Numerical prediction of the energy efficiency of the three-dimensional fish school using the discretized Adomian decomposition method

NASA Astrophysics Data System (ADS)

Lin, Yinwei

2018-06-01

A three-dimensional modeling of fish school performed by a modified Adomian decomposition method (ADM) discretized by the finite difference method is proposed. To our knowledge, few studies of the fish school are documented due to expensive cost of numerical computing and tedious three-dimensional data analysis. Here, we propose a simple model replied on the Adomian decomposition method to estimate the efficiency of energy saving of the flow motion of the fish school. First, the analytic solutions of Navier-Stokes equations are used for numerical validation. The influences of the distance between the side-by-side two fishes are studied on the energy efficiency of the fish school. In addition, the complete error analysis for this method is presented.

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

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.

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1992-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Reconstructing gravitational wave source parameters via direct comparisons to numerical relativity I: Method

NASA Astrophysics Data System (ADS)

Lange, Jacob; O'Shaughnessy, Richard; Healy, James; Lousto, Carlos; Shoemaker, Deirdre; Lovelace, Geoffrey; Scheel, Mark; Ossokine, Serguei

2016-03-01

In this talk, we describe a procedure to reconstruct the parameters of sufficiently massive coalescing compact binaries via direct comparison with numerical relativity simulations. For sufficiently massive sources, existing numerical relativity simulations are long enough to cover the observationally accessible part of the signal. Due to the signal's brevity, the posterior parameter distribution it implies is broad, simple, and easily reconstructed from information gained by comparing to only the sparse sample of existing numerical relativity simulations. We describe how followup simulations can corroborate and improve our understanding of a detected source. Since our method can include all physics provided by full numerical relativity simulations of coalescing binaries, it provides a valuable complement to alternative techniques which employ approximations to reconstruct source parameters. Supported by NSF Grant PHY-1505629.

Implicit level set algorithms for modelling hydraulic fracture propagation.

PubMed

Peirce, A

2016-10-13

Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture 'tip screen-out'; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research. This article is part of the themed issue 'Energy and the subsurface'. © 2016 The Author(s).

Implicit level set algorithms for modelling hydraulic fracture propagation

PubMed Central

2016-01-01

Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture ‘tip screen-out’; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research.  This article is part of the themed issue ‘Energy and the subsurface’. PMID:27597787

Convergence studies in meshfree peridynamic simulations

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

Seleson, Pablo; Littlewood, David J.

2016-04-15

Meshfree methods are commonly applied to discretize peridynamic models, particularly in numerical simulations of engineering problems. Such methods discretize peridynamic bodies using a set of nodes with characteristic volume, leading to particle-based descriptions of systems. In this article, we perform convergence studies of static peridynamic problems. We show that commonly used meshfree methods in peridynamics suffer from accuracy and convergence issues, due to a rough approximation of the contribution to the internal force density of nodes near the boundary of the neighborhood of a given node. We propose two methods to improve meshfree peridynamic simulations. The first method uses accuratemore » computations of volumes of intersections between neighbor cells and the neighborhood of a given node, referred to as partial volumes. The second method employs smooth influence functions with a finite support within peridynamic kernels. Numerical results demonstrate great improvements in accuracy and convergence of peridynamic numerical solutions, when using the proposed methods.« less

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

NASA Technical Reports Server (NTRS)

Wang, W.; Shu, C. W.; Yee, H. C.; Sjogreen, B.

2012-01-01

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

NASA Astrophysics Data System (ADS)

Xu, Ao; Shyy, Wei; Zhao, Tianshou

2017-06-01

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas-liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

Method of Lines Transpose an Implicit Vlasov Maxwell Solver for Plasmas

DTIC Science & Technology

2015-04-17

boundary crossings should be rare. Numerical results for the Bennett pinch are given in Figure 9. In order to resolve large gradients near the center of the...contributing to the large error at the center of the beam due to large gradients there) and with the finite beam cut-off radius and the outflow boundary...usable time step size can be limited by the numerical accuracy of the method when there are large gradients (high-frequency content) in the solution. We

Electromagnetic fields due to a horizontal electric dipole antenna laid on the surface of a two-layer medium

NASA Technical Reports Server (NTRS)

Tsang, L.; Kong, J. A.

1974-01-01

With applications to geophysical subsurface probings, electromagnetic fields due to a horizontal electric dipole laid on the surface of a two-layer medium are solved by a combination of analytic and numerical methods. Interference patterns are calculated for various layer thickness. The results are interpreted in terms of normal modes, and the accuracies of the methods are discussed.

Multi-scale sensitivity analysis of pile installation using DEM

NASA Astrophysics Data System (ADS)

Esposito, Ricardo Gurevitz; Velloso, Raquel Quadros; , Eurípedes do Amaral Vargas, Jr.; Danziger, Bernadete Ragoni

2017-12-01

The disturbances experienced by the soil due to the pile installation and dynamic soil-structure interaction still present major challenges to foundation engineers. These phenomena exhibit complex behaviors, difficult to measure in physical tests and to reproduce in numerical models. Due to the simplified approach used by the discrete element method (DEM) to simulate large deformations and nonlinear stress-dilatancy behavior of granular soils, the DEM consists of an excellent tool to investigate these processes. This study presents a sensitivity analysis of the effects of introducing a single pile using the PFC2D software developed by Itasca Co. The different scales investigated in these simulations include point and shaft resistance, alterations in porosity and stress fields and particles displacement. Several simulations were conducted in order to investigate the effects of different numerical approaches showing indications that the method of installation and particle rotation could influence greatly in the conditions around the numerical pile. Minor effects were also noted due to change in penetration velocity and pile-soil friction. The difference in behavior of a moving and a stationary pile shows good qualitative agreement with previous experimental results indicating the necessity of realizing a force equilibrium process prior to any load-test to be simulated.

Multi-scale sensitivity analysis of pile installation using DEM

NASA Astrophysics Data System (ADS)

Esposito, Ricardo Gurevitz; Velloso, Raquel Quadros; , Eurípedes do Amaral Vargas, Jr.; Danziger, Bernadete Ragoni

2018-07-01

The disturbances experienced by the soil due to the pile installation and dynamic soil-structure interaction still present major challenges to foundation engineers. These phenomena exhibit complex behaviors, difficult to measure in physical tests and to reproduce in numerical models. Due to the simplified approach used by the discrete element method (DEM) to simulate large deformations and nonlinear stress-dilatancy behavior of granular soils, the DEM consists of an excellent tool to investigate these processes. This study presents a sensitivity analysis of the effects of introducing a single pile using the PFC2D software developed by Itasca Co. The different scales investigated in these simulations include point and shaft resistance, alterations in porosity and stress fields and particles displacement. Several simulations were conducted in order to investigate the effects of different numerical approaches showing indications that the method of installation and particle rotation could influence greatly in the conditions around the numerical pile. Minor effects were also noted due to change in penetration velocity and pile-soil friction. The difference in behavior of a moving and a stationary pile shows good qualitative agreement with previous experimental results indicating the necessity of realizing a force equilibrium process prior to any load-test to be simulated.

Effect of joint spacing and joint dip on the stress distribution around tunnels using different numerical methods

NASA Astrophysics Data System (ADS)

Nikadat, Nooraddin; Fatehi Marji, Mohammad; Rahmannejad, Reza; Yarahmadi Bafghi, Alireza

2016-11-01

Different conditions may affect the stability of tunnels by the geometry (spacing and orientation) of joints in the surrounded rock mass. In this study, by comparing the results obtained by the three novel numerical methods i.e. finite element method (Phase2), discrete element method (UDEC) and indirect boundary element method (TFSDDM), the effects of joint spacing and joint dips on the stress distribution around rock tunnels are numerically studied. These comparisons indicate the validity of the stress analyses around circular rock tunnels. These analyses also reveal that for a semi-continuous environment, boundary element method gives more accurate results compared to the results of finite element and distinct element methods. In the indirect boundary element method, the displacements due to joints of different spacing and dips are estimated by using displacement discontinuity (DD) formulations and the total stress distribution around the tunnel are obtained by using fictitious stress (FS) formulations.

Second-order Poisson Nernst-Planck solver for ion channel transport

PubMed Central

Zheng, Qiong; Chen, Duan; Wei, Guo-Wei

2010-01-01

The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements. PMID:21552336

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

NASA Astrophysics Data System (ADS)

Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix

2018-03-01

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

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

Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

Simple numerical method for predicting steady compressible flows

NASA Technical Reports Server (NTRS)

Vonlavante, Ernst; Nelson, N. Duane

1986-01-01

A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Computation of Feedback Aeroacoustic System by the CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Wang, Xiao Y.; Chang, Sin-Chung; Jorgenson, Philip C. E.

2000-01-01

It is well known that due to vortex shedding in high speed flow over cutouts, cavities, and gaps, intense noise may be generated. Strong tonal oscillations occur in a feedback cycle in which the vortices shed from the upstream edge of the cavity convect downstream and impinge on the cavity lip, generating acoustic waves that propagate upstream to excite new vortices. Numerical simulation of such a complicated process requires a scheme that can: (1) resolve acoustic waves with low dispersion and numerical dissipation, (2) handle nonlinear and discontinuous waves (e.g. shocks), and (3) have an effective (near field) nonreflecting boundary condition (NRBC). The new space time conservation element and solution element method, or CE/SE for short, is a numerical method that meets the above requirements.

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

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mohebbi, Akbar

2018-02-01

In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

PubMed Central

Filobello-Nino, U.; Vazquez-Leal, H.; Sarmiento-Reyes, A.; Benhammouda, B.; Jimenez-Fernandez, V. M.; Pereyra-Diaz, D.; Perez-Sesma, A.; Cervantes-Perez, J.; Huerta-Chua, J.; Sanchez-Orea, J.; Contreras-Hernandez, A. D.

2014-01-01

The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient. PMID:27433526

Numerical form-finding method for large mesh reflectors with elastic rim trusses

NASA Astrophysics Data System (ADS)

Yang, Dongwu; Zhang, Yiqun; Li, Peng; Du, Jingli

2018-06-01

Traditional methods for designing a mesh reflector usually treat the rim truss as rigid. Due to large aperture, light weight and high accuracy requirements on spaceborne reflectors, the rim truss deformation is indeed not negligible. In order to design a cable net with asymmetric boundaries for the front and rear nets, a cable-net form-finding method is firstly introduced. Then, the form-finding method is embedded into an iterative approach for designing a mesh reflector considering the elasticity of the supporting rim truss. By iterations on form-findings of the cable-net based on the updated boundary conditions due to the rim truss deformation, a mesh reflector with a fairly uniform tension distribution in its equilibrium state could be finally designed. Applications on offset mesh reflectors with both circular and elliptical rim trusses are illustrated. The numerical results show the effectiveness of the proposed approach and that a circular rim truss is more stable than an elliptical rim truss.

Analysis of space charge fields using the Lienard-Wiechert potential and the method of images during the photoemission of the electron beam from the cathode

NASA Astrophysics Data System (ADS)

Salah, Wa'el

2017-01-01

We present a numerical analysis of the space charge effect and the effect of image charge force on the cathode surface for a laser-driven RF-photocathode gun. In this numerical analysis, in the vicinity of the cathode surface, we used an analytical method based on Lienard-Weichert retarded potentials. The analytical method allows us to calculate longitudinal and radial electric fields, and the azimuth magnetic field due to both space charge effect and the effect of the image charge force. We calculate the electro-magnetic fields in the following two conditions for the "ELSA" photoinjector. The first condition is in the progress of photoemission, which corresponds to the inside of the emitted beam, and the second condition is at the end of the photoemission. The electromagnetic fields due to the space charge effect and the effect of the image charge force, and the sum of them, which corresponds to the global electro-magnetic fields, are shown. Based on these numerical results, we discussed the effects of the space charge and the image charge in the immediate vicinity of the cathode.

Modified Finite Particle Methods for Stokes problems

NASA Astrophysics Data System (ADS)

Montanino, A.; Asprone, D.; Reali, A.; Auricchio, F.

2018-04-01

The Modified Finite Particle Method (MFPM) is a numerical method belonging to the class of meshless methods, nowadays widely investigated due to their characteristic of being capable to easily model large deformation and fluid-dynamic problems. Here we use the MFPM to approximate the Stokes problem. Since the classical formulation of the Stokes problem may lead to pressure spurious oscillations, we investigate alternative formulations and focus on how MFPM discretization behaves in those situations. Some of the investigated formulations, in fact, do not enforce strongly the incompressibility constraint, and therefore an important issue of the present work is to verify if the MFPM is able to correctly reproduce the incompressibility in those cases. The numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.

Dispersive effects on multicomponent transport through porous media

NASA Astrophysics Data System (ADS)

Dutta, Sourav; Daripa, Prabir

2017-11-01

We use a hybrid numerical method to solve a global pressure based porous media flow model of chemical enhanced oil recovery. This is an extension of our recent work. The numerical method is based on the use of a discontinuous finite element method and the modified method of characteristics. The impact of molecular diffusion and mechanical dispersion on the evolution of scalar concentration distributions are studied through numerical simulations of various flooding schemes. The relative importance of the advective, capillary diffusive and dispersive fluxes are compared over different flow regimes defined in the parameter space of Capillary number, Peclet number, longitudinal and transverse dispersion coefficients. Such studies are relevant for the design of effective injection policies and determining optimal combinations of chemical components for improving recovery. This work has been possible due to financial support from the U.S. National Science Foundation Grant DMS-1522782.

Reliability-Based Stability Analysis of Rock Slopes Using Numerical Analysis and Response Surface Method

NASA Astrophysics Data System (ADS)

Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.

2017-08-01

While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.

Hybrid RANS-LES using high order numerical methods

NASA Astrophysics Data System (ADS)

Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael

2017-11-01

Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

NASA Astrophysics Data System (ADS)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

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

Meyers, M.D., E-mail: mdmeyers@physics.ucla.edu; Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095; Huang, C.-K., E-mail: huangck@lanl.gov

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTDmore » scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.« less

Numerical solution for weight reduction model due to health campaigns in Spain

NASA Astrophysics Data System (ADS)

Mohammed, Maha A.; Noor, Noor Fadiya Mohd; Siri, Zailan; Ibrahim, Adriana Irawati Nur

2015-10-01

Transition model between three subpopulations based on Body Mass Index of Valencia community in Spain is considered. No changes in population nutritional habits and public health strategies on weight reduction until 2030 are assumed. The system of ordinary differential equations is solved using Runge-Kutta method of higher order. The numerical results obtained are compared with the predicted values of subpopulation proportion based on statistical estimation in 2013, 2015 and 2030. Relative approximate error is calculated. The consistency of the Runge-Kutta method in solving the model is discussed.

Application of symbolic/numeric matrix solution techniques to the NASTRAN program

NASA Technical Reports Server (NTRS)

Buturla, E. M.; Burroughs, S. H.

1977-01-01

The matrix solving algorithm of any finite element algorithm is extremely important since solution of the matrix equations requires a large amount of elapse time due to null calculations and excessive input/output operations. An alternate method of solving the matrix equations is presented. A symbolic processing step followed by numeric solution yields the solution very rapidly and is especially useful for nonlinear problems.

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

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.

Feature selection methods for object-based classification of sub-decimeter resolution digital aerial imagery

USDA-ARS?s Scientific Manuscript database

Due to the availability of numerous spectral, spatial, and contextual features, the determination of optimal features and class separabilities can be a time consuming process in object-based image analysis (OBIA). While several feature selection methods have been developed to assist OBIA, a robust c...

A study on Marangoni convection by the variational iteration method

NASA Astrophysics Data System (ADS)

Karaoǧlu, Onur; Oturanç, Galip

2012-09-01

In this paper, we will consider the use of the variational iteration method and Padé approximant for finding approximate solutions for a Marangoni convection induced flow over a free surface due to an imposed temperature gradient. The solutions are compared with the numerical (fourth-order Runge Kutta) solutions.

Numerical investigation of finite-volume effects for the HVP

NASA Astrophysics Data System (ADS)

Boyle, Peter; Gülpers, Vera; Harrison, James; Jüttner, Andreas; Portelli, Antonin; Sachrajda, Christopher

2018-03-01

It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

NASA Astrophysics Data System (ADS)

Yokota, Rio; Barba, L. A.; Narumi, Tetsu; Yasuoka, Kenji

2013-03-01

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on GPU hardware using single precision. The simulations use a vortex particle method to solve the Navier-Stokes equations, with a highly parallel fast multipole method (FMM) as numerical engine, and match the current record in mesh size for this application, a cube of 40963 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the FFT algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the FMM-based vortex method achieving 74% parallel efficiency on 4096 processes (one GPU per MPI process, 3 GPUs per node of the TSUBAME-2.0 system). The FFT-based spectral method is able to achieve just 14% parallel efficiency on the same number of MPI processes (using only CPU cores), due to the all-to-all communication pattern of the FFT algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

Numerical modeling of time-lapse monitoring of CO2 sequestration in a layered basalt reservoir

USGS Publications Warehouse

Khatiwada, M.; Van Wijk, K.; Clement, W.P.; Haney, M.

2008-01-01

As part of preparations in plans by The Big Sky Carbon Sequestration Partnership (BSCSP) to inject CO2 in layered basalt, we numerically investigate seismic methods as a noninvasive monitoring technique. Basalt seems to have geochemical advantages as a reservoir for CO2 storage (CO2 mineralizes quite rapidly while exposed to basalt), but poses a considerable challenge in term of seismic monitoring: strong scattering from the layering of the basalt complicates surface seismic imaging. We perform numerical tests using the Spectral Element Method (SEM) to identify possibilities and limitations of seismic monitoring of CO2 sequestration in a basalt reservoir. While surface seismic is unlikely to detect small physical changes in the reservoir due to the injection of CO2, the results from Vertical Seismic Profiling (VSP) simulations are encouraging. As a perturbation, we make a 5%; change in wave velocity, which produces significant changes in VSP images of pre-injection and post-injection conditions. Finally, we perform an analysis using Coda Wave Interferometry (CWI), to quantify these changes in the reservoir properties due to CO2 injection.

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

NASA Technical Reports Server (NTRS)

Bodonyi, R. J.; Duck, P. W.

1992-01-01

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

NASA Technical Reports Server (NTRS)

Bodonyi, R. J.; Duck, P. W.

1990-01-01

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

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).

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

Interfacial gauge methods for incompressible fluid dynamics

PubMed Central

Saye, Robert

2016-01-01

Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of “gauge freedom” to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena. PMID:27386567

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

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

Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion accordingmore » to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.« less

Numerical simulation of overflow at vertical weirs using a hybrid level set/VOF method

NASA Astrophysics Data System (ADS)

Lv, Xin; Zou, Qingping; Reeve, Dominic

2011-10-01

This paper presents the applications of a newly developed free surface flow model to the practical, while challenging overflow problems for weirs. Since the model takes advantage of the strengths of both the level set and volume of fluid methods and solves the Navier-Stokes equations on an unstructured mesh, it is capable of resolving the time evolution of very complex vortical motions, air entrainment and pressure variations due to violent deformations following overflow of the weir crest. In the present study, two different types of vertical weir, namely broad-crested and sharp-crested, are considered for validation purposes. The calculated overflow parameters such as pressure head distributions, velocity distributions, and water surface profiles are compared against experimental data as well as numerical results available in literature. A very good quantitative agreement has been obtained. The numerical model, thus, offers a good alternative to traditional experimental methods in the study of weir problems.

Faster methods for estimating arc centre position during VAR and results from Ti-6Al-4V and INCONEL 718 alloys

NASA Astrophysics Data System (ADS)

Nair, B. G.; Winter, N.; Daniel, B.; Ward, R. M.

2016-07-01

Direct measurement of the flow of electric current during VAR is extremely difficult due to the aggressive environment as the arc process itself controls the distribution of current. In previous studies the technique of “magnetic source tomography” was presented; this was shown to be effective but it used a computationally intensive iterative method to analyse the distribution of arc centre position. In this paper we present faster computational methods requiring less numerical optimisation to determine the centre position of a single distributed arc both numerically and experimentally. Numerical validation of the algorithms were done on models and experimental validation on measurements based on titanium and nickel alloys (Ti6Al4V and INCONEL 718). The results are used to comment on the effects of process parameters on arc behaviour during VAR.

Numerical noise prediction in fluid machinery

NASA Astrophysics Data System (ADS)

Pantle, Iris; Magagnato, Franco; Gabi, Martin

2005-09-01

Numerical methods successively became important in the design and optimization of fluid machinery. However, as noise emission is considered, one can hardly find standardized prediction methods combining flow and acoustical optimization. Several numerical field methods for sound calculations have been developed. Due to the complexity of the considered flow, approaches must be chosen to avoid exhaustive computing. In this contribution the noise of a simple propeller is investigated. The configurations of the calculations comply with an existing experimental setup chosen for evaluation. The used in-house CFD solver SPARC contains an acoustic module based on Ffowcs Williams-Hawkings Acoustic Analogy. From the flow results of the time dependent Large Eddy Simulation the time dependent acoustic sources are extracted and given to the acoustic module where relevant sound pressure levels are calculated. The difficulties, which arise while proceeding from open to closed rotors and from gas to liquid are discussed.

Numerical investigation of the flat band Bloch modes in a 2D photonic crystal with Dirac cones

DOE PAGES

Zhang, Peng; Fietz, Chris; Tassin, Philippe; ...

2015-04-14

A numerical method combining complex-k band calculations and absorbing boundary conditions for Bloch waves is presented. We use this method to study photonic crystals with Dirac cones. We demonstrate that the photonic crystal behaves as a zero-index medium when excited at normal incidence, but that the zero-index behavior is lost at oblique incidence due to excitation of modes on the flat band. We also investigate the formation of monomodal and multimodal cavity resonances inside the photonic crystals, and the physical origins of their different line-shape features.

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

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

Pant, Nidhi; Das, Santanu; Mitra, Sanjit

Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper,more » we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations.« less

Self-Scheduling Parallel Methods for Multiple Serial Codes with Application to WOPWOP

NASA Technical Reports Server (NTRS)

Long, Lyle N.; Brentner, Kenneth S.

2000-01-01

This paper presents a scheme for efficiently running a large number of serial jobs on parallel computers. Two examples are given of computer programs that run relatively quickly, but often they must be run numerous times to obtain all the results needed. It is very common in science and engineering to have codes that are not massive computing challenges in themselves, but due to the number of instances that must be run, they do become large-scale computing problems. The two examples given here represent common problems in aerospace engineering: aerodynamic panel methods and aeroacoustic integral methods. The first example simply solves many systems of linear equations. This is representative of an aerodynamic panel code where someone would like to solve for numerous angles of attack. The complete code for this first example is included in the appendix so that it can be readily used by others as a template. The second example is an aeroacoustics code (WOPWOP) that solves the Ffowcs Williams Hawkings equation to predict the far-field sound due to rotating blades. In this example, one quite often needs to compute the sound at numerous observer locations, hence parallelization is utilized to automate the noise computation for a large number of observers.

A numerical method for simulations of rigid fiber suspensions

NASA Astrophysics Data System (ADS)

Tornberg, Anna-Karin; Gustavsson, Katarina

2006-06-01

In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

An Unconditionally Stable Fully Conservative Semi-Lagrangian Method (PREPRINT)

DTIC Science & Technology

2010-08-07

Alessandrini. An Hamiltonian interface SPH formulation for multi-fluid and free surface flows . J. of Comput. Phys., 228(22):8380–8393, 2009. [11] J.T...and J. Welch. Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface . Phys. Fluids, 8:2182–2189, 1965. [14... flow is divergence free , one would generally expect these lines to be commensurate, however, due to numerical errors in interpolation there is some

A combined analytical and numerical analysis of the flow-acoustic coupling in a cavity-pipe system

NASA Astrophysics Data System (ADS)

Langthjem, Mikael A.; Nakano, Masami

2018-05-01

The generation of sound by flow through a closed, cylindrical cavity (expansion chamber) accommodated with a long tailpipe is investigated analytically and numerically. The sound generation is due to self-sustained flow oscillations in the cavity. These oscillations may, in turn, generate standing (resonant) acoustic waves in the tailpipe. The main interest of the paper is in the interaction between these two sound sources. An analytical, approximate solution of the acoustic part of the problem is obtained via the method of matched asymptotic expansions. The sound-generating flow is represented by a discrete vortex method, based on axisymmetric vortex rings. It is demonstrated through numerical examples that inclusion of acoustic feedback from the tailpipe is essential for a good representation of the sound characteristics.

Numerical simulation of artificial hip joint motion based on human age factor

NASA Astrophysics Data System (ADS)

Ramdhani, Safarudin; Saputra, Eko; Jamari, J.

2018-05-01

Artificial hip joint is a prosthesis (synthetic body part) which usually consists of two or more components. Replacement of the hip joint due to the occurrence of arthritis, ordinarily patients aged or older. Numerical simulation models are used to observe the range of motion in the artificial hip joint, the range of motion of joints used as the basis of human age. Finite- element analysis (FEA) is used to calculate stress von mises in motion and observes a probability of prosthetic impingement. FEA uses a three-dimensional nonlinear model and considers the position variation of acetabular liner cups. The result of numerical simulation shows that FEA method can be used to analyze the performance calculation of the artificial hip joint at this time more accurate than conventional method.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Numerical evaluation of heating in the human head due to magnetic resonance imaging (MRI)

NASA Astrophysics Data System (ADS)

Nguyen, Uyen; Brown, Steve; Chang, Isaac; Krycia, Joe; Mirotznik, Mark S.

2003-06-01

In this paper we present a numerical model for evaluating tissue heating during magnetic resonance imaging (MRI). Our method, which included a detailed anatomical model of a human head, calculated both the electromagnetic power deposition and the associated temperature elevations during a MRI head examination. Numerical studies were conducted using a realistic birdcage coil excited at frequencies ranging from 63 MHz to 500 MHz. The model was validated both experimentally and analytically. The experimental validation was performed at the MR test facility located at the FDA's Center for Devices and Radiological Health (CDRH).

New efficient optimizing techniques for Kalman filters and numerical weather prediction models

NASA Astrophysics Data System (ADS)

Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis

2016-06-01

The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.

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

Ion sound instability driven by the ion flows

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

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

2015-05-15

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

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

An efficient and guaranteed stable numerical method for continuous modeling of infiltration and redistribution with a shallow dynamic water table

NASA Astrophysics Data System (ADS)

Lai, Wencong; Ogden, Fred L.; Steinke, Robert C.; Talbot, Cary A.

2015-03-01

We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call "GARTO" can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a near-surface water table.

Reentry trajectory optimization based on a multistage pseudospectral method.

PubMed

Zhao, Jiang; Zhou, Rui; Jin, Xuelian

2014-01-01

Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control strategy based on the pseudospectral method, capable of dealing with the unexpected situations in reentry flight. The strategy typically includes two subproblems: the trajectory estimation and trajectory refining. In each processing stage, the proposed method generates a specified range of trajectory with the transition of the flight state. The full glide trajectory consists of several optimal trajectory sequences. The newly focused geographic constraints in actual flight are discussed thereafter. Numerical examples of free-space flight, target transition flight, and threat avoidance flight are used to show the feasible application of multistage pseudospectral method in reentry trajectory optimization.

Reentry Trajectory Optimization Based on a Multistage Pseudospectral Method

PubMed Central

Zhou, Rui; Jin, Xuelian

2014-01-01

Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control strategy based on the pseudospectral method, capable of dealing with the unexpected situations in reentry flight. The strategy typically includes two subproblems: the trajectory estimation and trajectory refining. In each processing stage, the proposed method generates a specified range of trajectory with the transition of the flight state. The full glide trajectory consists of several optimal trajectory sequences. The newly focused geographic constraints in actual flight are discussed thereafter. Numerical examples of free-space flight, target transition flight, and threat avoidance flight are used to show the feasible application of multistage pseudospectral method in reentry trajectory optimization. PMID:24574929

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

A free energy-based surface tension force model for simulation of multiphase flows by level-set method

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Chen, Z.; Shu, C.; Wang, Y.; Niu, X. D.; Shu, S.

2017-09-01

In this paper, a free energy-based surface tension force (FESF) model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method. By using the analytical form of order parameter along the normal direction to the interface in the phase-field method and the free energy principle, FESF model offers an explicit and analytical formulation for the surface tension force. The only variable in this formulation is the normal distance to the interface, which can be substituted by the distance function solved by the level set method. On one hand, as compared to conventional continuum surface force (CSF) model in the level set method, FESF model introduces no regularized delta function, due to which it suffers less from numerical diffusions and performs better in mass conservation. On the other hand, as compared to the phase field surface tension force (PFSF) model, the evaluation of surface tension force in FESF model is based on an analytical approach rather than numerical approximations of spatial derivatives. Therefore, better numerical stability and higher accuracy can be expected. Various numerical examples are tested to validate the robustness of the proposed FESF model. It turns out that FESF model performs better than CSF model and PFSF model in terms of accuracy, stability, convergence speed and mass conservation. It is also shown in numerical tests that FESF model can effectively simulate problems with high density/viscosity ratio, high Reynolds number and severe topological interfacial changes.

On the damping effect due to bolted junctions in space structures subjected to pyro-shock

NASA Astrophysics Data System (ADS)

de Benedetti, M.; Garofalo, G.; Zumpano, M.; Barboni, R.

2007-06-01

The damping due to bolted or riveted joints in the dynamics of assembled structures subjected to pyro-shock has been studied. A relevant effect in this phenomenon is the micro-slip between the jointed surfaces. In order to verify the feasibility and the reliability of the numerical analyses performed on structures with junctions, the numerical results obtained by the finite elements method have been compared with those obtained experimentally. Several numerical analyses, in which friction forces have been represented as nonlinear loads, have been carried out for the FE models of two application cases: an electronic unit mounted within the Radarsat-2 satellite, and the complete Cosmo-Skymed spacecraft. Considering the load type, involving a typical high frequency response spectrum between 100 and 10 000 Hz, both numerical and experimental data have been reduced to the shock response spectrum form. After the comparative evaluation, taking into account also the damping effect, the agreement between numerical results and experimental data has been evaluated. The proposed numerical approach yields an effective and less expensive instrument, able to provide indications in the design phase, to allow the prevision of the dynamic behaviour of the structure for the prevention of failures in units or systems mounted within the spacecraft or launch vehicle. With the proposed model, it is possible to determine in a simple and direct way the characteristics of the damping due to the single bolted and riveted joints, and use them in similar multiple joints in the complete structure assembling or substructuring.

An efficient impedance method for induced field evaluation based on a stabilized Bi-conjugate gradient algorithm.

PubMed

Wang, Hua; Liu, Feng; Xia, Ling; Crozier, Stuart

2008-11-21

This paper presents a stabilized Bi-conjugate gradient algorithm (BiCGstab) that can significantly improve the performance of the impedance method, which has been widely applied to model low-frequency field induction phenomena in voxel phantoms. The improved impedance method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional, successive over-relaxation (SOR)-based algorithm. The scheme has been validated against other numerical/analytical solutions on a lossy, multilayered sphere phantom excited by an ideal coil loop. To demonstrate the computational performance and application capability of the developed algorithm, the induced fields inside a human phantom due to a low-frequency hyperthermia device is evaluated. The simulation results show the numerical accuracy and superior performance of the 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.

Numerical study of droplet evaporation in an acoustic levitator

NASA Astrophysics Data System (ADS)

Bänsch, Eberhard; Götz, Michael

2018-03-01

We present a finite element method for the simulation of all relevant processes of the evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical model and the numerical implementation take into account heat and mass transfer across the interface between the liquid and gaseous phase and the influence of acoustic streaming on this process, as well as the displacement and deformation of the droplet due to acoustic radiation pressure. We apply this numerical method to several theoretical and experimental examples and compare our results with the well-known d2-law for the evaporation of spherical droplets and with theoretical predictions for the acoustic streaming velocity. We study the influence of acoustic streaming on the distribution of water vapor and temperature in the levitation device, with special attention to the vapor distribution in the emerging toroidal vortices. We also compare the evaporation rate of a droplet with and without acoustic streaming, as well as the evaporation rates in dependence of different temperatures and sound pressure levels. Finally, a simple model of protein inactivation due to heat damage is considered and studied for different evaporation settings and their respective influence on protein damage.

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.

Spacelike matching to null infinity

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

Zenginoglu, Anil; Tiglio, Manuel

2009-07-15

We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions of evolution equations so that both the radiation extraction problem and the outer boundary problem are solved. The first method is based on the geometric conformal approach, the second is a coordinate based approach. We apply these methods to the case of a massless scalar wave equation on a Kerr spacetime. Our methods are designed to allow existing codes to reach the radiative zone by including future null infinity in the computational domain with relatively minor modifications. We demonstrate the flexibilitymore » of the methods by considering both Boyer-Lindquist and ingoing Kerr coordinates near the black hole. We also confirm numerically predictions concerning tail decay rates for scalar fields at null infinity in Kerr spacetime due to Hod for the first time.« less

Realistic numerical modelling of human head tissue exposure to electromagnetic waves from cellular phones

NASA Astrophysics Data System (ADS)

Scarella, Gilles; Clatz, Olivier; Lanteri, Stéphane; Beaume, Grégory; Oudot, Steve; Pons, Jean-Philippe; Piperno, Sergo; Joly, Patrick; Wiart, Joe

2006-06-01

The ever-rising diffusion of cellular phones has brought about an increased concern for the possible consequences of electromagnetic radiation on human health. Possible thermal effects have been investigated, via experimentation or simulation, by several research projects in the last decade. Concerning numerical modeling, the power absorption in a user's head is generally computed using discretized models built from clinical MRI data. The vast majority of such numerical studies have been conducted using Finite Differences Time Domain methods, although strong limitations of their accuracy are due to heterogeneity, poor definition of the detailed structures of head tissues (staircasing effects), etc. In order to propose numerical modeling using Finite Element or Discontinuous Galerkin Time Domain methods, reliable automated tools for the unstructured discretization of human heads are also needed. Results presented in this article aim at filling the gap between human head MRI images and the accurate numerical modeling of wave propagation in biological tissues and its thermal effects. To cite this article: G. Scarella et al., C. R. Physique 7 (2006).

Interfacial gauge methods for incompressible fluid dynamics

DOE PAGES

Saye, R.

2016-06-10

Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work,more » high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.« less

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Alford, R. L.

1979-01-01

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case

NASA Astrophysics Data System (ADS)

Hojbotǎ, C. I.; Toşa, V.; Mercea, P. V.

2013-08-01

We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food.

Numerical simulation of temperature distribution in cylindrical ilmenite (FeTiO3) due to microwave heating

NASA Astrophysics Data System (ADS)

Hidayat, Mas Irfan P.; Fellicia, Dian Mughni; Rafandi, Ferdiansyah Iqbal

2018-04-01

Microwave assisted heating has been extensively used in materials processing particularly in extraction of TiO2 from Ilmenite (FeTiO3) minerals. Nevertheless, this method could generate non-uniform temperature distribution during the heating process. The observation of this phenomena in cylindrical ilmenite has been conducted by numerical simulation using finite element method according to the Poynthing's theorem. Four different cylinders with variation on its height were simulated in ANSYS 17 with input microwave power of 5.5 Kw. The results indicated that height of heated object could vigorously influence the uniformity of temperature inside the body.

Tunable properties of light propagation in photonic liquid crystal fibers

NASA Astrophysics Data System (ADS)

Szaniawska, K.; Nasilowski, T.; Woliński, T. R.; Thienpont, H.

