess development: Case studies in HT chromatography.

PubMed

Konstantinidis, Spyridon; Titchener-Hooker, Nigel; Velayudhan, Ajoy

2017-08-01

Bioprocess development studies often involve the investigation of numerical and categorical inputs via the adoption of Design of Experiments (DoE) techniques. An attractive alternative is the deployment of a grid compatible Simplex variant which has been shown to yield optima rapidly and consistently. In this work, the method is combined with dummy variables and it is deployed in three case studies wherein spaces are comprised of both categorical and numerical inputs, a situation intractable by traditional Simplex methods. The first study employs in silico data and lays out the dummy variable methodology. The latter two employ experimental data from chromatography based studies performed with the filter-plate and miniature column High Throughput (HT) techniques. The solute of interest in the former case study was a monoclonal antibody whereas the latter dealt with the separation of a binary system of model proteins. The implemented approach prevented the stranding of the Simplex method at local optima, due to the arbitrary handling of the categorical inputs, and allowed for the concurrent optimization of numerical and categorical, multilevel and/or dichotomous, inputs. The deployment of the Simplex method, combined with dummy variables, was therefore entirely successful in identifying and characterizing global optima in all three case studies. The Simplex-based method was further shown to be of equivalent efficiency to a DoE-based approach, represented here by D-Optimal designs. Such an approach failed, however, to both capture trends and identify optima, and led to poor operating conditions. It is suggested that the Simplex-variant is suited to development activities involving numerical and categorical inputs in early bioprocess development. © 2017 The Authors. Biotechnology Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

Gvozdic, Branko D.; Djurdjevic, Dusan Z.

2017-01-01

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

A feasible DY conjugate gradient method for linear equality constraints

NASA Astrophysics Data System (ADS)

LI, Can

2017-09-01

In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.

Methods for the identification of material parameters in distributed models for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Crowley, J. M.; Rosen, I. G.

1986-01-01

Theoretical and numerical results are presented for inverse problems involving estimation of spatially varying parameters such as stiffness and damping in distributed models for elastic structures such as Euler-Bernoulli beams. An outline of algorithms used and a summary of computational experiences are presented.

Reflections on Graduate Student PBL Experiences

ERIC Educational Resources Information Center

McDonald, Betty

2008-01-01

The study designed to contribute to existing research on Problem-Based Learning (PBL) chose a focus group comprising 16 MSc. Petroleum Engineering students (six females). Using PBL as the method of instruction, students examined a real-life petroleum engineering problem that highlighted numerous areas of their existing curriculum. They worked in…

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

NASA Astrophysics Data System (ADS)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Time Domain Strain/Stress Reconstruction Based on Empirical Mode Decomposition: Numerical Study and Experimental Validation.

PubMed

He, Jingjing; Zhou, Yibin; Guan, Xuefei; Zhang, Wei; Zhang, Weifang; Liu, Yongming

2016-08-16

Structural health monitoring has been studied by a number of researchers as well as various industries to keep up with the increasing demand for preventive maintenance routines. This work presents a novel method for reconstruct prompt, informed strain/stress responses at the hot spots of the structures based on strain measurements at remote locations. The structural responses measured from usage monitoring system at available locations are decomposed into modal responses using empirical mode decomposition. Transformation equations based on finite element modeling are derived to extrapolate the modal responses from the measured locations to critical locations where direct sensor measurements are not available. Then, two numerical examples (a two-span beam and a 19956-degree of freedom simplified airfoil) are used to demonstrate the overall reconstruction method. Finally, the present work investigates the effectiveness and accuracy of the method through a set of experiments conducted on an aluminium alloy cantilever beam commonly used in air vehicle and spacecraft. The experiments collect the vibration strain signals of the beam via optical fiber sensors. Reconstruction results are compared with theoretical solutions and a detailed error analysis is also provided.

A time-space domain stereo finite difference method for 3D scalar wave propagation

NASA Astrophysics Data System (ADS)

Chen, Yushu; Yang, Guangwen; Ma, Xiao; He, Conghui; Song, Guojie

2016-11-01

The time-space domain finite difference methods reduce numerical dispersion effectively by minimizing the error in the joint time-space domain. However, their interpolating coefficients are related with the Courant numbers, leading to significantly extra time costs for loading the coefficients consecutively according to velocity in heterogeneous models. In the present study, we develop a time-space domain stereo finite difference (TSSFD) method for 3D scalar wave equation. The method propagates both the displacements and their gradients simultaneously to keep more information of the wavefields, and minimizes the maximum phase velocity error directly using constant interpolation coefficients for different Courant numbers. We obtain the optimal constant coefficients by combining the truncated Taylor series approximation and the time-space domain optimization, and adjust the coefficients to improve the stability condition. Subsequent investigation shows that the TSSFD can suppress numerical dispersion effectively with high computational efficiency. The maximum phase velocity error of the TSSFD is just 3.09% even with only 2 sampling points per minimum wavelength when the Courant number is 0.4. Numerical experiments show that to generate wavefields with no visible numerical dispersion, the computational efficiency of the TSSFD is 576.9%, 193.5%, 699.0%, and 191.6% of those of the 4th-order and 8th-order Lax-Wendroff correction (LWC) method, the 4th-order staggered grid method (SG), and the 8th-order optimal finite difference method (OFD), respectively. Meanwhile, the TSSFD is compatible to the unsplit convolutional perfectly matched layer (CPML) boundary condition for absorbing artificial boundaries. The efficiency and capability to handle complex velocity models make it an attractive tool in imaging methods such as acoustic reverse time migration (RTM).

An adaptive time-stepping strategy for solving the phase field crystal model

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

Zhang, Zhengru, E-mail: zrzhang@bnu.edu.cn; Ma, Yuan, E-mail: yuner1022@gmail.com; Qiao, Zhonghua, E-mail: zqiao@polyu.edu.hk

2013-09-15

In this work, we will propose an adaptive time step method for simulating the dynamics of the phase field crystal (PFC) model. The numerical simulation of the PFC model needs long time to reach steady state, and then large time-stepping method is necessary. Unconditionally energy stable schemes are used to solve the PFC model. The time steps are adaptively determined based on the time derivative of the corresponding energy. It is found that the use of the proposed time step adaptivity cannot only resolve the steady state solution, but also the dynamical development of the solution efficiently and accurately. Themore » numerical experiments demonstrate that the CPU time is significantly saved for long time simulations.« less

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference

NASA Astrophysics Data System (ADS)

Shen, Cheng; Guo, Cheng; Tan, Jiubin; Liu, Shutian; Liu, Zhengjun

2018-06-01

Multi-image iterative phase retrieval methods have been successfully applied in plenty of research fields due to their simple but efficient implementation. However, there is a mismatch between the measurement of the first long imaging distance and the sequential interval. In this paper, an amplitude-phase retrieval algorithm with reference is put forward without additional measurements or priori knowledge. It gets rid of measuring the first imaging distance. With a designed update formula, it significantly raises the convergence speed and the reconstruction fidelity, especially in phase retrieval. Its superiority over the original amplitude-phase retrieval (APR) method is validated by numerical analysis and experiments. Furthermore, it provides a conceptual design of a compact holographic image sensor, which can achieve numerical refocusing easily.

Fluid-structure interaction of a pulsatile flow with an aortic valve model: A combined experimental and numerical study.

PubMed

Sigüenza, Julien; Pott, Desiree; Mendez, Simon; Sonntag, Simon J; Kaufmann, Tim A S; Steinseifer, Ulrich; Nicoud, Franck

2018-04-01

The complex fluid-structure interaction problem associated with the flow of blood through a heart valve with flexible leaflets is investigated both experimentally and numerically. In the experimental test rig, a pulse duplicator generates a pulsatile flow through a biomimetic rigid aortic root where a model of aortic valve with polymer flexible leaflets is implanted. High-speed recordings of the leaflets motion and particle image velocimetry measurements were performed together to investigate the valve kinematics and the dynamics of the flow. Large eddy simulations of the same configuration, based on a variant of the immersed boundary method, are also presented. A massively parallel unstructured finite-volume flow solver is coupled with a finite-element solid mechanics solver to predict the fluid-structure interaction between the unsteady flow and the valve. Detailed analysis of the dynamics of opening and closure of the valve are conducted, showing a good quantitative agreement between the experiment and the simulation regarding the global behavior, in spite of some differences regarding the individual dynamics of the valve leaflets. A multicycle analysis (over more than 20 cycles) enables to characterize the generation of turbulence downstream of the valve, showing similar flow features between the experiment and the simulation. The flow transitions to turbulence after peak systole, when the flow starts to decelerate. Fluctuations are observed in the wake of the valve, with maximum amplitude observed at the commissure side of the aorta. Overall, a very promising experiment-vs-simulation comparison is shown, demonstrating the potential of the numerical method. Copyright © 2017 John Wiley & Sons, Ltd.

PIV measurements of airflow past multiple cylinders

NASA Astrophysics Data System (ADS)

Wodziak, Waldemar; Sobczyk, Jacek

2018-06-01

Flow characteristics in vicinity of six circular cylinders aligned inline was investigated experimentally by means of PIV method. Experiments were conducted in a low speed closed circuit wind tunnel. Inflow velocity was 1.2 m/s which corresponds to Re=1600 based on the cylinder diameter. Spacing ratio between cylinders L/D was 1.5. Instantaneous and averaged velocity fields were presented. Experiments were designed in order to use their results as a test case for future numerical calculations.

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

PubMed Central

Butnariu, Dan; Censor, Yair; Gurfil, Pini; Hadar, Ethan

2010-01-01

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm’s behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method. PMID:20182556

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces.

PubMed

Butnariu, Dan; Censor, Yair; Gurfil, Pini; Hadar, Ethan

2008-07-03

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm's behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.

A comparison of solute-transport solution techniques based on inverse modelling results

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2000-01-01

Five common numerical techniques (finite difference, predictor-corrector, total-variation-diminishing, method-of-characteristics, and modified-method-of-characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using randomly distributed homogeneous blocks of five sand types. This experimental model provides an outstanding opportunity to compare the solution techniques because of the heterogeneous hydraulic conductivity distribution of known structure, and the availability of detailed measurements with which to compare simulated concentrations. The present work uses this opportunity to investigate how three common types of results-simulated breakthrough curves, sensitivity analysis, and calibrated parameter values-change in this heterogeneous situation, given the different methods of simulating solute transport. The results show that simulated peak concentrations, even at very fine grid spacings, varied because of different amounts of numerical dispersion. Sensitivity analysis results were robust in that they were independent of the solution technique. They revealed extreme correlation between hydraulic conductivity and porosity, and that the breakthrough curve data did not provide enough information about the dispersivities to estimate individual values for the five sands. However, estimated hydraulic conductivity values are significantly influenced by both the large possible variations in model dispersion and the amount of numerical dispersion present in the solution technique.Five common numerical techniques (finite difference, predictor-corrector, total-variation-diminishing, method-of-characteristics, and modified-method-of-characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using randomly distributed homogeneous blocks of five sand types. This experimental model provides an outstanding opportunity to compare the solution techniques because of the heterogeneous hydraulic conductivity distribution of known structure, and the availability of detailed measurements with which to compare simulated concentrations. The present work uses this opportunity to investigate how three common types of results - simulated breakthrough curves, sensitivity analysis, and calibrated parameter values - change in this heterogeneous situation, given the different methods of simulating solute transport. The results show that simulated peak concentrations, even at very fine grid spacings, varied because of different amounts of numerical dispersion. Sensitivity analysis results were robust in that they were independent of the solution technique. They revealed extreme correlation between hydraulic conductivity and porosity, and that the breakthrough curve data did not provide enough information about the dispersivities to estimate individual values for the five sands. However, estimated hydraulic conductivity values are significantly influenced by both the large possible variations in model dispersion and the amount of numerical dispersion present in the solution technique.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

NASA Astrophysics Data System (ADS)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Adaptive [theta]-methods for pricing American options

NASA Astrophysics Data System (ADS)

Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran

2008-12-01

We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.

Prediction of Quality Change During Thawing of Frozen Tuna Meat by Numerical Calculation I

NASA Astrophysics Data System (ADS)

Murakami, Natsumi; Watanabe, Manabu; Suzuki, Toru

A numerical calculation method has been developed to determine the optimum thawing method for minimizing the increase of metmyoglobin content (metMb%) as an indicator of color changes in frozen tuna meat during thawing. The calculation method is configured the following two steps: a) calculation of temperature history in each part of frozen tuna meat during thawing by control volume method under the assumption of one-dimensional heat transfer, and b) calculation of metMb% based on the combination of calculated temperature history, Arrenius equation and the first-order reaction equation for the increase rate of metMb%. Thawing experiments for measuring temperature history of frozen tuna meat were carried out under the conditions of rapid thawing and slow thawing to compare the experimental data with calculated temperature history as well as the increase of metMb%. The results were coincident with the experimental data. The proposed simulation method would be useful for predicting the optimum thawing conditions in terms of metMb%.

A Numerical Theory for Impedance Education in Three-Dimensional Normal Incidence Tubes

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Jones, Michael G.

2016-01-01

A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance.

Experimental study and finite element analysis based on equivalent load method for laser ultrasonic measurement of elastic constants.

PubMed

Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo

2016-07-01

The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. Copyright © 2016. Published by Elsevier B.V.

Spectral editing of weakly coupled spins using variable flip angles in PRESS constant echo time difference spectroscopy: Application to GABA

NASA Astrophysics Data System (ADS)

Snyder, Jeff; Hanstock, Chris C.; Wilman, Alan H.

2009-10-01

A general in vivo magnetic resonance spectroscopy editing technique is presented to detect weakly coupled spin systems through subtraction, while preserving singlets through addition, and is applied to the specific brain metabolite γ-aminobutyric acid (GABA) at 4.7 T. The new method uses double spin echo localization (PRESS) and is based on a constant echo time difference spectroscopy approach employing subtraction of two asymmetric echo timings, which is normally only applicable to strongly coupled spin systems. By utilizing flip angle reduction of one of the two refocusing pulses in the PRESS sequence, we demonstrate that this difference method may be extended to weakly coupled systems, thereby providing a very simple yet effective editing process. The difference method is first illustrated analytically using a simple two spin weakly coupled spin system. The technique was then demonstrated for the 3.01 ppm resonance of GABA, which is obscured by the strong singlet peak of creatine in vivo. Full numerical simulations, as well as phantom and in vivo experiments were performed. The difference method used two asymmetric PRESS timings with a constant total echo time of 131 ms and a reduced 120° final pulse, providing 25% GABA yield upon subtraction compared to two short echo standard PRESS experiments. Phantom and in vivo results from human brain demonstrate efficacy of this method in agreement with numerical simulations.

Numerical and experimental analyses of the radiant heat flux produced by quartz heating systems

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Ash, Robert L.

1994-01-01

A method is developed for predicting the radiant heat flux distribution produced by tungsten filament, tubular fused-quartz envelope heating systems with reflectors. The method is an application of Monte Carlo simulation, which takes the form of a random walk or ray tracing scheme. The method is applied to four systems of increasing complexity, including a single lamp without a reflector, a single lamp with a Hat reflector, a single lamp with a parabolic reflector, and up to six lamps in a six-lamp contoured-reflector heating unit. The application of the Monte Carlo method to the simulation of the thermal radiation generated by these systems is discussed. The procedures for numerical implementation are also presented. Experiments were conducted to study these quartz heating systems and to acquire measurements of the corresponding empirical heat flux distributions for correlation with analysis. The experiments were conducted such that several complicating factors could be isolated and studied sequentially. Comparisons of the experimental results with analysis are presented and discussed. Good agreement between the experimental and simulated results was obtained in all cases. This study shows that this method can be used to analyze very complicated quartz heating systems and can account for factors such as spectral properties, specular reflection from curved surfaces, source enhancement due to reflectors and/or adjacent sources, and interaction with a participating medium in a straightforward manner.

Design of a rapid magnetic microfluidic mixer

NASA Astrophysics Data System (ADS)

Ballard, Matthew; Owen, Drew; Mills, Zachary Grant; Hanasoge, Srinivas; Hesketh, Peter; Alexeev, Alexander

2015-11-01

Using three-dimensional simulations and experiments, we demonstrate rapid mixing of fluid streams in a microchannel using orbiting magnetic microbeads. We use a lattice Boltzmann model coupled to a Brownian dynamics model to perform numerical simulations that study in depth the effect of system parameters such as channel configuration and fluid and bead velocities. We use our findings to aid the design of an experimental micromixer. Using this experimental device, we demonstrate rapid microfluidic mixing over a compact channel length, and validate our numerical simulation results. Finally, we use numerical simulations to study the physical mechanisms leading to microfluidic mixing in our system. Our findings demonstrate a promising method of rapid microfluidic mixing over a short distance, with applications in lab-on-a-chip sample testing.

Performance evaluation of Bragg coherent diffraction imaging

NASA Astrophysics Data System (ADS)

Öztürk, H.; Huang, X.; Yan, H.; Robinson, I. K.; Noyan, I. C.; Chu, Y. S.

2017-10-01

In this study, we present a numerical framework for modeling three-dimensional (3D) diffraction data in Bragg coherent diffraction imaging (Bragg CDI) experiments and evaluating the quality of obtained 3D complex-valued real-space images recovered by reconstruction algorithms under controlled conditions. The approach is used to systematically explore the performance and the detection limit of this phase-retrieval-based microscopy tool. The numerical investigation suggests that the superb performance of Bragg CDI is achieved with an oversampling ratio above 30 and a detection dynamic range above 6 orders. The observed performance degradation subject to the data binning processes is also studied. This numerical tool can be used to optimize experimental parameters and has the potential to significantly improve the throughput of Bragg CDI method.