2006-12-01

Tunable properties of light propagation in photonic crystal fibers filled with liquid crystals, called photonic liquid crystal fibers (PLCFs) are presented. The propagation properties of PLCFs strongly depend on contrast between refractive indices of the solid core (pure silica glass) and liquid crystals (LCs) filing the holes of the fiber. Due to relatively strong thermo-optical effect, we can change the refractive index of the LC by changing its temperature. Numerical analysis of light propagation in PLCF, based on two simulation methods, such as finite difference (FD) and multipole method (MM) is presented. The numerical results obtained are in good agreement with our earlier experimental results presented elsewhere [1].

Heavy Metals in ToxCast: Relevance to Food Safety (SOT)

EPA Science Inventory

Human exposure to heavy metals occurs through food contamination due to industrial processes, vehicle emissions and farming methods. Specific toxicity endpoints have been associated with metal exposures, e.g. lead and neurotoxicity; however, numerous varieties of heavy metals hav...

CAN WE BELIEVE OUR RESULTS?

EPA Science Inventory

Numerous waterborne outbreaks of cryptosporidiosis have occurred recently with the most notable being the 1993 episode in Milwaukee. Due to these outbreaks and the concern for public health, the past decade has seen a massive effort expended on the development of methods to dete...

Chemical Transport in a Fissured Rock: Verification of a Numerical Model

NASA Astrophysics Data System (ADS)

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions, with or without decay and source terms. The method is based on an integrated finite difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem, as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10-3% or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters are likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. Work in this direction is in progress.

Numerical investigation of supercritical LNG convective heat transfer in a horizontal serpentine tube

NASA Astrophysics Data System (ADS)

Han, Chang-Liang; Ren, Jing-Jie; Dong, Wen-Ping; Bi, Ming-Shu

2016-09-01

The submerged combustion vaporizer (SCV) is indispensable general equipment for liquefied natural gas (LNG) receiving terminals. In this paper, numerical simulation was conducted to get insight into the flow and heat transfer characteristics of supercritical LNG on the tube-side of SCV. The SST model with enhanced wall treatment method was utilized to handle the coupled wall-to-LNG heat transfer. The thermal-physical properties of LNG under supercritical pressure were used for this study. After the validation of model and method, the effects of mass flux, outer wall temperature and inlet pressure on the heat transfer behaviors were discussed in detail. Then the non-uniformity heat transfer mechanism of supercritical LNG and effect of natural convection due to buoyancy change in the tube was discussed based on the numerical results. Moreover, different flow and heat transfer characteristics inside the bend tube sections were also analyzed. The obtained numerical results showed that the local surface heat transfer coefficient attained its peak value when the bulk LNG temperature approached the so-called pseudo-critical temperature. Higher mass flux could eliminate the heat transfer deteriorations due to the increase of turbulent diffusion. An increase of outer wall temperature had a significant influence on diminishing heat transfer ability of LNG. The maximum surface heat transfer coefficient strongly depended on inlet pressure. Bend tube sections could enhance the heat transfer due to secondary flow phenomenon. Furthermore, based on the current simulation results, a new dimensionless, semi-theoretical empirical correlation was developed for supercritical LNG convective heat transfer in a horizontal serpentine tube. The paper provided the mechanism of heat transfer for the design of high-efficiency SCV.

Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media

NASA Astrophysics Data System (ADS)

Quintal, Beatriz; Steeb, Holger; Frehner, Marcel; Schmalholz, Stefan M.

2011-01-01

The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u - p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.

Numerical simulation of liquid-layer breakup on a moving wall due to an impinging jet

NASA Astrophysics Data System (ADS)

Yu, Taejong; Moon, Hojoon; You, Donghyun; Kim, Dokyun; Ovsyannikov, Andrey

2014-11-01

Jet wiping, which is a hydrodynamic method for controlling the liquid film thickness in coating processes, is constrained by a rather violent film instability called splashing. The instability is characterized by the ejection of droplets from the runback flow and results in an explosion of the film. The splashing phenomenon degrades the final coating quality. In the present research, a volume-of-fluid (VOF)-based method, which is developed at Cascade Technologies, is employed to simulate the air-liquid multiphase flow dynamics. The present numerical method is based on an unstructured-grid unsplit geometric VOF scheme and guarantees strict conservation of mass of two-phase flow, The simulation results are compared with experimental measurements such as the liquid-film thickness before and after the jet wiping, wall pressure and shear stress distributions. The trajectories of liquid droplets due to the fluid motion entrained by the gas-jet operation, are also qualitatively compared with experimental visualization. Physical phenomena observed during the liquid-layer breakup due to an impinging jet is characterized in order to develop ideas for controlling the liquid-layer instability and resulting splash generation and propagation. Supported by the Grant NRF-2012R1A1A2003699, the Brain Korea 21+ program, POSCO, and 2014 CTR Summer Program.

A numerical study of axisymmetric compressible non-isothermal and reactive swirling flow

NASA Astrophysics Data System (ADS)

Tavernetti, William E.; Hafez, Mohamed M.

2017-09-01

Non-linear dynamical phenomena in combustion processes is an active area of experimental and theoretical research. This is in large part due to increasingly strict environmental pressures to make gas turbine engines and industrial burners more efficient. Using numerical methods, for steady and unsteady confined and unconfined compressible flow, this study examines the modeling influence of compressibility for axisymmetric swirling flow. The compressible reactive Navier-Stokes equations in terms of stream function, vorticity, circulation are used. Results, details of the numerical algorithms, as well as numerical verification techniques and validation with sources from the literature will be presented. Understanding how vortex breakdown phenomena are affected by modeling reactant consumption with compressibility effect is the main goal of this study.

Numerical Predictions of Wind Turbine Power and Aerodynamic Loads for the NREL Phase II and IV Combined Experiment Rotor

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Johnson, Wayne; vanDam, C. P.; Chao, David D.; Cortes, Regina; Yee, Karen

1999-01-01

Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.

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.

Numerical correction of distorted images in full-field optical coherence tomography

NASA Astrophysics Data System (ADS)

Min, Gihyeon; Kim, Ju Wan; Choi, Woo June; Lee, Byeong Ha

2012-03-01

We propose a numerical method which can numerically correct the distorted en face images obtained with a full field optical coherence tomography (FF-OCT) system. It is shown that the FF-OCT image of the deep region of a biological sample is easily blurred or degraded because the sample has a refractive index (RI) much higher than its surrounding medium in general. It is analyzed that the focal plane of the imaging system is segregated from the imaging plane of the coherence-gated system due to the RI mismatch. This image-blurring phenomenon is experimentally confirmed by imaging the chrome pattern of a resolution test target through its glass substrate in water. Moreover, we demonstrate that the blurred image can be appreciably corrected by using the numerical correction process based on the Fresnel-Kirchhoff diffraction theory. The proposed correction method is applied to enhance the image of a human hair, which permits the distinct identification of the melanin granules inside the cortex layer of the hair shaft.

Modeling viscoelastic deformation of the earth due to surface loading by commercial finite element package - ABAQUS

NASA Astrophysics Data System (ADS)

Kit Wong, Ching; Wu, Patrick

2017-04-01

Wu (2004) developed a transformation scheme to model viscoelatic deformation due to glacial loading by commercial finite element package - ABAQUS. Benchmark tests confirmed that this method works extremely well on incompressible earth model. Bangtsson & Lund (2008),however, showed that the transformation scheme would lead to incorrect results if compressible material parameters are used. Their study implies that Wu's method of stress transformation is inadequate to model the load induced deformation of a compressible earth under the framework of ABAQUS. In light of this, numerical experiments are carried out to find if there exist other methods that serve this purpose. All the tested methods are not satisfying as the results failed to converge through iterations, except at the elastic limit. Those tested methods will be outlined and the results will be presented. Possible reasons of failure will also be discussed. Bängtsson, E., & Lund, B. (2008). A comparison between two solution techniques to solve the equations of glacially induced deformation of an elastic Earth. International journal for numerical methods in engineering, 75(4), 479-502. Wu, P. (2004). Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress. Geophysical Journal International, 158(2), 401-408.

A Complex Prime Numerical Representation of Amino Acids for Protein Function Comparison.

PubMed

Chen, Duo; Wang, Jiasong; Yan, Ming; Bao, Forrest Sheng

2016-08-01

Computationally assessing the functional similarity between proteins is an important task of bioinformatics research. It can help molecular biologists transfer knowledge on certain proteins to others and hence reduce the amount of tedious and costly benchwork. Representation of amino acids, the building blocks of proteins, plays an important role in achieving this goal. Compared with symbolic representation, representing amino acids numerically can expand our ability to analyze proteins, including comparing the functional similarity of them. Among the state-of-the-art methods, electro-ion interaction pseudopotential (EIIP) is widely adopted for the numerical representation of amino acids. However, it could suffer from degeneracy that two different amino acid sequences have the same numerical representation, due to the design of EIIP. In light of this challenge, we propose a complex prime numerical representation (CPNR) of amino acids, inspired by the similarity between a pattern among prime numbers and the number of codons of amino acids. To empirically assess the effectiveness of the proposed method, we compare CPNR against EIIP. Experimental results demonstrate that the proposed method CPNR always achieves better performance than EIIP. We also develop a framework to combine the advantages of CPNR and EIIP, which enables us to improve the performance and study the unique characteristics of different representations.

Fluid-structure interaction with pipe-wall viscoelasticity during water hammer

NASA Astrophysics Data System (ADS)

Keramat, A.; Tijsseling, A. S.; Hou, Q.; Ahmadi, A.

2012-01-01

Fluid-structure interaction (FSI) due to water hammer in a pipeline which has viscoelastic wall behaviour is studied. Appropriate governing equations are derived and numerically solved. In the numerical implementation of the hydraulic and structural equations, viscoelasticity is incorporated using the Kelvin-Voigt mechanical model. The equations are solved by two different approaches, namely the Method of Characteristics-Finite Element Method (MOC-FEM) and full MOC. In both approaches two important effects of FSI in fluid-filled pipes, namely Poisson and junction coupling, are taken into account. The study proposes a more comprehensive model for studying fluid transients in pipelines as compared to previous works, which take into account either FSI or viscoelasticity. To verify the proposed mathematical model and its numerical solutions, the following problems are investigated: axial vibration of a viscoelastic bar subjected to a step uniaxial loading, FSI in an elastic pipe, and hydraulic transients in a pressurised polyethylene pipe without FSI. The results of each case are checked with available exact and experimental results. Then, to study the simultaneous effects of FSI and viscoelasticity, which is the new element of the present research, one problem is solved by the two different numerical approaches. Both numerical methods give the same results, thus confirming the correctness of the solutions.

A reconstruction method for cone-beam differential x-ray phase-contrast computed tomography.

PubMed

Fu, Jian; Velroyen, Astrid; Tan, Renbo; Zhang, Junwei; Chen, Liyuan; Tapfer, Arne; Bech, Martin; Pfeiffer, Franz

2012-09-10

Most existing differential phase-contrast computed tomography (DPC-CT) approaches are based on three kinds of scanning geometries, described by parallel-beam, fan-beam and cone-beam. Due to the potential of compact imaging systems with magnified spatial resolution, cone-beam DPC-CT has attracted significant interest. In this paper, we report a reconstruction method based on a back-projection filtration (BPF) algorithm for cone-beam DPC-CT. Due to the differential nature of phase contrast projections, the algorithm restrains from differentiation of the projection data prior to back-projection, unlike BPF algorithms commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a micro-focus x-ray tube source. Moreover, the numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated cone-beam datasets. We believe that this feature is of particular interest for future medical cone-beam phase-contrast CT imaging applications.

Freefield vibrations due to dynamic loading on a tunnel embedded in a stratified medium

NASA Astrophysics Data System (ADS)

Clouteau, D.; Arnst, M.; Al-Hussaini, T. M.; Degrande, G.

2005-05-01

An efficient and modular numerical prediction model is developed to predict vibration and re-radiated noise in adjacent buildings from excitation due to metro trains in tunnels for both newly built and existing situations. The three-dimensional dynamic tunnel-soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transform, limiting the discretization effort to a single bounded reference cell. It is demonstrated in the paper how the boundary element method can efficiently be extended to deal with periodic media, reusing the available three-dimensional Green's tensors for layered media. The efficiency of the method is demonstrated with a numerical example, where the case of harmonic and transient point loading on the invert of a shallow cut-and-cover masonry tunnel in Paris is considered. The work described here was carried out under the auspices of the CONVURT project sponsored by the European Community.

The stress intensity factors for a periodic array of interacting coplanar penny-shaped cracks

PubMed Central

Lekesiz, Huseyin; Katsube, Noriko; Rokhlin, Stanislav I.; Seghi, Robert R.

2013-01-01

The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar penny-shaped cracks. Kachanov’s approximate method for crack interactions (Int. J. Solid. Struct. 1987; 23(1):23–43) is employed to analyze both hexagonal and square crack configurations. In approximating crack interactions, the solution converges when the total truncation number of the cracks is 109. As expected, due to high density packing crack interaction in the hexagonal configuration is stronger than that in the square configuration. Based on the numerical results, convenient fitting equations for quick evaluation of the mode I stress intensity factors are obtained as a function of crack density and angle around the crack edge for both crack configurations. Numerical results for the mode II and III stress intensity factors are presented in the form of contour lines for the case of Poisson’s ratio ν =0.3. Possible errors for these problems due to Kachanov’s approximate method are estimated. Good agreement is observed with the limited number of results available in the literature and obtained by different methods. PMID:27175035

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

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1993-01-01

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

Numerical simulation of vessel dynamics in manoeuvrability and seakeeping problems

NASA Astrophysics Data System (ADS)

Blishchik, A. E.; Taranov, A. E.

2018-05-01

This paper deals with some examples of numerical modelling for ship's dynamics problems and data comparison with corresponding experimental results. It was considered two kinds of simulation: self-propelled turning motion of crude carrier KVLCC2 and changing position of container carrier S 175 due to wave loadings. Mesh generation and calculation were made in STAR-CCM+ package. URANS equations were used as system of equations closed by k-w SST turbulence model. The vessel had several degrees of freedom, which depend on task. Based on the results of this research, the conclusion was made concerning the applicability of used numerical methods.

Mixed time integration methods for transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Liu, W. K.

1982-01-01

The computational methods used to predict and optimize the thermal structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a different yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Mixed time integration methods for transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Liu, W. K.

1983-01-01

The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally-useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

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.

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.

Propagation characteristics of two-color laser pulses in homogeneous plasma

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

Hemlata,; Saroch, Akanksha; Jha, Pallavi

2015-11-15

An analytical and numerical study of the evolution of two-color, sinusoidal laser pulses in cold, underdense, and homogeneous plasma has been presented. The wave equations for the radiation fields driven by linear as well as nonlinear contributions due to the two-color laser pulses have been set up. A variational technique is used to obtain the simultaneous equations describing the evolution of the laser spot size, pulse length, and chirp parameter. Numerical methods are used to graphically analyze the simultaneous evolution of these parameters due to the combined effect of the two-color laser pulses. Further, the pulse parameters are compared withmore » those obtained for a single laser pulse. Significant focusing, compression, and enhanced positive chirp is obtained due to the combined effect of simultaneously propagating two-color pulses as compared to a single pulse propagating in plasma.« less

Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity

NASA Astrophysics Data System (ADS)

Voronych, Oksana; Buraczewski, Adam; Matuszewski, Michał; Stobińska, Magdalena

2017-06-01

A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge-Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which has been used for theoretical investigation of exciton-polaritons. Catalogue identifier: AFBQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD-3 No. of lines in distributed program, including test data, etc.: 2157 No. of bytes in distributed program, including test data, etc.: 498994 Distribution format: tar.gz Programming language: C++ with OpenMP extensions (main numerical program), Python (helper scripts). Computer: Modern PC (tested on AMD and Intel processors), HP BL2x220. Operating system: Unix/Linux and Windows. Has the code been vectorized or parallelized?: Yes (OpenMP) RAM: 200 MB for single run Classification: 7, 7.7. Nature of problem: An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose-Einstein condensation of exciton-polaritons-quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross-Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons. Solution method: A Runge-Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware. Running time: 6h for 100 ps evolution, depending on the values of parameters

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.

Computing Normal Shock-Isotropic Turbulence Interaction With Tetrahedral Meshes and the Space-Time CESE Method

NASA Astrophysics Data System (ADS)

Venkatachari, Balaji Shankar; Chang, Chau-Lyan

2016-11-01

The focus of this study is scale-resolving simulations of the canonical normal shock- isotropic turbulence interaction using unstructured tetrahedral meshes and the space-time conservation element solution element (CESE) method. Despite decades of development in unstructured mesh methods and its potential benefits of ease of mesh generation around complex geometries and mesh adaptation, direct numerical or large-eddy simulations of turbulent flows are predominantly carried out using structured hexahedral meshes. This is due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for unstructured meshes that can resolve multiple physical scales and flow discontinuities simultaneously. The CESE method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to accurately simulate turbulent flows using tetrahedral meshes. As part of the study, various regimes of the shock-turbulence interaction (wrinkled and broken shock regimes) will be investigated along with a study on how adaptive refinement of tetrahedral meshes benefits this problem. The research funding for this paper has been provided by Revolutionary Computational Aerosciences (RCA) subproject under the NASA Transformative Aeronautics Concepts Program (TACP).

Analytical model of cracking due to rebar corrosion expansion in concrete considering the structure internal force

NASA Astrophysics Data System (ADS)

Lin, Xiangyue; Peng, Minli; Lei, Fengming; Tan, Jiangxian; Shi, Huacheng

2017-12-01

Based on the assumptions of uniform corrosion and linear elastic expansion, an analytical model of cracking due to rebar corrosion expansion in concrete was established, which is able to consider the structure internal force. And then, by means of the complex variable function theory and series expansion technology established by Muskhelishvili, the corresponding stress component functions of concrete around the reinforcement were obtained. Also, a comparative analysis was conducted between the numerical simulation model and present model in this paper. The results show that the calculation results of both methods were consistent with each other, and the numerical deviation was less than 10%, proving that the analytical model established in this paper is reliable.

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.

Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading

NASA Astrophysics Data System (ADS)

Nasri, Mohamed Aziz; Robert, Camille; Ammar, Amine; El Arem, Saber; Morel, Franck

2018-02-01

The numerical modelling of the behaviour of materials at the microstructural scale has been greatly developed over the last two decades. Unfortunately, conventional resolution methods cannot simulate polycrystalline aggregates beyond tens of loading cycles, and they do not remain quantitative due to the plasticity behaviour. This work presents the development of a numerical solver for the resolution of the Finite Element modelling of polycrystalline aggregates subjected to cyclic mechanical loading. The method is based on two concepts. The first one consists in maintaining a constant stiffness matrix. The second uses a time/space model reduction method. In order to analyse the applicability and the performance of the use of a space-time separated representation, the simulations are carried out on a three-dimensional polycrystalline aggregate under cyclic loading. Different numbers of elements per grain and two time increments per cycle are investigated. The results show a significant CPU time saving while maintaining good precision. Moreover, increasing the number of elements and the number of time increments per cycle, the model reduction method is faster than the standard solver.

Numerical simulation of systems of shear bands in ductile metal with inclusions

NASA Astrophysics Data System (ADS)

Plohr, Jeeyeon

2017-06-01

We develop a method for numerical simulations of high strain-rate loading of mesoscale samples of ductile metal with inclusions. Because of its small-scale inhomogeneity, the composite material is prone to localized shear deformation. This method employs the Generalized Method of Cells to ensure that the micro mechanical behavior of the metal and inclusions is reflected properly in the behavior of the composite at the mesoscale. To find the effective plastic strain rate when shear bands are present, we extend and apply the analytic and numerical analysis of shear bands of Glimm, Plohr, and Sharp. Our tests of the method focus on the stress/strain response in uniaxial-strain flow, both compressive and tensile, of depleted uranium metal containing silicon carbide inclusions. In results, we verify the elevated temperature and thermal softening at shear bands in our simulations of pure DU and DU/SiC composites. We also note that in composites, due the asymmetry caused by the inclusions, shear band form at different times in different subcells. In particular, in the subcells near inclusions, shear band form much earlier than they do in pure DU.

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

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.

Multi-scale image segmentation and numerical modeling in carbonate rocks

NASA Astrophysics Data System (ADS)

Alves, G. C.; Vanorio, T.

2016-12-01

Numerical methods based on computational simulations can be an important tool in estimating physical properties of rocks. These can complement experimental results, especially when time constraints and sample availability are a problem. However, computational models created at different scales can yield conflicting results with respect to the physical laboratory. This problem is exacerbated in carbonate rocks due to their heterogeneity at all scales. We developed a multi-scale approach performing segmentation of the rock images and numerical modeling across several scales, accounting for those heterogeneities. As a first step, we measured the porosity and the elastic properties of a group of carbonate samples with varying micrite content. Then, samples were imaged by Scanning Electron Microscope (SEM) as well as optical microscope at different magnifications. We applied three different image segmentation techniques to create numerical models from the SEM images and performed numerical simulations of the elastic wave-equation. Our results show that a multi-scale approach can efficiently account for micro-porosities in tight micrite-supported samples, yielding acoustic velocities comparable to those obtained experimentally. Nevertheless, in high-porosity samples characterized by larger grain/micrite ratio, results show that SEM scale images tend to overestimate velocities, mostly due to their inability to capture macro- and/or intragranular- porosity. This suggests that, for high-porosity carbonate samples, optical microscope images would be more suited for numerical simulations.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface

NASA Astrophysics Data System (ADS)

Bibi, Madiha; Khalil-Ur-Rehman; Malik, M. Y.; Tahir, M.

2018-04-01

In the present article, unsteady flow field characteristics of the Williamson fluid model are explored. The nanosized particles are suspended in the flow regime having the interaction of a magnetic field. The fluid flow is induced due to a stretching permeable surface. The flow model is controlled through coupled partial differential equations to the used shooting method for a numerical solution. The obtained partial differential equations are converted into ordinary differential equations as an initial value problem. The shooting method is used to find a numerical solution. The mathematical modeling yields physical parameters, namely the Weissenberg number, the Prandtl number, the unsteadiness parameter, the magnetic parameter, the mass transfer parameter, the Lewis number, the thermophoresis parameter and Brownian parameters. It is found that the Williamson fluid velocity, temperature and nanoparticles concentration are a decreasing function of the unsteadiness parameter.

Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter With Enhanced Numerical Stability

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

Qi, Junjian; Sun, Kai; Wang, Jianhui

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKFGPS) is proposed and compared with five existing approaches, including UKFschol, UKF-kappa, UKFmodified, UKF-Delta Q, and the squareroot UKF (SRUKF). These methods and the extended Kalman filter (EKF) are tested by performing dynamic state estimation on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good estimates. However, for NPCC system, both EKF and the classic UKF fail. It is foundmore » that UKFschol, UKF-kappa, and UKF-Delta Q do not work well in some estimations while UKFGPS works well in most cases. UKFmodified and SRUKF can always work well, indicating their better scalability mainly due to the enhanced numerical stability.« less

Thermal radiation characteristics of nonisothermal cylindrical enclosures using a numerical ray tracing technique

NASA Technical Reports Server (NTRS)

Baumeister, Joseph F.

1990-01-01

Analysis of energy emitted from simple or complex cavity designs can lead to intricate solutions due to nonuniform radiosity and irradiation within a cavity. A numerical ray tracing technique was applied to simulate radiation propagating within and from various cavity designs. To obtain the energy balance relationships between isothermal and nonisothermal cavity surfaces and space, the computer code NEVADA was utilized for its statistical technique applied to numerical ray tracing. The analysis method was validated by comparing results with known theoretical and limiting solutions, and the electrical resistance network method. In general, for nonisothermal cavities the performance (apparent emissivity) is a function of cylinder length-to-diameter ratio, surface emissivity, and cylinder surface temperatures. The extent of nonisothermal conditions in a cylindrical cavity significantly affects the overall cavity performance. Results are presented over a wide range of parametric variables for use as a possible design reference.

Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory

NASA Astrophysics Data System (ADS)

MacDonald, Christopher L.; Bhattacharya, Nirupama; Sprouse, Brian P.; Silva, Gabriel A.

2015-09-01

Computing numerical solutions to fractional differential equations can be computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In general, numerical approaches that depend on truncating part of the system history while efficient, can suffer from high degrees of error and inaccuracy. Here we present an adaptive time step memory method for smooth functions applied to the Grünwald-Letnikov fractional diffusion derivative. This method is computationally efficient and results in smaller errors during numerical simulations. Sampled points along the system's history at progressively longer intervals are assumed to reflect the values of neighboring time points. By including progressively fewer points backward in time, a temporally 'weighted' history is computed that includes contributions from the entire past of the system, maintaining accuracy, but with fewer points actually calculated, greatly improving computational efficiency.

Simulation for Carbon Nanotube Dispersion and Microstructure Formation in CNTs/AZ91D Composite Fabricated by Ultrasonic Processing

NASA Astrophysics Data System (ADS)

Yang, Yuansheng; Zhao, Fuze; Feng, Xiaohui

2017-10-01

The dispersion of carbon nanotubes (CNTs) in AZ91D melt by ultrasonic processing and microstructure formation of CNTs/AZ91D composite were studied using numerical and physical simulations. The sound field and acoustic streaming were predicted using finite element method. Meanwhile, optimal immersion depth of the ultrasonic probe and suitable ultrasonic power were obtained. Single-bubble model was used to predict ultrasonic cavitation in AZ91D melt. The relationship between sound pressure amplitude and ultrasonic cavitation was established. Physical simulations of acoustic streaming and ultrasonic cavitation agreed well with the numerical simulations. It was confirmed that the dispersion of carbon nanotubes was remarkably improved by ultrasonic processing. Microstructure formation of CNTs/AZ91D composite was numerically simulated using cellular automation method. In addition, grain refinement was achieved and the growth of dendrites was changed due to the uniform dispersion of CNTs.

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.

Computational investigations and grid refinement study of 3D transient flow in a cylindrical tank using OpenFOAM

NASA Astrophysics Data System (ADS)

Mohd Sakri, F.; Mat Ali, M. S.; Sheikh Salim, S. A. Z.

2016-10-01

The study of physic fluid for a liquid draining inside a tank is easily accessible using numerical simulation. However, numerical simulation is expensive when the liquid draining involves the multi-phase problem. Since an accurate numerical simulation can be obtained if a proper method for error estimation is accomplished, this paper provides systematic assessment of error estimation due to grid convergence error using OpenFOAM. OpenFOAM is an open source CFD-toolbox and it is well-known among the researchers and institutions because of its free applications and ready to use. In this study, three types of grid resolution are used: coarse, medium and fine grids. Grid Convergence Index (GCI) is applied to estimate the error due to the grid sensitivity. A monotonic convergence condition is obtained in this study that shows the grid convergence error has been progressively reduced. The fine grid has the GCI value below 1%. The extrapolated value from Richardson Extrapolation is in the range of the GCI obtained.

Phase segregation in multiphase turbulent channel flow

NASA Astrophysics Data System (ADS)

Bianco, Federico; Soldati, Alfredo

2014-11-01

The phase segregation of a rapidly quenched mixture (namely spinodal decomposition) is numerically investigated. A phase field approach is considered. Direct numerical simulation of the coupled Navier-Stokes and Cahn-Hilliard equations is performed with spectral accuracy and focus has been put on domain growth scaling laws, in a wide range of regimes. The numerical method has been first validated against well known results of literature, then spinodal decomposition in a turbulent bounded flow (channel flow) has been considered. As for homogeneous isotropic case, turbulent fluctuations suppress the segregation process when surface tension at the interfaces is relatively low (namely low Weber number regimes). For these regimes, segregated domains size reaches a statistically steady state due to mixing and break-up phenomena. In contrast with homogenous and isotropic turbulence, the presence of mean shear, leads to a typical domain size that show a wall-distance dependence. Finally, preliminary results on the effects to the drag forces at the wall, due to phase segregation, have been discussed. Regione FVG, program PAR-FSC.

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Boby-Vortex Interaction, Sound Generation and Destructive Interference

NASA Technical Reports Server (NTRS)

Kao, Hsiao C.

2000-01-01

It is generally recognized that interaction of vortices with downstream blades is a major source of noise production. To analyze this problem numerically, a two-dimensional model of inviscid flow together with the method of matched asymptotic expansions is proposed. The method of matched asymptotic expansions is used to match the inner region of incompressible flow to the outer region of compressible flow. Because of incompressibility, relatively simple numerical methods are available to treat multiple vortices and multiple bodies of arbitrary shape. Disturbances from vortices and bodies propagate outward as sound waves. Due to their interactions, either constructive or destructive interference may result. When it is destructive, the combined sound intensity can be reduced, sometimes substantially. In addition, an analytical solution to sound generation by the cascade-vonex interaction is given.

A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry

NASA Technical Reports Server (NTRS)

Bodonyi, R. J.; Tadjfar, M.; Welch, W. J. C.; Duck, P. W.

1989-01-01

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite-difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves.

Detection of admittivity anomaly on high-contrast heterogeneous backgrounds using frequency difference EIT.

PubMed

Jang, J; Seo, J K

2015-06-01

This paper describes a multiple background subtraction method in frequency difference electrical impedance tomography (fdEIT) to detect an admittivity anomaly from a high-contrast background conductivity distribution. The proposed method expands the use of the conventional weighted frequency difference EIT method, which has been used limitedly to detect admittivity anomalies in a roughly homogeneous background. The proposed method can be viewed as multiple weighted difference imaging in fdEIT. Although the spatial resolutions of the output images by fdEIT are very low due to the inherent ill-posedness, numerical simulations and phantom experiments of the proposed method demonstrate its feasibility to detect anomalies. It has potential application in stroke detection in a head model, which is highly heterogeneous due to the skull.

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.

Co-Teaching: A Mixed Methods Study of the Effectiveness of a Secondary Co-Taught Classroom versus a Traditional Model

ERIC Educational Resources Information Center

Chilcoat, Eric R.

2011-01-01

Due to numerous mandates in the educational field, it is imperative to schools that teachers incorporate effective instructional methods to reach the diverse student population within a classroom. One way some educators have chosen to meet these challenges is by using the co-teaching model. In this setting, two or more teachers work in a…

Time-dependent wave splitting and source separation

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nataf, Frédéric; Assous, Franck

2017-02-01

Starting from classical absorbing boundary conditions, we propose a method for the separation of time-dependent scattered wave fields due to multiple sources or obstacles. In contrast to previous techniques, our method is local in space and time, deterministic, and avoids a priori assumptions on the frequency spectrum of the signal. Numerical examples in two space dimensions illustrate the usefulness of wave splitting for time-dependent scattering problems.

Discontinuous Galerkin Method with Numerical Roe Flux for Spherical Shallow Water Equations

NASA Astrophysics Data System (ADS)

Yi, T.; Choi, S.; Kang, S.

2013-12-01

In developing the dynamic core of a numerical weather prediction model with discontinuous Galerkin method, a numerical flux at the boundaries of grid elements plays a vital role since it preserves the local conservation properties and has a significant impact on the accuracy and stability of numerical solutions. Due to these reasons, we developed the numerical Roe flux based on an approximate Riemann problem for spherical shallow water equations in Cartesian coordinates [1] to find out its stability and accuracy. In order to compare the performance with its counterpart flux, we used the Lax-Friedrichs flux, which has been used in many dynamic cores such as NUMA [1], CAM-DG [2] and MCore [3] because of its simplicity. The Lax-Friedrichs flux is implemented by a flux difference between left and right states plus the maximum characteristic wave speed across the boundaries of elements. It has been shown that the Lax-Friedrichs flux with the finite volume method is more dissipative and unstable than other numerical fluxes such as HLLC, AUSM+ and Roe. The Roe flux implemented in this study is based on the decomposition of flux difference over the element boundaries where the nonlinear equations are linearized. It is rarely used in dynamic cores due to its complexity and thus computational expensiveness. To compare the stability and accuracy of the Roe flux with the Lax-Friedrichs, two- and three-dimensional test cases are performed on a plane and cubed-sphere, respectively, with various numbers of element and polynomial order. For the two-dimensional case, the Gaussian bell is simulated on the plane with two different numbers of elements at the fixed polynomial orders. In three-dimensional cases on the cubed-sphere, we performed the test cases of a zonal flow over an isolated mountain and a Rossby-Haurwitz wave, of which initial conditions are the same as those of Williamson [4]. This study presented that the Roe flux with the discontinuous Galerkin method is less dissipative and has stronger numerical stability than the Lax-Friedrichs. Reference 1. 2002, Giraldo, F.X., Hesthaven, J.S. and Warburton, T., "Nodal High-Order Discontinous Galerkin Methods for the Spherical Shallow Water Equations," Journal of Computational Physics, Vol.181, pp.499-525. 2. 2005, Nair, R.D., Thomas, S.J. and Loft, R.D., "A Discontinuous Galerkin Transport Scheme on the Cubed Sphere," Monthly Weather Review, Vol.133, pp.814-828. 3. 2010, Ullrich, P.A., Jablonowski, C. and Leer, van B., "High-Order Finite-Volume Methods for the Shallow-Water Equations on the Sphere," Journal of Computational Physics, Vol.229, pp.6104-6134. 4. 1992, Williamson, D.L., Drake, J.B., Hack, J., Jacob, R. and Swartztrauber, P.N., "A Standard Test Set for Numerical Approximations to the Shallow Water Equations in Spherical Geometry," Journal of Computational Physics, Vol.102, pp.211-224.

Modeling of nonequilibrium space plasma flows

NASA Technical Reports Server (NTRS)

Gombosi, Tamas

1995-01-01

Godunov-type numerical solution of the 20 moment plasma transport equations. One of the centerpieces of our proposal was the development of a higher order Godunov-type numerical scheme to solve the gyration dominated 20 moment transport equations. In the first step we explored some fundamental analytic properties of the 20 moment transport equations for a low b plasma, including the eigenvectors and eigenvalues of propagating disturbances. The eigenvalues correspond to wave speeds, while the eigenvectors characterize the transported physical quantities. In this paper we also explored the physically meaningful parameter range of the normalized heat flow components. In the second step a new Godunov scheme type numerical method was developed to solve the coupled set of 20 moment transport equations for a quasineutral single-ion plasma. The numerical method and the first results were presented at several national and international meetings and a paper describing the method has been published in the Journal of Computational Physics. To our knowledge this is the first numerical method which is capable of producing stable time-dependent solutions to the full 20 (or 16) moment set of transport equations, including the full heat flow equation. Previous attempts resulted in unstable (oscillating) solutions of the heat flow equations. Our group invested over two man-years into the development and implementation of the new method. The present model solves the 20 moment transport equations for an ion species and thermal electrons in 8 domain extending from a collision dominated to a collisionless region (200 km to 12,000 km). This model has been applied to study O+ acceleration due to Joule heating in the lower ionosphere.

Artificial acoustic stiffness reduction in fully compressible, direct numerical simulation of combustion

NASA Astrophysics Data System (ADS)

Wang, Yi; Trouvé, Arnaud

2004-09-01

A pseudo-compressibility method is proposed to modify the acoustic time step restriction found in fully compressible, explicit flow solvers. The method manipulates terms in the governing equations of order Ma2, where Ma is a characteristic flow Mach number. A decrease in the speed of acoustic waves is obtained by adding an extra term in the balance equation for total energy. This term is proportional to flow dilatation and uses a decomposition of the dilatational field into an acoustic component and a component due to heat transfer. The present method is a variation of the pressure gradient scaling (PGS) method proposed in Ramshaw et al (1985 Pressure gradient scaling method for fluid flow with nearly uniform pressure J. Comput. Phys. 58 361-76). It achieves gains in computational efficiencies similar to PGS: at the cost of a slightly more involved right-hand-side computation, the numerical time step increases by a full order of magnitude. It also features the added benefit of preserving the hydrodynamic pressure field. The original and modified PGS methods are implemented into a parallel direct numerical simulation solver developed for applications to turbulent reacting flows with detailed chemical kinetics. The performance of the pseudo-compressibility methods is illustrated in a series of test problems ranging from isothermal sound propagation to laminar premixed flame problems.

Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

USGS Publications Warehouse

Cox, T.J.; Runkel, R.L.

2008-01-01

Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

QUANTIFYING UNCERTAINTY DUE TO RANDOM ERRORS FOR MOMENT ANALYSES OF BREAKTHROUGH CURVES

EPA Science Inventory

The uncertainty in moments calculated from breakthrough curves (BTCs) is investigated as a function of random measurement errors in the data used to define the BTCs. The method presented assumes moments are calculated by numerical integration using the trapezoidal rule, and is t...

Numerical Study on Density Gradient Carbon-Carbon Composite for Vertical Launching System

NASA Astrophysics Data System (ADS)

Yoon, Jin-Young; Kim, Chun-Gon; Lim, Juhwan

2018-04-01

This study presents new carbon-carbon (C/C) composite that has a density gradient within single material, and estimates its heat conduction performance by a numerical method. To address the high heat conduction of a high-density C/C, which can cause adhesion separation in the steel structures of vertical launching systems, density gradient carbon-carbon (DGCC) composite is proposed due to its exhibiting low thermal conductivity as well as excellent ablative resistance. DGCC is manufactured by hybridizing two different carbonization processes into a single carbon preform. One part exhibits a low density using phenolic resin carbonization to reduce heat conduction, and the other exhibits a high density using thermal gradient-chemical vapor infiltration for excellent ablative resistance. Numerical analysis for DGCC is performed with a heat conduction problem, and internal temperature distributions are estimated by the forward finite difference method. Material properties of the transition density layer, which is inevitably formed during DGCC manufacturing, are assumed to a combination of two density layers for numerical analysis. By comparing numerical results with experimental data, we validate that DGCC exhibits a low thermal conductivity, and it can serve as highly effective ablative material for vertical launching systems.

Study on unsteady hydrodynamic performance of propeller in waves

NASA Astrophysics Data System (ADS)

Zhao, Qingxin; Guo, Chunyu; Su, Yumin; Liu, Tian; Meng, Xiangyin

2017-09-01

The speed of a ship sailing in waves always slows down due to the decrease in efficiency of the propeller. So it is necessary and essential to analyze the unsteady hydrodynamic performance of propeller in waves. This paper is based on the numerical simulation and experimental research of hydrodynamics performance when the propeller is under wave conditions. Open-water propeller performance in calm water is calculated by commercial codes and the results are compared to experimental values to evaluate the accuracy of the numerical simulation method. The first-order Volume of Fluid (VOF) wave method in STAR CCM+ is utilized to simulate the three-dimensional numerical wave. According to the above prerequisite, the numerical calculation of hydrodynamic performance of the propeller under wave conditions is conducted, and the results reveal that both thrust and torque of the propeller under wave conditions reveal intense unsteady behavior. With the periodic variation of waves, ventilation, and even an effluent phenomenon appears on the propeller. Calculation results indicate, when ventilation or effluent appears, the numerical calculation model can capture the dynamic characteristics of the propeller accurately, thus providing a significant theory foundation for further studying the hydrodynamic performance of a propeller in waves.

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

NASA Astrophysics Data System (ADS)

Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot

2018-05-01

The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.

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.

Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2018-03-01

In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Reτ = 180 are compared systematically with both published experimental and other DNS results based on solving the Navier-Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.

On the numerical treatment of selected oscillatory evolutionary problems

NASA Astrophysics Data System (ADS)

Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice

2017-07-01

We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.

SPH Simulation of Impact of a Surge on a Wall

NASA Astrophysics Data System (ADS)

Diwakar, Manoj Kumar; Mohapatra, Pranab Kumar; Tripathi, Shivam

2014-05-01

Structures located on the downstream of a dam are prone to impact of the surge due to dam break flow. Ramsden (1996) experimentally studied the run-up height on a vertical wall due to propagation of bore and surge on dry bed and measured their impact on the wall. Mohapatra et al. (2000) applied Navier Stokes equations to numerically study the impact of bore on vertical and inclined walls. They also obtained the evolution of surge on dry bed. In the present work, the impact of a surge wave due to dam break flow against the wall is modeled with a two-dimensional smoothed particle hydrodynamics (SPH) model. SPH is a mesh-free method that relies on the particle view of the field problem and approximates the continuity and momentum equations on a set of particles. The method solves the strong form of Navier-Stokes equations. The governing equations are solved numerically in the vertical plane. The propagation of the surge wave, its impact and the maximum run-up on the wall located at the boundary are analyzed. Surface profile, velocity field and pressure distributions are simulated. Non-dimensional run-up height obtained from the present numerical model is 0.86 and is in good agreement with the available experimental data of Ramsden (1996) which is in the range of 0.75-0.9. Also, the simulated profile of the surge tip was comparable to the empirical equations refereed in Ramsden (1996). The model is applied to the study the maximum force and the run-up height on inclined walls with different inclinations. The results indicate that the maximum force and the run-up height on the wall increase with the increment of wall inclination. Comparison of numerical results with analytical solutions derived from shallow water equations clearly shows the breakdown of shallow water assumption during the impact. In addition to these results, the numerical simulation yields the complete velocity and pressure ?elds which may be used to design structures located in the path of a dam-break wave. The study shows that the smoothed particle hydrodynamics can effectively simulate fluid flow dynamics. References: Mohapatra, P. K., Bhallamudi, S. M., and Eswaran, V. (2000). 'Numerical simulation of impact of bores against inclined walls.' J. Hydraulic. Engg., ASCE, 126(12), 942-945. Ramsden, J. D. (1996). 'Forces on a vertical wall due to long waves, bores, and dry-bed surges.' J. Waterway, Port, Coastal, and Ocean Engg., ASCE, 122(3), 134-141.

Numerical study on microbubble-enhanced heating for various parameters in EUS-FUS

NASA Astrophysics Data System (ADS)

Okita, Kohei; Maezawa, Miyuki; Takagi, Shu; Matsumoto, Yoichiro

2012-11-01

Endoscopic ultrasonography guided focused ultrasound surgery (EUS-FUS) have been developed as a less-invasive treatment for pancreatic cancer. In the present study, microbubble-enhanced heating for various parameters in EUS-FUS is investigated numerically. Mass and momentum equations for bubbly mixture are solved to reproduce the propagation of ultrasound of 4.8MHz through the gel containing microbubbles as Sonazoid®. The dynamics of bubble is governed by the equation which considers the elasticity of both shell and surrounding media. Additionally, the heat equation with the time averaged heat source is solved to obtain a temperature distribution. The basic equations are discretized by the 6th-order finite difference method and developed based on FDTD method. The mixture and bubbles are coupled by Euler-Lagrange method. As the results, the temperature around the target increased due to the microbubble oscillation with increasing the initial void fraction fG0 from 10-5 to 10-4%. However, at fG0=10-3%, ultrasounds were too attenuated to heat the target. The heating region moved from the target to the transducer side. By comparing the results with and without shell, the shell of bubble induced the heating around focus. This is because the decrease of the attenuation due to the elasticity of the shell and the increase of the viscous dissipation rate due to the viscosity of the shell.

The method of characteristics for the determination of supersonic flow over bodies of revolution at small angles of attack

NASA Technical Reports Server (NTRS)

Ferri, Antonio

1951-01-01

The method of characteristics has been applied for the determination of the supersonic-flow properties around bodies of revolution at a small angle of attack. The system developed considers the effect of the variation of entropy due to the curved shock and determines a flow that exactly satisfies the boundary conditions in the limits of the simplifications assumed. Two practical methods for numerical calculations are given. (author)

Integrated Reconfigurable Intelligent Systems (IRIS) for Complex Naval Systems

DTIC Science & Technology

2010-02-21

RKF45] and Adams Variable Step- Size Predictor - Corrector methods). While such algorithms naturally are usually used to numerically solve differential...verified by yet another function call. Due to their nature, such methods are referred to as predictor - corrector methods. While computationally expensive...CONTRACT NUMBER N00014-09- C -0394 5b. GRANT NUMBER N/A 5c. PROGRAM ELEMENT NUMBER N/A 6. Author(s) Dr. Dimitri N. Mavris Dr. Yongchang Li 5d

Symplectic discretization for spectral element solution of Maxwell's equations

NASA Astrophysics Data System (ADS)

Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo

2009-08-01

Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

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.

Numerical analysis of heat transfer in the exhaust gas flow in a diesel power generator

NASA Astrophysics Data System (ADS)

Brito, C. H. G.; Maia, C. B.; Sodré, J. R.

2016-09-01

This work presents a numerical study of heat transfer in the exhaust duct of a diesel power generator. The analysis was performed using two different approaches: the Finite Difference Method (FDM) and the Finite Volume Method (FVM), this last one by means of a commercial computer software, ANSYS CFX®. In FDM, the energy conservation equation was solved taking into account the estimated velocity profile for fully developed turbulent flow inside a tube and literature correlations for heat transfer. In FVM, the mass conservation, momentum, energy and transport equations were solved for turbulent quantities by the K-ω SST model. In both methods, variable properties were considered for the exhaust gas composed by six species: CO2, H2O, H2, O2, CO and N2. The entry conditions for the numerical simulations were given by experimental data available. The results were evaluated for the engine operating under loads of 0, 10, 20, and 37.5 kW. Test mesh and convergence were performed to determine the numerical error and uncertainty of the simulations. The results showed a trend of increasing temperature gradient with load increase. The general behaviour of the velocity and temperature profiles obtained by the numerical models were similar, with some divergence arising due to the assumptions made for the resolution of the models.

Improvement to the Convergence-Confinement Method: Inclusion of Support Installation Proximity and Stiffness

NASA Astrophysics Data System (ADS)

Oke, Jeffrey; Vlachopoulos, Nicholas; Diederichs, Mark

2018-05-01

The convergence-confinement method (CCM) is a method that has been introduced in tunnel construction that considers the ground response to the advancing tunnel face and the interaction with installed support. One limitation of the CCM is due to the numerically or empirically driven nature of the longitudinal displacement profile and the incomplete consideration of the longitudinal arching effect that occurs during tunnelling operations as part of the face effect. In this paper, the authors address the issue associated with when the CCM is used within squeezing ground conditions at depth. Based on numerical analysis, the authors have proposed a methodology and solution to improving the CCM in order to allow for more accurate results for squeezing ground conditions for three different excavation cases involving various excavation-support increments and distances from the face to the supported front. The tunnelling methods of consideration include: tunnel boring machine, mechanical (conventional), and drill and blast.

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Faegri, Knut, Jr.; Taylor, Peter R.

1990-01-01

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

Near Field Trailing Edge Tone Noise Computation

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2002-01-01

Blunt trailing edges in a flow often generate tone noise due to wall-jet shear layer and vortex shedding. In this paper, the space-time conservation element (CE/SE) method is employed to numerically study the near-field noise of blunt trailing edges. Two typical cases, namely, flow past a circular cylinder (aeolian noise problem) and flow past a flat plate of finite thickness are considered. The computed frequencies compare well with experimental data. For the aeolian noise problem, comparisons with the results of other numerical approaches are also presented.

On Computations of Duct Acoustics with Near Cut-Off Frequency

NASA Technical Reports Server (NTRS)

Dong, Thomas Z.; Povinelli, Louis A.

1997-01-01

The cut-off is a unique feature associated with duct acoustics due to the presence of duct walls. A study of this cut-off effect on the computations of duct acoustics is performed in the present work. The results show that the computation of duct acoustic modes near cut-off requires higher numerical resolutions than others to avoid being numerically cut off. Duct acoustic problems in Category 2 are solved by the DRP finite difference scheme with the selective artificial damping method and results are presented and compared to reference solutions.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

Evaluation of Test Methods for Triaxially Braided Composites using a Meso-Scale Finite Element Model

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

Zhang, Chao

The characterization of triaxially braided composite is complicate due to the nonuniformity of deformation within the unit cell as well as the possibility of the freeedge effect related to the large size of the unit cell. Extensive experimental investigation has been conducted to develop more accurate test approaches in characterizing the actual mechanical properties of the material we are studying. In this work, a meso-scale finite element model is utilized to simulate two complex specimens: notched tensile specimen and tube tensile specimen, which are designed to avoid the free-edge effect and free-edge effect induced premature edge damage. The full fieldmore » strain data is predicted numerically and compared with experimental data obtained by Digit Image Correlation. The numerically predicted tensile strength values are compared with experimentally measured results. The discrepancy between numerically predicted and experimentally measured data, the capability of different test approaches are analyzed and discussed. The presented numerical model could serve as assistance to the evaluation of different test methods, and is especially useful in identifying potential local damage events.« less

Comparative In vivo, Ex vivo, and In vitro Toxicity Studies of Engineered Nanomaterials

EPA Science Inventory

Efforts to reduce the number of animals in engineered nanomaterials (ENM) toxicity testing have resulted in the development of numerous alternative toxicity testing methods, but in vivo and in vitro results are still evolving and variable. This inconsistency could be due to the f...

A flow-injection mass spectrometry fingerprinting method for authentication and quality assessment of Scutellaria lateriflora-based dietary supplements

USDA-ARS?s Scientific Manuscript database

Scutellaria lateriflora, commonly known as skullcap, is used as an ingredient in numerous herbal products. However, it has been occasionally adulterated/contaminated with Teucrium canadense and/or Teucrium chamaedrys, commonly known as germander, due to the morphological similarities between the tw...

Mass spectroscopic fingerprinting method for to differentiation between Scutellaria lateriflora and the Germander (Teucrium canadens and T. chamaedrys species

USDA-ARS?s Scientific Manuscript database

Scutellaria lateriflora, commonly known as skullcap, is used as an ingredient in numerous herbal products. However, it has been occasionally adulterated/contaminated with Teucrium canadense and Teucrium chamaedrys, commonly known as germander, which contain potentially hepatotoxic diterpenes. Due ...

Chemical transport in a fissured rock: Verification of a numerical model

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

Rasmuson, A.; Narasimhan, T. N.; Neretnieks, I.

1982-10-01

Numerical models for simulating chemical transport in fissured rocks constitute powerful tools for evaluating the acceptability of geological nuclear waste repositories. Due to the very long-term, high toxicity of some nuclear waste products, the models are required to predict, in certain cases, the spatial and temporal distribution of chemical concentration less than 0.001% of the concentration released from the repository. Whether numerical models can provide such accuracies is a major question addressed in the present work. To this end, we have verified a numerical model, TRUMP, which solves the advective diffusion equation in general three dimensions with or without decaymore » and source terms. The method is based on an integrated finite-difference approach. The model was verified against known analytic solution of the one-dimensional advection-diffusion problem as well as the problem of advection-diffusion in a system of parallel fractures separated by spherical particles. The studies show that as long as the magnitude of advectance is equal to or less than that of conductance for the closed surface bounding any volume element in the region (that is, numerical Peclet number <2), the numerical method can indeed match the analytic solution within errors of ±10{sup -3} % or less. The realistic input parameters used in the sample calculations suggest that such a range of Peclet numbers is indeed likely to characterize deep groundwater systems in granitic and ancient argillaceous systems. Thus TRUMP in its present form does provide a viable tool for use in nuclear waste evaluation studies. A sensitivity analysis based on the analytic solution suggests that the errors in prediction introduced due to uncertainties in input parameters is likely to be larger than the computational inaccuracies introduced by the numerical model. Currently, a disadvantage in the TRUMP model is that the iterative method of solving the set of simultaneous equations is rather slow when time constants vary widely over the flow region. Although the iterative solution may be very desirable for large three-dimensional problems in order to minimize computer storage, it seems desirable to use a direct solver technique in conjunction with the mixed explicit-implicit approach whenever possible. work in this direction is in progress.« less

A Numerical Combination of Extended Boundary Condition Method and Invariant Imbedding Method Applied to Light Scattering by Large Spheroids and Cylinders

NASA Technical Reports Server (NTRS)

Bi, Lei; Yang, Ping; Kattawar, George W.; Mishchenko, Michael I.

2013-01-01

The extended boundary condition method (EBCM) and invariant imbedding method (IIM) are two fundamentally different T-matrix methods for the solution of light scattering by nonspherical particles. The standard EBCM is very efficient but encounters a loss of precision when the particle size is large, the maximum size being sensitive to the particle aspect ratio. The IIM can be applied to particles in a relatively large size parameter range but requires extensive computational time due to the number of spherical layers in the particle volume discretization. A numerical combination of the EBCM and the IIM (hereafter, the EBCM+IIM) is proposed to overcome the aforementioned disadvantages of each method. Even though the EBCM can fail to obtain the T-matrix of a considered particle, it is valuable for decreasing the computational domain (i.e., the number of spherical layers) of the IIM by providing the initial T-matrix associated with an iterative procedure in the IIM. The EBCM+IIM is demonstrated to be more efficient than the IIM in obtaining the optical properties of large size parameter particles beyond the convergence limit of the EBCM. The numerical performance of the EBCM+IIM is illustrated through representative calculations in spheroidal and cylindrical particle cases.

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.

Structures to Resist the Effects of Accidental Explosions. Volume 3. Principles of Dynamic Analysis

DTIC Science & Technology

1984-06-01

multi-degree-of-freedom systems) is presented. A step-by-step numerical integration of an element’s motion under dynamic loads using the...structural arrangements; providing closures, and preventing damage to interior portions of structures due to structual motion , shock, and fragment...an element’s motion under dynamic loads utilizing the Acceleration-Impulse- Extrapolation Method or the Average Acceleration Method and design charts

Calculation of wing response to gusts and blast waves with vortex lift effect

NASA Technical Reports Server (NTRS)

Chao, D. C.; Lan, C. E.

1983-01-01

A numerical study of the response of aircraft wings to atmospheric gusts and to nuclear explosions when flying at subsonic speeds is presented. The method is based upon unsteady quasi-vortex lattice method, unsteady suction analogy and Pade approximant. The calculated results, showing vortex lag effect, yield reasonable agreement with experimental data for incremental lift on wings in gust penetration and due to nuclear blast waves.

Numerical modelling and experimental study of liquid evaporation during gel formation

NASA Astrophysics Data System (ADS)

Pokusaev, B. G.; Khramtsov, D. P.

2017-11-01

Gels are promising materials in biotechnology and medicine as a medium for storing cells for bioprinting applications. Gel is a two-phase system consisting of solid medium and liquid phase. Understanding of a gel structure evolution and gel aging during liquid evaporation is a crucial step in developing new additive bioprinting technologies. A numerical and experimental study of liquid evaporation was performed. In experimental study an evaporation process of an agarose gel layer located on Petri dish was observed and mass difference was detected using electronic scales. Numerical model was based on a smoothed particle hydrodynamics method. Gel in a model was represented as a solid-liquid system and liquid evaporation was modelled due to capillary forces and heat transfer. Comparison of experimental data and numerical results demonstrated that model can adequately represent evaporation process in agarose gel.

Combined Effect of Random Transmit Power Control and Inter-Path Interference Cancellation on DS-CDMA Packet Mobile Communications

NASA Astrophysics Data System (ADS)

Kudoh, Eisuke; Ito, Haruki; Wang, Zhisen; Adachi, Fumiyuki

In mobile communication systems, high speed packet data services are demanded. In the high speed data transmission, throughput degrades severely due to severe inter-path interference (IPI). Recently, we proposed a random transmit power control (TPC) to increase the uplink throughput of DS-CDMA packet mobile communications. In this paper, we apply IPI cancellation in addition to the random TPC. We derive the numerical expression of the received signal-to-interference plus noise power ratio (SINR) and introduce IPI cancellation factor. We also derive the numerical expression of system throughput when IPI is cancelled ideally to compare with the Monte Carlo numerically evaluated system throughput. Then we evaluate, by Monte-Carlo numerical computation method, the combined effect of random TPC and IPI cancellation on the uplink throughput of DS-CDMA packet mobile communications.

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.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

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.

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Numerical investigation of field enhancement by metal nano-particles using a hybrid FDTD-PSTD algorithm.

PubMed

Pernice, W H; Payne, F P; Gallagher, D F

2007-09-03

We present a novel numerical scheme for the simulation of the field enhancement by metal nano-particles in the time domain. The algorithm is based on a combination of the finite-difference time-domain method and the pseudo-spectral time-domain method for dispersive materials. The hybrid solver leads to an efficient subgridding algorithm that does not suffer from spurious field spikes as do FDTD schemes. Simulation of the field enhancement by gold particles shows the expected exponential field profile. The enhancement factors are computed for single particles and particle arrays. Due to the geometry conforming mesh the algorithm is stable for long integration times and thus suitable for the simulation of resonance phenomena in coupled nano-particle structures.

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Hadaegh, F. Y.

1996-01-01

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Computational domain discretization in numerical analysis of flow within granular materials

NASA Astrophysics Data System (ADS)

Sosnowski, Marcin

2018-06-01

The discretization of computational domain is a crucial step in Computational Fluid Dynamics (CFD) because it influences not only the numerical stability of the analysed model but also the agreement of obtained results and real data. Modelling flow in packed beds of granular materials is a very challenging task in terms of discretization due to the existence of narrow spaces between spherical granules contacting tangentially in a single point. Standard approach to this issue results in a low quality mesh and unreliable results in consequence. Therefore the common method is to reduce the diameter of the modelled granules in order to eliminate the single-point contact between the individual granules. The drawback of such method is the adulteration of flow and contact heat resistance among others. Therefore an innovative method is proposed in the paper: single-point contact is extended to a cylinder-shaped volume contact. Such approach eliminates the low quality mesh elements and simultaneously introduces only slight distortion to the flow as well as contact heat transfer. The performed analysis of numerous test cases prove the great potential of the proposed method of meshing the packed beds of granular materials.

A variational approach to multi-phase motion of gas, liquid and solid based on the level set method

NASA Astrophysics Data System (ADS)

Yokoi, Kensuke

2009-07-01

We propose a simple and robust numerical algorithm to deal with multi-phase motion of gas, liquid and solid based on the level set method [S. Osher, J.A. Sethian, Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79 (1988) 12; M. Sussman, P. Smereka, S. Osher, A level set approach for capturing solution to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146; J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999; S. Osher, R. Fedkiw, Level Set Methods and Dynamics Implicit Surface, Applied Mathematical Sciences, vol. 153, Springer, 2003]. In Eulerian framework, to simulate interaction between a moving solid object and an interfacial flow, we need to define at least two functions (level set functions) to distinguish three materials. In such simulations, in general two functions overlap and/or disagree due to numerical errors such as numerical diffusion. In this paper, we resolved the problem using the idea of the active contour model [M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision 1 (1988) 321; V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, International Journal of Computer Vision 22 (1997) 61; G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001; R. Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications, Springer-Verlag, 2003] introduced in the field of image processing.

Supratransmission in a metastable modular metastructure for tunable non-reciprocal wave transmission

NASA Astrophysics Data System (ADS)

Wu, Zhen; Wang, K. W.

2018-03-01

In this research, we numerically and analytically investigate the nonlinear energy transmission phenomenon in a metastable modular metastructure. Numerical studies on a 1D metastable chain provide clear evidence that when driving frequency is within the stopband of the periodic structure, there exists a threshold for the driving amplitude, above which sudden increase in the energy transmission can be observed. This onset of transmission is due to nonlinear instability and is known as supratransmission. We discover that due to spatial asymmetry of strategically configured constituents, such transmission thresholds are considerably different when structure is excited from different ends and this discrepancy creates a region of non-reciprocal energy transmission. We demonstrate that when the loss of stability is due to saddlenode bifurcation, the transmission threshold can be predicted analytically using a localized nonlinear-linear system model, and analyzed via combining harmonic balancing and transfer matrix methods. These investigations elucidate the rich and complex dynamics achievable by nonlinearity and metastabilities, and provide synthesize tools for tunable bandgaps and non-reciprocal wave transmissions.

ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Mokhtari, Simin

1990-01-01

For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

Fast solver for large scale eddy current non-destructive evaluation problems

NASA Astrophysics Data System (ADS)

Lei, Naiguang

Eddy current testing plays a very important role in non-destructive evaluations of conducting test samples. Based on Faraday's law, an alternating magnetic field source generates induced currents, called eddy currents, in an electrically conducting test specimen. The eddy currents generate induced magnetic fields that oppose the direction of the inducing magnetic field in accordance with Lenz's law. In the presence of discontinuities in material property or defects in the test specimen, the induced eddy current paths are perturbed and the associated magnetic fields can be detected by coils or magnetic field sensors, such as Hall elements or magneto-resistance sensors. Due to the complexity of the test specimen and the inspection environments, the availability of theoretical simulation models is extremely valuable for studying the basic field/flaw interactions in order to obtain a fuller understanding of non-destructive testing phenomena. Theoretical models of the forward problem are also useful for training and validation of automated defect detection systems. Theoretical models generate defect signatures that are expensive to replicate experimentally. In general, modelling methods can be classified into two categories: analytical and numerical. Although analytical approaches offer closed form solution, it is generally not possible to obtain largely due to the complex sample and defect geometries, especially in three-dimensional space. Numerical modelling has become popular with advances in computer technology and computational methods. However, due to the huge time consumption in the case of large scale problems, accelerations/fast solvers are needed to enhance numerical models. This dissertation describes a numerical simulation model for eddy current problems using finite element analysis. Validation of the accuracy of this model is demonstrated via comparison with experimental measurements of steam generator tube wall defects. These simulations generating two-dimension raster scan data typically takes one to two days on a dedicated eight-core PC. A novel direct integral solver for eddy current problems and GPU-based implementation is also investigated in this research to reduce the computational time.

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.

Boundary element methods for the analysis of crack growth in the presence of residual stress fields

NASA Astrophysics Data System (ADS)

Leitao, V. M. A.; Aliabadi, M. H.; Rooke, D. P.; Cook, R.

1998-06-01

Two boundary element methods of simulating crack growth in the presence of residual stress fields are presented, and the results are compared to experimental measurements. The first method utilizes linear elastic fracture mechanics (LEFM) and superimposes the solutions due to the applied load and the residual stress field. In this method, the residual stress fields are obtained from an elastoplastic BEM analysis, and numerical weight functions are used to obtain the stress intensity factors due to the fatigue loading. The second method presented is an elastoplastic fracture mechanics (EPFM) approach for crack growth simulation. A nonlinear J-integral is used in the fatigue life calculations. The methods are shown to agree well with experimental measurements of crack growth in prestressed open hole specimens. Results are also presented for the case where the prestress is applied to specimens that have been precracked.

An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

NASA Astrophysics Data System (ADS)

Karwas, Alex

Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach is capable of accurately simulating sailcraft motion. Sailcraft and spacecraft simulations are compared to flight data and to other numerical solution techniques. The new formulation shows an increase in accuracy over a widely used trajectory propagation technique. Simulations for two-dimensional, three-dimensional, and variable attitude trajectories are presented to show the multiple capabilities of the new technique. An element of optimal control is also part of the new technique. An additional equation is added to the sailcraft equations of motion that maximizes thrust in a specific direction. A technical description and results of an example optimization problem are presented. The spacecraft attitude dynamics equations take the simulation a step further by providing control torques using the angular rate and acceleration outputs of the numerical formulation.

Effects of non-homogeneous flow on ADCP data processing in a hydroturbine forebay

DOE PAGES

Harding, S. F.; Richmond, M. C.; Romero-Gomez, P.; ...

2016-01-02

Accurate modeling of the velocity field in the forebay of a hydroelectric power station is important for both power generation and fish passage, and is able to be increasingly well represented by computational fluid dynamics (CFD) simulations. Acoustic Doppler Current Profiler (ADCP) are investigated herein as a method of validating the numerical flow solutions, particularly in observed and calculated regions of non-homogeneous flow velocity. By using a numerical model of an ADCP operating in a velocity field calculated using CFD, the errors due to the spatial variation of the flow velocity are quantified. Furthermore, the numerical model of the ADCPmore » is referred to herein as a Virtual ADCP (VADCP).« less

The liquid fuel jet in subsonic crossflow

NASA Technical Reports Server (NTRS)

Nguyen, T. T.; Karagozian, A. R.

1990-01-01

An analytical/numerical model is described which predicts the behavior of nonreacting and reacting liquid jets injected transversely into subsonic cross flow. The compressible flowfield about the elliptical jet cross section is solved at various locations along the jet trajectory by analytical means for free-stream local Mach number perpendicular to jet cross section smaller than 0.3 and by numerical means for free-stream local Mach number perpendicular to jet cross section in the range 0.3-1.0. External and internal boundary layers along the jet cross section are solved by integral and numerical methods, and the mass losses due to boundary layer shedding, evaporation, and combustion are calculated and incorporated into the trajectory calculation. Comparison of predicted trajectories is made with limited experimental observations.

RT DDA: A hybrid method for predicting the scattering properties by densely packed media

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D.

2017-12-01

The most accurate approaches to predicting the scattering properties of particulate media are based on exact solutions of the Maxwell's equations (MEs), such as the T-matrix and discrete dipole methods. Applying these techniques for optically thick targets is challenging problem due to the large-scale computations and are usually substituted by phenomenological radiative transfer (RT) methods. On the other hand, the RT technique is of questionable validity in media with large particle packing densities. In recent works, we used numerically exact ME solvers to examine the effects of particle concentration on the polarized reflection properties of plane parallel random media. The simulations were performed for plane parallel layers of wavelength-sized spherical particles, and results were compared with RT predictions. We have shown that RTE results monotonically converge to the exact solution as the particle volume fraction becomes smaller and one can observe a nearly perfect fit for packing densities of 2%-5%. This study describes the hybrid technique composed of exact and numerical scalar RT methods. The exact methodology in this work is the plane parallel discrete dipole approximation whereas the numerical method is based on the adding and doubling method. This approach not only decreases the computational time owing to the RT method but also includes the interference and multiple scattering effects, so it may be applicable to large particle density conditions.

Technical Workshop on Human Milk Surveillance and Research on Environmental Chemicals in the U.S.: An Overview

EPA Science Inventory

Interest in human milk research and monitoring for environmental chemicals is growing, and as studies of chemicals in human milk are initiated, it is of the utmost importance that these studies be conducted using harmonized methods. Due to numerous limitations in previous studies...

Epistasis-list.org: A Curated Database of Gene-Gene and Gene-Environment Interactions in Human Epidemiology

EPA Science Inventory

The field of human genetics has experienced a paradigm shift in that common diseases are now thought to be due to the complex interactions among numerous genetic and environmental factors. This paradigm shift has prompted the development of myriad novel methods to detect such int...

Odor and chemical emissions from dairy and swine facilities: Part 1 - project overview and collection methods

USDA-ARS?s Scientific Manuscript database

Livestock facilities have received numerous criticisms due to their emissions of odorous air and chemicals. Hence, there is a significant need for odor emission factors and identification of principle odorous chemicals. Odor emission factors are used as inputs to odor setback models, while chemica...

TECHNICAL WORKSHOP ON HUMAN MILK SURVEILLANCE AND RESEARCH ON ENVIRONMENTAL CHEMICALS IN THE U.S.: AN OVERVIEW

EPA Science Inventory

Interest in human milk research and monitoring for environmental chemicals is growing, and as studies of chemicals in human milk are initiated, it is of the utmost importance that these studies be conducted using harmonized methods. Due to numerous limitations in previous studies...

A Network Analysis of the American Library Association: Defining a Profession

ERIC Educational Resources Information Center

Battleson, Brenda L.

2010-01-01

The term "librarianship" is a generic one, suggesting one overarching discipline despite the numerous specializations and areas of research within the profession. While many disciplines use bibliometric analysis of their literature to define subfields of study within, such methods are not appropriate to librarianship due to the nature of…

Thirty years of change in forest soils of the Allegheny Plateau, Pennsylvania

Treesearch

S.W. Bailey; S.B. Horsley; R.P. Long

2005-01-01

Numerous studies have investigated the potential depletion of available base cation pools from forest soils in regions impacted by acid deposition. However, these studies mostly used indirect methods. Retrospective studies, providing direct evidence of chemical changes in forest soils, are relatively rare due to a lack of appropriate sampling, documentation, and...

Handbook of Research on Hybrid Learning Models: Advanced Tools, Technologies, and Applications

ERIC Educational Resources Information Center

Wang, Fu Lee, Ed.; Fong, Joseph, Ed.; Kwan, Reggie, Ed.

2010-01-01

Hybrid learning is now the single-greatest trend in education today due to the numerous educational advantages when both traditional classroom learning and e-learning are implemented collectively. This handbook collects emerging research and pedagogies related to the convergence of teaching and learning methods. This significant "Handbook of…

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Modeling Pulse Transmission in the Monterey Bay Using Parabolic Equation Methods

DTIC Science & Technology

1991-12-01

Collins 9-13 was chosen for this purpose due its energy conservation scheme , and its ability to efficiently incorporate higher order terms in its...pressure field generated by the PE model into normal modes. Additionally, this process provides increased physical understanding of mode coupling and...separation of variables (i.e. normal modes or fast field), as well as pure numerical schemes such as the parabolic equation methods, can be used. However, as

Comment on 'Shang S. 2012. Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes 26: 3338-3343. DOI: 10.1002/hyp.8405'

NASA Technical Reports Server (NTRS)

Yatheendradas, Soni; Narapusetty, Balachandrudu; Peters-Lidard, Christa; Funk, Christopher; Verdin, James

2014-01-01

A previous study analyzed errors in the numerical calculation of actual crop evapotranspiration (ET(sub a)) under soil water stress. Assuming no irrigation or precipitation, it constructed equations for ET(sub a) over limited soil-water ranges in a root zone drying out due to evapotranspiration. It then used a single crop-soil composite to provide recommendations about the appropriate usage of numerical methods under different values of the time step and the maximum crop evapotranspiration (ET(sub c)). This comment reformulates those ET(sub a) equations for applicability over the full range of soil water values, revealing a dependence of the relative error in numerical ET(sub a) on the initial soil water that was not seen in the previous study. It is shown that the recommendations based on a single crop-soil composite can be invalid for other crop-soil composites. Finally, a consideration of the numerical error in the time-cumulative value of ET(sub a) is discussed besides the existing consideration of that error over individual time steps as done in the previous study. This cumulative ET(sub a) is more relevant to the final crop yield.

Detection of multiple thin surface cracks using vibrothermography with low-power piezoceramic-based ultrasonic actuator—a numerical study with experimental verification

NASA Astrophysics Data System (ADS)

Parvasi, Seyed Mohammad; Xu, Changhang; Kong, Qingzhao; Song, Gangbing

2016-05-01

Ultrasonic vibrations in cracked structures generate heat at the location of defects mainly due to frictional rubbing and viscoelastic losses at the defects. Vibrothermography is an effective nondestructive evaluation method which uses infrared imaging (IR) techniques to locate defects such as cracks and delaminations by detecting the heat generated at the defects. In this paper a coupled thermo-electro-mechanical analysis with the use of implicit finite element method was used to simulate a low power (10 W) piezoceramic-based ultrasonic actuator and the corresponding heat generation in a metallic plate with multiple surface cracks. Numerical results show that the finite element software Abaqus can be used to simultaneously model the electrical properties of the actuator, the ultrasonic waves propagating within the plate, as well as the thermal properties of the plate. Obtained numerical results demonstrate the ability of these low power transducers in detecting multiple cracks in the simulated aluminum plate. The validity of the numerical simulations was verified through experimental studies on a physical aluminum plate with multiple surface cracks while the same low power piezoceramic stack actuator was used to excite the plate and generate heat at the cracks. An excellent qualitative agreement exists between the experimental results and the numerical simulation’s results.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

PubMed

Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PubMed Central

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

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.

Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Christiansen, Ove

2018-06-01

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μEh regime.