Free energy calculation of single molecular interaction using Jarzynski's identity method: the case of HIV-1 protease inhibitor system

NASA Astrophysics Data System (ADS)

Li, De-Chang; Ji, Bao-Hua

2012-06-01

Jarzynski' identity (JI) method was suggested a promising tool for reconstructing free energy landscape of biomolecular interactions in numerical simulations and experiments. However, JI method has not yet been well tested in complex systems such as ligand-receptor molecular pairs. In this paper, we applied a huge number of steered molecular dynamics (SMD) simulations to dissociate the protease of human immunodeficiency type I virus (HIV-1 protease) and its inhibitors. We showed that because of intrinsic complexity of the ligand-receptor system, the energy barrier predicted by JI method at high pulling rates is much higher than experimental results. However, with a slower pulling rate and fewer switch times of simulations, the predictions of JI method can approach to the experiments. These results suggested that the JI method is more appropriate for reconstructing free energy landscape using the data taken from experiments, since the pulling rates used in experiments are often much slower than those in SMD simulations. Furthermore, we showed that a higher loading stiffness can produce higher precision of calculation of energy landscape because it yields a lower mean value and narrower bandwidth of work distribution in SMD simulations.

A simple finite element method for the Stokes equations

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-21

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

A simple finite element method for the Stokes equations

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

Mu, Lin; Ye, Xiu

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

Comparison of OpenFOAM and EllipSys3D actuator line methods with (NEW) MEXICO results

NASA Astrophysics Data System (ADS)

Nathan, J.; Meyer Forsting, A. R.; Troldborg, N.; Masson, C.

2017-05-01

The Actuator Line Method exists for more than a decade and has become a well established choice for simulating wind rotors in computational fluid dynamics. Numerous implementations exist and are used in the wind energy research community. These codes were verified by experimental data such as the MEXICO experiment. Often the verification against other codes were made on a very broad scale. Therefore this study attempts first a validation by comparing two different implementations, namely an adapted version of SOWFA/OpenFOAM and EllipSys3D and also a verification by comparing against experimental results from the MEXICO and NEW MEXICO experiments.

A parallel Jacobson-Oksman optimization algorithm. [parallel processing (computers)

NASA Technical Reports Server (NTRS)

Straeter, T. A.; Markos, A. T.

1975-01-01

A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities.

Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies

PubMed Central

Borazjani, Iman; Ge, Liang; Sotiropoulos, Fotis

2010-01-01

The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782–1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken’s acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and an upper bound of the required for stability under-relaxation coefficient is derived. PMID:20981246

Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Ge, Liang; Sotiropoulos, Fotis

2008-08-01

The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries, Journal of Computational Physics 225 (2007) 1782-1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions the FSI algorithm is unconditionally unstable even when strong coupling FSI is employed. For such cases, however, combining the strong coupling iteration with under-relaxation in conjunction with the Aitken's acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and the upper bound of the under-relaxation coefficient, required for stability, is derived.

Inverse Regional Modeling with Adjoint-Free Technique

NASA Astrophysics Data System (ADS)

Yaremchuk, M.; Martin, P.; Panteleev, G.; Beattie, C.

2016-02-01

The ongoing parallelization trend in computer technologies facilitates the use ensemble methods in geophysical data assimilation. Of particular interest are ensemble techniques which do not require the development of tangent linear numerical models and their adjoints for optimization. These ``adjoint-free'' methods minimize the cost function within the sequence of subspaces spanned by a carefully chosen sets perturbations of the control variables. In this presentation, an adjoint-free variational technique (a4dVar) is demonstrated in an application estimating initial conditions of two numerical models: the Navy Coastal Ocean Model (NCOM), and the surface wave model (WAM). With the NCOM, performance of both adjoint and adjoint-free 4dVar data assimilation techniques is compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea in 2006. Numerical experiments have shown that a4dVar is capable of providing forecast skill similar to that of conventional 4dVar at comparable computational expense while being less susceptible to excitation of ageostrophic modes that are not supported by observations. Adjoint-free technique constrained by the WAM model is tested in a series of data assimilation experiments with synthetic observations in the southern Chukchi Sea. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars and along-track SWH observations by satellite altimeters. The a4dVar forecast skill is shown to be 30-40% better than the skill of the sequential assimilaiton method based on optimal interpolation which is currently used in operations. Prospects of further development of the a4dVar methods in regional applications are discussed.

Hardness of H13 Tool Steel After Non-isothermal Tempering

NASA Astrophysics Data System (ADS)

Nelson, E.; Kohli, A.; Poirier, D. R.

2018-04-01

A direct method to calculate the tempering response of a tool steel (H13) that exhibits secondary hardening is presented. Based on the traditional method of presenting tempering response in terms of isothermal tempering, we show that the tempering response for a steel undergoing a non-isothermal tempering schedule can be predicted. Experiments comprised (1) isothermal tempering, (2) non-isothermal tempering pertaining to a relatively slow heating to process-temperature and (3) fast-heating cycles that are relevant to tempering by induction heating. After establishing the tempering response of the steel under simple isothermal conditions, the tempering response can be applied to non-isothermal tempering by using a numerical method to calculate the tempering parameter. Calculated results are verified by the experiments.

Prototyping method for Bragg-type atom interferometers

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

Benton, Brandon; Krygier, Michael; Heward, Jeffrey

2011-10-15

We present a method for rapid modeling of new Bragg ultracold atom-interferometer (AI) designs useful for assessing the performance of such interferometers. The method simulates the overall effect on the condensate wave function in a given AI design using two separate elements. These are (1) modeling the effect of a Bragg pulse on the wave function and (2) approximating the evolution of the wave function during the intervals between the pulses. The actual sequence of these pulses and intervals is then followed to determine the approximate final wave function from which the interference pattern can be calculated. The exact evolutionmore » between pulses is assumed to be governed by the Gross-Pitaevskii (GP) equation whose solution is approximated using a Lagrangian variational method to facilitate rapid estimation of performance. The method presented here is an extension of an earlier one that was used to analyze the results of an experiment [J. E. Simsarian et al., Phys. Rev. Lett. 85, 2040 (2000)], where the phase of a Bose-Einstein condensate was measured using a Mach-Zehnder-type Bragg AI. We have developed both 1D and 3D versions of this method and we have determined their validity by comparing their predicted interference patterns with those obtained by numerical integration of the 1D GP equation and with the results of the above experiment. We find excellent agreement between the 1D interference patterns predicted by this method and those found by the GP equation. We show that we can reproduce all of the results of that experiment without recourse to an ad hoc velocity-kick correction needed by the earlier method, including some experimental results that the earlier model did not predict. We also found that this method provides estimates of 1D interference patterns at least four orders-of-magnitude faster than direct numerical solution of the 1D GP equation.« less

Numerical simulation of premixed flame propagation in a closed tube

NASA Astrophysics Data System (ADS)

Kuzuu, Kazuto; Ishii, Katsuya; Kuwahara, Kunio

1996-08-01

Premixed flame propagation of methane-air mixture in a closed tube is estimated through a direct numerical simulation of the three-dimensional unsteady Navier-Stokes equations coupled with chemical reaction. In order to deal with a combusting flow, an extended version of the MAC method, which can be applied to a compressible flow with strong density variation, is employed as a numerical method. The chemical reaction is assumed to be an irreversible single step reaction between methane and oxygen. The chemical species are CH 4, O 2, N 2, CO 2, and H 2O. In this simulation, we reproduce a formation of a tulip flame in a closed tube during the flame propagation. Furthermore we estimate not only a two-dimensional shape but also a three-dimensional structure of the flame and flame-induced vortices, which cannot be observed in the experiments. The agreement between the calculated results and the experimental data is satisfactory, and we compare the phenomenon near the side wall with the one in the corner of the tube.

Novel permanent magnet linear motor with isolated movers: analytical, numerical and experimental study.

PubMed

Yan, Liang; Peng, Juanjuan; Jiao, Zongxia; Chen, Chin-Yin; Chen, I-Ming

2014-10-01

This paper proposes a novel permanent magnet linear motor possessing two movers and one stator. The two movers are isolated and can interact with the stator poles to generate independent forces and motions. Compared with conventional multiple motor driving system, it helps to increase the system compactness, and thus improve the power density and working efficiency. The magnetic field distribution is obtained by using equivalent magnetic circuit method. Following that, the formulation of force output considering armature reaction is carried out. Then inductances are analyzed with finite element method to investigate the relationships of the two movers. It is found that the mutual-inductances are nearly equal to zero, and thus the interaction between the two movers is negligible. A research prototype of the linear motor and a measurement apparatus on thrust force have been developed. Both numerical computation and experiment measurement are conducted to validate the analytical model of thrust force. Comparison shows that the analytical model matches the numerical and experimental results well.

Numerical simulation of water hammer in low pressurized pipe: comparison of SimHydraulics and Lax-Wendroff method with experiment

NASA Astrophysics Data System (ADS)

Himr, D.

2013-04-01

Article describes simulation of unsteady flow during water hammer with two programs, which use different numerical approaches to solve ordinary one dimensional differential equations describing the dynamics of hydraulic elements and pipes. First one is Matlab-Simulink-SimHydraulics, which is a commercial software developed to solve the dynamics of general hydraulic systems. It defines them with block elements. The other software is called HYDRA and it is based on the Lax-Wendrff numerical method, which serves as a tool to solve the momentum and continuity equations. This program was developed in Matlab by Brno University of Technology. Experimental measurements were performed on a simple test rig, which consists of an elastic pipe with strong damping connecting two reservoirs. Water hammer is induced with fast closing the valve. Physical properties of liquid and pipe elasticity parameters were considered in both simulations, which are in very good agreement and differences in comparison with experimental data are minimal.

Computation of the sound generated by isotropic turbulence

NASA Technical Reports Server (NTRS)

Sarkar, S.; Hussaini, M. Y.

1993-01-01

The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries.

PubMed

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries

PubMed Central

Ge, Liang; Sotiropoulos, Fotis

2008-01-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533

A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

DOE PAGES

Tuo, Rui; Jeff Wu, C. F.

2016-07-19

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2-inconsistent calibration. This L 2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the Lmore » 2 calibration, is proposed and proven to be L 2-consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2-inconsistency problem.« less

Chaotic time series prediction for prenatal exposure to polychlorinated biphenyls in umbilical cord blood using the least squares SEATR model

NASA Astrophysics Data System (ADS)

Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia

2016-04-01

Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field.

Chaotic time series prediction for prenatal exposure to polychlorinated biphenyls in umbilical cord blood using the least squares SEATR model

PubMed Central

Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia

2016-01-01

Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field. PMID:27118260

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

NASA Astrophysics Data System (ADS)

Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

2008-12-01

A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.

A Method for Large Eddy Simulation of Acoustic Combustion Instabilities

NASA Astrophysics Data System (ADS)

Wall, Clifton; Moin, Parviz

2003-11-01

A method for performing Large Eddy Simulation of acoustic combustion instabilities is presented. By extending the low Mach number pressure correction method to the case of compressible flow, a numerical method is developed in which the Poisson equation for pressure is replaced by a Helmholtz equation. The method avoids the acoustic CFL condition by using implicit time advancement, leading to large efficiency gains at low Mach number. The method also avoids artificial damping of acoustic waves. The numerical method is attractive for the simulation of acoustics combustion instabilities, since these flows are typically at low Mach number, and the acoustic frequencies of interest are usually low. Additionally, new boundary conditions based on the work of Poinsot and Lele have been developed to model the acoustic effect of a long channel upstream of the computational inlet, thus avoiding the need to include such a channel in the computational domain. The turbulent combustion model used is the Level Set model of Duchamp de Lageneste and Pitsch for premixed combustion. Comparison of LES results to the reacting experiments of Besson et al. will be presented.

Linear information retrieval method in X-ray grating-based phase contrast imaging and its interchangeability with tomographic reconstruction

NASA Astrophysics Data System (ADS)

Wu, Z.; Gao, K.; Wang, Z. L.; Shao, Q. G.; Hu, R. F.; Wei, C. X.; Zan, G. B.; Wali, F.; Luo, R. H.; Zhu, P. P.; Tian, Y. C.

2017-06-01

In X-ray grating-based phase contrast imaging, information retrieval is necessary for quantitative research, especially for phase tomography. However, numerous and repetitive processes have to be performed for tomographic reconstruction. In this paper, we report a novel information retrieval method, which enables retrieving phase and absorption information by means of a linear combination of two mutually conjugate images. Thanks to the distributive law of the multiplication as well as the commutative law and associative law of the addition, the information retrieval can be performed after tomographic reconstruction, thus simplifying the information retrieval procedure dramatically. The theoretical model of this method is established in both parallel beam geometry for Talbot interferometer and fan beam geometry for Talbot-Lau interferometer. Numerical experiments are also performed to confirm the feasibility and validity of the proposed method. In addition, we discuss its possibility in cone beam geometry and its advantages compared with other methods. Moreover, this method can also be employed in other differential phase contrast imaging methods, such as diffraction enhanced imaging, non-interferometric imaging, and edge illumination.

Physical mechanisms of longitudinal vortexes formation, appearance of zones with high heat fluxes and early transition in hypersonic flow over delta wing with blunted leading edges

NASA Astrophysics Data System (ADS)

Alexandrov, S. V.; Vaganov, A. V.; Shalaev, V. I.

2016-10-01

Processes of vortex structures formation and they interactions with the boundary layer in the hypersonic flow over delta wing with blunted leading edges are analyzed on the base of experimental investigations and numerical solutions of Navier-Stokes equations. Physical mechanisms of longitudinal vortexes formation, appearance of abnormal zones with high heat fluxes and early laminar turbulent transition are studied. These phenomena were observed in many high-speed wind tunnel experiments; however they were understood only using the detailed analysis of numerical modeling results with the high resolution. Presented results allowed explaining experimental phenomena. ANSYS CFX code (the DAFE MIPT license) on the grid with 50 million nodes was used for the numerical modeling. The numerical method was verified by comparison calculated heat flux distributions on the wing surface with experimental data.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

Numerical simulation for turbulent heating around the forebody fairing of H-II rocket

NASA Astrophysics Data System (ADS)

Nomura, Shigeaki; Yamamoto, Yukimitsu; Fukushima, Yukio

Concerning the heat transfer distributions around the nose fairing of the Japanese new launch vehicle H-II rocket, numerical simulations have been conducted for the conditions along its nominal ascent trajectory and some experimental tests have been conducted additionally to confirm the numerical results. The thin layer approximated Navier-Stokes equations with Baldwin-Lomax's algebraic turbulent model were solved by the time dependent finite difference method. Results of numerical simulations showed that a high peak heating would occur near the stagnation point on the spherical nose portion due to the transition to turbulent flow during the period when large stagnation point heating was predicted. The experiments were conducted under the condition of M = 5 and Re = 10 to the 6th which was similar to the flight condition where the maximum stagnation point heating would occur. The experimental results also showed a high peak heating near the stagnation point over the spherical nose portion.

Local mechanical properties of LFT injection molded parts: Numerical simulations versus experiments

NASA Astrophysics Data System (ADS)

Desplentere, F.; Soete, K.; Bonte, H.; Debrabandere, E.

2014-05-01

In predictive engineering for polymer processes, the proper prediction of material microstructure from known processing conditions and constituent material properties is a critical step forward properly predicting bulk properties in the finished composite. Operating within the context of long-fiber thermoplastics (LFT, length < 15mm) this investigation concentrates on the prediction of the local mechanical properties of an injection molded part. To realize this, the Autodesk Simulation Moldflow Insight 2014 software has been used. In this software, a fiber breakage algorithm for the polymer flow inside the mold is available. Using well known micro mechanic formulas allow to combine the local fiber length with the local orientation into local mechanical properties. Different experiments were performed using a commercially available glass fiber filled compound to compare the measured data with the numerical simulation results. In this investigation, tensile tests and 3 point bending tests are considered. To characterize the fiber length distribution of the polymer melt entering the mold (necessary for the numerical simulations), air shots were performed. For those air shots, similar homogenization conditions were used as during the injection molding tests. The fiber length distribution is characterized using automated optical method on samples for which the matrix material is burned away. Using the appropriate settings for the different experiments, good predictions of the local mechanical properties are obtained.

W17_geonuc “Application of the Spectral Element Method to improvement of Ground-based Nuclear Explosion Monitoring”

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

Larmat, Carene; Rougier, Esteban; Lei, Zhou

This project is in support of the Source Physics Experiment SPE (Snelson et al. 2013), which aims to develop new seismic source models of explosions. One priority of this program is first principle numerical modeling to validate and extend current empirical models.

What Motivates Introductory Geology Students to Study for an Exam?

ERIC Educational Resources Information Center

Lukes, Laura A.; McConnell, David A.

2014-01-01

There is a need to understand why some students succeed and persist in STEM fields and others do not. While numerous studies have focused on the positive results of using empirically validated teaching methods in introductory science, technology, engineering, and math (STEM) courses, little data has been collected about the student experience in…

A note on the radial solutions for the supercritical Hénon equation

NASA Astrophysics Data System (ADS)

Barutello, Vivina; Secchi, Simone; Serra, Enrico

2008-05-01

We prove the existence of a positive radial solution for the Hénon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.

More on Systematic Error in a Boyle's Law Experiment

ERIC Educational Resources Information Center

McCall, Richard P.

2012-01-01

A recent article in "The Physics Teacher" describes a method for analyzing a systematic error in a Boyle's law laboratory activity. Systematic errors are important to consider in physics labs because they tend to bias the results of measurements. There are numerous laboratory examples and resources that discuss this common source of error.