Development of a vehicle-track model assembly and numerical method for simulation of wheel-rail dynamic interaction due to unsupported sleepers

NASA Astrophysics Data System (ADS)

Zhu, Jian Jun; Ahmed, A. K. W.; Rakheja, Subhash; Khajepour, Amir

2010-12-01

In practice, it is not very uncommon to find railway track systems with unsupported sleepers due to the uneven settlement of a ballasted track system. These unsupported sleepers are among the major vibration excitations for a train and track system when a train moves forwards on a track. The vibration induced by unsupported sleepers can cause a large dynamic contact force between wheels and rails. For heavily loaded high-speed trains, the deteriorated sleeper support may lead to accelerated degradation of the railway track and vehicle components, and may thus impose safety risk to the operation. This paper presents analyses of a coupled vehicle-track assembly consisting of a roll plane vehicle model, a continuous track system model and an adaptive wheel-rail contact model. In order to improve the simulation efficiency, a numerical approach based on the central finite difference method is proposed in this investigation. The developed model assembly and proposed simulation method are utilised to simulate the vehicle-track dynamic interaction in the presence of unsupported sleepers. The dynamic response in terms of the dynamic wheel-rail interaction force due to one or multiple unsupported sleepers is studied. Important factors influencing the dynamic wheel-rail interaction force in the presence of sleeper voids are also investigated. The results show that the vehicle speed, the gap size and the number of unsupported sleepers primarily dictate the magnitude of impact load which can be significant.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

New Numerical Approaches To thermal Convection In A Compositionally Stratified Fluid

NASA Astrophysics Data System (ADS)

Puckett, E. G.; Turcotte, D. L.; Kellogg, L. H.; Lokavarapu, H. V.; He, Y.; Robey, J.

2016-12-01

Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations propose that the heterogeneities are compositional in nature, differing from the overlying mantle, an interpretation that would be consistent with chemical geodynamic models. The LLSVP's are thought to be very old, meaning they have persisted thoughout much of Earth's history. Numerical modeling of persistent compositional interfaces present challenges to even state-of-the-art numerical methodology. It is extremely difficult to maintain sharp composition boundaries which migrate and distort with time dependent fingering without compositional diffusion and / or artificial diffusion. The compositional boundary must persist indefinitely. In this work we present computations of an initial compositionally stratified fluid that is subject to a thermal gradient ΔT = T1 - T0 across the height D of a rectangular domain over a range of buoyancy numbers B and Rayleigh numbers Ra. In these computations we compare three numerical approaches to modeling the movement of two distinct, thermally driven, compositional fields; namely, a high-order Finte Element Method (FEM) that employs artifical viscosity to preserve the maximum and minimum values of the compositional field, a Discontinous Galerkin (DG) method with a Bound Preserving (BP) limiter, and a Volume-of-Fluid (VOF) interface tracking algorithm. Our computations demonstrate that the FEM approach has far too much numerical diffusion to yield meaningful results, the DGBP method yields much better resuts but with small amounts of each compositional field being (numerically) entrained within the other compositional field, while the VOF method maintains a sharp interface between the two compositions throughout the computation. In the figure we show a comparison of between the three methods for a computation made with B = 1.111 and Ra = 10,000 after the flow has reached 'steady state'. (R) the images computed with the standard FEM method (with artifical viscosity), (C) the images computed with the DGBP method (with no artifical viscosity or diffusion due to discretization errors) and (L) the images computed with the VOF algorithm.

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.

Experimental and Numerical Study of the Buckling of Composite Profiles with Open Cross Section under Axial Compression

NASA Astrophysics Data System (ADS)

Rozylo, Patryk; Teter, Andrzej; Debski, Hubert; Wysmulski, Pawel; Falkowicz, Katarzyna

2017-10-01

The object of the research are short, thin-walled columns with an open top-hat cross section made of multilayer laminate. The walls of the investigated profiles are made of plate elements. The entire columns are subjected to uniform compression. A detailed analysis allowed us to determine critical forces and post-critical equilibrium paths. It is assumed that the columns are articulately supported on the edges forming their ends. The numerical investigation is performed by the finite element method. The study involves solving the problem of eigenvalue and the non-linear problem of stability of the structure. The numerical analysis is performed by the commercial simulation software ABAQUS®. The numerical results are then validated experimentally. In the discussed cases, it is assumed that the material operates within a linearly-elastic range, and the non-linearity of the FEM model is due to large displacements.

The Numerical Simulation of Coupling Behavior of Soil with Chemical Pollutant Effects

NASA Astrophysics Data System (ADS)

Liu, Z. J.; Li, X. K.; Tang, L. Q.

2010-05-01

The coupling behavior of clay plays a role in the integrity of clay barriers used in landfills. The clay barriers are subjected to mechanical and thermal effects coupled with hydraulic behavior, also, if the leachates become in contact with the clay liner, chemical effects may lead to some drastic changes in the properties of the clay. A numerical method to simulate the coupling behavior of soil with chemical pollutant effects is presented. Within the framework of Gens-Alonso model describing the constitutive behavior of unsaturated clay presented in reference[1], basing on the work of Wu[2] and Hueckel[3], a constitutive model describing the chemo-thermo-hydro-mechanical(CTHM) coupling behavior of clays in contact with a single organic contaminant is presented. The thermical softening and chemical softening is considered in the presented model. The strain arising in the material due to chemical and thermical effects can be decomposed into two parts: elastic expansion and plastic compaction. The chemical effects are described in terms of the mass concentration of the contaminant. The increases in temperature and contaminant concentration cause decreases of the pre-consolidation pressure and the cohesion. The mechanisms are called thermical softening and chemical softening. The presented coupled CTHM constitutive model has been integrated into the coupled thermo-hydro-mechanical mathematical model including contaminant transport in porous media. To solve the equilibrium equations, the grogram of finite element methods is developed with a stagger algorithm. The mechanisms taking place due to the coupling behaviour of the clay with a single contaminant solute are analysed with the presented numerical method.

Postbuckling failure of composite plates with central holes. Interim Report, Feb. 1990 - Dec. 1991 Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lee, H. H.; Hyer, M. W.

1992-01-01

The postbuckling failure of square composite plates with central holes is analyzed numerically and experimentally. The particular plates studies have stacking sequences of: (+ and - 45/0/90)(sub 2S); (+ and - 45/0(sub 2))(sub 2S); (+ and - 45/0(sub 6))(sub S); and (+ and - 45)(sub 4S). A simple plate geometry, one with a hole diameter to plate width ratio of 0.3 is compared. Failure load, failure mode, and failure location are predicted numerically by using the finite element method. Predictions are compared with experimental results. In numerical failure analysis the interlaminar shear stresses, as well as the inplane stresses are taken into account. An issue addressed in this study is the possible mode shape change of the plate during loading. It is predicted that the first three laminates fail due to excessive stresses in the fiber direction, and more importantly, that the load level is independent of whether the laminate is deformed in a one-half or two-half wave configuration. It is predicted that the fourth laminate fails due to excessive inplane shear stress. Interlaminar shear failure is not predicted for any laminates. For the first two laminates the experimental observations correlated well with the predictions. Experimentally, the third laminate failed along the side support due to interlaminar shear strength S(sub 23). The fourth experimental laminate failed due to inplane shear in the location predicted, however material softening resulted in a different failure load from predictions.

Local phase method for designing and optimizing metasurface devices.

PubMed

Hsu, Liyi; Dupré, Matthieu; Ndao, Abdoulaye; Yellowhair, Julius; Kanté, Boubacar

2017-10-16

Metasurfaces have attracted significant attention due to their novel designs for flat optics. However, the approach usually used to engineer metasurface devices assumes that neighboring elements are identical, by extracting the phase information from simulations with periodic boundaries, or that near-field coupling between particles is negligible, by extracting the phase from single particle simulations. This is not the case most of the time and the approach thus prevents the optimization of devices that operate away from their optimum. Here, we propose a versatile numerical method to obtain the phase of each element within the metasurface (meta-atoms) while accounting for near-field coupling. Quantifying the phase error of each element of the metasurfaces with the proposed local phase method paves the way to the design of highly efficient metasurface devices including, but not limited to, deflectors, high numerical aperture metasurface concentrators, lenses, cloaks, and modulators.

Dynamics of inductors for heating of the metal under deformation

NASA Astrophysics Data System (ADS)

Zimin, L. S.; Yeghiazaryan, A. S.; Protsenko, A. N.

2018-01-01

Current issues of creating powerful systems for hot sheet rolling with induction heating application in mechanical engineering and metallurgy were discussed. Electrodynamical and vibroacoustic problems occurring due to the induction heating of objects with complex shapes, particularly the slabs heating prior to rolling, were analysed. The numerical mathematical model using the method of related contours and the principle of virtual displacements is recommended for electrodynamical calculations. For the numerical solution of the vibrational problem, it is reasonable to use the finite element method (FEM). In general, for calculating the distribution forces, the law of Biot-Savart-Laplace method providing the determination of the current density of the skin layer in slab was used. The form of the optimal design of the inductor based on maximum hardness was synthesized while researching the vibrodynamic model of the system "inductor-metal" which provided allowable sound level meeting all established sanitary standards.

Peelle's pertinent puzzle using the Monte Carlo technique

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

Kawano, Toshihiko; Talou, Patrick; Burr, Thomas

2009-01-01

We try to understand the long-standing problem of the Peelle's Pertinent Puzzle (PPP) using the Monte Carlo technique. We allow the probability density functions to be any kind of form to assume the impact of distribution, and obtain the least-squares solution directly from numerical simulations. We found that the standard least squares method gives the correct answer if a weighting function is properly provided. Results from numerical simulations show that the correct answer of PPP is 1.1 {+-} 0.25 if the common error is multiplicative. The thought-provoking answer of 0.88 is also correct, if the common error is additive, andmore » if the error is proportional to the measured values. The least squares method correctly gives us the most probable case, where the additive component has a negative value. Finally, the standard method fails for PPP due to a distorted (non Gaussian) joint distribution.« less

Phase Space Approach to Dynamics of Interacting Fermions

NASA Astrophysics Data System (ADS)

Davidson, Shainen; Sels, Dries; Kasper, Valentin; Polkovnikov, Anatoli

Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of this. Already in equilibrium, fermions are notoriously hard to handle due to the sign problem. Out of equilibrium, an important outstanding problem is the efficient numerical simulation of the dynamics of these systems. In this work we develop a new semiclassical phase-space approach (a.k.a. the truncated Wigner approximation) for simulating the dynamics of interacting lattice fermions in arbitrary dimensions. We demonstrate the strength of the method by comparing the results to exact diagonalization (ED) on small 1D and 2D systems. We furthermore present results on Many-Body Localized (MBL) systems in 1D and 2D, and demonstrate how the method can be used to determine the MBL transition.

Numerical Simulation of Two Phase Flows

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2001-01-01

Two phase flows can be found in broad situations in nature, biology, and industry devices and can involve diverse and complex mechanisms. While the physical models may be specific for certain situations, the mathematical formulation and numerical treatment for solving the governing equations can be general. Hence, we will require information concerning each individual phase as needed in a single phase. but also the interactions between them. These interaction terms, however, pose additional numerical challenges because they are beyond the basis that we use to construct modern numerical schemes, namely the hyperbolicity of equations. Moreover, due to disparate differences in time scales, fluid compressibility and nonlinearity become acute, further complicating the numerical procedures. In this paper, we will show the ideas and procedure how the AUSM-family schemes are extended for solving two phase flows problems. Specifically, both phases are assumed in thermodynamic equilibrium, namely, the time scales involved in phase interactions are extremely short in comparison with those in fluid speeds and pressure fluctuations. Details of the numerical formulation and issues involved are discussed and the effectiveness of the method are demonstrated for several industrial examples.

Numerical model of the polymer electro-optic waveguide

NASA Astrophysics Data System (ADS)

Fan, Guofang; Li, Yuan; Han, Bing; Wang, Qi; Liu, Xinhou; Zhen, Zhen

2012-09-01

A numerical design model is presented for the polymer waveguide in an electro-optic modulator. The effective index method is used to analyze the height of the core waveguide and rib waveguide, an improved Marcatili method is presented to design the rib waveguide width in order to keep the strong single mode operation and have a good match with the standard fiber. Also, the thickness of the upper cladding layer is discussed through calculating the effective index of the multilayer planar waveguide structure has been obtained by setting the optical loss due to the metallic absorption to an acceptable value (<0.1 dB/cm). As a consequence, we take the EO polymer waveguide structure of UV15:CLD/APC:UFC170 as an example, an optimized design is reported.

Computationally efficient method for optical simulation of solar cells and their applications

NASA Astrophysics Data System (ADS)

Semenikhin, I.; Zanuccoli, M.; Fiegna, C.; Vyurkov, V.; Sangiorgi, E.

2013-01-01

This paper presents two novel implementations of the Differential method to solve the Maxwell equations in nanostructured optoelectronic solid state devices. The first proposed implementation is based on an improved and computationally efficient T-matrix formulation that adopts multiple-precision arithmetic to tackle the numerical instability problem which arises due to evanescent modes. The second implementation adopts the iterative approach that allows to achieve low computational complexity O(N logN) or better. The proposed algorithms may work with structures with arbitrary spatial variation of the permittivity. The developed two-dimensional numerical simulator is applied to analyze the dependence of the absorption characteristics of a thin silicon slab on the morphology of the front interface and on the angle of incidence of the radiation with respect to the device surface.

Numerical and Experimental Study on the Residual Stresses in the Nitrided Steel

NASA Astrophysics Data System (ADS)

Song, X.; Zhang, Zhi-Qian; Narayanaswamy, S.; Huang, Y. Z.; Zarinejad, M.

2016-09-01

In the present work, residual stresses distribution in the gas nitrided AISI 4140 sample has been studied using finite element (FE) simulation. The nitrogen concentration profile is obtained from the diffusion-controlled compound layer growth model, and nitrogen concentration controls the material volume change through phase transformation and lattice interstitials which results in residual stresses. Such model is validated through residual stress measurement technique—micro-ring-core method, which is applied to the nitriding process to obtain the residual stresses profiles in both the compound and diffusion layer. The numerical and experimental results are in good agreement with each other; they both indicate significant stress variation in the compound layer, which was not captured in previous research works due to the resolution limit of the traditional methods.

Un algorithme efficace d'intégration plastique pour un matériau obéissant au critère anisotrope de Hill

NASA Astrophysics Data System (ADS)

Titeux, Isabelle; Li, Yuming M.; Debray, Karl; Guo, Ying-Qiao

2004-11-01

This Note deals with an efficient algorithm to carry out the plastic integration and compute the stresses due to large strains for materials satisfying the Hill's anisotropic yield criterion. The classical algorithm of plastic integration such as 'Return Mapping Method' is largely used for nonlinear analyses of structures and numerical simulations of forming processes, but it requires an iterative schema and may have convergence problems. A new direct algorithm based on a scalar method is developed which allows us to directly obtain the plastic multiplier without an iteration procedure; thus the computation time is largely reduced and the numerical problems are avoided. To cite this article: I. Titeux et al., C. R. Mecanique 332 (2004).

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

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

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

A comparative analysis of numerical approaches to the mechanics of elastic sheets

NASA Astrophysics Data System (ADS)

Taylor, Michael; Davidovitch, Benny; Qiu, Zhanlong; Bertoldi, Katia

2015-06-01

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

Numerical methods for large eddy simulation of acoustic combustion instabilities

NASA Astrophysics Data System (ADS)

Wall, Clifton T.

Acoustic combustion instabilities occur when interaction between the combustion process and acoustic modes in a combustor results in periodic oscillations in pressure, velocity, and heat release. If sufficiently large in amplitude, these instabilities can cause operational difficulties or the failure of combustor hardware. In many situations, the dominant instability is the result of the interaction between a low frequency acoustic mode of the combustor and the large scale hydrodynamics. Large eddy simulation (LES), therefore, is a promising tool for the prediction of these instabilities, since both the low frequency acoustic modes and the large scale hydrodynamics are well resolved in LES. Problems with the tractability of such simulations arise, however, due to the difficulty of solving the compressible Navier-Stokes equations efficiently at low Mach number and due to the large number of acoustic periods that are often required for such instabilities to reach limit cycles. An implicit numerical method for the solution of the compressible Navier-Stokes equations has been developed which avoids the acoustic CFL restriction, allowing for significant efficiency gains at low Mach number, while still resolving the low frequency acoustic modes of interest. In the limit of a uniform grid the numerical method causes no artificial damping of acoustic waves. New, non-reflecting boundary conditions have also been developed for use with the characteristic-based approach of Poinsot and Lele (1992). The new boundary conditions are implemented in a manner which allows for significant reduction of the computational domain of an LES by eliminating the need to perform LES in regions where one-dimensional acoustics significantly affect the instability but details of the hydrodynamics do not. These new numerical techniques have been demonstrated in an LES of an experimental combustor. The new techniques are shown to be an efficient means of performing LES of acoustic combustion instabilities and are shown to accurately predict the occurrence and frequency of the dominant mode of the instability observed in the experiment.

High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities

DTIC Science & Technology

2015-03-31

FD scheme is only consistent for classical solutions of the PDE . For this reason, we implement the method of singularity subtraction as a means for...regularity due to the boundary conditions. This is because the FD scheme is only consistent for classical solutions of the PDE . For this reason, we...Introduction In the present work, we develop a high-order numerical method for solving linear elliptic PDEs with well-behaved variable coefficients on

Numerical study on non-locally reacting behavior of nacelle liners incorporating drainage slots

NASA Astrophysics Data System (ADS)

Chen, Chao; Li, Xiaodong; Thiele, Frank

2018-06-01

For acoustic liners used in current commercial nacelles, in order to prevent any liquid accumulating in the resonators, drainage slots are incorporated on the partition walls between closely packed cavities. Recently, an experimental study conducted by Busse-Gerstengarbe et al. shown that the cell interaction introduced by drainage slots causes an additional dissipation peak which increases with the size of the slot. However, the variation of damping process due to drainage slots is still not fully understood. Therefore, a numerical study based on computational aeroacoustic methods is carried out to investigate the mechanism of the changed attenuation characteristics due to drainage slots in presence of grazing incident sound waves with low or high intensities. Different slot configurations are designed based on the generic non-locally reacting liner model adopted in the experimental investigation. Both 2-D and 3-D numerical simulations of only slit resonators are carried out. Numerical results indicate that the extra peak is a result of a resonance excited in the second cavity at specific frequency. Under high sound pressure level incoming waves, the basic characteristics of the acoustic performance remain. However, vortex shedding transpires at the resonances around both the slits and the drainage slot. Vorticity contours show that the connection of two coupled cavities decreases the strength of vortex shedding around the basic Helmholtz resonance due to a higher energy reflection. Meanwhile, the cell interaction significantly increases the vorticity magnitude near the extra resonant frequency. Finally, a semi-empirical model is derived to predict the extra attenuation peak frequency.

Advanced nodal neutron diffusion method with space-dependent cross sections: ILLICO-VX

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

Rajic, H.L.; Ougouag, A.M.

1987-01-01

Advanced transverse integrated nodal methods for neutron diffusion developed since the 1970s require that node- or assembly-homogenized cross sections be known. The underlying structural heterogeneity can be accurately accounted for in homogenization procedures by the use of heterogeneity or discontinuity factors. Other (milder) types of heterogeneity, burnup-induced or due to thermal-hydraulic feedback, can be resolved by explicitly accounting for the spatial variations of material properties. This can be done during the nodal computations via nonlinear iterations. The new method has been implemented in the code ILLICO-VX (ILLICO variable cross-section method). Numerous numerical tests were performed. As expected, the convergence ratemore » of ILLICO-VX is lower than that of ILLICO, requiring approx. 30% more outer iterations per k/sub eff/ computation. The methodology has also been implemented as the NOMAD-VX option of the NOMAD, multicycle, multigroup, two- and three-dimensional nodal diffusion depletion code. The burnup-induced heterogeneities (space dependence of cross sections) are calculated during the burnup steps.« less

Numerical simulations of motion-insensitive diffusion imaging based on the distant dipolar field effects.

PubMed

Lin, Tao; Sun, Huijun; Chen, Zhong; You, Rongyi; Zhong, Jianhui

2007-12-01

Diffusion weighting in MRI is commonly achieved with the pulsed-gradient spin-echo (PGSE) method. When combined with spin-warping image formation, this method often results in ghosts due to the sample's macroscopic motion. It has been shown experimentally (Kennedy and Zhong, MRM 2004;52:1-6) that these motion artifacts can be effectively eliminated by the distant dipolar field (DDF) method, which relies on the refocusing of spatially modulated transverse magnetization by the DDF within the sample itself. In this report, diffusion-weighted images (DWIs) using both DDF and PGSE methods in the presence of macroscopic sample motion were simulated. Numerical simulation results quantify the dependence of signals in DWI on several key motion parameters and demonstrate that the DDF DWIs are much less sensitive to macroscopic sample motion than the traditional PGSE DWIs. The results also show that the dipolar correlation distance (d(c)) can alter contrast in DDF DWIs. The simulated results are in good agreement with the experimental results reported previously.

Numerical simulations of incompressible laminar flows using viscous-inviscid interaction procedures

NASA Astrophysics Data System (ADS)

Shatalov, Alexander V.

The present method is based on Helmholtz velocity decomposition where velocity is written as a sum of irrotational (gradient of a potential) and rotational (correction due to vorticity) components. Substitution of the velocity decomposition into the continuity equation yields an equation for the potential, while substitution into the momentum equations yields equations for the velocity corrections. A continuation approach is used to relate the pressure to the gradient of the potential through a modified Bernoulli's law, which allows the elimination of the pressure variable from the momentum equations. The present work considers steady and unsteady two-dimensional incompressible flows over an infinite cylinder and NACA 0012 airfoil shape. The numerical results are compared against standard methods (stream function-vorticity and SMAC methods) and data available in literature. The results demonstrate that the proposed formulation leads to a good approximation with some possible benefits compared to the available formulations. The method is not restricted to two-dimensional flows and can be used for viscous-inviscid domain decomposition calculations.

On the interaction between the external magnetic field and nanofluid inside a vertical square duct

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

Ali, Kashif; Ahmad, Shabbir; Ahmad, Shahzad, E-mail: shahzadahmadbzu@gmail.com

In this paper, we numerically study how the external magnetic field influences the flow and thermal characteristics of nanofluid inside a vertical square duct. The flow is considered to be laminar and hydrodynamically as well as thermally developed, whereas the thermal boundary condition of constant heat flux per unit axial length with constant peripheral temperature at any cross section, is assumed. The governing equations are solved using the spectral method and the finite difference method. Excellent comparison is noted in the numerical results given by the two methods but the spectral method is found to be superior in terms ofmore » both efficiency and accuracy. We have noted that the flow reversal due to high Raleigh number may be controlled by applying an external magnetic field of suitable strength. Moreover, the Nusselt number is found to be almost a linear function of the nanoparticle volume fraction parameter, for different values of the Raleigh number and the magnetic parameter.« less

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

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.

Quantifying Rock Weakening Due to Decreasing Calcite Mineral Content by Numerical Simulations

PubMed Central

2018-01-01

The quantification of changes in geomechanical properties due to chemical reactions is of paramount importance for geological subsurface utilisation, since mineral dissolution generally reduces rock stiffness. In the present study, the effective elastic moduli of two digital rock samples, the Fontainebleau and Bentheim sandstones, are numerically determined based on micro-CT images. Reduction in rock stiffness due to the dissolution of 10% calcite cement by volume out of the pore network is quantified for three synthetic spatial calcite distributions (coating, partial filling and random) using representative sub-cubes derived from the digital rock samples. Due to the reduced calcite content, bulk and shear moduli decrease by 34% and 38% in maximum, respectively. Total porosity is clearly the dominant parameter, while spatial calcite distribution has a minor impact, except for a randomly chosen cement distribution within the pore network. Moreover, applying an initial stiffness reduced by 47% for the calcite cement results only in a slightly weaker mechanical behaviour. Using the quantitative approach introduced here substantially improves the accuracy of predictions in elastic rock properties compared to general analytical methods, and further enables quantification of uncertainties related to spatial variations in porosity and mineral distribution. PMID:29614776

Quantifying Rock Weakening Due to Decreasing Calcite Mineral Content by Numerical Simulations.

PubMed

Wetzel, Maria; Kempka, Thomas; Kühn, Michael

2018-04-01

The quantification of changes in geomechanical properties due to chemical reactions is of paramount importance for geological subsurface utilisation, since mineral dissolution generally reduces rock stiffness. In the present study, the effective elastic moduli of two digital rock samples, the Fontainebleau and Bentheim sandstones, are numerically determined based on micro-CT images. Reduction in rock stiffness due to the dissolution of 10% calcite cement by volume out of the pore network is quantified for three synthetic spatial calcite distributions (coating, partial filling and random) using representative sub-cubes derived from the digital rock samples. Due to the reduced calcite content, bulk and shear moduli decrease by 34% and 38% in maximum, respectively. Total porosity is clearly the dominant parameter, while spatial calcite distribution has a minor impact, except for a randomly chosen cement distribution within the pore network. Moreover, applying an initial stiffness reduced by 47% for the calcite cement results only in a slightly weaker mechanical behaviour. Using the quantitative approach introduced here substantially improves the accuracy of predictions in elastic rock properties compared to general analytical methods, and further enables quantification of uncertainties related to spatial variations in porosity and mineral distribution.

Two-Relaxation-Time Lattice Boltzmann Method for Advective-Diffusive-Reactive Transport

NASA Astrophysics Data System (ADS)

Yan, Z.; Hilpert, M.

2016-12-01

The lattice Boltzmann method (LBM) has been applied to study a wide range of reactive transport in porous and fractured media. The single-relaxation-time (SRT) LBM, employing single relaxation time, is the most popular LBM due to its simplicity of understanding and implementation. Nevertheless, the SRT LBM may suffer from numerical instability for small value of the relaxation time. By contrast, the multiple-relaxation-time (MRT) LBM, employing multiple relaxation times, can improve the numerical stability through tuning the multiple relaxation times, but the complexity of implementing this method restricts its applications. The two-relaxation-time (TRT) LBM, which employs two relaxation times, combines the advantages of SRT and MRT LBMs. The TRT LBM can produce simulations with better accuracy and stability than the SRT one, and is easier to implement than the MRT one. This work evaluated the numerical accuracy and stability of the TRT method by comparing the simulation results with analytical solutions of Gaussian hill transport and Taylor dispersion under different advective velocities. The accuracy generally increased with the tunable relaxation time τ, and the stability first increased and then decreased as τ increased, showing an optimal TRT method emerging the best numerical stability. The free selection of τ enabled the TRT LBM to simulate the Gaussian hill transport and Taylor dispersion under relatively high advective velocity, under which the SRT LBM suffered from numerical instability. Finally, the TRT method was applied to study the contaminant degradation by chemotactic microorganisms in porous media, which acted as a reprehensive of reactive transport in this study, and well predicted the evolution of microorganisms and degradation of contaminants for different transport scenarios. To sum up, the TRT LBM produced simulation results with good accuracy and stability for various advective-diffusive-reactive transport through tuning the relaxation time τ, illustrating its potential to study various biogeochemical behaviors in the subsurface environment.

Numerical simulation of nonequilibrium flows by using the state-to-state approach in commercial software

NASA Astrophysics Data System (ADS)

Kunova, O. V.; Shoev, G. V.; Kudryavtsev, A. N.

2017-01-01

Nonequilibrium flows of a two-component oxygen mixture O2/O behind a shock wave are studied with due allowance for the state-to-state vibrational and chemical kinetics. The system of gas-dynamic equations is supplemented with kinetic equations including contributions of VT (TV)-exchange and dissociation processes. A method of the numerical solution of this system with the use of the ANSYS Fluent commercial software package is proposed, which is used in a combination with the authors' code that takes into account nonequilibrium kinetics. The computed results are compared with parameters obtained by solving the problem in the shock-fitting formulation. The vibrational temperature is compared with experimental data. The numerical tool proposed in the present paper is applied to study the flow around a cylinder.

Numerical study of unsteady MHD oblique stagnation point flow and heat transfer due to an oscillating stream

NASA Astrophysics Data System (ADS)

Javed, T.; Ghaffari, A.; Ahmad, H.

2016-05-01

The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.

Numerical analysis of turbulent coaxial flow with internal heat generation

NASA Technical Reports Server (NTRS)

Lin, A.; Weinstein, H.

1981-01-01

A computational method with which to obtain a physical understanding of the turbulent field of two coaxial jets entering an axisymmetric chamber is developed. Even the laminar field of this flow is quite complicated. This is due to the many different domains which exist in the field especially in the entrance region. Physically, three regions may be identified: the wall region, the initial region near the axis of symmetry and the mixing region. Advancing downstream, these regions change relative size with the ratio of the two jets' mass fluxes as the main parameter. The turbulent field of these flows is much more complicated due to the difference in the effective transport coefficients and turbulence level from region to region. However, being aware beforehand of the complications and the different regions of this field, the appropriate turbulence model and numerical scheme can be adjusted to treat the problem.

Full wave two-dimensional modeling of scattering and inverse scattering for layered rough surfaces with buried objects

NASA Astrophysics Data System (ADS)

Kuo, Chih-Hao

Efficient and accurate modeling of electromagnetic scattering from layered rough surfaces with buried objects finds applications ranging from detection of landmines to remote sensing of subsurface soil moisture. The formulation of a hybrid numerical/analytical solution to electromagnetic scattering from layered rough surfaces is first presented in this dissertation. The solution to scattering from each rough interface is sought independently based on the extended boundary condition method (EBCM), where the scattered fields of each rough interface are expressed as a summation of plane waves and then cast into reflection/transmission matrices. To account for interactions between multiple rough boundaries, the scattering matrix method (SMM) is applied to recursively cascade reflection and transmission matrices of each rough interface and obtain the composite reflection matrix from the overall scattering medium. The validation of this method against the Method of Moments (MoM) and Small Perturbation Method (SPM) is addressed and the numerical results which investigate the potential of low frequency radar systems in estimating deep soil moisture are presented. Computational efficiency of the proposed method is also discussed. In order to demonstrate the capability of this method in modeling coherent multiple scattering phenomena, the proposed method has been employed to analyze backscattering enhancement and satellite peaks due to surface plasmon waves from layered rough surfaces. Numerical results which show the appearance of enhanced backscattered peaks and satellite peaks are presented. Following the development of the EBCM/SMM technique, a technique which incorporates a buried object in layered rough surfaces by employing the T-matrix method and the cylindrical-to-spatial harmonics transformation is proposed. Validation and numerical results are provided. Finally, a multi-frequency polarimetric inversion algorithm for the retrieval of subsurface soil properties using VHF/UHF band radar measurements is devised. The top soil dielectric constant is first determined using an L-band inversion algorithm. For the retrieval of subsurface properties, a time-domain inversion technique is employed together with a parameter optimization for the pulse shape of time delay echoes from VHF/UHF band radar observations. Numerical studies to investigate the accuracy of the proposed inversion technique in presence of errors are addressed.

Numerical simulation of photocurrent generation in bilayer organic solar cells: Comparison of master equation and kinetic Monte Carlo approaches

NASA Astrophysics Data System (ADS)

Casalegno, Mosè; Bernardi, Andrea; Raos, Guido

2013-07-01

Numerical approaches can provide useful information about the microscopic processes underlying photocurrent generation in organic solar cells (OSCs). Among them, the Kinetic Monte Carlo (KMC) method is conceptually the simplest, but computationally the most intensive. A less demanding alternative is potentially represented by so-called Master Equation (ME) approaches, where the equations describing particle dynamics rely on the mean-field approximation and their solution is attained numerically, rather than stochastically. The description of charge separation dynamics, the treatment of electrostatic interactions and numerical stability are some of the key issues which have prevented the application of these methods to OSC modelling, despite of their successes in the study of charge transport in disordered system. Here we describe a three-dimensional ME approach to photocurrent generation in OSCs which attempts to deal with these issues. The reliability of the proposed method is tested against reference KMC simulations on bilayer heterojunction solar cells. Comparison of the current-voltage curves shows that the model well approximates the exact result for most devices. The largest deviations in current densities are mainly due to the adoption of the mean-field approximation for electrostatic interactions. The presence of deep traps, in devices characterized by strong energy disorder, may also affect result quality. Comparison of the simulation times reveals that the ME algorithm runs, on the average, one order of magnitude faster than KMC.

Stress analysis and damage evaluation of flawed composite laminates by hybrid-numerical methods

NASA Technical Reports Server (NTRS)

Yang, Yii-Ching

1992-01-01

Structural components in flight vehicles is often inherited flaws, such as microcracks, voids, holes, and delamination. These defects will degrade structures the same as that due to damages in service, such as impact, corrosion, and erosion. It is very important to know how a structural component can be useful and survive after these flaws and damages. To understand the behavior and limitation of these structural components researchers usually do experimental tests or theoretical analyses on structures with simulated flaws. However, neither approach has been completely successful. As Durelli states that 'Seldom does one method give a complete solution, with the most efficiency'. Examples of this principle is seen in photomechanics which additional strain-gage testing can only average stresses at locations of high concentration. On the other hand, theoretical analyses including numerical analyses are implemented with simplified assumptions which may not reflect actual boundary conditions. Hybrid-Numerical methods which combine photomechanics and numerical analysis have been used to correct this inefficiency since 1950's. But its application is limited until 1970's when modern computer codes became available. In recent years, researchers have enhanced the data obtained from photoelasticity, laser speckle, holography and moire' interferometry for input of finite element analysis on metals. Nevertheless, there is only few of literature being done on composite laminates. Therefore, this research is dedicated to this highly anisotropic material.

Numerical simulation of stress amplification induced by crack interaction in human femur bone

NASA Astrophysics Data System (ADS)

Alia, Noor; Daud, Ruslizam; Ramli, Mohammad Fadzli; Azman, Wan Zuki; Faizal, Ahmad; Aisyah, Siti

2015-05-01

This research is about numerical simulation using a computational method which study on stress amplification induced by crack interaction in human femur bone. Cracks in human femur bone usually occur because of large load or stress applied on it. Usually, the fracture takes longer time to heal itself. At present, the crack interaction is still not well understood due to bone complexity. Thus, brittle fracture behavior of bone may be underestimated and inaccurate. This study aims to investigate the geometrical effect of double co-planar edge cracks on stress intensity factor (K) in femur bone. This research focuses to analyze the amplification effect on the fracture behavior of double co-planar edge cracks, where numerical model is developed using computational method. The concept of fracture mechanics and finite element method (FEM) are used to solve the interacting cracks problems using linear elastic fracture mechanics (LEFM) theory. As a result, this study has shown the identification of the crack interaction limit (CIL) and crack unification limit (CUL) exist in the human femur bone model developed. In future research, several improvements will be made such as varying the load, applying thickness on the model and also use different theory or method in calculating the stress intensity factor (K).

Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques

NASA Astrophysics Data System (ADS)

Elliott, Louie C.

This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.

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.

Electromagnetic Field Penetration Studies

NASA Technical Reports Server (NTRS)

Deshpande, M.D.

2000-01-01

A numerical method is presented to determine electromagnetic shielding effectiveness of rectangular enclosure with apertures on its wall used for input and output connections, control panels, visual-access windows, ventilation panels, etc. Expressing EM fields in terms of cavity Green's function inside the enclosure and the free space Green's function outside the enclosure, integral equations with aperture tangential electric fields as unknown variables are obtained by enforcing the continuity of tangential electric and magnetic fields across the apertures. Using the Method of Moments, the integral equations are solved for unknown aperture fields. From these aperture fields, the EM field inside a rectangular enclosure due to external electromagnetic sources are determined. Numerical results on electric field shielding of a rectangular cavity with a thin rectangular slot obtained using the present method are compared with the results obtained using simple transmission line technique for code validation. The present technique is applied to determine field penetration inside a Boeing-757 by approximating its passenger cabin as a rectangular cavity filled with a homogeneous medium and its passenger windows by rectangular apertures. Preliminary results for, two windows, one on each side of fuselage were considered. Numerical results for Boeing-757 at frequencies 26 MHz, 171-175 MHz, and 428-432 MHz are presented.

Analysis of small-angle X-ray scattering data in the presence of significant instrumental smearing

PubMed Central

Bergenholtz, Johan; Ulama, Jeanette; Zackrisson Oskolkova, Malin

2016-01-01

A laboratory-scale small-angle X-ray scattering instrument with pinhole collimation has been used to assess smearing effects due to instrumental resolution. A new, numerically efficient method to smear ideal model intensities is developed and presented. It allows for directly using measured profiles of isotropic but otherwise arbitrary beams in smearing calculations. Samples of low-polydispersity polymer spheres have been used to show that scattering data can in this way be quantitatively modeled even when there is substantial distortion due to instrumental resolution. PMID:26937235

Comparison of the quasi-static method and the dynamic method for simulating fracture processes in concrete

NASA Astrophysics Data System (ADS)

Liu, J. X.; Deng, S. C.; Liang, N. G.

2008-02-01

Concrete is heterogeneous and usually described as a three-phase material, where matrix, aggregate and interface are distinguished. To take this heterogeneity into consideration, the Generalized Beam (GB) lattice model is adopted. The GB lattice model is much more computationally efficient than the beam lattice model. Numerical procedures of both quasi-static method and dynamic method are developed to simulate fracture processes in uniaxial tensile tests conducted on a concrete panel. Cases of different loading rates are compared with the quasi-static case. It is found that the inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, an unrealistic result will be obtained if a fracture process including unstable cracking is simulated by the quasi-static procedure.

Effects of centrifugal acceleration on the flows and segregation in vertical Bridgman crystal growth with steady ampoule rotation

NASA Astrophysics Data System (ADS)

Lan, C. W.

2001-07-01

The effects of centrifugal acceleration on the flows and segregation in vertical Bridgman crystal growth with steady ampoule rotation are investigated through numerical simulation. The numerical model is based on the Boussinesq approximation in a rotating frame, and the fluid flow, heat and mass transfer, and the growth interface are solved simultaneously by a robust finite-volume/Newton method. The growth of gallium-doped germanium (GaGe) in the Grenoble furnace is adopted as an example. The calculated results at small Froude number (Fr<<1) are consistent with the previous prediction (Lan, J. Crystal growth 197 (1999) 983). However, at a high rotation speed or in reduced gravity, where the centrifugal acceleration becomes important (Fr˜1), the results are quite different due to the secondary flow induced. Since the direction of the induced flow is different from that of the buoyancy convection due to the concave interface, the flow damping is more effective than that due to the Coriolis force alone. More importantly, radial segregation can be reversed during the flow transition from one to the other.

Shape adjustment optimization and experiment of cable-membrane reflectors

NASA Astrophysics Data System (ADS)

Du, Jingli; Gu, Yongzhen; Bao, Hong; Wang, Congsi; Chen, Xiaofeng

2018-05-01

Cable-membrane structures are widely employed for large space reflectors due to their lightweight, compact and easy package. In these structures, membranes are attached to cable net, serving as reflectors themselves or as supporting structures for other reflective surface. The cable length and membrane shape have to be carefully designed and fabricated to guarantee the desired reflector surface shape. However, due to inevitable error in cable length and membrane shape during the manufacture and assembly of cable-membrane reflectors, some cables have to be designed to be capable of length adjustment. By carefully adjusting the length of these cables, the degeneration in reflector shape precision due to this inevitable error can be effectively reduced. In the paper a shape adjustment algorithm for cable-membrane reflectors is proposed. Meanwhile, model updating is employed during shape adjustment to decrease the discrepancy of the numerical model with respect to the actual reflector. This discrepancy has to be considered because during attaching membranes to cable net, the accuracy of the membrane shape is hard to guarantee. Numerical examples and experimental results demonstrate the proposed method.

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.

A Semi-implicit Method for Resolution of Acoustic Waves in Low Mach Number Flows

NASA Astrophysics Data System (ADS)

Wall, Clifton; Pierce, Charles D.; Moin, Parviz

2002-09-01

A semi-implicit numerical method for time accurate simulation of compressible flow is presented. By extending the low Mach number pressure correction method, a Helmholtz equation for pressure is obtained in the case of compressible flow. The method avoids the acoustic CFL limitation, allowing a time step restricted only by the convective velocity, resulting in significant efficiency gains. Use of a discretization that is centered in both time and space results in zero artificial damping of acoustic waves. The method is attractive for problems in which Mach numbers are low, and the acoustic waves of most interest are those having low frequency, such as acoustic combustion instabilities. Both of these characteristics suggest the use of time steps larger than those allowable by an acoustic CFL limitation. In some cases it may be desirable to include a small amount of numerical dissipation to eliminate oscillations due to small-wavelength, high-frequency, acoustic modes, which are not of interest; therefore, a provision for doing this in a controlled manner is included in the method. Results of the method for several model problems are presented, and the performance of the method in a large eddy simulation is examined.

Checking the validity of superimposing analytical deformation models and implications for numerical modelling of dikes and magma chambers

NASA Astrophysics Data System (ADS)

Pascal, K.; Neuberg, J. W.; Rivalta, E.

2011-12-01

The displacement field due to magma movements in the subsurface is commonly modelled using the solutions for a point source (Mogi, 1958), a finite spherical source (McTigue, 1987), or a dislocation source (Okada, 1992) embedded in a homogeneous elastic half-space. When the magmatic system is represented by several sources, their respective deformation fields are summed, and the assumption of homogeneity in the half-space is violated. We have investigated the effects of neglecting the interaction between sources on the surface deformation field. To do so, we calculated the vertical and horizontal displacements for models with adjacent sources and we tested them against the solutions of corresponding numerical 3D finite element models. We implemented several models combining spherical pressure sources and dislocation sources, varying the pressure or opening of the sources and their relative position. We also investigated various numerical methods to model a dike as a dislocation tensile source or as a pressurized tabular crack. In the former case, the dike opening was either defined as two boundaries displaced from a central location, or as one boundary displaced relative to the other. We finally considered two case studies based on Soufrière Hills Volcano (Montserrat, West Indies) and the Dabbahu rift segment (Afar, Ethiopia) magmatic systems. We found that the discrepancies between simple superposition of the displacement field and a fully interacting numerical solution depend mostly on the source types and on their spacing. Their magnitude may be comparable with the errors due to neglecting the topography, the inhomogeneities in crustal properties or more realistic rheologies. In the models considered, the errors induced when neglecting the source interaction can be neglected (<5%) when the sources are separated by at least 4 radii for two combined Mogi sources and by at least 3 radii for juxtaposed Mogi and Okada sources. Furthermore, this study underlines fundamental issues related to the numerical method chosen to model a dike or a magma chamber. It clearly demonstrates that, while the magma compressibility can be neglected to model the deformation due to one source or distant sources, it is necessary to take it into account in models combining close sources.

Adaptive numerical algorithms to simulate the dynamical Casimir effect in a closed cavity with different boundary conditions

NASA Astrophysics Data System (ADS)

Villar, Paula I.; Soba, Alejandro

2017-07-01

We present an alternative numerical approach to compute the number of particles created inside a cavity due to time-dependent boundary conditions. The physical model consists of a rectangular cavity, where a wall always remains still while the other wall of the cavity presents a smooth movement in one direction. The method relies on the setting of the boundary conditions (Dirichlet and Neumann) and the following resolution of the corresponding equations of modes. By a further comparison between the ground state before and after the movement of the cavity wall, we finally compute the number of particles created. To demonstrate the method, we investigate the creation of particle production in vibrating cavities, confirming previously known results in the appropriate limits. Within this approach, the dynamical Casimir effect can be investigated, making it possible to study a variety of scenarios where no analytical results are known. Of special interest is, of course, the realistic case of the electromagnetic field in a three-dimensional cavity, with transverse electric (TE)-mode and transverse magnetic (TM)-mode photon production. Furthermore, with our approach we are able to calculate numerically the particle creation in a tuneable resonant superconducting cavity by the use of the generalized Robin boundary condition. We compare the numerical results with analytical predictions as well as a different numerical approach. Its extension to three dimensions is also straightforward.

Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model

NASA Astrophysics Data System (ADS)

Wang, Huimin

2017-01-01

In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.

Distributed structural control using multilayered piezoelectric actuators

NASA Technical Reports Server (NTRS)

Cudney, Harley H.; Inman, Daniel J.; Oshman, Yaakov

1990-01-01

A method of segmenting piezoelectric sensors and actuators is proposed which can preclude the currently experienced cancelation of sensor signals, or the reduction of actuator effectiveness, due to the integration of the property undergoing measurement or control. The segmentation method is demonstrated by a model developed for beam structures, to which multiple layers of piezoelectric materials are attached. A numerical study is undertaken of increasing active and passive damping of a beam using the segmented sensors and actuators over unsegmented sensors and actuators.

Solution of nonlinear time-dependent PDEs through componentwise approximation of matrix functions

NASA Astrophysics Data System (ADS)

Cibotarica, Alexandru; Lambers, James V.; Palchak, Elisabeth M.

2016-09-01

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODEs, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this paper, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. Numerical experiments demonstrate that this modification causes the number of Krylov projection steps to become bounded independently of the grid size, thus dramatically improving efficiency and scalability. As a result, for each test problem featured, as the total number of grid points increases, the growth in computation time is just below linear, while other methods achieved this only on selected test problems or not at all.

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

NASA Astrophysics Data System (ADS)

Van der Kelen, C.; Göransson, P.; Pluymers, B.; Desmet, W.

2014-12-01

The aspects related to modelling the frequency dependence of the elastic properties of air-saturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke's law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.

A Modified Kirchhoff plate theory for Free Vibration analysis of functionally graded material plates using meshfree method

NASA Astrophysics Data System (ADS)

Nguyen Van Do, Vuong

2018-04-01

In this paper, a modified Kirchhoff theory is presented for free vibration analyses of functionally graded material (FGM) plate based on modified radial point interpolation method (RPIM). The shear deformation effects are taken account into modified theory to ignore the locking phenomenon of thin plates. Due to the proposed refined plate theory, the number of independent unknowns reduces one variable and exists with four degrees of freedom per node. The simulated free vibration results employed by the modified RPIM are compared with the other analytical solutions to verify the effectiveness and the accuracy of the developed mesh-free method. Detail parametric studies of the proposed method are then conducted including the effectiveness of thickness ratio, boundary condition and material inhomogeneity on the sample problems of square plates. Results illustrated that the modified mesh-free RPIM can effectively predict the numerical calculation as compared to the exact solutions. The obtained numerical results are indicated that the proposed method are stable and well accurate prediction to evaluate with other published analyses.

Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

NASA Technical Reports Server (NTRS)

Barry, B. F.; Pimm, R. S.; Rowe, C. K.

1971-01-01

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.

Biomedical implications of dental-ceramic defects investigated by numerical simulation, radiographic, microcomputer tomography, and time-domain optical coherence tomography

NASA Astrophysics Data System (ADS)

Sinescu, Cosmin; Negrutiu, Meda Lavinia; Ionita, Ciprian; Marsavina, Liviu; Negru, Radu; Topala, Florin; Petrescu, Emanuela; Rominu, Roxana; Fabriky, Mihai; Bradu, Adrian; Rominu, Mihai; Podoleanu, Adrian Gh.

2011-10-01

Imagistic investigation of the metal-ceramic crowns and fixed partial prostheses represent a very important issue in nowadays dentistry. At this time, in dental office, it is difficult or even impossible to evaluate a metal ceramic crown or bridge before setting it in the oral cavity. The possibilities of ceramic fractures are due to small fracture lines or material defects inside the esthetic layers. Material and methods: In this study 25 metal ceramic crowns and fixed partial prostheses were investigated by radiographic method (Rx), micro computer tomography (MicroCT) and optical coherence tomography (OCT) working in Time Domain, at 1300 nm. The OCT system contains two interferometers and one scanner. For each incident analysis a stuck made of 100 slices was obtain. These slices were used in order to obtain a 3D model of the ceramic interface. After detecting the presence and the positions of the ceramic defects the numerical simulation method was used to estimate the biomechanical effect of the masticatory forces on fractures propagations in ceramic materials. Results: For all the dental ceramic defects numerical simulation analysis was performed. The simulation of crack propagation shows that the crack could initiate from the upper, lower or both parts of the defect and propagates through the ceramic material where tensile stress field is present. RX and MicroCT are very powerful instruments that provide a good characterization of the dental construct. It is important to observe the reflections due to the metal infrastructure that could affect the evaluation of the metal ceramic crowns and bridges. The OCT investigations could complete the imagistic evaluation of the dental construct by offering important information when it is need it.

Numerical Simulation of Monitoring Corrosion in Reinforced Concrete Based on Ultrasonic Guided Waves

PubMed Central

Zheng, Zhupeng; Lei, Ying; Xue, Xin

2014-01-01

Numerical simulation based on finite element method is conducted to predict the location of pitting corrosion in reinforced concrete. Simulation results show that it is feasible to predict corrosion monitoring based on ultrasonic guided wave in reinforced concrete, and wavelet analysis can be used for the extremely weak signal of guided waves due to energy leaking into concrete. The characteristic of time-frequency localization of wavelet transform is adopted in the corrosion monitoring of reinforced concrete. Guided waves can be successfully used to identify corrosion defects in reinforced concrete with the analysis of suitable wavelet-based function and its scale. PMID:25013865

Role of electromagnetic navigational bronchoscopy in pulmonary nodule management

PubMed Central

Dahagam, Chanukya; Breen, David P.; Sarkar, Saiyad

2016-01-01

The incidence of pulmonary nodules and lung cancer is rising. Some of this increase in incidence is due to improved pick up by newer imaging modalities. However, the goal is to diagnose these lesion, many of which are located in the periphery, by safe and relatively non-invasive methods. This has led to the emergence of numerous techniques such as electromagnetic navigational bronchoscopy (ENB). Current evidence supports a role for these techniques in the diagnostic pathway. However, numerous factor influence the diagnostic accuracy. Thus despite significant advances, more research needs to be undertaken to further improve the currently available diagnostic technologies. PMID:27606080

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

NASA Astrophysics Data System (ADS)

Hayat, T.; Ahmad, Salman; Ijaz Khan, M.; Alsaedi, A.

2018-05-01

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODE’s. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.

Dissipative nonlinear waves in a gravitating quantum fluid

NASA Astrophysics Data System (ADS)

Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

2018-02-01

Nonlinear wave propagation is studied in a dissipative, self-gravitating Bose-Einstein condensate, starting from the Gross-Pitaevskii equation. In the absence of an exact analytical result, approximate methods like the linear analysis and perturbative approach are applied. The linear dispersion relation puts a restriction on the permissible range of the dissipation parameter. The waves get damped due to dissipation. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation, which is solved both analytically as well as numerically. Interestingly, the analytical and numerical plots match excellently with each other, in the realm of weak dissipation.

Simulation of Helical Flow Hydrodynamics in Meanders and Advection-Turbulent Diffusion Using Smoothed Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Gusti, T. P.; Hertanti, D. R.; Bahsan, E.; Soeryantono, H.

2013-12-01

Particle-based numerical methods, such as Smoothed Particle Hydrodynamics (SPH), may be able to simulate some hydrodynamic and morphodynamic behaviors better than grid-based numerical methods. This study simulates hydrodynamics in meanders and advection and turbulent diffusion in straight river channels using Microsoft Excel and Visual Basic. The simulators generate three-dimensional data for hydrodynamics and one-dimensional data for advection-turbulent diffusion. Fluid at rest, sloshing, and helical flow are simulated in the river meanders. Spill loading and step loading are done to simulate concentration patterns associated with advection-turbulent diffusion. Results indicate that helical flow is formed due to disturbance in morphology and particle velocity in the stream and the number of particles does not have a significant effect on the pattern of advection-turbulent diffusion concentration.

Calculated Low-Speed Steady and Time-Dependent Aerodynamic Derivatives for Some Airfoils Using a Discrete Vortex Method

NASA Technical Reports Server (NTRS)

Riley, Donald R.

2015-01-01

This paper contains a collection of some results of four individual studies presenting calculated numerical values for airfoil aerodynamic stability derivatives in unseparated inviscid incompressible flow due separately to angle-of-attack, pitch rate, flap deflection, and airfoil camber using a discrete vortex method. Both steady conditions and oscillatory motion were considered. Variables include the number of vortices representing the airfoil, the pitch axis / moment center chordwise location, flap chord to airfoil chord ratio, and circular or parabolic arc camber. Comparisons with some experimental and other theoretical information are included. The calculated aerodynamic numerical results obtained using a limited number of vortices provided in each study compared favorably with thin airfoil theory predictions. Of particular interest are those aerodynamic results calculated herein (such as induced drag) that are not readily available elsewhere.

Fracture mechanics life analytical methods verification testing

NASA Technical Reports Server (NTRS)

Favenesi, J. A.; Clemons, T. G.; Riddell, W. T.; Ingraffea, A. R.; Wawrzynek, P. A.

1994-01-01

The objective was to evaluate NASCRAC (trademark) version 2.0, a second generation fracture analysis code, for verification and validity. NASCRAC was evaluated using a combination of comparisons to the literature, closed-form solutions, numerical analyses, and tests. Several limitations and minor errors were detected. Additionally, a number of major flaws were discovered. These major flaws were generally due to application of a specific method or theory, not due to programming logic. Results are presented for the following program capabilities: K versus a, J versus a, crack opening area, life calculation due to fatigue crack growth, tolerable crack size, proof test logic, tearing instability, creep crack growth, crack transitioning, crack retardation due to overloads, and elastic-plastic stress redistribution. It is concluded that the code is an acceptable fracture tool for K solutions of simplified geometries, for a limited number of J and crack opening area solutions, and for fatigue crack propagation with the Paris equation and constant amplitude loads when the Paris equation is applicable.

Linear diffusion-wave channel routing using a discrete Hayami convolution method

Treesearch

Li Wang; Joan Q. Wu; William J. Elliot; Fritz R. Feidler; Sergey Lapin

2014-01-01

The convolution of an input with a response function has been widely used in hydrology as a means to solve various problems analytically. Due to the high computation demand in solving the functions using numerical integration, it is often advantageous to use the discrete convolution instead of the integration of the continuous functions. This approach greatly reduces...

Assessing the performances of low impact development alternatives by long-term simulation for a semi-arid area in Tianjin, northern China.

PubMed

Huang, Jinhui Jeanne; Li, Yu; Niu, Shuai; Zhou, Shu H

2014-01-01

For areas that are urbanized rapidly, the practice of low impact development (LID) has gained an important place in stormwater management and urban planning due to its capability and beneficial effects in restoring the original hydrological cycle. The performances of LID alternatives can vary substantially due to different climate conditions. This study investigated the performances of five LID alternatives under a semi-arid climate in northern China on water balance and flood control. A numerical model, Storm Water Management Model version 5 (US Environmental Protection Agency), was employed to run 10 years' rainfall events for these objectives. Two evaluation methods were proposed in this study: the efficiency index for water balance and a performance radar chart. The investigation of the five LID alternatives revealed that these LID alternatives functioned differently in flood control and water balance, and porous pavement performed best in all indices except the lag time. The two evaluation methods, in conjunction with the long-term numerical simulation, can facilitate design and decision making by providing a clear picture of the performance and functions for these LID alternatives.

Investigation of the complex electroviscous effects on electrolyte (single and multiphase) flow in porous medi.

NASA Astrophysics Data System (ADS)

Bolet, A. J. S.; Linga, G.; Mathiesen, J.

2017-12-01

Surface charge is an important control parameter for wall-bounded flow of electrolyte solution. The electroviscous effect has been studied theoretically in model geometries such as infinite capillaries. However, in more complex geometries a quantification of the electroviscous effect is a non-trival task due to strong non-linarites of the underlying equations. In general, one has to rely on numerical methods. Here we present numerical studies of the full three-dimensional steady state Stokes-Poisson-Nernst-Planck problem in order to model electrolyte transport in artificial porous samples. The simulations are performed using the finite element method. From the simulation, we quantity how the electroviscous effect changes the general flow permeability in complex three-dimensional porous media. The porous media we consider are mostly generated artificially by connecting randomly dispersed cylindrical pores. Furthermore, we present results of electric driven two-phase immiscible flow in two dimensions. The simulations are performed by augmenting the above equations with a phase field model to handle and track the interaction between the two fluids (using parameters corresponding to oil-water interfaces, where oil non-polar). In particular, we consider the electro-osmotic effect on imbibition due to charged walls and electrolyte-solution.

Center vortices in confinement

NASA Astrophysics Data System (ADS)

Alexandru, Viorel-Andrei

2001-11-01

The confinement property of quarks is still one of the puzzles of today's physics. Although QCD is believed to accurately describe the interaction between quarks, due to the peculiar nature of the theory we are still unable to prove that it confines the quarks. Most analytical efforts in QCD are based on perturbative techniques which are useless in studying confinement. Lattice gauge theory enables us to get non-perturbative results. We use lattice techniques to investigate one of the proposed mechanisms of quark confinement, namely the center vortex idea. We first present a cursory introduction to lattice theory and the methods used to detect confinement on the lattices. We then show how the center vortices are suppose to produce confinement using center vortices to study Z2 lattice gauge theory. A review of the current studies regarding the idea of center vortices follows. The last chapter is dedicated to studying a particular definition of center vortices due to Tomboulis. We show how to implement this definition of vortices in numerical simulations and use numerical simulations to check the assumptions underlying the formalism. We also compare Tomboulis definition with other methods used to identify vortices on lattice.

SiMon: Simulation Monitor for Computational Astrophysics

NASA Astrophysics Data System (ADS)

Xuran Qian, Penny; Cai, Maxwell Xu; Portegies Zwart, Simon; Zhu, Ming

2017-09-01

Scientific discovery via numerical simulations is important in modern astrophysics. This relatively new branch of astrophysics has become possible due to the development of reliable numerical algorithms and the high performance of modern computing technologies. These enable the analysis of large collections of observational data and the acquisition of new data via simulations at unprecedented accuracy and resolution. Ideally, simulations run until they reach some pre-determined termination condition, but often other factors cause extensive numerical approaches to break down at an earlier stage. In those cases, processes tend to be interrupted due to unexpected events in the software or the hardware. In those cases, the scientist handles the interrupt manually, which is time-consuming and prone to errors. We present the Simulation Monitor (SiMon) to automatize the farming of large and extensive simulation processes. Our method is light-weight, it fully automates the entire workflow management, operates concurrently across multiple platforms and can be installed in user space. Inspired by the process of crop farming, we perceive each simulation as a crop in the field and running simulation becomes analogous to growing crops. With the development of SiMon we relax the technical aspects of simulation management. The initial package was developed for extensive parameter searchers in numerical simulations, but it turns out to work equally well for automating the computational processing and reduction of observational data reduction.

Numerical modeling of separated flows at moderate Reynolds numbers appropriate for turbine blades and unmanned aero vehicles

NASA Astrophysics Data System (ADS)

Castiglioni, Giacomo

Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble and transition to turbulence further downstream. Typical Reynolds averaged Navier-Stokes turbulence models are inadequate for such flows. Direct numerical simulation is the most reliable, but is also the most computationally expensive alternative. This work assesses the capability of immersed boundary methods and large eddy simulations to reduce the computational requirements for such flows and still provide high quality results. Two-dimensional and three-dimensional simulations of a laminar separation bubble on a NACA-0012 airfoil at Rec = 5x104 and at 5° of incidence have been performed with an immersed boundary code and a commercial code using body fitted grids. Several sub-grid scale models have been implemented in both codes and their performance evaluated. For the two-dimensional simulations with the immersed boundary method the results show good agreement with the direct numerical simulation benchmark data for the pressure coefficient Cp and the friction coefficient Cf, but only when using dissipative numerical schemes. There is evidence that this behavior can be attributed to the ability of dissipative schemes to damp numerical noise coming from the immersed boundary. For the three-dimensional simulations the results show a good prediction of the separation point, but an inaccurate prediction of the reattachment point unless full direct numerical simulation resolution is used. The commercial code shows good agreement with the direct numerical simulation benchmark data in both two and three-dimensional simulations, but the presence of significant, unquantified numerical dissipation prevents a conclusive assessment of the actual prediction capabilities of very coarse large eddy simulations with low order schemes in general cases. Additionally, a two-dimensional sweep of angles of attack from 0° to 5° is performed showing a qualitative prediction of the jump in lift and drag coefficients due to the appearance of the laminar separation bubble. The numerical dissipation inhibits the predictive capabilities of large eddy simulations whenever it is of the same order of magnitude or larger than the sub-grid scale dissipation. The need to estimate the numerical dissipation is most pressing for low-order methods employed by commercial computational fluid dynamics codes. Following the recent work of Schranner et al., the equations and procedure for estimating the numerical dissipation rate and the numerical viscosity in a commercial code are presented. The method allows for the computation of the numerical dissipation rate and numerical viscosity in the physical space for arbitrary sub-domains in a self-consistent way, using only information provided by the code in question. The method is first tested for a three-dimensional Taylor-Green vortex flow in a simple cubic domain and compared with benchmark results obtained using an accurate, incompressible spectral solver. Afterwards the same procedure is applied for the first time to a realistic flow configuration, specifically to the above discussed laminar separation bubble flow over a NACA 0012 airfoil. The method appears to be quite robust and its application reveals that for the code and the flow in question the numerical dissipation can be significantly larger than the viscous dissipation or the dissipation of the classical Smagorinsky sub-grid scale model, confirming the previously qualitative finding.

Fractal analysis of GPS time series for early detection of disastrous seismic events

NASA Astrophysics Data System (ADS)

Filatov, Denis M.; Lyubushin, Alexey A.

2017-03-01

A new method of fractal analysis of time series for estimating the chaoticity of behaviour of open stochastic dynamical systems is developed. The method is a modification of the conventional detrended fluctuation analysis (DFA) technique. We start from analysing both methods from the physical point of view and demonstrate the difference between them which results in a higher accuracy of the new method compared to the conventional DFA. Then, applying the developed method to estimate the measure of chaoticity of a real dynamical system - the Earth's crust, we reveal that the latter exhibits two distinct mechanisms of transition to a critical state: while the first mechanism has already been known due to numerous studies of other dynamical systems, the second one is new and has not previously been described. Using GPS time series, we demonstrate efficiency of the developed method in identification of critical states of the Earth's crust. Finally we employ the method to solve a practically important task: we show how the developed measure of chaoticity can be used for early detection of disastrous seismic events and provide a detailed discussion of the numerical results, which are shown to be consistent with outcomes of other researches on the topic.

Self-similar solutions to isothermal shock problems

NASA Astrophysics Data System (ADS)

Deschner, Stephan C.; Illenseer, Tobias F.; Duschl, Wolfgang J.

We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant initial density is not allowed for isothermal EPs. Reasonable restrictions for this parameter are given. Both, the (genuinely) isothermal implosion as well as the explosion problem are solved for the first time.

Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM

NASA Astrophysics Data System (ADS)

Idelsohn, S. R.; Marti, J.; Souto-Iglesias, A.; Oñate, E.

2008-12-01

The paper aims to introduce new fluid structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) [1] for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.

Inspiration of slip effects on electromagnetohydrodynamics (EMHD) nanofluid flow through a horizontal Riga plate

NASA Astrophysics Data System (ADS)

Ayub, M.; Abbas, T.; Bhatti, M. M.

2016-06-01

The boundary layer flow of nanofluid that is electrically conducting over a Riga plate is considered. The Riga plate is an electromagnetic actuator which comprises a spanwise adjusted cluster of substituting terminal and lasting magnets mounted on a plane surface. The numerical model fuses the Brownian motion and the thermophoresis impacts because of the nanofluid and the Grinberg term for the wall parallel Lorentz force due to the Riga plate in the presence of slip effects. The numerical solution of the problem is presented using the shooting method. The novelties of all the physical parameters such as modified Hartmann number, Richardson number, nanoparticle concentration flux parameter, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter and slip parameter are demonstrated graphically. Numerical values of reduced Nusselt number, Sherwood number are discussed in detail.

Numerical and experimental investigation of turbine blade film cooling

NASA Astrophysics Data System (ADS)

Berkache, Amar; Dizene, Rabah

2017-12-01

The blades in a gas turbine engine are exposed to extreme temperature levels that exceed the melting temperature of the material. Therefore, efficient cooling is a requirement for high performance of the gas turbine engine. The present study investigates film cooling by means of 3D numerical simulations using a commercial code: Fluent. Three numerical models, namely k-ɛ, RSM and SST turbulence models; are applied and then prediction results are compared to experimental measurements conducted by PIV technique. The experimental model realized in the ENSEMA laboratory uses a flat plate with several rows of staggered holes. The performance of the injected flow into the mainstream is analyzed. The comparison shows that the RANS closure models improve the over-predictions of center-line film cooling velocities that is caused by the limitations of the RANS method due to its isotropy eddy diffusivity.

Behaviors of printed circuit boards due to microwave supported curing process of coating materials.

PubMed

Bremerkamp, Felix; Nowottnick, Mathias; Seehase, Dirk; Bui, Trinh Dung

2012-01-01

The Application of a microwave supported curing process for coatings in the field of electronic industry poses a challenge. Here the implementation of this technology is represented. Within the scope of the investigation special PCB Test Layouts were designed and the polymer curing process examined by the method of dielectric analysis. Furthermore the coupling of microwave radiation with conductive PCB structures was analyzed experimentally by means of special test boards. The formation of standing waves and regular heating distribution along the conductive wires on the PCB could be observed. The experimental results were compared with numerical simulation. In this context the numerical analysis of microwave PCB interaction led to important findings concerning wave propagation on wired PCB. The final valuation demonstrated a substantial similarity between numerical simulations and experimental results.

Aerodynamic shape optimization using control theory

NASA Technical Reports Server (NTRS)

Reuther, James

1996-01-01

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Validation of a numerical method for interface-resolving simulation of multicomponent gas-liquid mass transfer and evaluation of multicomponent diffusion models

NASA Astrophysics Data System (ADS)

Woo, Mino; Wörner, Martin; Tischer, Steffen; Deutschmann, Olaf

2018-03-01

The multicomponent model and the effective diffusivity model are well established diffusion models for numerical simulation of single-phase flows consisting of several components but are seldom used for two-phase flows so far. In this paper, a specific numerical model for interfacial mass transfer by means of a continuous single-field concentration formulation is combined with the multicomponent model and effective diffusivity model and is validated for multicomponent mass transfer. For this purpose, several test cases for one-dimensional physical or reactive mass transfer of ternary mixtures are considered. The numerical results are compared with analytical or numerical solutions of the Maxell-Stefan equations and/or experimental data. The composition-dependent elements of the diffusivity matrix of the multicomponent and effective diffusivity model are found to substantially differ for non-dilute conditions. The species mole fraction or concentration profiles computed with both diffusion models are, however, for all test cases very similar and in good agreement with the analytical/numerical solutions or measurements. For practical computations, the effective diffusivity model is recommended due to its simplicity and lower computational costs.

The Formation of a Milky Way-sized Disk Galaxy. I. A Comparison of Numerical Methods

NASA Astrophysics Data System (ADS)

Zhu, Qirong; Li, Yuexing

2016-11-01

The long-standing challenge of creating a Milky Way- (MW-) like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of an MW-sized galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: an improved smoothed particle hydrodynamics (SPH) code Gadget, and a Lagrangian Meshless Finite-Mass (MFM) code Gizmo. All the simulations in this paper use the same initial conditions and physical models, which include star formation, “energy-driven” outflows, metal-dependent cooling, stellar evolution, and metal enrichment. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star-formation history, gas content, disk structure, and kinematics. Compared to Gizmo, the Gadget simulation produced a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by 20% and a lower gas fraction by 10% at z = 0, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the Gizmo simulation, which shows a more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that the MFM method is a promising alternative to SPH in cosmological hydrodynamic simulations.

THE FORMATION OF A MILKY WAY-SIZED DISK GALAXY. I. A COMPARISON OF NUMERICAL METHODS

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

Zhu, Qirong; Li, Yuexing, E-mail: qxz125@psu.edu

The long-standing challenge of creating a Milky Way- (MW-) like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of an MW-sized galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: an improved smoothed particle hydrodynamics (SPH) code Gadget, and a Lagrangian Meshless Finite-Mass (MFM) code Gizmo. All the simulations in this paper use the same initial conditions and physical models, which include star formation, “energy-driven” outflows, metal-dependent cooling, stellarmore » evolution, and metal enrichment. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star-formation history, gas content, disk structure, and kinematics. Compared to Gizmo, the Gadget simulation produced a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by 20% and a lower gas fraction by 10% at z = 0, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the Gizmo simulation, which shows a more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that the MFM method is a promising alternative to SPH in cosmological hydrodynamic simulations.« less

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

NASA Astrophysics Data System (ADS)

Del Carpio R., Maikol; Hashemi, M. Javad; Mosqueda, Gilberto

2017-10-01

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

NASA Astrophysics Data System (ADS)

Franceschini, Andrea; Ferronato, Massimiliano; Janna, Carlo; Teatini, Pietro

2016-06-01

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions.

Measurement of SAR-induced temperature increase in a phantom and in vivo with comparison to numerical simulation

PubMed Central

Oh, Sukhoon; Ryu, Yeun-Chul; Carluccio, Giuseppe; Sica, Christopher T.; Collins, Christopher M.

2013-01-01

Purpose Compare numerically-simulated and experimentally-measured temperature increase due to Specific energy Absorption Rate (SAR) from radiofrequency fields. Methods Temperature increase induced in both a phantom and in the human forearm when driving an adjacent circular surface coil was mapped using the proton resonance frequency shift technique of Magnetic Resonance (MR) thermography. The phantom and forearm were also modeled from MR image data, and both SAR and temperature change as induced by the same coil were simulated numerically. Results The simulated and measured temperature increase distributions were generally in good agreement for the phantom. The relative distributions for the human forearm were very similar, with the simulations giving maximum temperature increase about 25% higher than measured. Conclusion Although a number of parameters and uncertainties are involved, it should be possible to use numerical simulations to produce reasonably accurate and conservative estimates of temperature distribution to ensure safety in MR imaging. PMID:23804188

Numerical Simulation of Transitional, Hypersonic Flows using a Hybrid Particle-Continuum Method

NASA Astrophysics Data System (ADS)

Verhoff, Ashley Marie

Analysis of hypersonic flows requires consideration of multiscale phenomena due to the range of flight regimes encountered, from rarefied conditions in the upper atmosphere to fully continuum flow at low altitudes. At transitional Knudsen numbers there are likely to be localized regions of strong thermodynamic nonequilibrium effects that invalidate the continuum assumptions of the Navier-Stokes equations. Accurate simulation of these regions, which include shock waves, boundary and shear layers, and low-density wakes, requires a kinetic theory-based approach where no prior assumptions are made regarding the molecular distribution function. Because of the nature of these types of flows, there is much to be gained in terms of both numerical efficiency and physical accuracy by developing hybrid particle-continuum simulation approaches. The focus of the present research effort is the continued development of the Modular Particle-Continuum (MPC) method, where the Navier-Stokes equations are solved numerically using computational fluid dynamics (CFD) techniques in regions of the flow field where continuum assumptions are valid, and the direct simulation Monte Carlo (DSMC) method is used where strong thermodynamic nonequilibrium effects are present. Numerical solutions of transitional, hypersonic flows are thus obtained with increased physical accuracy relative to CFD alone, and improved numerical efficiency is achieved in comparison to DSMC alone because this more computationally expensive method is restricted to those regions of the flow field where it is necessary to maintain physical accuracy. In this dissertation, a comprehensive assessment of the physical accuracy of the MPC method is performed, leading to the implementation of a non-vacuum supersonic outflow boundary condition in particle domains, and more consistent initialization of DSMC simulator particles along hybrid interfaces. The relative errors between MPC and full DSMC results are greatly reduced as a direct result of these improvements. Next, a new parameter for detecting rotational nonequilibrium effects is proposed and shown to offer advantages over other continuum breakdown parameters, achieving further accuracy gains. Lastly, the capabilities of the MPC method are extended to accommodate multiple chemical species in rotational nonequilibrium, each of which is allowed to equilibrate independently, enabling application of the MPC method to more realistic atmospheric flows.