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.; Tang, Harry (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

Frequency-independent approach to calculate physical optics radiations with the quadratic concave phase variations

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

Wu, Yu Mao, E-mail: yumaowu@fudan.edu.cn; Teng, Si Jia, E-mail: sjteng12@fudan.edu.cn

In this work, we develop the numerical steepest descent path (NSDP) method to calculate the physical optics (PO) radiations with the quadratic concave phase variations. With the surface integral equation method, the physical optics (PO) scattered fields are formulated and further reduced to the surface integrals. The high frequency physical critical points contributions, including the stationary phase points, the boundary resonance points and the vertex points are comprehensively studied via the proposed NSDP method. The key contributions of this work are twofold. One is that together with the PO integrals taking the quadratic parabolic and hyperbolic phase terms, this workmore » makes the NSDP theory be complete for treating the PO integrals with quadratic phase variations. Another is that, in order to illustrate the transition effect of the high frequency physical critical points, in this work, we consider and further extend the NSDP method to calculate the PO integrals with the coalescence of the high frequency critical points. Numerical results for the highly oscillatory PO integral with the coalescence of the critical points are given to verify the efficiency of the proposed NSDP method. The NSDP method could achieve the frequency independent computational workload and error controllable accuracy in all the numerical experiments, especially for the case of the coalescence of the high frequency critical points.« less

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

DOE PAGES

Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

2015-09-08

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics

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

Leimkuhler, Benedict, E-mail: b.leimkuhler@ed.ac.uk; Shang, Xiaocheng, E-mail: x.shang@brown.edu

2016-11-01

We examine the formulation and numerical treatment of dissipative particle dynamics (DPD) and momentum-conserving molecular dynamics. We show that it is possible to improve both the accuracy and the stability of DPD by employing a pairwise adaptive Langevin thermostat that precisely matches the dynamical characteristics of DPD simulations (e.g., autocorrelation functions) while automatically correcting thermodynamic averages using a negative feedback loop. In the low friction regime, it is possible to replace DPD by a simpler momentum-conserving variant of the Nosé–Hoover–Langevin method based on thermostatting only pairwise interactions; we show that this method has an extra order of accuracy for anmore » important class of observables (a superconvergence result), while also allowing larger timesteps than alternatives. All the methods mentioned in the article are easily implemented. Numerical experiments are performed in both equilibrium and nonequilibrium settings; using Lees–Edwards boundary conditions to induce shear flow.« less

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Visualization of flow separation and control by vortex generators on an single flap in landing configuration

NASA Astrophysics Data System (ADS)

Součková, Natálie; Kuklová, Jana; Popelka, Lukáš; Matějka, Milan

2012-04-01

This paper focuses on a suppression of the flow separation, which occurs on a deflected flap, by means of vortex generators (VG's). An airfoil NACA 63A421 with a simple flap and vane-type vortex generators were used. The investigation was carried out by using experimental and numerical methods. The data from the numerical simulation of the flapped airfoil without VG's control were used for the vortex generator design. Two sizes, two different shapes and various spacing of the vortex generators were tested. The flow past the airfoil was visualized through three methods, namely tuft filaments technique, oil and thermo camera visualization. The experiments were performed in closed circuit wind tunnels with closed and open test sections. The lift curves for both cases without and with vortex generators were acquired for a lift coefficient improvement determination. The improvement was achieved for several cases by means all of the applied methods.

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Development of Numerical Methods to Estimate the Ohmic Breakdown Scenarios of a Tokamak

NASA Astrophysics Data System (ADS)

Yoo, Min-Gu; Kim, Jayhyun; An, Younghwa; Hwang, Yong-Seok; Shim, Seung Bo; Lee, Hae June; Na, Yong-Su

2011-10-01

The ohmic breakdown is a fundamental method to initiate the plasma in a tokamak. For the robust breakdown, ohmic breakdown scenarios have to be carefully designed by optimizing the magnetic field configurations to minimize the stray magnetic fields. This research focuses on development of numerical methods to estimate the ohmic breakdown scenarios by precise analysis of the magnetic field configurations. This is essential for the robust and optimal breakdown and start-up of fusion devices especially for ITER and its beyond equipped with low toroidal electric field (ET <= 0.3 V/m). A field-line-following analysis code based on the Townsend avalanche theory and a particle simulation code are developed to analyze the breakdown characteristics of actual complex magnetic field configurations including the stray magnetic fields in tokamaks. They are applied to the ohmic breakdown scenarios of tokamaks such as KSTAR and VEST and compared with experiments.

The spectral cell method in nonlinear earthquake modeling

NASA Astrophysics Data System (ADS)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

Multi-objective Optimization Strategies Using Adjoint Method and Game Theory in Aerodynamics

NASA Astrophysics Data System (ADS)

Tang, Zhili

2006-08-01

There are currently three different game strategies originated in economics: (1) Cooperative games (Pareto front), (2) Competitive games (Nash game) and (3) Hierarchical games (Stackelberg game). Each game achieves different equilibria with different performance, and their players play different roles in the games. Here, we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multi-criteria aerodynamic optimization problems. The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments. We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method. The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front. Non-dominated Pareto front solutions are obtained, however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.

Immunomagnetic separation for MEMS-based biosensor of waterborne pathogens detection

NASA Astrophysics Data System (ADS)

Guo, Jianjiang; Zhang, Rongbiao

2017-07-01

Rapid isolation and detection of special pathogens present in environmental drinking water is critical for water quality monitoring. Numerical analysis and experimental investigations on immunomagnetic capture and isolation of waterborne pathogens with magnetic nanoparticles (MNPs) in microfluidic channel are performed. A finite-element COMSOL-based model is established to demonstrate the novel method of on-chip capturing pathogens using MNPs together with periodic pulse magnetic field. Simulation results determine the optimum magnetic pole current and switching frequency for magnetic separation. With the magnetic isolation experiment platform built up, as a pathogen example of Escherichia coli O157:H7, the performance of the method is experimentally verified. Both numerical and experimental results are found to agree reasonably well. Results of these investigations show that the capture efficiency of the immunomagnetic separation method is more than 92%, which could be encouraging for the design and optimization of MEMS-based biosensor of waterborne pathogen detection.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

NASA Technical Reports Server (NTRS)

Lin, Ray-Quing; Kuang, Weijia

2011-01-01

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

Exploring the nonequilibrium dynamics of ultracold quantum gases by using numerical tools

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian

Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al., in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis, nonequilibrium mass transport, dynamical fermionization, and transient phenomena such as quantum distillation or dynamical quasicondensation. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems and in determining the asymptotic state after a quantum quench. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 801.

Ex Vivo and in Silico Study of Human Common Carotid Arteries Pressure Response in Physiological and Inverted State

NASA Astrophysics Data System (ADS)

Piechna, A.; Cieślicki, K.; Lombarski, L.; Ciszek, B.

2015-02-01

Arterial walls are a multilayer structures with nonlinear material characteristics. Furthermore, residual stresses exist in unloaded state (zero-pressure condition) and they affect arterial behavior. To investigate these phenomena a number of theoretical and numerical studies were performed, however no experimental validation was proposed and realized yet. We cannot get rid of residual stresses without damaging the arterial segment. In this paper we propose a novel experiment to validate a numerical model of artery with residual stresses. The inspiration for our study originates from experiments made by Dobrin on dogs' arteries (1999). We applied the idea of turning the artery inside out. After such an operation the sequence of layer is reversed and the residual stresses are re-ordered. We performed several pressure-inflation tests on human Common Carotid Arteries (CCA) in normal and inverted configurations. The nonlinear responses of arterial behavior were obtained and compared to the numerical model. Computer simulations were carried out using the commercial software which applied the finite element method (FEM). Then, these results were discussed.

Background field removal technique based on non-regularized variable kernels sophisticated harmonic artifact reduction for phase data for quantitative susceptibility mapping.

PubMed

Kan, Hirohito; Arai, Nobuyuki; Takizawa, Masahiro; Omori, Kazuyoshi; Kasai, Harumasa; Kunitomo, Hiroshi; Hirose, Yasujiro; Shibamoto, Yuta

2018-06-11

We developed a non-regularized, variable kernel, sophisticated harmonic artifact reduction for phase data (NR-VSHARP) method to accurately estimate local tissue fields without regularization for quantitative susceptibility mapping (QSM). We then used a digital brain phantom to evaluate the accuracy of the NR-VSHARP method, and compared it with the VSHARP and iterative spherical mean value (iSMV) methods through in vivo human brain experiments. Our proposed NR-VSHARP method, which uses variable spherical mean value (SMV) kernels, minimizes L2 norms only within the volume of interest to reduce phase errors and save cortical information without regularization. In a numerical phantom study, relative local field and susceptibility map errors were determined using NR-VSHARP, VSHARP, and iSMV. Additionally, various background field elimination methods were used to image the human brain. In a numerical phantom study, the use of NR-VSHARP considerably reduced the relative local field and susceptibility map errors throughout a digital whole brain phantom, compared with VSHARP and iSMV. In the in vivo experiment, the NR-VSHARP-estimated local field could sufficiently achieve minimal boundary losses and phase error suppression throughout the brain. Moreover, the susceptibility map generated using NR-VSHARP minimized the occurrence of streaking artifacts caused by insufficient background field removal. Our proposed NR-VSHARP method yields minimal boundary losses and highly precise phase data. Our results suggest that this technique may facilitate high-quality QSM. Copyright © 2017. Published by Elsevier Inc.

A Fast Fourier transform stochastic analysis of the contaminant transport problem

USGS Publications Warehouse

Deng, F.W.; Cushman, J.H.; Delleur, J.W.

1993-01-01

A three-dimensional stochastic analysis of the contaminant transport problem is developed in the spirit of Naff (1990). The new derivation is more general and simpler than previous analysis. The fast Fourier transformation is used extensively to obtain numerical estimates of the mean concentration and various spatial moments. Data from both the Borden and Cape Cod experiments are used to test the methodology. Results are comparable to results obtained by other methods, and to the experiments themselves.