On vertical advection truncation errors in terrain-following numerical models: Comparison to a laboratory model for upwelling over submarine canyons

NASA Astrophysics Data System (ADS)

Allen, S. E.; Dinniman, M. S.; Klinck, J. M.; Gorby, D. D.; Hewett, A. J.; Hickey, B. M.

2003-01-01

Submarine canyons which indent the continental shelf are frequently regions of steep (up to 45°), three-dimensional topography. Recent observations have delineated the flow over several submarine canyons during 2-4 day long upwelling episodes. Thus upwelling episodes over submarine canyons provide an excellent flow regime for evaluating numerical and physical models. Here we compare a physical and numerical model simulation of an upwelling event over a simplified submarine canyon. The numerical model being evaluated is a version of the S-Coordinate Rutgers University Model (SCRUM). Careful matching between the models is necessary for a stringent comparison. Results show a poor comparison for the homogeneous case due to nonhydrostatic effects in the laboratory model. Results for the stratified case are better but show a systematic difference between the numerical results and laboratory results. This difference is shown not to be due to nonhydrostatic effects. Rather, the difference is due to truncation errors in the calculation of the vertical advection of density in the numerical model. The calculation is inaccurate due to the terrain-following coordinates combined with a strong vertical gradient in density, vertical shear in the horizontal velocity and topography with strong curvature.

Numerical investigation of the air injection effect on the cavitating flow in Francis hydro turbine

NASA Astrophysics Data System (ADS)

Chirkov, D. V.; Shcherbakov, P. K.; Cherny, S. G.; Skorospelov, V. A.; Turuk, P. A.

2017-09-01

At full and over load operating points, some Francis turbines experience strong self-excited pressure and power oscillations. These oscillations are occuring due to the hydrodynamic instability of the cavitating fluid flow. In many cases, the amplitude of such pulsations may be reduced substantially during the turbine operation by the air injection/ admission below the runner. Such an effect is investigated numerically in the present work. To this end, the hybrid one-three-dimensional model of the flow of the mixture "liquid-vapor" in the duct of a hydroelectric power station, which was proposed previously by the present authors, is augmented by the second gaseous component — the noncondensable air. The boundary conditions and the numerical method for solving the equations of the model are described. To check the accuracy of computing the interface "liquid-gas", the numerical method was applied at first for solving the dam break problem. The algorithm was then used for modeling the flow in a hydraulic turbine with air injection below the runner. It is shown that with increasing flow rate of the injected air, the amplitude of pressure pulsations decreases. The mechanism of the flow structure alteration in the draft tube cone has been elucidated, which leads to flow stabilization at air injection.

Numerical Capture of Wing-tip Vortex Using Vorticity Confinement

NASA Astrophysics Data System (ADS)

Zhang, Baili; Lou, Jing; Kang, Chang Wei; Wilson, Alexander; Lundberg, Johan; Bensow, Rickard

2012-11-01

Tracking vortices accurately over large distances is very important in many areas of engineering, for instance flow over rotating helicopter blades, ship propeller blades and aircraft wings. However, due to the inherent numerical dissipation in the advection step of flow simulation, current Euler and RANS field solvers tend to damp these vortices too fast. One possible solution to reduce the unphysical decay of these vortices is the application of vorticity confinement methods. In this study, a vorticity confinement term is added to the momentum conservation equations which is a function of the local element size, the vorticity and the gradient of the absolute value of vorticity. The approach has been evaluated by a systematic numerical study on the tip vortex trailing from a rectangular NACA0012 half-wing. The simulated structure and development of the wing-tip vortex agree well with experiments both qualitatively and quantitatively without any adverse effects on the global flow field. It is shown that vorticity confinement can negate the effect of numerical dissipation, leading to a more or less constant vortex strength. This is an approximate method in that genuine viscous diffusion of the vortex is not modeled, but it can be appropriate for vortex dominant flows over short to medium length scales where viscous diffusion can be neglected.

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.

Performance issues for iterative solvers in device simulation

NASA Technical Reports Server (NTRS)

Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai

1994-01-01

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches.

PubMed

Pahle, Jürgen

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches

PubMed Central

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem. PMID:19151097

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.

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.

Distribution of Plasmoids in Post-Coronal Mass Ejection Current Sheets

NASA Astrophysics Data System (ADS)

Bhattacharjee, A.; Guo, L.; Huang, Y.

2013-12-01

Recently, the fragmentation of a current sheet in the high-Lundquist-number regime caused by the plasmoid instability has been proposed as a possible mechanism for fast reconnection. In this work, we investigate this scenario by comparing the distribution of plasmoids obtained from Large Angle and Spectrometric Coronagraph (LASCO) observational data of a coronal mass ejection event with a resistive magnetohydrodynamic simulation of a similar event. The LASCO/C2 data are analyzed using visual inspection, whereas the numerical data are analyzed using both visual inspection and a more precise topological method. Contrasting the observational data with numerical data analyzed with both methods, we identify a major limitation of the visual inspection method, due to the difficulty in resolving smaller plasmoids. This result raises questions about reports of log-normal distributions of plasmoids and other coherent features in the recent literature. Based on nonlinear scaling relations of the plasmoid instability, we infer a lower bound on the current sheet width, assuming the underlying mechanism of current sheet broadening is resistive diffusion.

Numerical assessment of pulsating water jet in the conical diffusers

NASA Astrophysics Data System (ADS)

Tanasa, Constantin; Ciocan, Tiberiu; Muntean, Sebastian

2017-11-01

The hydraulic fluctuations associated with partial load operating conditions of Francis turbines are often periodic and characterized by the presence of a vortex rope. Two types of pressure fluctuations associated with the draft tube surge are identified in the literature. The first is an asynchronous (rotating) pressure fluctuation due to the precession of the helical vortex around the axis of the draft tube. The second type of fluctuation is a synchronous (plunging) fluctuation. The plunging fluctuations correspond to the flow field oscillations in the whole hydraulic passage, and are generally propagated overall in the hydraulic system. The paper introduced a new control method, which consists in injecting a pulsating axial water jet along to the draft tube axis. Nevertheless, the great calling of this control method is to mitigate the vortex rope effects targeting the vortex sheet and corresponding plunging component. In this paper, is presented our 3D numerical investigations with and without pulsating axial water jet control method in order to evaluate the concept.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Numerical Investigation of the Ability of Salt Tracers to Represent the Residence Time Distribution of Fluidized Catalytic Cracking Particles

DOE PAGES

Lu, Liqiang; Gao, Xi; Li, Tingwen; ...

2017-11-02

For a long time, salt tracers have been used to measure the residence time distribution (RTD) of fluidized catalytic cracking (FCC) particles. However, due to limitations in experimental measurements and simulation methods, the ability of salt tracers to faithfully represent RTDs has never been directly investigated. Our current simulation results using coarse-grained computational fluid dynamic coupled with discrete element method (CFD-DEM) with filtered drag models show that the residence time of salt tracers with the same terminal velocity as FCC particles is slightly larger than that of FCC particles. This research also demonstrates the ability of filtered drag models tomore » predict the correct RTD curve for FCC particles while the homogeneous drag model may only be used in the dilute riser flow of Geldart type B particles. The RTD of large-scale reactors can then be efficiently investigated with our proposed numerical method as well as by using the old-fashioned salt tracer technology.« less

A multi-scale Q1/P0 approach to langrangian shock hydrodynamics.

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

Shashkov, Mikhail; Love, Edward; Scovazzi, Guglielmo

A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the form of a pressure correction. With respect to currently implemented hourglass control approaches, the novelty of the method resides in its residual-based character. The stabilizing residual has a definite physical meaning, since it embeds a discrete form of the Clausius-Duhem inequality. Effectively, the proposed stabilization samples and acts to counter the production of entropy due to numerical instabilities. The proposed techniquemore » is applicable to materials with no shear strength, for which there exists a caloric equation of state. The stabilization operator is incorporated into a mid-point, predictor/multi-corrector time integration algorithm, which conserves mass, momentum and total energy. Encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method.« less

Swimming in a two-dimensional Brinkman fluid: Computational modeling and regularized solutions

NASA Astrophysics Data System (ADS)

Leiderman, Karin; Olson, Sarah D.

2016-02-01

The incompressible Brinkman equation represents the homogenized fluid flow past obstacles that comprise a small volume fraction. In nondimensional form, the Brinkman equation can be characterized by a single parameter that represents the friction or resistance due to the obstacles. In this work, we derive an exact fundamental solution for 2D Brinkman flow driven by a regularized point force and describe the numerical method to use it in practice. To test our solution and method, we compare numerical results with an analytic solution of a stationary cylinder in a uniform Brinkman flow. Our method is also compared to asymptotic theory; for an infinite-length, undulating sheet of small amplitude, we recover an increasing swimming speed as the resistance is increased. With this computational framework, we study a model swimmer of finite length and observe an enhancement in propulsion and efficiency for small to moderate resistance. Finally, we study the interaction of two swimmers where attraction does not occur when the initial separation distance is larger than the screening length.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

Visually lossless compression of digital hologram sequences

NASA Astrophysics Data System (ADS)

Darakis, Emmanouil; Kowiel, Marcin; Näsänen, Risto; Naughton, Thomas J.

2010-01-01

Digital hologram sequences have great potential for the recording of 3D scenes of moving macroscopic objects as their numerical reconstruction can yield a range of perspective views of the scene. Digital holograms inherently have large information content and lossless coding of holographic data is rather inefficient due to the speckled nature of the interference fringes they contain. Lossy coding of still holograms and hologram sequences has shown promising results. By definition, lossy compression introduces errors in the reconstruction. In all of the previous studies, numerical metrics were used to measure the compression error and through it, the coding quality. Digital hologram reconstructions are highly speckled and the speckle pattern is very sensitive to data changes. Hence, numerical quality metrics can be misleading. For example, for low compression ratios, a numerically significant coding error can have visually negligible effects. Yet, in several cases, it is of high interest to know how much lossy compression can be achieved, while maintaining the reconstruction quality at visually lossless levels. Using an experimental threshold estimation method, the staircase algorithm, we determined the highest compression ratio that was not perceptible to human observers for objects compressed with Dirac and MPEG-4 compression methods. This level of compression can be regarded as the point below which compression is perceptually lossless although physically the compression is lossy. It was found that up to 4 to 7.5 fold compression can be obtained with the above methods without any perceptible change in the appearance of video sequences.

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Stability Analysis of Algebraic Reconstruction for Immersed Boundary Methods with Application in Flow and Transport in Porous Media

NASA Astrophysics Data System (ADS)

Yousefzadeh, M.; Battiato, I.

2017-12-01

Flow and reactive transport problems in porous media often involve complex geometries with stationary or evolving boundaries due to absorption and dissolution processes. Grid based methods (e.g. finite volume, finite element, etc.) are a vital tool for studying these problems. Yet, implementing these methods requires one to answer a very first question of what type of grid is to be used. Among different possible answers, Cartesian grids are one of the most attractive options as they possess simple discretization stencil and are usually straightforward to generate at roughly no computational cost. The Immersed Boundary Method, a Cartesian based methodology, maintains most of the useful features of the structured grids while exhibiting a high-level resilience in dealing with complex geometries. These features make it increasingly more attractive to model transport in evolving porous media as the cost of grid generation reduces greatly. Yet, stability issues and severe time-step restriction due to explicit-time implementation combined with limited studies on the implementation of Neumann (constant flux) and linear and non-linear Robin (e.g. reaction) boundary conditions (BCs) have significantly limited the applicability of IBMs to transport in porous media. We have developed an implicit IBM capable of handling all types of BCs and addressed some numerical issues, including unconditional stability criteria, compactness and reduction of spurious oscillations near the immersed boundary. We tested the method for several transport and flow scenarios, including dissolution processes in porous media, and demonstrate its capabilities. Successful validation against both experimental and numerical data has been carried out.

Spectral element method for elastic and acoustic waves in frequency domain

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

Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the usemore » of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.« less

Concrete Infill Monitoring in Concrete-Filled FRP Tubes Using a PZT-Based Ultrasonic Time-of-Flight Method.

PubMed

Luo, Mingzhang; Li, Weijie; Hei, Chuang; Song, Gangbing

2016-12-07

Concrete-filled fiber-reinforced polymer tubes (CFFTs) have attracted interest for their structural applications in corrosive environments. However, a weak interfacial strength between the fiber-reinforced polymer (FRP) tube and the concrete infill may develop due to concrete shrinkage and inadequate concrete compaction during concrete casting, which will destroy the confinement effect and thereby reduce the load bearing capacity of a CFFT. In this paper, the lead zirconate titanate (PZT)-based ultrasonic time-of-flight (TOF) method was adopted to assess the concrete infill condition of CFFTs. The basic idea of this method is that the velocity of the ultrasonic wave propagation in the FRP material is about half of that in concrete material. Any voids or debonding created along the interface between the FRP tube and the concrete will delay the arrival time between the pairs of PZT transducers. A comparison of the arrival times of the PZT pairs between the intact and the defected CFFT was made to assess the severity of the voids or the debonding. The feasibility of the methodology was analyzed using a finite-difference time-domain-based numerical simulation. Experiments were setup to validate the numerical results, which showed good agreement with the numerical findings. The results showed that the ultrasonic time-of-flight method is able to detect the concrete infill condition of CFFTs.

Concrete Infill Monitoring in Concrete-Filled FRP Tubes Using a PZT-Based Ultrasonic Time-of-Flight Method

PubMed Central

Luo, Mingzhang; Li, Weijie; Hei, Chuang; Song, Gangbing

2016-01-01

Concrete-filled fiber-reinforced polymer tubes (CFFTs) have attracted interest for their structural applications in corrosive environments. However, a weak interfacial strength between the fiber-reinforced polymer (FRP) tube and the concrete infill may develop due to concrete shrinkage and inadequate concrete compaction during concrete casting, which will destroy the confinement effect and thereby reduce the load bearing capacity of a CFFT. In this paper, the lead zirconate titanate (PZT)-based ultrasonic time-of-flight (TOF) method was adopted to assess the concrete infill condition of CFFTs. The basic idea of this method is that the velocity of the ultrasonic wave propagation in the FRP material is about half of that in concrete material. Any voids or debonding created along the interface between the FRP tube and the concrete will delay the arrival time between the pairs of PZT transducers. A comparison of the arrival times of the PZT pairs between the intact and the defected CFFT was made to assess the severity of the voids or the debonding. The feasibility of the methodology was analyzed using a finite-difference time-domain-based numerical simulation. Experiments were setup to validate the numerical results, which showed good agreement with the numerical findings. The results showed that the ultrasonic time-of-flight method is able to detect the concrete infill condition of CFFTs. PMID:27941617

Assessment of head injury of children due to golf ball impact.

PubMed

Lee, Heow Pueh; Wang, Fang

2010-10-01

Head trauma injury due to impact by a flying golf ball is one of the most severe possible injury accidents on the golf course. Numerical simulations based on the finite element method are presented to investigate head injury in children due to impact by a flying golf ball. The stress and energy flow patterns in a head model during the golf ball impact are computed for various combinations of striking speed, falling angle of the golf ball before impact, and impact location. It is found that a child is more prone to head injury due to golf ball impact on the frontal and side/temporal areas. The simulated results are found to conform to the clinical reports on children's head injuries from flying golf balls.

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Heterojunction Solid-State Devices for Millimeter-Wave Sources.

DTIC Science & Technology

1983-10-01

technology such as MBE and/or OK-CVD will be required. Our large-signal, numerical WATT device simulations are the first to predict from basic transport...results are due to an improved method for determining semiconductor material parameters. We use a theoretical Monte Carlo materials simulation ... simulations . These calculations have helped provide insight into velocity overshoot and ballistic transport phenomena. We find that ballistic or near

[Anorexia nervosa].

PubMed

Nogal, Paweł; Lewiński, Andrzej

2008-01-01

Anorexia nervosa is an eating disorder characterized by conscious restriction of food intake, which causes numerous metabolic and hormonal disorders. Knowledge of these changes is important due to growing morbidity and mortality of anorexia. Treatment is difficult and requires cooperation of a group of specialists, including an endocrinologist. The authors presented a clinical picture, view of etiopathogenesis and typical disorders found in patients with this illness. Furthermore, treatment methods were also discussed.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

NASA Astrophysics Data System (ADS)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Highly accurate symplectic element based on two variational principles

NASA Astrophysics Data System (ADS)

Qing, Guanghui; Tian, Jia

2018-02-01

For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.

Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal

NASA Astrophysics Data System (ADS)

Krčmár, Roman; Šamaj, Ladislav

2018-01-01

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ηe and δe which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.

Numerical and Experimental Investigation on a Thermo-Photovoltaic Module for Higher Efficiency Energy Generation

NASA Astrophysics Data System (ADS)

Karami-Lakeh, Hossein; Hosseini-Abardeh, Reza; Kaatuzian, Hassan

2017-05-01

One major problem of solar cells is the decrease in efficiency due to an increase in temperature when operating under constant irradiation of solar energy. The combination of solar cell and a thermoelectric generator is one of the methods proposed to solve this problem. In this paper, the performance of thermo-photovoltaic system is studied experimentally as well as through numerical simulation. In the experimental part, design, manufacture and test of a novel thermo-photovoltaic system assembly are presented. Results of the assembled system showed that with reduction of one degree (Centigrade) in the temperature of solar cell under investigation, and about 0.2 % increase in the efficiency will be obtained in comparison with given efficiency at that specified temperature. The solar cell in a hybrid-assembled system under two cooling conditions (air cooling and water cooling) obtained an efficiency of 8 % and 9.5 %, respectively, while the efficiency of a single cell under the same radiation condition was 6 %. In numerical simulation part, photo-thermoelectric performance of system was analyzed. Two methods for evaluation of thermoelectric performance were used: average properties and finite element method. Results of simulation also demonstrate an increase in solar cell efficiency in the combined system in comparison with that of the single cell configuration.

A Parallel Compact Multi-Dimensional Numerical Algorithm with Aeroacoustics Applications

NASA Technical Reports Server (NTRS)

Povitsky, Alex; Morris, Philip J.

1999-01-01

In this study we propose a novel method to parallelize high-order compact numerical algorithms for the solution of three-dimensional PDEs (Partial Differential Equations) in a space-time domain. For this numerical integration most of the computer time is spent in computation of spatial derivatives at each stage of the Runge-Kutta temporal update. The most efficient direct method to compute spatial derivatives on a serial computer is a version of Gaussian elimination for narrow linear banded systems known as the Thomas algorithm. In a straightforward pipelined implementation of the Thomas algorithm processors are idle due to the forward and backward recurrences of the Thomas algorithm. To utilize processors during this time, we propose to use them for either non-local data independent computations, solving lines in the next spatial direction, or local data-dependent computations by the Runge-Kutta method. To achieve this goal, control of processor communication and computations by a static schedule is adopted. Thus, our parallel code is driven by a communication and computation schedule instead of the usual "creative, programming" approach. The obtained parallelization speed-up of the novel algorithm is about twice as much as that for the standard pipelined algorithm and close to that for the explicit DRP algorithm.

A Semi-implicit Treatment of Porous Media in Steady-State CFD.

PubMed

Domaingo, Andreas; Langmayr, Daniel; Somogyi, Bence; Almbauer, Raimund

There are many situations in computational fluid dynamics which require the definition of source terms in the Navier-Stokes equations. These source terms not only allow to model the physics of interest but also have a strong impact on the reliability, stability, and convergence of the numerics involved. Therefore, sophisticated numerical approaches exist for the description of such source terms. In this paper, we focus on the source terms present in the Navier-Stokes or Euler equations due to porous media-in particular the Darcy-Forchheimer equation. We introduce a method for the numerical treatment of the source term which is independent of the spatial discretization and based on linearization. In this description, the source term is treated in a fully implicit way whereas the other flow variables can be computed in an implicit or explicit manner. This leads to a more robust description in comparison with a fully explicit approach. The method is well suited to be combined with coarse-grid-CFD on Cartesian grids, which makes it especially favorable for accelerated solution of coupled 1D-3D problems. To demonstrate the applicability and robustness of the proposed method, a proof-of-concept example in 1D, as well as more complex examples in 2D and 3D, is presented.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Review of the results of the in vivo dosimetry during total skin electron beam therapy

PubMed Central

Guidi, Gabriele; Gottardi, Giovanni; Ceroni, Paola; Costi, Tiziana

2013-01-01

This work reviews results of in vivo dosimetry (IVD) for total skin electron beam (TSEB) therapy, focusing on new methods, data emerged within 2012. All quoted data are based on a careful review of the literature reporting IVD results for patients treated by means of TSEB therapy. Many of the reviewed papers refer mainly to now old studies and/or old guidelines and recommendations (by IAEA, AAPM and EORTC), because (due to intrinsic rareness of TSEB-treated pathologies) only a limited number of works and reports with a large set of numerical data and proper statistical analysis is up-to-day available in scientific literature. Nonetheless, a general summary of the results obtained by the now numerous IVD techniques available is reported; innovative devices and methods, together with areas of possible further and possibly multicenter investigations for TSEB therapies are highlighted. PMID:24936333

Numerical Analysis on Seepage in the deep overburden CFRD

NASA Astrophysics Data System (ADS)

Zeyu, GUO; Junrui, CHAI; Yuan, QIN

2017-12-01

There are many problems in the construction of hydraulic structures on deep overburden because of its complex foundation structure and poor geological condition. Seepage failure is one of the main problems. The Combination of the seepage control system of the face rockfill dam and the deep overburden can effectively control the seepage of construction of the concrete face rockfill dam on the deep overburden. Widely used anti-seepage measures are horizontal blanket, waterproof wall, curtain grouting and so on, but the method, technique and its effect of seepage control still have many problems thus need further study. Due to the above considerations, Three-dimensional seepage field numerical analysis based on practical engineering case is conducted to study the seepage prevention effect under different seepage prevention methods, which is of great significance to the development of dam technology and the development of hydropower resources in China.

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.

Prediction of sound absorption in rigid porous media with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

da Silva, Andrey Ricardo; Mareze, Paulo; Brandão, Eric

2016-02-01

In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques.

Analysis and Assessment of Environmental Load of Vending Machines by a LCA Method, and Eco-Improvement Effect

NASA Astrophysics Data System (ADS)

Kimura, Yukio; Sadamichi, Yucho; Maruyama, Naoki; Kato, Seizo

These days the environmental impact due to vending machines'(VM) diffusion has greatly been discussed. This paper describes the numerical evaluation of the environmental impact by using the LCA (Life Cycle Assessment) scheme and then proposes eco-improvements' strategy toward environmentally conscious products(ECP). A new objective and universal consolidated method for the LCA-evaluation, so-called LCA-NETS(Numerical Eco-load Standardization ) developed by the authors is applied to the present issue. As a result, the environmental loads at the 5years' operation and the material procurement stages are found to dominate others over the life cycle. Further eco-improvement is realized by following the order of the LCA-NETS magnitude; namely, energy saving, materials reducing, parts' re-using, and replacing with low environmental load material. Above all, parts' re-using is specially recommendable for significant reduction of the environmental loads toward ECP.

Building of fuzzy decision trees using ID3 algorithm

NASA Astrophysics Data System (ADS)

Begenova, S. B.; Avdeenko, T. V.

2018-05-01

Decision trees are widely used in the field of machine learning and artificial intelligence. Such popularity is due to the fact that with the help of decision trees graphic models, text rules can be built and they are easily understood by the final user. Because of the inaccuracy of observations, uncertainties, the data, collected in the environment, often take an unclear form. Therefore, fuzzy decision trees becoming popular in the field of machine learning. This article presents a method that includes the features of the two above-mentioned approaches: a graphical representation of the rules system in the form of a tree and a fuzzy representation of the data. The approach uses such advantages as high comprehensibility of decision trees and the ability to cope with inaccurate and uncertain information in fuzzy representation. The received learning method is suitable for classifying problems with both numerical and symbolic features. In the article, solution illustrations and numerical results are given.

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

NASA Technical Reports Server (NTRS)

Starlinger, Alois; Duffy, Stephen F.; Palko, Joseph L.

1993-01-01

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Numerical modelling of thin-walled Z-columns made of general laminates subjected to uniform shortening

NASA Astrophysics Data System (ADS)

Teter, Andrzej; Kolakowski, Zbigniew

2018-01-01

The numerical modelling of a plate structure was performed with the finite element method and a one-mode approach based on Koiter's method. The first order approximation of Koiter's method enables one to solve the eigenvalue problem. The second order approximation describes post-buckling equilibrium paths. In the finite element analysis, the Lanczos method was used to solve the linear problem of buckling. Simulations of the non-linear problem were performed with the Newton-Raphson method. Detailed calculations were carried out for a short Z-column made of general laminates. Configurations of laminated layers were non-symmetric. Due to possibilities of its application, the general laminate is very interesting. The length of the samples was chosen to obtain the lowest value of local buckling load. The amplitude of initial imperfections was 10% of the wall thickness. Thin-walled structures were simply supported on both ends. The numerical results were verified in experimental tests. A strain-gauge technique was applied. A static compression test was performed on a universal testing machine and a special grip, which consisted of two rigid steel plates and clamping sleeves, was used. Specimens were obtained with an autoclave technique. Tests were performed at a constant velocity of the cross-bar equal to 2 mm/min. The compressive load was less than 150% of the bifurcation load. Additionally, soft and thin pads were used to reduce inaccuracy of the sample ends.

Green's functions for analysis of dynamic response of wheel/rail to vertical excitation

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2007-09-01

An analytical model to simulate wheel/rail interaction using the Green's functions method is proposed in this paper. The model consists of a moving wheel on a discretely supported rail. Particularly for this model of rail, the bending and the longitudinal displacement are coupled due to the rail pad and a complex model of the rail pad is adopted. An efficient method for solving a time-domain analysis for wheel/rail interaction is presented. The method is based on the properties of the rail's Green functions and starting to these functions, a track's Green matrix is assembled for the numerical simulations of wheel/rail response due to three kinds of vertical excitations: the steady-state interaction, the rail corrugation and the wheel flat. The study points to influence of the worn rail—rigid contact—on variation in the wheel/rail contact force. The concept of pinned-pinned inhibitive rail pad is also presented.

Float-zone crystal growth of CdGeAs 2 in microgravity: numerical simulation and experiment

NASA Astrophysics Data System (ADS)

Saghir, M. Z.; Labrie, D.; Ginovker, A.; Paton, B. E.; George, A. E.; Olson, K.; Simpson, A. M.

2000-01-01

Two CdGeAs 2 samples have been successfully grown under microgravity on SPACEHAB-SH04 during the STS-77 Space Shuttle Endeavour mission. One polycrystalline and one single crystal CdGeAs 2 feed rods with 9 mm diameter were processed by the float-zone method. An eutectic salt of LiCl and KCl was used as an encapsulant to suppress Cd and As evaporation from the melt. Numerical modeling of the float zone shows that salt encapsulation plays an important role in reducing Marangoni convection. The interface between the salt and CdGeAs 2 was shown not to deform in the float zone due to the weak capillary pressure.

Double-Zero-Index Structural Phononic Waveguides

NASA Astrophysics Data System (ADS)

Zhu, Hongfei; Semperlotti, Fabio

2017-12-01

We report on the theoretical and experimental realization of a double-zero-index elastic waveguide and the corresponding acoustic cloaking and supercoupling effects. The proposed waveguide uses geometric tapers in order to induce Dirac-like cones at k → =0 due to accidental degeneracy. The nature of the degeneracy is explored by a k .p perturbation method adapted to thin structural waveguides. The results confirm the linear nature of the dispersion around the degeneracy and the possibility to map the material to effective-medium properties. Effective parameters numerically extracted using boundary medium theory confirm that the phononic waveguide maps into a double-zero-index material. Numerical and experimental results confirm the expected cloaking and supercoupling effects.

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.

Estimation of the curvature of the solid liquid interface during Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Barat, Catherine; Duffar, Thierry; Garandet, Jean-Paul

1998-11-01

An approximate solution for the solid/liquid interface curvature due to the crucible effect in crystal growth is derived from simple heat flux considerations. The numerical modelling of the problem carried out with the help of the finite element code FIDAP supports the predictions of our analytical expression and allows to identify its range of validity. Experimental interface curvatures, measured in gallium antimonide samples grown by the vertical Bridgman method, are seen to compare satisfactorily to analytical and numerical results. Other literature data are also in fair agreement with the predictions of our models in the case where the amount of heat carried by the crucible is small compared to the overall heat flux.

Numerical simulation of transmission coefficient using c-number Langevin equation

NASA Astrophysics Data System (ADS)

Barik, Debashis; Bag, Bidhan Chandra; Ray, Deb Shankar

2003-12-01

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik et al., J. Chem. Phys. 119, 680 (2003); Banerjee et al., Phys. Rev. E 65, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the T2 enhancement of the rate at low temperatures and other related features of temporal behavior of the transmission coefficient over a range of temperature down to absolute zero, noise correlation, and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order.

Model of a Frame of Dynamic Routing and Its Equilibrium

NASA Astrophysics Data System (ADS)

Zhang, Shu; Yuan, Yuan; Xu, Jian

Dynamic routing algorithm based on the shortest path principle is criticized due to the oscillation induced by such routing scheme. In the present work, we propose the model of TCP/RED algorithm by a new frame of dynamic routing, based on the measurement of occupation ratio of router buffer for different links, which only requires the information of the queue size at the buffer of the router, to stabilize the system. We classify several types of equilibrium and employ the numerical method to study the stability of the steady state. Our numerical results show that the careful selection of the parameters characterizing the dynamic routing algorithm can stabilize the system in some cases.

Optical ablation/temperature gage (COTA)

NASA Astrophysics Data System (ADS)

Cassaing, J.; Balageas, D.

ONERA has ground and flight tested for heat-shield recession a novel technique, different from current radiation and acoustic measurement methods. It uses a combined ablation/temperature gage that views the radiation optically from a cavity embedded within the heat shield. Flight measurements, both of temperature and of passage of the ablation front, are compared with data generated by a predictive numerical code. The ablation and heat diffusion into the instrumented ablator can be simulated numerically to evaluate accurately the errors due to the presence of the gage. This technology was established in 1978 and finally adopted after ground tests in arc heater facilities. After four years of flight evaluations, it is possible to evaluate and criticize the sensor reliability.

Joint Center Estimation Using Single-Frame Optimization: Part 1: Numerical Simulation.

PubMed

Frick, Eric; Rahmatalla, Salam

2018-04-04

The biomechanical models used to refine and stabilize motion capture processes are almost invariably driven by joint center estimates, and any errors in joint center calculation carry over and can be compounded when calculating joint kinematics. Unfortunately, accurate determination of joint centers is a complex task, primarily due to measurements being contaminated by soft-tissue artifact (STA). This paper proposes a novel approach to joint center estimation implemented via sequential application of single-frame optimization (SFO). First, the method minimizes the variance of individual time frames’ joint center estimations via the developed variance minimization method to obtain accurate overall initial conditions. These initial conditions are used to stabilize an optimization-based linearization of human motion that determines a time-varying joint center estimation. In this manner, the complex and nonlinear behavior of human motion contaminated by STA can be captured as a continuous series of unique rigid-body realizations without requiring a complex analytical model to describe the behavior of STA. This article intends to offer proof of concept, and the presented method must be further developed before it can be reasonably applied to human motion. Numerical simulations were introduced to verify and substantiate the efficacy of the proposed methodology. When directly compared with a state-of-the-art inertial method, SFO reduced the error due to soft-tissue artifact in all cases by more than 45%. Instead of producing a single vector value to describe the joint center location during a motion capture trial as existing methods often do, the proposed method produced time-varying solutions that were highly correlated ( r > 0.82) with the true, time-varying joint center solution.

Thermal Pollution Mathematical Model. Volume 2; Verification of One-Dimensional Numerical Model at Lake Keowee

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.

Joint denoising, demosaicing, and chromatic aberration correction for UHD video

NASA Astrophysics Data System (ADS)

Jovanov, Ljubomir; Philips, Wilfried; Damstra, Klaas Jan; Ellenbroek, Frank

2017-09-01

High-resolution video capture is crucial for numerous applications such as surveillance, security, industrial inspection, medical imaging and digital entertainment. In the last two decades, we are witnessing a dramatic increase of the spatial resolution and the maximal frame rate of video capturing devices. In order to achieve further resolution increase, numerous challenges will be facing us. Due to the reduced size of the pixel, the amount of light also reduces, leading to the increased noise level. Moreover, the reduced pixel size makes the lens imprecisions more pronounced, which especially applies to chromatic aberrations. Even in the case when high quality lenses are used some chromatic aberration artefacts will remain. Next, noise level additionally increases due to the higher frame rates. To reduce the complexity and the price of the camera, one sensor captures all three colors, by relying on Color Filter Arrays. In order to obtain full resolution color image, missing color components have to be interpolated, i.e. demosaicked, which is more challenging than in the case of lower resolution, due to the increased noise and aberrations. In this paper, we propose a new method, which jointly performs chromatic aberration correction, denoising and demosaicking. By jointly performing the reduction of all artefacts, we are reducing the overall complexity of the system and the introduction of new artefacts. In order to reduce possible flicker we also perform temporal video enhancement. We evaluate the proposed method on a number of publicly available UHD sequences and on sequences recorded in our studio.

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

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

NASA Astrophysics Data System (ADS)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime

NASA Astrophysics Data System (ADS)

Kumar, Rakesh; Sood, Shilpa; Shehzad, Sabir Ali; Sheikholeslami, Mohsen

A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM). The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number) on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables.

Numerical theory of the motion of Jupiter's Galilean satellites

NASA Astrophysics Data System (ADS)

Kosmodamianskii, G. A.

2009-12-01

A numerical theory of the motion of Jupiter’s Galilean satellites was constructed using 3767 absolute observations of the satellites. The theory was based on the numerical integration of the equations of motion of the satellites. The integration was carried out by Everhart’s method using the ERA software package developed at the Institute of Applied Astronomy (IAA). Perturbations due to the oblateness of the central planet, perturbations from Saturn and the Sun, and the mutual attraction of the satellites were taken into account in the integration. As a result, the coefficients of the Chebyshev series expansion for coordinates and velocities were found for the period from 1962 to 2010. The initial coordinates and velocities of the satellites, as well as their masses, the mass of Jupiter, and the harmonic coefficient J 2 of the potential of Jupiter, were adjusted. The resulting ephemerides were compared to those of Lieske and Lainey.

Corrigendum to "A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves" [J. Comput. Phys. 259 (2014) 331-357

NASA Astrophysics Data System (ADS)

Pelanti, Marica; Shyue, Keh-Ming

2015-05-01

The authors regret that one erroneous plot of the numerical results for a dodecane liquid-vapor shock tube problem was included in Fig. 3, p. 346, of the article [1]. Specifically, the graph of the vapor-liquid temperature difference (Tv -Tl) displayed at the bottom-right corner of Fig. 3 in [1] is not correct due to some wrong settings introduced in the temperature visualization tool. The error pertains solely to simulation data post-processing, and it is not related to the numerical methods and programs employed to run the experiment. We display here in Fig. 1 the correct temperature difference plot, generated from our original results computed for the dodecane shock tube test described in [1]. We think that is important to notify this correction to avoid any confusion.