An improvement of convergence of a dispersion-relation preserving method for the classical Boussinesq equation

NASA Astrophysics Data System (ADS)

Jang, T. S.

2018-03-01

A dispersion-relation preserving (DRP) method, as a semi-analytic iterative procedure, has been proposed by Jang (2017) for integrating the classical Boussinesq equation. It has been shown to be a powerful numerical procedure for simulating a nonlinear dispersive wave system because it preserves the dispersion-relation, however, there still exists a potential flaw, e.g., a restriction on nonlinear wave amplitude and a small region of convergence (ROC) and so on. To remedy the flaw, a new DRP method is proposed in this paper, aimed at improving convergence performance. The improved method is proved to have convergence properties and dispersion-relation preserving nature for small waves; of course, unique existence of the solutions is also proved. In addition, by a numerical experiment, the method is confirmed to be good at observing nonlinear wave phenomena such as moving solitary waves and their binary collision with different wave amplitudes. Especially, it presents a ROC (much) wider than that of the previous method by Jang (2017). Moreover, it gives the numerical simulation of a high (or large-amplitude) nonlinear dispersive wave. In fact, it is demonstrated to simulate a large-amplitude solitary wave and the collision of two solitary waves with large-amplitudes that we have failed to simulate with the previous method. Conclusively, it is worth noting that better convergence results are achieved compared to Jang (2017); i.e., they represent a major improvement in practice over the previous method.

Methodenvergleich zur Bestimmung der hydraulischen Durchlässigkeit

NASA Astrophysics Data System (ADS)

Storz, Katharina; Steger, Hagen; Wagner, Valentin; Bayer, Peter; Blum, Philipp

2017-06-01

Knowing the hydraulic conductivity (K) is a precondition for understanding groundwater flow processes in the subsurface. Numerous laboratory and field methods for the determination of hydraulic conductivity exist, which can lead to significantly different results. In order to quantify the variability of these various methods, the hydraulic conductivity was examined for an industrial silica sand (Dorsilit) using four different methods: (1) grain-size analysis, (2) Kozeny-Carman approach, (3) permeameter tests and (4) flow rate experiments in large-scale tank experiments. Due to the large volume of the artificially built aquifer, the tank experiment results are assumed to be the most representative. Hydraulic conductivity values derived from permeameter tests show only minor deviation, while results of the empirically evaluated grain-size analysis are about one magnitude higher and show great variances. The latter was confirmed by the analysis of several methods for the determination of K-values found in the literature, thus we generally question the suitability of grain-size analyses and strongly recommend the use of permeameter tests.

Numerical simulation of evolutionary erodible bedforms using the particle finite element method

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Becker, Pablo; Ortiz, Pablo

2017-07-01

This paper presents a numerical strategy for the simulation of flows with evolutionary erodible boundaries. The fluid equations are fully resolved in 3D, while the sediment transport is modelled using the Exner equation and solved with an explicit Lagrangian procedure based on a fixed 2D mesh. Flow and sediment are coupled in geometry by deforming the fluid mesh in the vertical direction and in velocities with the experimental sediment flux computed using the Meyer Peter Müller model. A comparison with real experiments on channels is performed, giving good agreement.

Automated Testcase Generation for Numerical Support Functions in Embedded Systems

NASA Technical Reports Server (NTRS)

Schumann, Johann; Schnieder, Stefan-Alexander

2014-01-01

We present a tool for the automatic generation of test stimuli for small numerical support functions, e.g., code for trigonometric functions, quaternions, filters, or table lookup. Our tool is based on KLEE to produce a set of test stimuli for full path coverage. We use a method of iterative deepening over abstractions to deal with floating-point values. During actual testing the stimuli exercise the code against a reference implementation. We illustrate our approach with results of experiments with low-level trigonometric functions, interpolation routines, and mathematical support functions from an open source UAS autopilot.

Quasistatic packings of droplets in flat microfluidic channels

NASA Astrophysics Data System (ADS)

Kadivar, Erfan

2016-02-01

As observed in recent experiments, monodisperse droplets self-assemble spontaneously in different ordered packings. In this work, we present a numerical study of the droplet packings in the flat rectangular microfluidic channels. Employing the boundary element method, we numerically solve the Stokes equation in two-dimension and investigate the appearance of droplet packing and transition between one and two-row packings of monodisperse emulsion droplets. By calculating packing force applied on the droplet interface, we investigate the effect of flow rate, droplet size, and surface tension on the packing configurations of droplets and transition between different topological packings.

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

Numerical prediction of a draft tube flow taking into account uncertain inlet conditions

NASA Astrophysics Data System (ADS)

Brugiere, O.; Balarac, G.; Corre, C.; Metais, O.; Flores, E.; Pleroy

2012-11-01

The swirling turbulent flow in a hydroturbine draft tube is computed with a non-intrusive uncertainty quantification (UQ) method coupled to Reynolds-Averaged Navier-Stokes (RANS) modelling in order to take into account in the numerical prediction the physical uncertainties existing on the inlet flow conditions. The proposed approach yields not only mean velocity fields to be compared with measured profiles, as is customary in Computational Fluid Dynamics (CFD) practice, but also variance of these quantities from which error bars can be deduced on the computed profiles, thus making more significant the comparison between experiment and computation.

The Numerical Studies Program for the Atmospheric General Circulation Experiment (AGCE) for Spacelab Flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W. (Editor); Davis, M. H. (Editor)

1981-01-01

The atmospheric general circulation experiment (AGCE) numerical design for Spacelab flights was studied. A spherical baroclinic flow experiment which models the large scale circulations of the Earth's atmosphere was proposed. Gravity is simulated by a radial dielectric body force. The major objective of the AGCE is to study nonlinear baroclinic wave flows in spherical geometry. Numerical models must be developed which accurately predict the basic axisymmetric states and the stability of nonlinear baroclinic wave flows. A three dimensional, fully nonlinear, numerical model and the AGCE based on the complete set of equations is required. Progress in the AGCE numerical design studies program is reported.

A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface

NASA Astrophysics Data System (ADS)

Cao, Huijun; Cao, Yong; Chu, Yuchuan; He, Xiaoming; Lin, Tao

2018-06-01

Surface evolution is an unavoidable issue in engineering plasma applications. In this article an iterative method for modeling plasma-surface interactions with moving interface is proposed and validated. In this method, the plasma dynamics is simulated by an immersed finite element particle-in-cell (IFE-PIC) method, and the surface evolution is modeled by the Huygens wavelet method which is coupled with the iteration of the IFE-PIC method. Numerical experiments, including prototypical engineering applications, such as the erosion of Hall thruster channel wall, are presented to demonstrate features of this Huygens IFE-PIC method for simulating the dynamic plasma-surface interactions.

Selecting an appropriate method to remove cyanide from the wastewater of Moteh gold mine using a mathematical approach.

PubMed

Seyyed Alizadeh Ganji, Seyyed Mohammad; Hayati, Mohammad

2018-06-05

The presence of cyanide ions in wastewater is dangerous to the health and life of living creatures, especially humans. Cyanide concentration should not exceed the acceptable limit in wastewaters to avoid their adverse effects to the environment. In this paper, in order to select the most appropriate method to remove cyanide from the wastewater of the Moteh gold mine, based on the experts' opinions, the use of calcium hypochlorite, sodium hypochlorite, and hydrogen peroxide was chosen as forerunning alternative in the form of a multi-stage model. Then, seven criteria including the amount of material consumed, ease of implementation, safety, ability to remove cyanide, pH, time, and cost of the process to assess the considered methods were determined. Afterwards, seven experts conducted numerous experiments to examine the conditions of each of these criteria. Then, by employing a mathematical method called "numerical taxonomy," the use of sodium hypochlorite was suggested as the best method to remove cyanide from the wastewater of the Moteh gold mine. Finally, the TOPSIS model was used to validate the proposed model, which led to the same results of the suggested method. Also, the results of employing taxonomic analysis and TOPSIS method suggested the use of sodium hypochlorite as the best method for cyanide removal from wastewater. In addition, according to the analysis of various experiments, conditions for complete removal of cyanide using sodium hypochlorite included concentration (8.64 g/L), pH (12.3), and temperature (12 °C).

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Maximizing and minimizing investment concentration with constraints of budget and investment risk

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-01-01

In this paper, as a first step in examining the properties of a feasible portfolio subset that is characterized by budget and risk constraints, we assess the maximum and minimum of the investment concentration using replica analysis. To do this, we apply an analytical approach of statistical mechanics. We note that the optimization problem considered in this paper is the dual problem of the portfolio optimization problem discussed in the literature, and we verify that these optimal solutions are also dual. We also present numerical experiments, in which we use the method of steepest descent that is based on Lagrange's method of undetermined multipliers, and we compare the numerical results to those obtained by replica analysis in order to assess the effectiveness of our proposed approach.

A non-oscillatory energy-splitting method for the computation of compressible multi-fluid flows

NASA Astrophysics Data System (ADS)

Lei, Xin; Li, Jiequan

2018-04-01

This paper proposes a new non-oscillatory energy-splitting conservative algorithm for computing multi-fluid flows in the Eulerian framework. In comparison with existing multi-fluid algorithms in the literature, it is shown that the mass fraction model with isobaric hypothesis is a plausible choice for designing numerical methods for multi-fluid flows. Then we construct a conservative Godunov-based scheme with the high order accurate extension by using the generalized Riemann problem solver, through the detailed analysis of kinetic energy exchange when fluids are mixed under the hypothesis of isobaric equilibrium. Numerical experiments are carried out for the shock-interface interaction and shock-bubble interaction problems, which display the excellent performance of this type of schemes and demonstrate that nonphysical oscillations are suppressed around material interfaces substantially.

Dynamic earthquake rupture simulation on nonplanar faults embedded in 3D geometrically complex, heterogeneous Earth models

NASA Astrophysics Data System (ADS)

Duru, K.; Dunham, E. M.; Bydlon, S. A.; Radhakrishnan, H.

2014-12-01

Dynamic propagation of shear ruptures on a frictional interface is a useful idealization of a natural earthquake.The conditions relating slip rate and fault shear strength are often expressed as nonlinear friction laws.The corresponding initial boundary value problems are both numerically and computationally challenging.In addition, seismic waves generated by earthquake ruptures must be propagated, far away from fault zones, to seismic stations and remote areas.Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods.We present a numerical method for:a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration;b) dynamic propagation of earthquake ruptures along rough faults; c) accurate propagation of seismic waves in heterogeneous media with free surface topography.We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts finite differences in space. The finite difference stencils are 6th order accurate in the interior and 3rd order accurate close to the boundaries. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme. We have performed extensive numerical experiments using a slip-weakening friction law on non-planar faults, including recent SCEC benchmark problems. We also show simulations on fractal faults revealing the complexity of rupture dynamics on rough faults. We are presently extending our method to rate-and-state friction laws and off-fault plasticity.

Surface tension of undercooled liquid cobalt

NASA Astrophysics Data System (ADS)

Yao, W. J.; Han, X. J.; Chen, M.; Wei, B.; Guo, Z. Y.

2002-08-01

This paper provides the results on experimentally measured and numerically predicted surface tensions of undercooled liquid cobalt. The experiments were performed by using the oscillation drop technique combined with electromagnetic levitation. The simulations are carried out with the Monte Carlo (MC) method, where the surface tension is predicted through calculations of the work of cohesion, and the interatomic interaction is described with an embedded-atom method. The maximum undercooling of the liquid cobalt is reached at 231 K (0.13Tm) in the experiment and 268 K (0.17Tm) in the simulation. The surface tension and its relationship with temperature obtained in the experiment and simulation are σexp = 1.93 - 0.000 33 (T - T m) N m-1 and σcal = 2.26 - 0.000 32 (T - T m) N m-1 respectively. The temperature dependence of the surface tension calculated from the MC simulation is in reasonable agreement with that measured in the experiment.

Impact of air temperature on physically-based maximum precipitation estimation through change in moisture holding capacity of air

NASA Astrophysics Data System (ADS)

Ishida, K.; Ohara, N.; Kavvas, M. L.; Chen, Z. Q.; Anderson, M. L.

2018-01-01

Impact of air temperature on the Maximum Precipitation (MP) estimation through change in moisture holding capacity of air was investigated. A series of previous studies have estimated the MP of 72-h basin-average precipitation over the American River watershed (ARW) in Northern California by means of the Maximum Precipitation (MP) estimation approach, which utilizes a physically-based regional atmospheric model. For the MP estimation, they have selected 61 severe storm events for the ARW, and have maximized them by means of the atmospheric boundary condition shifting (ABCS) and relative humidity maximization (RHM) methods. This study conducted two types of numerical experiments in addition to the MP estimation by the previous studies. First, the air temperature on the entire lateral boundaries of the outer model domain was increased uniformly by 0.0-8.0 °C with 0.5 °C increments for the two severest maximized historical storm events in addition to application of the ABCS + RHM method to investigate the sensitivity of the basin-average precipitation over the ARW to air temperature rise. In this investigation, a monotonous increase was found in the maximum 72-h basin-average precipitation over the ARW with air temperature rise for both of the storm events. The second numerical experiment used specific amounts of air temperature rise that is assumed to happen under future climate change conditions. Air temperature was increased by those specified amounts uniformly on the entire lateral boundaries in addition to application of the ABCS + RHM method to investigate the impact of air temperature on the MP estimate over the ARW under changing climate. The results in the second numerical experiment show that temperature increases in the future climate may amplify the MP estimate over the ARW. The MP estimate may increase by 14.6% in the middle of the 21st century and by 27.3% in the end of the 21st century compared to the historical period.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Observing system simulation experiments with multiple methods

NASA Astrophysics Data System (ADS)

Ishibashi, Toshiyuki

2014-11-01

An observing System Simulation Experiment (OSSE) is a method to evaluate impacts of hypothetical observing systems on analysis and forecast accuracy in numerical weather prediction (NWP) systems. Since OSSE requires simulations of hypothetical observations, uncertainty of OSSE results is generally larger than that of observing system experiments (OSEs). To reduce such uncertainty, OSSEs for existing observing systems are often carried out as calibration of the OSSE system. The purpose of this study is to achieve reliable OSSE results based on results of OSSEs with multiple methods. There are three types of OSSE methods. The first one is the sensitivity observing system experiment (SOSE) based OSSE (SOSEOSSE). The second one is the ensemble of data assimilation cycles (ENDA) based OSSE (ENDA-OSSE). The third one is the nature-run (NR) based OSSE (NR-OSSE). These three OSSE methods have very different properties. The NROSSE evaluates hypothetical observations in a virtual (hypothetical) world, NR. The ENDA-OSSE is very simple method but has a sampling error problem due to a small size ensemble. The SOSE-OSSE requires a very highly accurate analysis field as a pseudo truth of the real atmosphere. We construct these three types of OSSE methods in the Japan meteorological Agency (JMA) global 4D-Var experimental system. In the conference, we will present initial results of these OSSE systems and their comparisons.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

NASA Astrophysics Data System (ADS)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

Joint multifractal analysis based on wavelet leaders

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Yang, Yan-Hong; Wang, Gang-Jin; Zhou, Wei-Xing

2017-12-01

Mutually interacting components form complex systems and these components usually have long-range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and determine intriguing joint multifractal behavior.

A composite experimental dynamic substructuring method based on partitioned algorithms and localized Lagrange multipliers

NASA Astrophysics Data System (ADS)

Abbiati, Giuseppe; La Salandra, Vincenzo; Bursi, Oreste S.; Caracoglia, Luca

2018-02-01

Successful online hybrid (numerical/physical) dynamic substructuring simulations have shown their potential in enabling realistic dynamic analysis of almost any type of non-linear structural system (e.g., an as-built/isolated viaduct, a petrochemical piping system subjected to non-stationary seismic loading, etc.). Moreover, owing to faster and more accurate testing equipment, a number of different offline experimental substructuring methods, operating both in time (e.g. the impulse-based substructuring) and frequency domains (i.e. the Lagrange multiplier frequency-based substructuring), have been employed in mechanical engineering to examine dynamic substructure coupling. Numerous studies have dealt with the above-mentioned methods and with consequent uncertainty propagation issues, either associated with experimental errors or modelling assumptions. Nonetheless, a limited number of publications have systematically cross-examined the performance of the various Experimental Dynamic Substructuring (EDS) methods and the possibility of their exploitation in a complementary way to expedite a hybrid experiment/numerical simulation. From this perspective, this paper performs a comparative uncertainty propagation analysis of three EDS algorithms for coupling physical and numerical subdomains with a dual assembly approach based on localized Lagrange multipliers. The main results and comparisons are based on a series of Monte Carlo simulations carried out on a five-DoF linear/non-linear chain-like systems that include typical aleatoric uncertainties emerging from measurement errors and excitation loads. In addition, we propose a new Composite-EDS (C-EDS) method to fuse both online and offline algorithms into a unique simulator. Capitalizing from the results of a more complex case study composed of a coupled isolated tank-piping system, we provide a feasible way to employ the C-EDS method when nonlinearities and multi-point constraints are present in the emulated system.

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

NASA Astrophysics Data System (ADS)

Belyaev, V. A.; Shapeev, V. P.

2017-10-01

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

High performance computation of residual stress and distortion in laser welded 301L stainless sheets

DOE PAGES

Huang, Hui; Tsutsumi, Seiichiro; Wang, Jiandong; ...