A new method to compute lunisolar perturbations in satellite motions

NASA Technical Reports Server (NTRS)

Kozai, Y.

1973-01-01

A new method to compute lunisolar perturbations in satellite motion is proposed. The disturbing function is expressed by the orbital elements of the satellite and the geocentric polar coordinates of the moon and the sun. The secular and long periodic perturbations are derived by numerical integrations, and the short periodic perturbations are derived analytically. The perturbations due to the tides can be included in the same way. In the Appendix, the motion of the orbital plane for a synchronous satellite is discussed; it is concluded that the inclination cannot stay below 7 deg.

A fuzzy inventory model with acceptable shortage using graded mean integration value method

NASA Astrophysics Data System (ADS)

Saranya, R.; Varadarajan, R.

2018-04-01

In many inventory models uncertainty is due to fuzziness and fuzziness is the closed possible approach to reality. In this paper, we proposed a fuzzy inventory model with acceptable shortage which is completely backlogged. We fuzzily the carrying cost, backorder cost and ordering cost using Triangular and Trapezoidal fuzzy numbers to obtain the fuzzy total cost. The purpose of our study is to defuzzify the total profit function by Graded Mean Integration Value Method. Further a numerical example is also given to demonstrate the developed crisp and fuzzy models.

Improvment of short cut numerical method for determination of periods of free oscillations for basins with irregular geometry and bathymetry

NASA Astrophysics Data System (ADS)

Chernov, Anton; Kurkin, Andrey; Pelinovsky, Efim; Yalciner, Ahmet; Zaytsev, Andrey

2010-05-01

A short cut numerical method for evaluation of the modes of free oscillations of the basins which have irregular geometry and bathymetry was presented in the paper (Yalciner A.C., Pelinovsky E., 2007). In the method, a single wave is inputted to the basin as an initial impulse. The respective agitation in the basin is computed by using the numerical method solving the nonlinear form of long wave equations. The time histories of water surface fluctuations at different locations due to propagation of the waves in relation to the initial impulse are stored and analyzed by the fast Fourier transform technique (FFT) and energy spectrum curves for each location are obtained. The frequencies of each mode of free oscillations are determined from the peaks of the spectrum curves. Some main features were added for this method and will be discussed here: 1. Instead of small number of gauges which were manually installed in the studied area the information from numerical simulation now is recorded on the regular net of the «simulation» gauges which was place everywhere on the sea surface in the depth deeper than "coast" level with the fixed presetted distance between gauges. The spectral analysis of wave records was produced by Welch periodorgam method instead of simple FFT so it's possible to get spectral power estimation for wave process and determine confidence interval for spectra peaks. 2. After the power spectral estimation procedure the common peak of studied seiche can be found and mean spectral amplitudes for this peak were calculated numerically by a Simpson integration method for all gauges in the basin and the mean spectral amplitudes spatial distribution map can be ploted. The spatial distribution helps to study structure of seiche and determine effected dangerous areas. 3. Nested grid module in the NAMI-DANCE - nonlinear shallow water equations calculation software package was developed. This is very important feature for complicated different scale (ocean - sea - bay - harbor) phenomenons studying. The new developed software was tested for Mediterranian, Sea of Okhotsk and South China sea regions. This software can be usefull in local tsunami mapping and tsunami propagation in the coastal zone. References: Yalciner A.C., Pelinovsky E. A short cut numerical method for determination of periods of free oscillations for basins with irregular geometry and bathymetry // Ocean engineering. V. 34. 2007. С. 747 - 757

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Probabilistic analysis and fatigue damage assessment of offshore mooring system due to non-Gaussian bimodal tension processes

NASA Astrophysics Data System (ADS)

Chang, Anteng; Li, Huajun; Wang, Shuqing; Du, Junfeng

2017-08-01

Both wave-frequency (WF) and low-frequency (LF) components of mooring tension are in principle non-Gaussian due to nonlinearities in the dynamic system. This paper conducts a comprehensive investigation of applicable probability density functions (PDFs) of mooring tension amplitudes used to assess mooring-line fatigue damage via the spectral method. Short-term statistical characteristics of mooring-line tension responses are firstly investigated, in which the discrepancy arising from Gaussian approximation is revealed by comparing kurtosis and skewness coefficients. Several distribution functions based on present analytical spectral methods are selected to express the statistical distribution of the mooring-line tension amplitudes. Results indicate that the Gamma-type distribution and a linear combination of Dirlik and Tovo-Benasciutti formulas are suitable for separate WF and LF mooring tension components. A novel parametric method based on nonlinear transformations and stochastic optimization is then proposed to increase the effectiveness of mooring-line fatigue assessment due to non-Gaussian bimodal tension responses. Using time domain simulation as a benchmark, its accuracy is further validated using a numerical case study of a moored semi-submersible platform.

Cement bond evaluation method in horizontal wells using segmented bond tool

NASA Astrophysics Data System (ADS)

Song, Ruolong; He, Li

2018-06-01

Most of the existing cement evaluation technologies suffer from tool eccentralization due to gravity in highly deviated wells and horizontal wells. This paper proposes a correction method to lessen the effects of tool eccentralization on evaluation results of cement bond using segmented bond tool, which has an omnidirectional sonic transmitter and eight segmented receivers evenly arranged around the tool 2 ft from the transmitter. Using 3-D finite difference parallel numerical simulation method, we investigate the logging responses of centred and eccentred segmented bond tool in a variety of bond conditions. From the numerical results, we find that the tool eccentricity and channel azimuth can be estimated from measured sector amplitude. The average of the sector amplitude when the tool is eccentred can be corrected to the one when the tool is centred. Then the corrected amplitude will be used to calculate the channel size. The proposed method is applied to both synthetic and field data. For synthetic data, it turns out that this method can estimate the tool eccentricity with small error and the bond map is improved after correction. For field data, the tool eccentricity has a good agreement with the measured well deviation angle. Though this method still suffers from the low accuracy of calculating channel azimuth, the credibility of corrected bond map is improved especially in horizontal wells. It gives us a choice to evaluate the bond condition for horizontal wells using existing logging tool. The numerical results in this paper can provide aids for understanding measurements of segmented tool in both vertical and horizontal wells.

A numerical method for shock driven multiphase flow with evaporating particles

NASA Astrophysics Data System (ADS)

Dahal, Jeevan; McFarland, Jacob A.

2017-09-01

A numerical method for predicting the interaction of active, phase changing particles in a shock driven flow is presented in this paper. The Particle-in-Cell (PIC) technique was used to couple particles in a Lagrangian coordinate system with a fluid in an Eulerian coordinate system. The Piecewise Parabolic Method (PPM) hydrodynamics solver was used for solving the conservation equations and was modified with mass, momentum, and energy source terms from the particle phase. The method was implemented in the open source hydrodynamics software FLASH, developed at the University of Chicago. A simple validation of the methods is accomplished by comparing velocity and temperature histories from a single particle simulation with the analytical solution. Furthermore, simple single particle parcel simulations were run at two different sizes to study the effect of particle size on vorticity deposition in a shock-driven multiphase instability. Large particles were found to have lower enstrophy production at early times and higher enstrophy dissipation at late times due to the advection of the particle vorticity source term through the carrier gas. A 2D shock-driven instability of a circular perturbation is studied in simulations and compared to previous experimental data as further validation of the numerical methods. The effect of the particle size distribution and particle evaporation is examined further for this case. The results show that larger particles reduce the vorticity deposition, while particle evaporation increases it. It is also shown that for a distribution of particles sizes the vorticity deposition is decreased compared to single particle size case at the mean diameter.

Effect of Blast-Induced Vibration from New Railway Tunnel on Existing Adjacent Railway Tunnel in Xinjiang, China

NASA Astrophysics Data System (ADS)

Liang, Qingguo; Li, Jie; Li, Dewu; Ou, Erfeng

2013-01-01

The vibrations of existing service tunnels induced by blast-excavation of adjacent tunnels have attracted much attention from both academics and engineers during recent decades in China. The blasting vibration velocity (BVV) is the most widely used controlling index for in situ monitoring and safety assessment of existing lining structures. Although numerous in situ tests and simulations had been carried out to investigate blast-induced vibrations of existing tunnels due to excavation of new tunnels (mostly by bench excavation method), research on the overall dynamical response of existing service tunnels in terms of not only BVV but also stress/strain seemed limited for new tunnels excavated by the full-section blasting method. In this paper, the impacts of blast-induced vibrations from a new tunnel on an existing railway tunnel in Xinjiang, China were comprehensively investigated by using laboratory tests, in situ monitoring and numerical simulations. The measured data from laboratory tests and in situ monitoring were used to determine the parameters needed for numerical simulations, and were compared with the calculated results. Based on the results from in situ monitoring and numerical simulations, which were consistent with each other, the original blasting design and corresponding parameters were adjusted to reduce the maximum BVV, which proved to be effective and safe. The effect of both the static stress before blasting vibrations and the dynamic stress induced by blasting on the total stresses in the existing tunnel lining is also discussed. The methods and related results presented could be applied in projects with similar ground and distance between old and new tunnels if the new tunnel is to be excavated by the full-section blasting method.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Yee, H. C.; Shinn, J. L.

1986-01-01

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A new weak Galerkin finite element method for elliptic interface problems

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

Mu, Lin; Wang, Junping; Ye, Xiu

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Aiding flow Thermo-Solutal Convection in Porous Cavity: ANN approach

NASA Astrophysics Data System (ADS)

Jafer Kazi1, Mohammed; Ameer Ahamad, N.; Yunus Khan, T. M.

2017-08-01

The transfer of thermal energy along with the diffusion of mass is common phenomenon that occurs in nature. The thermos-solutal convection in porous medium arises due to combined effect of diffusion of heat as well as mass inside the domain. The density variation of fluid due to absorbed heat at one end of porous cavity leads to fluid movement which in turn initiates the heat transfer. The mass diffusion inside the porous regime occurs due to concentration difference between two ends of cavity. Generally this phenomenon is studied with the help of numerical methods but current work emphasis the successful usage of artificial neural network in predicting the thermos-solutal convection of aiding flow in porous medium.

Seismic behavior of breakwaters on complex ground by numerical tests: Liquefaction and post liquefaction ground settlements

NASA Astrophysics Data System (ADS)

Gu, Linlin; Zhang, Feng; Bao, Xiaohua; Shi, Zhenming; Ye, Guanlin; Ling, Xianzhang

2018-04-01

A large number of breakwaters have been constructed along coasts to protect humans and infrastructures from tsunamis. There is a risk that foundation soils of these structures may liquefy, or partially liquefy during the earthquake preceding a tsunami, which would greatly reduce the structures' capacity to resist the tsunami. It is necessary to consider not only the soil's liquefaction behavior due to earthquake motions but also its post-liquefaction behavior because this behavior will affect the breakwater's capacity to resist an incoming tsunami. In this study, numerical tests based on a sophisticated constitutive model and a soil-water coupled finite element method are used to predict the mechanical behavior of breakwaters and the surrounding soils. Two real breakwaters subjected to two different seismic excitations are examined through numerical simulation. The simulation results show that, earthquakes affect not only the immediate behavior of breakwaters and the surrounding soils but also their long-term settlements due to post-earthquake consolidation. A soil profile with thick clayey layers beneath liquefied soil is more vulnerable to tsunami than a soil profile with only sandy layers. Therefore, quantitatively evaluating the seismic behavior of breakwaters and surrounding soils is important for the design of breakwater structures to resist tsunamis.

Determination and characterization by numerical simulations of flow mixing due to electrokinetic instabilities in cross-shaped microchannels

NASA Astrophysics Data System (ADS)

Guerrero, Esteban; Chen, Daming; Hageman, Logan; Guzman, Amador

2017-11-01

This article describes a computational study of flow mixing in microchannels due to electrokinetic instabilities that are compared to experimental results obtained in a cross- microchannel with an ionic solution of potassium chloride with two different ionic concentrations, with the purpose of determining the parameter combinations to produce the onset of flow mixing and its characteristics. For the numerical simulation process carried out using a finite element method-based commercial code, we applied a typical zeta potential used in other articles as a boundary condition for the microchannel walls. For the experiments, we used a commercial silicon glass (Caliper NS95) microchannel. For determining a flow mixing regime, we use the concept of ``mixing index'' established by (Fu et al., 2005) for an electrical conductivity ratio range of 18 to 52 with an electric field range of 1100 to 1900 V/cm. From our numerical simulation results we have found a threshold for the electrical Rayleigh number for starting a flow mixing regime, and a minimum microchannel characteristic length for achieving a 90% of flow mixing that will allow us to significantly reduce the mixing time. Vicerrectoria de Investigacion y Departamento de Ingeniera Mecánica y Metalúrgica Pontificia Universidad Catolica de Chile.

Numerical modeling of the agricultural-hydrologic system in Punjab, India

NASA Astrophysics Data System (ADS)

Nyblade, M.; Russo, T. A.; Zikatanov, L.; Zipp, K.

2017-12-01

The goal of food security for India's growing population is threatened by the decline in freshwater resources due to unsustainable water use for irrigation. The issue is acute in parts of Punjab, India, where small landholders produce a major quantity of India's food with declining groundwater resources. To further complicate this problem, other regions of the state are experiencing groundwater logging and salinization, and are reliant on canal systems for fresh water delivery. Due to the lack of water use records, groundwater consumption for this study is estimated with available data on crop yields, climate, and total canal water delivery. The hydrologic and agricultural systems are modeled using appropriate numerical methods and software. This is a state-wide hydrologic numerical model of Punjab that accounts for multiple aquifer layers, agricultural water demands, and interactions between the surface canal system and groundwater. To more accurately represent the drivers of agricultural production and therefore water use, we couple an economic crop optimization model with the hydrologic model. These tools will be used to assess and optimize crop choice scenarios based on farmer income, food production, and hydrologic system constraints. The results of these combined models can be used to further understand the hydrologic system response to government crop procurement policies and climate change, and to assess the effectiveness of possible water conservation solutions.

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.

Utility indifference pricing of insurance catastrophe derivatives.

PubMed

Eichler, Andreas; Leobacher, Gunther; Szölgyenyi, Michaela

2017-01-01

We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes. A numerical study illustrates our results.

Numerical analysis of projectile impact in woven texile structures

NASA Technical Reports Server (NTRS)

Roylance, D.

1977-01-01

Computer codes were developed for simulating the dynamic fracture and viscoelastic constitutive response due to stress wave interaction and reflections caused by ballistic impact on woven textiles. The method, which was developed for use in the design and analysis of protection devices for personnel armor, has potential for use in studies of rotor blade burst containment at high velocity. Alterations in coding required for burst containment problems are discussed.

Investigation of the stochastic nature of wave processes for renewable resources management: a pilot application in a remote island in the Aegean sea

NASA Astrophysics Data System (ADS)

Moschos, Evangelos; Manou, Georgia; Georganta, Xristina; Dimitriadis, Panayiotis; Iliopoulou, Theano; Tyralis, Hristos; Koutsoyiannis, Demetris; Tsoukala, Vicky

2017-04-01

The large energy potential of ocean dynamics is not yet being efficiently harvested mostly due to several technological and financial drawbacks. Nevertheless, modern renewable energy systems include wave and tidal energy in cases of nearshore locations. Although the variability of tidal waves can be adequately predictable, wind-generated waves entail a much larger uncertainty due to their dependence to the wind process. Recent research has shown, through estimation of the wave energy potential in coastal areas of the Aegean Sea, that installation of wave energy converters in nearshore locations could be an applicable scenario, assisting the electrical network of Greek islands. In this context, we analyze numerous of observations and we investigate the long-term behaviour of wave height and wave period processes. Additionally, we examine the case of a remote island in the Aegean sea, by estimating the local wave climate through past analysis data and numerical methods, and subsequently applying a parsimonious stochastic model to a theoretical scenario of wave energy production. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

Modeling shape selection of buckled dielectric elastomers

NASA Astrophysics Data System (ADS)

Langham, Jacob; Bense, Hadrien; Barkley, Dwight

2018-02-01

A dielectric elastomer whose edges are held fixed will buckle, given a sufficiently applied voltage, resulting in a nontrivial out-of-plane deformation. We study this situation numerically using a nonlinear elastic model which decouples two of the principal electrostatic stresses acting on an elastomer: normal pressure due to the mutual attraction of oppositely charged electrodes and tangential shear ("fringing") due to repulsion of like charges at the electrode edges. These enter via physically simplified boundary conditions that are applied in a fixed reference domain using a nondimensional approach. The method is valid for small to moderate strains and is straightforward to implement in a generic nonlinear elasticity code. We validate the model by directly comparing the simulated equilibrium shapes with the experiment. For circular electrodes which buckle axisymetrically, the shape of the deflection profile is captured. Annular electrodes of different widths produce azimuthal ripples with wavelengths that match our simulations. In this case, it is essential to compute multiple equilibria because the first model solution obtained by the nonlinear solver (Newton's method) is often not the energetically favored state. We address this using a numerical technique known as "deflation." Finally, we observe the large number of different solutions that may be obtained for the case of a long rectangular strip.

Risk assessment of consuming agricultural products irrigated with reclaimed wastewater: An exposure model

NASA Astrophysics Data System (ADS)

van Ginneken, Meike; Oron, Gideon

2000-09-01

This study assesses health risks to consumers due to the use of agricultural products irrigated with reclaimed wastewater. The analysis is based on a definition of an exposure model which takes into account several parameters: (1) the quality of the applied wastewater, (2) the irrigation method, (3) the elapsed times between irrigation, harvest, and product consumption, and (4) the consumers' habits. The exposure model is used for numerical simulation of human consumers' risks using the Monte Carlo simulation method. The results of the numerical simulation show large deviations, probably caused by uncertainty (impreciseness in quality of input data) and variability due to diversity among populations. There is a 10-orders of magnitude difference in the risk of infection between the different exposure scenarios with the same water quality. This variation indicates the need for setting risk-based criteria for wastewater reclamation rather than single water quality guidelines. Extra data are required to decrease uncertainty in the risk assessment. Future research needs to include definition of acceptable risk criteria, more accurate dose-response modeling, information regarding pathogen survival in treated wastewater, additional data related to the passage of pathogens into and in the plants during irrigation, and information regarding the behavior patterns of the community of human consumers.

A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search

NASA Astrophysics Data System (ADS)

Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd

2017-08-01

A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.

A biomolecular detection method based on charge pumping in a nanogap embedded field-effect-transistor biosensor

NASA Astrophysics Data System (ADS)

Kim, Sungho; Ahn, Jae-Hyuk; Park, Tae Jung; Lee, Sang Yup; Choi, Yang-Kyu

2009-06-01

A unique direct electrical detection method of biomolecules, charge pumping, was demonstrated using a nanogap embedded field-effect-transistor (FET). With aid of a charge pumping method, sensitivity can fall below the 1 ng/ml concentration regime in antigen-antibody binding of an avian influenza case. Biomolecules immobilized in the nanogap are mainly responsible for the acute changes of the interface trap density due to modulation of the energy level of the trap. This finding is supported by a numerical simulation. The proposed detection method for biomolecules using a nanogap embedded FET represents a foundation for a chip-based biosensor capable of high sensitivity.

Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods

DOE PAGES

Zou, Ling; Zhao, Haihua; Kim, Seung Jun

2016-11-16

In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to themore » low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.« less

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.

Identification of delamination interface in composite laminates using scattering characteristics of lamb wave: numerical and experimental studies

NASA Astrophysics Data System (ADS)

Singh, Rakesh Kumar; Ramadas, C.; Balachandra Shetty, P.; Satyanarayana, K. G.

2017-04-01

Considering the superior strength properties of polymer based composites over metallic materials, they are being used in primary structures of aircrafts. However, these polymeric materials are much more complex in behaviour due to their structural anisotropy along with existence of different materials unlike in metallic alloys. These pose challenge in flaw detection, residual strength determination and life of a structure with their high susceptibility to impact damage in the form of delaminations/disbonds or cracks. This reduces load-bearing capability and potentially leads to structural failure. With this background, this study presents a method to identify location of delamination interface along thickness of a laminate. Both numerical and experimental studies have been carried out with a view to identify the defect, on propagation, mode conversion and scattering characteristics of fundamental anti-symmetric Lamb mode (Ao) when it passed through a semi-infinite delamination. Further, the reflection and transmission scattering coefficients based on power and amplitude ratios of the scattered waves have been computed. The methodology was applied on numerically simulated delaminations to illustrate the efficacy of the method. Results showed that it could successfully identify delamination interface.

Numerical Simulation of the Layer-Bylayer Destruction of Cylindrical Shells Under Explosive Loading

NASA Astrophysics Data System (ADS)

Abrosimov, N. A.; Novoseltseva, N. A.

2015-09-01

A technique of numerical analysis of the influence of reinforcement structure on the nature of the dynamic response and the process of layer-by-layer destruction of layered fiberglass cylindrical shells under an axisymmetric internal explosive loading is elaborated. The kinematic model of deformation of the laminate package is based on a nonclassical theory of shells. The geometric dependences are based on simple quadratic relations of the nonlinear theory of elasticity. The relationship between the stress and strain tensors are established by using Hooke's law for orthotropic bodies with account of degradation of stiffness characteristics of the multilayer composite due to the local destruction of some its elementary layers. An energetically consistent system of dynamic equations for composite cylindrical shells is obtained by minimizing the functional of total energy of the shell as a three-dimensional body. The numerical method for solving the formulated initial boundary-value problem is based on an explicit variational-difference scheme. Results confirming the reliability of the method used to analyze the influence of reinforcement structure on the character of destruction and the bearing capacity of pulse-loaded cylindrical shells are presented.

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

NASA Astrophysics Data System (ADS)

Luo, Xiao-Ping; Wang, Cun-Hai; Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

2018-06-01

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

A study on the sensitivity of self-powered neutron detectors (SPNDs)

NASA Astrophysics Data System (ADS)

Lee, Wanno; Cho, Gyuseong; Kim, Kwanghyun; Kim, Hee Joon; choi, Yuseon; Park, Moon Chu; Kim, Soongpyung

2001-08-01

Self-powered neutron detectors (SPNDs) are widely used in reactors to monitor neutron flux, while they have several advantages such as small size, and relatively simple electronics required in conjunction with those usages, they have some intrinsic problems of the low level of output current-a slow response time and the rapid change of sensitivity-that make it difficult to use for a long term. Monte Carlo simulation was used to calculate the escape probability as a function of the birth position of emitted beta particle for geometry of rhodium-based SPNDs. A simple numerical method calculated the initial generation rate of beta particles and the change of generation rate due to rhodium burnup. Using results of the simulation and the simple numerical method, the burnup profile of rhodium number density and the neutron sensitivity were calculated as a function of burnup time in reactors. This method was verified by the comparison of this and other papers, and data of YGN3.4 (Young Gwang Nuclear plant 3, 4) about the initial sensitivity. In addition, for improvement of some properties of rhodium-based SPNDs, which are currently used, a modified geometry is proposed. The proposed geometry, which is tube-type, is able to increase the initial sensitivity due to increase of the escape probability. The escape probability was calculated by changing the thickness of the insulator and compared solid-type with tube-type about each insulator thickness. The method used here can be applied to the analysis and design of other types of SPNDs.

Black hole evolution by spectral methods

NASA Astrophysics Data System (ADS)

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

2000-10-01

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

Extension of a hybrid particle-continuum method for a mixture of chemical species

NASA Astrophysics Data System (ADS)

Verhoff, Ashley M.; Boyd, Iain D.

2012-11-01

Due to the physical accuracy and numerical efficiency achieved by analyzing transitional, hypersonic flow fields with hybrid particle-continuum methods, this paper describes a Modular Particle-Continuum (MPC) method and its extension to include multiple chemical species. Considerations that are specific to a hybrid approach for simulating gas mixtures are addressed, including a discussion of the Chapman-Enskog velocity distribution function (VDF) for near-equilibrium flows, and consistent viscosity models for the individual CFD and DSMC modules of the MPC method. Representative results for a hypersonic blunt-body flow are then presented, where the flow field properties, surface properties, and computational performance are compared for simulations employing full CFD, full DSMC, and the MPC method.

The estimation of 3D SAR distributions in the human head from mobile phone compliance testing data for epidemiological studies

NASA Astrophysics Data System (ADS)

Wake, Kanako; Varsier, Nadège; Watanabe, Soichi; Taki, Masao; Wiart, Joe; Mann, Simon; Deltour, Isabelle; Cardis, Elisabeth

2009-10-01

A worldwide epidemiological study called 'INTERPHONE' has been conducted to estimate the hypothetical relationship between brain tumors and mobile phone use. In this study, we proposed a method to estimate 3D distribution of the specific absorption rate (SAR) in the human head due to mobile phone use to provide the exposure gradient for epidemiological studies. 3D SAR distributions due to exposure to an electromagnetic field from mobile phones are estimated from mobile phone compliance testing data for actual devices. The data for compliance testing are measured only on the surface in the region near the device and in a small 3D region around the maximum on the surface in a homogeneous phantom with a specific shape. The method includes an interpolation/extrapolation and a head shape conversion. With the interpolation/extrapolation, SAR distributions in the whole head are estimated from the limited measured data. 3D SAR distributions in the numerical head models, where the tumor location is identified in the epidemiological studies, are obtained from measured SAR data with the head shape conversion by projection. Validation of the proposed method was performed experimentally and numerically. It was confirmed that the proposed method provided good estimation of 3D SAR distribution in the head, especially in the brain, which is the tissue of major interest in epidemiological studies. We conclude that it is possible to estimate 3D SAR distributions in a realistic head model from the data obtained by compliance testing measurements to provide a measure for the exposure gradient in specific locations of the brain for the purpose of exposure assessment in epidemiological studies. The proposed method has been used in several studies in the INTERPHONE.

The estimation of 3D SAR distributions in the human head from mobile phone compliance testing data for epidemiological studies.

PubMed

Wake, Kanako; Varsier, Nadège; Watanabe, Soichi; Taki, Masao; Wiart, Joe; Mann, Simon; Deltour, Isabelle; Cardis, Elisabeth

2009-10-07

A worldwide epidemiological study called 'INTERPHONE' has been conducted to estimate the hypothetical relationship between brain tumors and mobile phone use. In this study, we proposed a method to estimate 3D distribution of the specific absorption rate (SAR) in the human head due to mobile phone use to provide the exposure gradient for epidemiological studies. 3D SAR distributions due to exposure to an electromagnetic field from mobile phones are estimated from mobile phone compliance testing data for actual devices. The data for compliance testing are measured only on the surface in the region near the device and in a small 3D region around the maximum on the surface in a homogeneous phantom with a specific shape. The method includes an interpolation/extrapolation and a head shape conversion. With the interpolation/extrapolation, SAR distributions in the whole head are estimated from the limited measured data. 3D SAR distributions in the numerical head models, where the tumor location is identified in the epidemiological studies, are obtained from measured SAR data with the head shape conversion by projection. Validation of the proposed method was performed experimentally and numerically. It was confirmed that the proposed method provided good estimation of 3D SAR distribution in the head, especially in the brain, which is the tissue of major interest in epidemiological studies. We conclude that it is possible to estimate 3D SAR distributions in a realistic head model from the data obtained by compliance testing measurements to provide a measure for the exposure gradient in specific locations of the brain for the purpose of exposure assessment in epidemiological studies. The proposed method has been used in several studies in the INTERPHONE.

Numerical modeling and optimization of the Iguassu gas centrifuge

NASA Astrophysics Data System (ADS)

Bogovalov, S. V.; Borman, V. D.; Borisevich, V. D.; Tronin, V. N.; Tronin, I. V.

2017-07-01

The full procedure of the numerical calculation of the optimized parameters of the Iguassu gas centrifuge (GC) is under discussion. The procedure consists of a few steps. On the first step the problem of a hydrodynamical flow of the gas in the rotating rotor of the GC is solved numerically. On the second step the problem of diffusion of the binary mixture of isotopes is solved. The separation power of the gas centrifuge is calculated after that. On the last step the time consuming procedure of optimization of the GC is performed providing us the maximum of the separation power. The optimization is based on the BOBYQA method exploring the results of numerical simulations of the hydrodynamics and diffusion of the mixture of isotopes. Fast convergence of calculations is achieved due to exploring of a direct solver at the solution of the hydrodynamical and diffusion parts of the problem. Optimized separative power and optimal internal parameters of the Iguassu GC with 1 m rotor were calculated using the developed approach. Optimization procedure converges in 45 iterations taking 811 minutes.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Improved computational fluid dynamic simulations of blood flow in membrane oxygenators from X-ray imaging.

PubMed

Jones, Cameron C; McDonough, James M; Capasso, Patrizio; Wang, Dongfang; Rosenstein, Kyle S; Zwischenberger, Joseph B

2013-10-01

Computational fluid dynamics (CFD) is a useful tool in characterizing artificial lung designs by providing predictions of device performance through analyses of pressure distribution, perfusion dynamics, and gas transport properties. Validation of numerical results in membrane oxygenators has been predominantly based on experimental pressure measurements with little emphasis placed on confirmation of the velocity fields due to opacity of the fiber membrane and limitations of optical velocimetric methods. Biplane X-ray digital subtraction angiography was used to visualize flow of a blood analogue through a commercial membrane oxygenator at 1-4.5 L/min. Permeability and inertial coefficients of the Ergun equation were experimentally determined to be 180 and 2.4, respectively. Numerical simulations treating the fiber bundle as a single momentum sink according to the Ergun equation accurately predicted pressure losses across the fiber membrane, but significantly underestimated velocity magnitudes in the fiber bundle. A scaling constant was incorporated into the numerical porosity and reduced the average difference between experimental and numerical values in the porous media regions from 44 ± 4% to 6 ± 5%.

Study of the long-time dynamics of a viscous vortex sheet with a fully adaptive nonstiff method

NASA Astrophysics Data System (ADS)

Ceniceros, Hector D.; Roma, Alexandre M.

2004-12-01

A numerical investigation of the long-time dynamics of two immiscible two-dimensional fluids shearing past one another is presented. The fluids are incompressible and the interface between the bulk phases is subjected to surface tension. The simple case of density and viscosity matched fluids is considered. The two-dimensional Navier-Stokes equations are solved numerically with a fully adaptive nonstiff strategy based on the immersed boundary method. Dynamically adaptive mesh refinements are used to cover at all times the separately tracked fluid interface at the finest grid level. In addition, by combining adaptive front tracking, in the form of continuous interface marker equidistribution, with a predictor-corrector discretization an efficient method is introduced to successfully treat the well-known numerical difficulties associated with surface tension. The resulting numerical method can be used to compute stably and with high resolution the flow for wide-ranging Weber numbers but this study focuses on the computationally challenging cases for which elongated fingering and interface roll-up are observed. To assess the importance of the viscous and vortical effects in the interfacial dynamics the full viscous flow simulations are compared with inviscid counterparts computed with a state-of-the-art boundary integral method. In the examined cases of roll-up, it is found that in contrast to the inviscid flow in which the interface undergoes a topological reconfiguration, the viscous interface remarkably escapes self-intersection and rich long-time dynamics due to separation, transport, and diffusion of vorticity is observed. An even more striking motion occurs at an intermediate Weber number for which elongated interpenetrating fingers of fluid develop. In this case, it is found that the Kelvin-Helmholtz instability weakens due to shedding of vorticity and unlike the inviscid counterpart in which there is indefinite finger growth the viscous interface is pulled back by surface tension. As the interface recedes, thin necks connecting pockets of fluid with the rest of the fingers form. Narrow jets are observed at the necking regions but the vorticity there ultimately appears to be insufficient to drain all the fluid and cause reconnection. However, at another point, two disparate portions of the interface come in close proximity as the interface continues to contract. Large curvature points and an intense concentration of vorticity are observed in this region and then the motion is abruptly terminated by the collapse of the interface.

On the simulation of indistinguishable fermions in the many-body Wigner formalism

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

Sellier, J.M., E-mail: jeanmichel.sellier@gmail.com; Dimov, I.

2015-01-01

The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature.more » In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.« less

Numerical simulation of systems of shear bands in ductile metal with inclusions

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

Plohr, JeeYeon N., E-mail: jplohr@lanl.gov; Plohr, Bradley J.

2016-02-15

We develop a method for numerical simulations of high strain-rate loading of mesoscale samples of ductile metal with inclusions. Because of its small-scale inhomogeneity, the composite material is prone to localized shear deformation (adiabatic shear bands). This method employs the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. 127–139, 1992] to ensure that the micro mechanical behavior of the metal and inclusions is reflected properly in the behavior of the composite at the mesoscale. To find the effective plastic strain rate when shear bands are present, we extend and apply the analytic and numerical analysismore » of shear bands of Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31–41, 1996]. Our tests of the method focus on the stress/strain response in uniaxial-strain flow, both compressive and tensile, of depleted uranium metal containing silicon carbide inclusions. We use the Preston-Tonks-Wallace viscoplasticity model [J. Appl. Phys., vol. 93, pp. 211–220, 2003], which applies to the high strain-rate regime of an isotropic viscoplastic solid. In results, we verify the elevated temperature and thermal softening at shear bands in our simulations of pure DU and DU/SiC composites. We also note that in composites, due the asymmetry caused by the inclusions, shear band form at different times in different subcells. In particular, in the subcells near inclusions, shear band form much earlier than they do in pure DU.« less

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

NASA Technical Reports Server (NTRS)

Clark, William S.; Hall, Kenneth C.

1994-01-01

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

Fast Numerical Simulation of Focused Ultrasound Treatments During Respiratory Motion With Discontinuous Motion Boundaries.

PubMed

Schwenke, Michael; Georgii, Joachim; Preusser, Tobias

2017-07-01

Focused ultrasound (FUS) is rapidly gaining clinical acceptance for several target tissues in the human body. Yet, treating liver targets is not clinically applied due to a high complexity of the procedure (noninvasiveness, target motion, complex anatomy, blood cooling effects, shielding by ribs, and limited image-based monitoring). To reduce the complexity, numerical FUS simulations can be utilized for both treatment planning and execution. These use-cases demand highly accurate and computationally efficient simulations. We propose a numerical method for the simulation of abdominal FUS treatments during respiratory motion of the organs and target. Especially, a novel approach is proposed to simulate the heating during motion by solving Pennes' bioheat equation in a computational reference space, i.e., the equation is mathematically transformed to the reference. The approach allows for motion discontinuities, e.g., the sliding of the liver along the abdominal wall. Implementing the solver completely on the graphics processing unit and combining it with an atlas-based ultrasound simulation approach yields a simulation performance faster than real time (less than 50-s computing time for 100 s of treatment time) on a modern off-the-shelf laptop. The simulation method is incorporated into a treatment planning demonstration application that allows to simulate real patient cases including respiratory motion. The high performance of the presented simulation method opens the door to clinical applications. The methods bear the potential to enable the application of FUS for moving organs.

A penalty-based nodal discontinuous Galerkin method for spontaneous rupture dynamics

NASA Astrophysics Data System (ADS)

Ye, R.; De Hoop, M. V.; Kumar, K.