2017-07-11

Transient thermo-mechanical simulation of stainless plate laser welding process was performed by a highly efficient and accurate approach-hybrid iterative substructure and adaptive mesh method. Especially, residual stress prediction was enhanced by considering various heat effects in the numerical model. The influence of laser welding heat input on residual stress and welding distortion of stainless thin sheets were investigated by experiment and simulation. X-ray diffraction (XRD) and contour method were used to measure the surficial and internal residual stress respectively. Effect of strain hardening, annealing and melting on residual stress prediction was clarified through a parametric study. It was shown thatmore » these heat effects must be taken into account for accurate prediction of residual stresses in laser welded stainless sheets. Reasonable agreement among residual stresses by numerical method, XRD and contour method was obtained. Buckling type welding distortion was also well reproduced by the developed thermo-mechanical FEM.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

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

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

High performance computation of residual stress and distortion in laser welded 301L stainless sheets

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

Huang, Hui; Tsutsumi, Seiichiro; Wang, Jiandong

Transient thermo-mechanical simulation of stainless plate laser welding process was performed by a highly efficient and accurate approach-hybrid iterative substructure and adaptive mesh method. Especially, residual stress prediction was enhanced by considering various heat effects in the numerical model. The influence of laser welding heat input on residual stress and welding distortion of stainless thin sheets were investigated by experiment and simulation. X-ray diffraction (XRD) and contour method were used to measure the surficial and internal residual stress respectively. Effect of strain hardening, annealing and melting on residual stress prediction was clarified through a parametric study. It was shown thatmore » these heat effects must be taken into account for accurate prediction of residual stresses in laser welded stainless sheets. Reasonable agreement among residual stresses by numerical method, XRD and contour method was obtained. Buckling type welding distortion was also well reproduced by the developed thermo-mechanical FEM.« less

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Numerical modeling of local scour around hydraulic structure in sandy beds by dynamic mesh method

NASA Astrophysics Data System (ADS)

Fan, Fei; Liang, Bingchen; Bai, Yuchuan; Zhu, Zhixia; Zhu, Yanjun

2017-10-01

Local scour, a non-negligible factor in hydraulic engineering, endangers the safety of hydraulic structures. In this work, a numerical model for simulating local scour was constructed, based on the open source code computational fluid dynamics model OpenFOAM. We consider both the bedload and suspended load sediment transport in the scour model and adopt the dynamic mesh method to simulate the evolution of the bed elevation. We use the finite area method to project data between the three-dimensional flow model and the two-dimensional (2D) scour model. We also improved the 2D sand slide method and added it to the scour model to correct the bed bathymetry when the bed slope angle exceeds the angle of repose. Moreover, to validate our scour model, we conducted and compared the results of three experiments with those of the developed model. The validation results show that our developed model can reliably simulate local scour.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

An engineering study of hybrid adaptation of wind tunnel walls for three-dimensional testing

NASA Technical Reports Server (NTRS)

Brown, Clinton; Kalumuck, Kenneth; Waxman, David

1987-01-01

Solid wall tunnels having only upper and lower walls flexing are described. An algorithm for selecting the wall contours for both 2 and 3 dimensional wall flexure is presented and numerical experiments are used to validate its applicability to the general test case of 3 dimensional lifting aircraft models in rectangular cross section wind tunnels. The method requires an initial approximate representation of the model flow field at a given lift with wallls absent. The numerical methods utilized are derived by use of Green's source solutions obtained using the method of images; first order linearized flow theory is employed with Prandtl-Glauert compressibility transformations. Equations are derived for the flexed shape of a simple constant thickness plate wall under the influence of a finite number of jacks in an axial row along the plate centerline. The Green's source methods are developed to provide estimations of residual flow distortion (interferences) with measured wall pressures and wall flow inclinations as inputs.

Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling

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

Tavakoli, Rouhollah, E-mail: rtavakoli@sharif.ir

An unconditionally energy stable time stepping scheme is introduced to solve Cahn–Morral-like equations in the present study. It is constructed based on the combination of David Eyre's time stepping scheme and Schur complement approach. Although the presented method is general and independent of the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi-component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments demonstrate themore » success and performance of the presented method. According to the numerical results, the method is convergent and energy stable, independent of the choice of time stepsize. Its MATLAB implementation is included in the appendix for the numerical evaluation of algorithm and reproduction of the presented results. -- Highlights: •Extension of Eyre's convex–concave splitting scheme to multiphase systems. •Efficient solution of spinodal decomposition in multi-component systems. •Efficient solution of least perimeter periodic space partitioning problem. •Developing a penalization strategy to avoid trivial solutions. •Presentation of MATLAB implementation of the introduced algorithm.« less

On numerical model of time-dependent processes in three-dimensional porous heat-releasing objects

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2016-10-01

The gas flows in the gravity field through porous objects with heat-releasing sources are investigated when the self-regulation of the flow rate of the gas passing through the porous object takes place. Such objects can appear after various natural or man-made disasters (like the exploded unit of the Chernobyl NPP). The mathematical model and the original numerical method, based on a combination of explicit and implicit finite difference schemes, are developed for investigating the time-dependent processes in 3D porous energy-releasing objects. The advantage of the numerical model is its ability to describe unsteady processes under both natural convection and forced filtration. The gas cooling of 3D porous objects with different distribution of heat sources is studied using computational experiment.

Thermal engineering research. [Runge-Kutta investigation of gas flow inside multilayer insulation system for rocket booster fuel tanks

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

NASA Technical Reports Server (NTRS)

Chen, C. P.

1990-01-01

An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

Evaluation of mechanical deformation and distributive magnetic loads with different mechanical constraints in two parallel conducting bars

NASA Astrophysics Data System (ADS)

Lee, Ho-Young; Lee, Se-Hee

2017-08-01

Mechanical deformation, bending deformation, and distributive magnetic loads were evaluated numerically and experimentally for conducting materials excited with high current. Until now, many research works have extensively studied the area of magnetic force and mechanical deformation by using coupled approaches such as multiphysics solvers. In coupled analysis for magnetoelastic problems, some articles and commercial software have presented the resultant mechanical deformation and stress on the body. To evaluate the mechanical deformation, the Lorentz force density method (LZ) and the Maxwell stress tensor method (MX) have been widely used for conducting materials. However, it is difficult to find any experimental verification regarding mechanical deformation or bending deformation due to magnetic force density. Therefore, we compared our numerical results to those from experiments with two parallel conducting bars to verify our numerical setup for bending deformation. Before showing this, the basic and interesting coupled simulation was conducted to test the mechanical deformations by the LZ (body force density) and the MX (surface force density) methods. This resulted in MX gave the same total force as LZ, but the local force distribution in MX introduced an incorrect mechanical deformation in the simulation of a solid conductor.

Thermal dynamic behavior during selective laser melting of K418 superalloy: numerical simulation and experimental verification

NASA Astrophysics Data System (ADS)

Chen, Zhen; Xiang, Yu; Wei, Zhengying; Wei, Pei; Lu, Bingheng; Zhang, Lijuan; Du, Jun

2018-04-01

During selective laser melting (SLM) of K418 powder, the influence of the process parameters, such as laser power P and scanning speed v, on the dynamic thermal behavior and morphology of the melted tracks was investigated numerically. A 3D finite difference method was established to predict the dynamic thermal behavior and flow mechanism of K418 powder irradiated by a Gaussian laser beam. A three-dimensional randomly packed powder bed composed of spherical particles was established by discrete element method. The powder particle information including particle size distribution and packing density were taken into account. The volume shrinkage and temperature-dependent thermophysical parameters such as thermal conductivity, specific heat, and other physical properties were also considered. The volume of fluid method was applied to reconstruct the free surface of the molten pool during SLM. The geometrical features, continuity boundaries, and irregularities of the molten pool were proved to be largely determined by the laser energy density. The numerical results are in good agreement with the experiments, which prove to be reasonable and effective. The results provide us some in-depth insight into the complex physical behavior during SLM and guide the optimization of process parameters.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Methods for describing the electromagnetic properties of silver and gold nanoparticles.

PubMed

Zhao, Jing; Pinchuk, Anatoliy O; McMahon, Jeffrey M; Li, Shuzhou; Ausman, Logan K; Atkinson, Ariel L; Schatz, George C

2008-12-01

This Account provides an overview of the methods that are currently being used to study the electromagnetics of silver and gold nanoparticles, with an emphasis on the determination of extinction and surface-enhanced Raman scattering (SERS) spectra. These methods have proven to be immensely useful in recent years for interpreting a wide range of nanoscience experiments and providing the capability to describe optical properties of particles up to several hundred nanometers in dimension, including arbitrary particle structures and complex dielectric environments (adsorbed layers of molecules, nearby metal films, and other particles). While some of the methods date back to Mie's celebrated work a century ago, others are still at the forefront of algorithm development in computational electromagnetics. This Account gives a qualitative description of the physical and mathematical basis behind the most commonly used methods, including both analytical and numerical methods, as well as representative results of applications that are relevant to current experiments. The analytical methods that we discuss are either derived from Mie theory for spheres or from the quasistatic (Gans) model as applied to spheres and spheroids. In this discussion, we describe the use of Mie theory to determine electromagnetic contributions to SERS enhancements that include for retarded dipole emission effects, and the use of the quasistatic approximation for spheroidal particles interacting with dye adsorbate layers. The numerical methods include the discrete dipole approximation (DDA), the finite difference time domain (FDTD) method, and the finite element method (FEM) based on Whitney forms. We discuss applications such as using DDA to describe the interaction of two gold disks to define electromagnetic hot spots, FDTD for light interacting with metal wires that go from particle-like plasmonic response to the film-like transmission as wire dimension is varied, and FEM studies of electromagnetic fields near cubic particles.