2017-12-01

Numerical simulation of the dynamic rupture processes with slip is critical to understand the earthquake source process and the generation of ground motions. However, it can be challenging due to the nonlinear friction laws interacting with seismicity, coupled with the discontinuous boundary conditions across the rupture plane. In practice, the inhomogeneities in topography, fault geometry, elastic parameters and permiability add extra complexity. We develop a nodal discontinuous Galerkin method to simulate seismic wave phenomenon with slipping boundary conditions, including the fluid-solid boundaries and ruptures. By introducing a novel penalty flux, we avoid solving Riemann problems on interfaces, which makes our method capable for general anisotropic and poro-elastic materials. Based on unstructured tetrahedral meshes in 3D, the code can capture various geometries in geological model, and use polynomial expansion to achieve high-order accuracy. We consider the rate and state friction law, in the spontaneous rupture dynamics, as part of a nonlinear transmitting boundary condition, which is weakly enforced across the fault surface as numerical flux. An iterative coupling scheme is developed based on implicit time stepping, containing a constrained optimization process that accounts for the nonlinear part. To validate the method, we proof the convergence of the coupled system with error estimates. We test our algorithm on a well-established numerical example (TPV102) of the SCEC/USGS Spontaneous Rupture Code Verification Project, and benchmark with the simulation of PyLith and SPECFEM3D with agreeable results.

Numerical simulation of systems of shear bands in ductile metal with inclusions

NASA Astrophysics Data System (ADS)

Plohr, JeeYeon N.; Plohr, Bradley J.

2016-02-01

We develop a method for numerical simulations of high strain-rate loading of mesoscale samples of ductile metal with inclusions. Because of its small-scale inhomogeneity, the composite material is prone to localized shear deformation (adiabatic shear bands). This method employs the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. 127-139, 1992] to ensure that the micro mechanical behavior of the metal and inclusions is reflected properly in the behavior of the composite at the mesoscale. To find the effective plastic strain rate when shear bands are present, we extend and apply the analytic and numerical analysis of shear bands of Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31-41, 1996]. Our tests of the method focus on the stress/strain response in uniaxial-strain flow, both compressive and tensile, of depleted uranium metal containing silicon carbide inclusions. We use the Preston-Tonks-Wallace viscoplasticity model [J. Appl. Phys., vol. 93, pp. 211-220, 2003], which applies to the high strain-rate regime of an isotropic viscoplastic solid. In results, we verify the elevated temperature and thermal softening at shear bands in our simulations of pure DU and DU/SiC composites. We also note that in composites, due the asymmetry caused by the inclusions, shear band form at different times in different subcells. In particular, in the subcells near inclusions, shear band form much earlier than they do in pure DU.

Breast cancer detection using interferometric MUSIC: experimental and numerical assessment.

PubMed

Ruvio, Giuseppe; Solimene, Raffaele; Cuccaro, Antonio; Gaetano, Domenico; Browne, Jacinta E; Ammann, Max J

2014-10-01

In microwave breast cancer detection, it is often beneficial to arrange sensors in close proximity to the breast. The resultant coupling generally changes the antenna response. As an a priori characterization of the radio frequency system becomes difficult, this can lead to severe degradation of the detection efficacy. The purpose of this paper is to demonstrate the advantages of adopting an interferometric multiple signal classification (I-MUSIC) approach due to its limited dependence from a priori information on the antenna. The performance of I-MUSIC detection was measured in terms of signal-to-clutter ratio (SCR), signal-to-mean ratio (SMR), and spatial displacement (SD) and compared to other common linear noncoherent imaging methods, such as migration and the standard wideband MUSIC (WB-MUSIC) which also works when the antenna is not accounted for. The data were acquired by scanning a synthetic oil-in-gelatin phantom that mimics the dielectric properties of breast tissues across the spectrum 1-3 GHz using a proprietary breast microwave multi-monostatic radar system. The phantom is a multilayer structure that includes skin, adipose, fibroconnective, fibroglandular, and tumor tissue with an adipose component accounting for 60% of the whole structure. The detected tumor has a diameter of 5 mm and is inserted inside a fibroglandular region with a permittivity contrast εr-tumor/εr-fibroglandular < 1.5 over the operating band. Three datasets were recorded corresponding to three antennas with different coupling mechanisms. This was done to assess the independence of the I-MUSIC method from antenna characterizations. The datasets were processed by using I-MUSIC, noncoherent migration, and wideband MUSIC under equivalent conditions (i.e., operative bandwidth, frequency samples, and scanning positions). SCR, SMR, and SD figures were measured from all reconstructed images. In order to benchmark experimental results, numerical simulations of equivalent scenarios were carried out by using CST Microwave Studio. The three numerical datasets were then processed following the same procedure that was designed for the experimental case. Detection results are presented for both experimental and numerical phantoms, and higher performance of the I-MUSIC method in comparison with the WB-MUSIC and noncoherent migration is achieved. This finding is confirmed for the three different antennas in this study. Although a delocalization effect occurs, experimental datasets show that the signal-to-clutter ratio and the signal-to-mean performance with the I-MUSIC are at least 5 and 2.3 times better than the other methods, respectively. The numerical datasets calculated on an equivalent phantom for cross-testing confirm the improved performance of the I-MUSIC in terms of SCR and SMR. In numerical simulations, the delocalization effect is dramatically reduced up to an SD value of 1.61 achieved with the I-MUSIC in combination with the antipodal Vivaldi antenna. This shows that mechanical uncertainties are the main reason for the delocalization effect in the measurements. Experimental results show that the I-MUSIC generates images with signal-to-clutter levels higher than 5.46 dB across all working conditions and it reaches 7.84 dB in combination with the antipodal Vivaldi antenna. Numerical simulations confirm this trend and due to ideal mechanical conditions return a signal-to-clutter level higher than 7.61 dB. The I-MUSIC largely outperforms the methods under comparison and is able to detect a 5-mm tumor with a permittivity contrast of 1.5.

Space Flows and Disturbances Due to Bodies in Motion Through the Magnetoplasma

NASA Astrophysics Data System (ADS)

Ponomarjov, Maxim G.

2000-10-01

In this paper a method is concerned which makes it possible to describe numerically and analytically the most famous structures in the non-equilibrium ionosphere, such as stratified and yacht sail like structures, flute jets, wakes and clouds. These problems are of practical interest in space sciences, astrophysics and in turbulence theory, and also of fundamental interest since they enable one to concentrate on the effects of the ambient electric and magnetic fields. Disturbances of charged particle flows due to the ambient flow interactions with bodies are simulated with taking into account the ambient magnetic field effect. The effects of interactions between solid surfaces and the flows was simulated by making use of an original image method. The flow disturbances were described by the Boltzmann equation. In the case of the ambient homogeneous magnetic field the Boltzmann equation is solved analytically. The case of diffuse reflection of particles by surface is considered in detail. The disturbances of charged particle concentration are calculated in 3D space. The contours of constant particle concentration obtained from numerical simulations illustrate the dynamics of developing stratifications and flute structures in charged particle jets and wakes under the ambient magnetic field effect. The basic goal of this paper is to present the method and to demonstate its possibility for simulations of turbulence, plasma jets, wakes and clouds in the ionosphere and Space when effects of electric and magnetic fields are taken into account.

Numerical simulation and validation of helicopter blade-vortex interaction using coupled CFD/CSD and three levels of aerodynamic modeling

NASA Astrophysics Data System (ADS)

Amiraux, Mathieu

Rotorcraft Blade-Vortex Interaction (BVI) remains one of the most challenging flow phenomenon to simulate numerically. Over the past decade, the HART-II rotor test and its extensive experimental dataset has been a major database for validation of CFD codes. Its strong BVI signature, with high levels of intrusive noise and vibrations, makes it a difficult test for computational methods. The main challenge is to accurately capture and preserve the vortices which interact with the rotor, while predicting correct blade deformations and loading. This doctoral dissertation presents the application of a coupled CFD/CSD methodology to the problem of helicopter BVI and compares three levels of fidelity for aerodynamic modeling: a hybrid lifting-line/free-wake (wake coupling) method, with modified compressible unsteady model; a hybrid URANS/free-wake method; and a URANS-based wake capturing method, using multiple overset meshes to capture the entire flow field. To further increase numerical correlation, three helicopter fuselage models are implemented in the framework. The first is a high resolution 3D GPU panel code; the second is an immersed boundary based method, with 3D elliptic grid adaption; the last one uses a body-fitted, curvilinear fuselage mesh. The main contribution of this work is the implementation and systematic comparison of multiple numerical methods to perform BVI modeling. The trade-offs between solution accuracy and computational cost are highlighted for the different approaches. Various improvements have been made to each code to enhance physical fidelity, while advanced technologies, such as GPU computing, have been employed to increase efficiency. The resulting numerical setup covers all aspects of the simulation creating a truly multi-fidelity and multi-physics framework. Overall, the wake capturing approach showed the best BVI phasing correlation and good blade deflection predictions, with slightly under-predicted aerodynamic loading magnitudes. However, it proved to be much more expensive than the other two methods. Wake coupling with RANS solver had very good loading magnitude predictions, and therefore good acoustic intensities, with acceptable computational cost. The lifting-line based technique often had over-predicted aerodynamic levels, due to the degree of empiricism of the model, but its very short run-times, thanks to GPU technology, makes it a very attractive approach.

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

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

Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain

In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strongmore » laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to increase the local character in phase-space of the numerical scheme, by considering multiscale reconstruction with more compact support and by replacing the semi-Lagrangian method with more local - in space - numerical scheme as compact finite difference schemes, discontinuous-Galerkin method or finite element residual schemes which are well suited for parallel domain decomposition techniques.« less

Spherical harmonic analysis of a harmonic function given on a spheroid

NASA Astrophysics Data System (ADS)

Claessens, S. J.

2016-07-01

A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

Phase-Shifted Based Numerical Method for Modeling Frequency-Dependent Effects on Seismic Reflections

NASA Astrophysics Data System (ADS)

Chen, Xuehua; Qi, Yingkai; He, Xilei; He, Zhenhua; Chen, Hui

2016-08-01

The significant velocity dispersion and attenuation has often been observed when seismic waves propagate in fluid-saturated porous rocks. Both the magnitude and variation features of the velocity dispersion and attenuation are frequency-dependent and related closely to the physical properties of the fluid-saturated porous rocks. To explore the effects of frequency-dependent dispersion and attenuation on the seismic responses, in this work, we present a numerical method for seismic data modeling based on the diffusive and viscous wave equation (DVWE), which introduces the poroelastic theory and takes into account diffusive and viscous attenuation in diffusive-viscous-theory. We derive a phase-shift wave extrapolation algorithm in frequencywavenumber domain for implementing the DVWE-based simulation method that can handle the simultaneous lateral variations in velocity, diffusive coefficient and viscosity. Then, we design a distributary channels model in which a hydrocarbon-saturated sand reservoir is embedded in one of the channels. Next, we calculated the synthetic seismic data to analytically and comparatively illustrate the seismic frequency-dependent behaviors related to the hydrocarbon-saturated reservoir, by employing DVWE-based and conventional acoustic wave equation (AWE) based method, respectively. The results of the synthetic seismic data delineate the intrinsic energy loss, phase delay, lower instantaneous dominant frequency and narrower bandwidth due to the frequency-dependent dispersion and attenuation when seismic wave travels through the hydrocarbon-saturated reservoir. The numerical modeling method is expected to contribute to improve the understanding of the features and mechanism of the seismic frequency-dependent effects resulted from the hydrocarbon-saturated porous rocks.

Prediction of the interaction between a simple moving vehicle and an infinite periodically supported rail - Green's functions approach

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2010-09-01

This paper herein describes the interaction between a simple moving vehicle and an infinite periodically supported rail, in order to signalise the basic features of the vehicle/track vibration behaviour in general, and wheel/rail vibration, in particular. The rail is modelled as an infinite Timoshenko beam resting on semi-sleepers via three-directional rail pads and ballast. The time-domain analysis was performed applying Green's matrix of the track method. This method allows taking into account the nonlinearities of the wheel/rail contact and the Doppler effect. The numerical analysis is dedicated to the wheel/rail response due to two types of excitation: the steady-state interaction and rail irregularities. The study points out to certain aspects regarding the parametric resonance, the amplitude-modulated vibration due to corrugation and the Doppler effect.

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential.

PubMed

Pérez, Alejandro; von Lilienfeld, O Anatole

2011-08-09

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.

Acceleration and Transport of Particles in Collisionless Plasmas: Wakes due to the Interaction with Moving Bodies

NASA Astrophysics Data System (ADS)

Ponomarjov, Maxim G.

2001-06-01

A method is developed that allows the numerical and analytical description of the effects of ambient magnetic field on the time-dependent 3D structures of space plasma flows due to bodies in motion through a plasma. Some of these effects have been observed in space and ionosphere as stratified, flute and yacht sail like structures of plasma disturbances, jets, wakes and clouds. The method can be used for the simulations of Solar Wind flow taking into account the magnetic field effects and the interactions with the Interstellar Medium. These problems are of practical interest in fluid mechanics, space sciences, astrophysics, in turbulence theory. They also have some fundamental interest in their own right, as they enable one to concentrate on the effects of the ambient electric and magnetic fields.

The Reduced Basis Method in Geosciences: Practical examples for numerical forward simulations

NASA Astrophysics Data System (ADS)

Degen, D.; Veroy, K.; Wellmann, F.

2017-12-01

Due to the highly heterogeneous character of the earth's subsurface, the complex coupling of thermal, hydrological, mechanical, and chemical processes, and the limited accessibility we have to face high-dimensional problems associated with high uncertainties in geosciences. Performing the obviously necessary uncertainty quantifications with a reasonable number of parameters is often not possible due to the high-dimensional character of the problem. Therefore, we are presenting the reduced basis (RB) method, being a model order reduction (MOR) technique, that constructs low-order approximations to, for instance, the finite element (FE) space. We use the RB method to address this computationally challenging simulations because this method significantly reduces the degrees of freedom. The RB method is decomposed into an offline and online stage, allowing to make the expensive pre-computations beforehand to get real-time results during field campaigns. Generally, the RB approach is most beneficial in the many-query and real-time context.We will illustrate the advantages of the RB method for the field of geosciences through two examples of numerical forward simulations.The first example is a geothermal conduction problem demonstrating the implementation of the RB method for a steady-state case. The second examples, a Darcy flow problem, shows the benefits for transient scenarios. In both cases, a quality evaluation of the approximations is given. Additionally, the runtimes for both the FE and the RB simulations are compared. We will emphasize the advantages of this method for repetitive simulations by showing the speed-up for the RB solution in contrast to the FE solution. Finally, we will demonstrate how the used implementation is usable in high-performance computing (HPC) infrastructures and evaluate its performance for such infrastructures. Hence, we will especially point out its scalability, yielding in an optimal usage on HPC infrastructures and normal working stations.

Couette flow through a porous medium with heat and mass transfer in the presence of tranverse magnetic field

NASA Astrophysics Data System (ADS)

Lawanya, T.; Vidhya, M.; Govindarajan, A.

2018-04-01

This present paper deals with the investigation of couette flow of a viscous electrically conducting incompressible fluid three dimensionally through a porous medium in presence of transverse magnetic field. Approximate Solution of equations of motion and energy equations are derived using series solution method. Hartmann number, Schmidt number and Grashoff number (or) modified Grashoff number for mass transfer on the velocity and temperature distribution are numerically discussed and shown graphically. The Nusselt number and skin friction coefficients atthe plate are derived and their numerical values are shown graphically. It is seen that in the main flow direction the velocity profiles decreases due to either an increase in Schmidt number (Or) Hartmann number.

Simulating Damage Due to a Lightning Strike Event: Effects of Temperature Dependent Properties on Interlaminar Damage

NASA Technical Reports Server (NTRS)

Ghezeljeh, Paria Naghipour; Pineda, Evan Jorge

2014-01-01

A multidirectional, carbon fiber-epoxy, composite panel is subjected to a simulated lightning strike, within a finite element method framework, and the effect of material properties on the failure (delamination) response is investigated through a detailed numerical study. The numerical model of the composite panel consists of individual homogenized plies with user-defined, cohesive interface elements between them. Lightning strikes are simulated as an assumed combination of excessive heat and high pressure loadings. It is observed that the initiation and propagation of lightning-induced delamination is a significant function of the temperature dependency of interfacial fracture toughness. This dependency must be defined properly in order to achieve reliable predictions of the present lightning-induced delamination in the composite panel.

MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect

NASA Astrophysics Data System (ADS)

Zokri, S. M.; Arifin, N. S.; Salleh, M. Z.; Kasim, A. R. M.; Mohammad, N. F.; Yusoff, W. N. S. W.

2017-09-01

This study investigates the influence of viscous dissipation on magnetohydrodynamic (MHD) flow of Jeffrey nanofluid over a stretching sheet with convective boundary conditions. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by utilizing the similarity transformation variables. The Runge-Kutta Fehlberg method is used to solve the problem numerically. The numerical solutions obtained are presented graphically for several dimensionless parameters such as Brownian motion, Lewis number and Eckert number on the specified temperature and concentration profiles. It is noted that the temperature profile is accelerated due to increasing values of Brownian motion parameter and Eckert number. In contrast, both the Brownian motion parameter and Lewis number have caused the deceleration in the concentration profiles.

A computer program for predicting nonlinear uniaxial material responses using viscoplastic models

NASA Technical Reports Server (NTRS)

Chang, T. Y.; Thompson, R. L.

1984-01-01

A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.

Theoretical model of a polarization diffractive elements for the light beams conversion holographic formation in PDLCs

NASA Astrophysics Data System (ADS)

Sharangovich, Sergey N.; Semkin, Artem O.

2017-12-01

In this work a theoretical model of the holographic formation of the polarization diffractive optical elements for the transformation of Gaussian light beams into Bessel-like ones in polymer-dispersed liquid crystals (PDLC) is developed. The model is based on solving the equations of photo-induced Fredericks transition processes for polarization diffractive elements formation by orthogonally polarized light beams with inhomogeneous amplitude and phase profiles. The results of numerical simulation of the material's dielectric tensor changing due to the structure's formation process are presented for various recording beams' polarization states. Based on the results of numerical simulation, the ability to form the diffractive optical elements for light beams transformation by the polarization holography methods is shown.

solveME: fast and reliable solution of nonlinear ME models.

PubMed

Yang, Laurence; Ma, Ding; Ebrahim, Ali; Lloyd, Colton J; Saunders, Michael A; Palsson, Bernhard O

2016-09-22

Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints. Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints. Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.

Numerical modelling of methane oxidation efficiency and coupled water-gas-heat reactive transfer in a sloping landfill cover.

PubMed

Feng, S; Ng, C W W; Leung, A K; Liu, H W

2017-10-01

Microbial aerobic methane oxidation in unsaturated landfill cover involves coupled water, gas and heat reactive transfer. The coupled process is complex and its influence on methane oxidation efficiency is not clear, especially in steep covers where spatial variations of water, gas and heat are significant. In this study, two-dimensional finite element numerical simulations were carried out to evaluate the performance of unsaturated sloping cover. The numerical model was calibrated using a set of flume model test data, and was then subsequently used for parametric study. A new method that considers transient changes of methane concentration during the estimation of the methane oxidation efficiency was proposed and compared against existing methods. It was found that a steeper cover had a lower oxidation efficiency due to enhanced downslope water flow, during which desaturation of soil promoted gas transport and hence landfill gas emission. This effect was magnified as the cover angle and landfill gas generation rate at the bottom of the cover increased. Assuming the steady-state methane concentration in a cover would result in a non-conservative overestimation of oxidation efficiency, especially when a steep cover was subjected to rainfall infiltration. By considering the transient methane concentration, the newly-modified method can give a more accurate oxidation efficiency. Copyright © 2017. Published by Elsevier Ltd.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

An approach to solve replacement problems under intuitionistic fuzzy nature

NASA Astrophysics Data System (ADS)

Balaganesan, M.; Ganesan, K.

2018-04-01

Due to impreciseness to solve the day to day problems the researchers use fuzzy sets in their discussions of the replacement problems. The aim of this paper is to solve the replacement theory problems with triangular intuitionistic fuzzy numbers. An effective methodology based on fuzziness index and location index is proposed to determine the optimal solution of the replacement problem. A numerical example is illustrated to validate the proposed method.

Numerical investigation of optimal layout of rockbolts for ground structures

NASA Astrophysics Data System (ADS)

Kato, Junji; Ishi, Keiichiro; Terada, Kenjiro; Kyoya, Takashi

Due to difficulty to obtain reliable ground data, layout of rockbolts is determined entirely in a classical way assuming an isotropic rock stress condition. The present study assumes anisotropic stress condition and optimizes layout of rockbolts in order to maximize the stiffness of unstable ground of tunnels and slopes by applying multiphase layout optimization. It was verified that this method has a certain possibility to improve the stiffness of unstable ground.

Numerical simulation of tornado wind loading on structures

NASA Technical Reports Server (NTRS)

Maiden, D. E.

1976-01-01

A numerical simulation of a tornado interacting with a building was undertaken in order to compare the pressures due to a rotational unsteady wind with that due to steady straight winds used in design of nuclear facilities. The numerical simulations were performed on a two-dimensional compressible hydrodynamics code. Calculated pressure profiles for a typical building were then subjected to a tornado wind field and the results were compared with current quasisteady design calculations. The analysis indicates that current design practices are conservative.

An architecture for efficient gravitational wave parameter estimation with multimodal linear surrogate models

NASA Astrophysics Data System (ADS)

O'Shaughnessy, Richard; Blackman, Jonathan; Field, Scott E.

2017-07-01

The recent direct observation of gravitational waves has further emphasized the desire for fast, low-cost, and accurate methods to infer the parameters of gravitational wave sources. Due to expense in waveform generation and data handling, the cost of evaluating the likelihood function limits the computational performance of these calculations. Building on recently developed surrogate models and a novel parameter estimation pipeline, we show how to quickly generate the likelihood function as an analytic, closed-form expression. Using a straightforward variant of a production-scale parameter estimation code, we demonstrate our method using surrogate models of effective-one-body and numerical relativity waveforms. Our study is the first time these models have been used for parameter estimation and one of the first ever parameter estimation calculations with multi-modal numerical relativity waveforms, which include all \\ell ≤slant 4 modes. Our grid-free method enables rapid parameter estimation for any waveform with a suitable reduced-order model. The methods described in this paper may also find use in other data analysis studies, such as vetting coincident events or the computation of the coalescing-compact-binary detection statistic.

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Numerical Simulation of Response Characteristics of Audio-magnetotelluric for Gas Hydrate in the Qilian Mountain Permafrost, China

NASA Astrophysics Data System (ADS)

Xiao, Kun; Zou, Changchun; Yu, Changqing; Pi, Jinyun

2015-10-01

Audio-magnetotelluric (AMT) method is a kind of frequency-domain sounding technique, which can be applied to gas hydrate prospecting and assessments in the permafrost region due to its high frequency band. Based on the geological conditions of gas hydrate reservoir in the Qilian Mountain permafrost, by establishing high-resistance abnormal model for gas hydrate and carrying out numerical simulation using finite element method (FEM) and nonlinear conjugate gradient (NLCG) method, this paper analyzed the application range of AMT method and the best acquisition parameters setting scheme. When porosity of gas hydrate reservoir is less than 5%, gas hydrate saturation is greater than 70%, occurrence scale is less than 50 m, or bury depth is greater than 500 m, AMT technique cannot identify and delineate the favorable gas hydrate reservoir. Survey line should be more than twice the length of probable occurrence scale, while tripling the length will make the best result. The number of stations should be no less than 6, and 11 stations are optimal. At the high frequency section (10˜1000 Hz), there should be no less than 3 frequency points, 4 being the best number.

Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory

NASA Astrophysics Data System (ADS)

Richter, Martin; Fingerhut, Benjamin P.

2017-06-01

The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

Numerical Modeling of 3D Seismic Wave Propagation around Yogyakarta, the Southern Part of Central Java, Indonesia, Using Spectral-Element Method on MPI-GPU Cluster

NASA Astrophysics Data System (ADS)

Sudarmaji; Rudianto, Indra; Eka Nurcahya, Budi

2018-04-01

A strong tectonic earthquake with a magnitude of 5.9 Richter scale has been occurred in Yogyakarta and Central Java on May 26, 2006. The earthquake has caused severe damage in Yogyakarta and the southern part of Central Java, Indonesia. The understanding of seismic response of earthquake among ground shaking and the level of building damage is important. We present numerical modeling of 3D seismic wave propagation around Yogyakarta and the southern part of Central Java using spectral-element method on MPI-GPU (Graphics Processing Unit) computer cluster to observe its seismic response due to the earthquake. The homogeneous 3D realistic model is generated with detailed topography surface. The influences of free surface topography and layer discontinuity of the 3D model among the seismic response are observed. The seismic wave field is discretized using spectral-element method. The spectral-element method is solved on a mesh of hexahedral elements that is adapted to the free surface topography and the internal discontinuity of the model. To increase the data processing capabilities, the simulation is performed on a GPU cluster with implementation of MPI (Message Passing Interface).

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.

M-Adapting Low Order Mimetic Finite Differences for Dielectric Interface Problems

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

McGregor, Duncan A.; Gyrya, Vitaliy; Manzini, Gianmarco

2016-03-07

We consider a problem of reducing numerical dispersion for electromagnetic wave in the domain with two materials separated by a at interface in 2D with a factor of two di erence in wave speed. The computational mesh in the homogeneous parts of the domain away from the interface consists of square elements. Here the method construction is based on m-adaptation construction in homogeneous domain that leads to fourth-order numerical dispersion (vs. second order in non-optimized method). The size of the elements in two domains also di ers by a factor of two, so as to preserve the same value ofmore » Courant number in each. Near the interface where two meshes merge the mesh with larger elements consists of degenerate pentagons. We demonstrate that prior to m-adaptation the accuracy of the method falls from second to rst due to breaking of symmetry in the mesh. Next we develop m-adaptation framework for the interface region and devise an optimization criteria. We prove that for the interface problem m-adaptation cannot produce increase in method accuracy. This is in contrast to homogeneous medium where m-adaptation can increase accuracy by two orders.« less

Rapid tomographic reconstruction based on machine learning for time-resolved combustion diagnostics

NASA Astrophysics Data System (ADS)

Yu, Tao; Cai, Weiwei; Liu, Yingzheng

2018-04-01

Optical tomography has attracted surged research efforts recently due to the progress in both the imaging concepts and the sensor and laser technologies. The high spatial and temporal resolutions achievable by these methods provide unprecedented opportunity for diagnosis of complicated turbulent combustion. However, due to the high data throughput and the inefficiency of the prevailing iterative methods, the tomographic reconstructions which are typically conducted off-line are computationally formidable. In this work, we propose an efficient inversion method based on a machine learning algorithm, which can extract useful information from the previous reconstructions and build efficient neural networks to serve as a surrogate model to rapidly predict the reconstructions. Extreme learning machine is cited here as an example for demonstrative purpose simply due to its ease of implementation, fast learning speed, and good generalization performance. Extensive numerical studies were performed, and the results show that the new method can dramatically reduce the computational time compared with the classical iterative methods. This technique is expected to be an alternative to existing methods when sufficient training data are available. Although this work is discussed under the context of tomographic absorption spectroscopy, we expect it to be useful also to other high speed tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence which have been demonstrated for combustion diagnostics.

Rapid tomographic reconstruction based on machine learning for time-resolved combustion diagnostics.

PubMed

Yu, Tao; Cai, Weiwei; Liu, Yingzheng

2018-04-01

Optical tomography has attracted surged research efforts recently due to the progress in both the imaging concepts and the sensor and laser technologies. The high spatial and temporal resolutions achievable by these methods provide unprecedented opportunity for diagnosis of complicated turbulent combustion. However, due to the high data throughput and the inefficiency of the prevailing iterative methods, the tomographic reconstructions which are typically conducted off-line are computationally formidable. In this work, we propose an efficient inversion method based on a machine learning algorithm, which can extract useful information from the previous reconstructions and build efficient neural networks to serve as a surrogate model to rapidly predict the reconstructions. Extreme learning machine is cited here as an example for demonstrative purpose simply due to its ease of implementation, fast learning speed, and good generalization performance. Extensive numerical studies were performed, and the results show that the new method can dramatically reduce the computational time compared with the classical iterative methods. This technique is expected to be an alternative to existing methods when sufficient training data are available. Although this work is discussed under the context of tomographic absorption spectroscopy, we expect it to be useful also to other high speed tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence which have been demonstrated for combustion diagnostics.

Error in the determination of the deformed shape of prismatic beams using the double integration of curvature

NASA Astrophysics Data System (ADS)

Sigurdardottir, Dorotea H.; Stearns, Jett; Glisic, Branko

2017-07-01

The deformed shape is a consequence of loading the structure and it is defined by the shape of the centroid line of the beam after deformation. The deformed shape is a universal parameter of beam-like structures. It is correlated with the curvature of the cross-section; therefore, any unusual behavior that affects the curvature is reflected through the deformed shape. Excessive deformations cause user discomfort, damage to adjacent structural members, and may ultimately lead to issues in structural safety. However, direct long-term monitoring of the deformed shape in real-life settings is challenging, and an alternative is indirect determination of the deformed shape based on curvature monitoring. The challenge of the latter is an accurate evaluation of error in the deformed shape determination, which is directly correlated with the number of sensors needed to achieve the desired accuracy. The aim of this paper is to study the deformed shape evaluated by numerical double integration of the monitored curvature distribution along the beam, and create a method to predict the associated errors and suggest the number of sensors needed to achieve the desired accuracy. The error due to the accuracy in the curvature measurement is evaluated within the scope of this work. Additionally, the error due to the numerical integration is evaluated. This error depends on the load case (i.e., the shape of the curvature diagram), the magnitude of curvature, and the density of the sensor network. The method is tested on a laboratory specimen and a real structure. In a laboratory setting, the double integration is in excellent agreement with the beam theory solution which was within the predicted error limits of the numerical integration. Consistent results are also achieved on a real structure—Streicker Bridge on Princeton University campus.

Alternatives to Re-Planning: Methods for Plan Re-Evaluation at Runtime

NASA Technical Reports Server (NTRS)

Benazera, Emmanuel

2005-01-01

Current planning algorithms have difficulty handling the complexity that is due to an increase in domain uncertainty, and especially in the case of multi-dimensional continuous spaces. Therefore, they produce plans that do not take into account numerous situations that can occur at runtime, such as faults or other changes in the planning domain itself. Thus there is a gap between the plan generation and the reality experienced at runtime. Here we present two methods that allow the plan conditionals to be revised w.r.t. uncertainty on the system as estimated at runtime.

A preliminary study of numerical simulation of thermosolutal convection of interest to crystal growth

NASA Technical Reports Server (NTRS)

Miller, T. L.

1984-01-01

Calculations were performed with computer models using three types of finite difference methods of thermosolutal convection: horizontal heating of a container filled with a stably stratified solution, finger convection in a container, and finger convection in a horizontally infinite channel. The importance of including thermosolutal convection in models of crystal growth is emphasized, and the difficulties in doing so are demonstrated. It is pointed out that these difficulties, due primarily to the fine structure of the convection, may be partly overcome by the use of fine grids and implicit time stepping methods.

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.

A moment projection method for population balance dynamics with a shrinkage term

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

Wu, Shaohua; Yapp, Edward K.Y.; Akroyd, Jethro

A new method of moments for solving the population balance equation is developed and presented. The moment projection method (MPM) is numerically simple and easy to implement and attempts to address the challenge of particle shrinkage due to processes such as oxidation, evaporation or dissolution. It directly solves the moment transport equation for the moments and tracks the number of the smallest particles using the algorithm by Blumstein and Wheeler (1973) . The performance of the new method is measured against the method of moments (MOM) and the hybrid method of moments (HMOM). The results suggest that MPM performs muchmore » better than MOM and HMOM where shrinkage is dominant. The new method predicts mean quantities which are almost as accurate as a high-precision stochastic method calculated using the established direct simulation algorithm (DSA).« less

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

Zou, Ling; Zhao, Haihua; Kim, Seung Jun

In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to themore » low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.« less

Application of Bayesian Maximum Entropy Filter in parameter calibration of groundwater flow model in PingTung Plain

NASA Astrophysics Data System (ADS)

Cheung, Shao-Yong; Lee, Chieh-Han; Yu, Hwa-Lung

2017-04-01

Due to the limited hydrogeological observation data and high levels of uncertainty within, parameter estimation of the groundwater model has been an important issue. There are many methods of parameter estimation, for example, Kalman filter provides a real-time calibration of parameters through measurement of groundwater monitoring wells, related methods such as Extended Kalman Filter and Ensemble Kalman Filter are widely applied in groundwater research. However, Kalman Filter method is limited to linearity. This study propose a novel method, Bayesian Maximum Entropy Filtering, which provides a method that can considers the uncertainty of data in parameter estimation. With this two methods, we can estimate parameter by given hard data (certain) and soft data (uncertain) in the same time. In this study, we use Python and QGIS in groundwater model (MODFLOW) and development of Extended Kalman Filter and Bayesian Maximum Entropy Filtering in Python in parameter estimation. This method may provide a conventional filtering method and also consider the uncertainty of data. This study was conducted through numerical model experiment to explore, combine Bayesian maximum entropy filter and a hypothesis for the architecture of MODFLOW groundwater model numerical estimation. Through the virtual observation wells to simulate and observe the groundwater model periodically. The result showed that considering the uncertainty of data, the Bayesian maximum entropy filter will provide an ideal result of real-time parameters estimation.

Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient.

PubMed

Hindasageri, V; Vedula, R P; Prabhu, S V

2013-02-01

Temperature measurement by thermocouples is prone to errors due to conduction and radiation losses and therefore has to be corrected for precise measurement. The temperature dependent emissivity of the thermocouple wires is measured by the use of thermal infrared camera. The measured emissivities are found to be 20%-40% lower than the theoretical values predicted from theory of electromagnetism. A transient technique is employed for finding the heat transfer coefficients for the lead wire and the bead of the thermocouple. This method does not require the data of thermal properties and velocity of the burnt gases. The heat transfer coefficients obtained from the present method have an average deviation of 20% from the available heat transfer correlations in literature for non-reacting convective flow over cylinders and spheres. The parametric study of thermocouple error using the numerical code confirmed the existence of a minimum wire length beyond which the conduction loss is a constant minimal. Temperature of premixed methane-air flames stabilised on 16 mm diameter tube burner is measured by three B-type thermocouples of wire diameters: 0.15 mm, 0.30 mm, and 0.60 mm. The measurements are made at three distances from the burner tip (thermocouple tip to burner tip/burner diameter = 2, 4, and 6) at an equivalence ratio of 1 for the tube Reynolds number varying from 1000 to 2200. These measured flame temperatures are corrected by the present numerical procedure, the multi-element method, and the extrapolation method. The flame temperatures estimated by the two-element method and extrapolation method deviate from numerical results within 2.5% and 4%, respectively.

Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient

NASA Astrophysics Data System (ADS)

Hindasageri, V.; Vedula, R. P.; Prabhu, S. V.

2013-02-01

Temperature measurement by thermocouples is prone to errors due to conduction and radiation losses and therefore has to be corrected for precise measurement. The temperature dependent emissivity of the thermocouple wires is measured by the use of thermal infrared camera. The measured emissivities are found to be 20%-40% lower than the theoretical values predicted from theory of electromagnetism. A transient technique is employed for finding the heat transfer coefficients for the lead wire and the bead of the thermocouple. This method does not require the data of thermal properties and velocity of the burnt gases. The heat transfer coefficients obtained from the present method have an average deviation of 20% from the available heat transfer correlations in literature for non-reacting convective flow over cylinders and spheres. The parametric study of thermocouple error using the numerical code confirmed the existence of a minimum wire length beyond which the conduction loss is a constant minimal. Temperature of premixed methane-air flames stabilised on 16 mm diameter tube burner is measured by three B-type thermocouples of wire diameters: 0.15 mm, 0.30 mm, and 0.60 mm. The measurements are made at three distances from the burner tip (thermocouple tip to burner tip/burner diameter = 2, 4, and 6) at an equivalence ratio of 1 for the tube Reynolds number varying from 1000 to 2200. These measured flame temperatures are corrected by the present numerical procedure, the multi-element method, and the extrapolation method. The flame temperatures estimated by the two-element method and extrapolation method deviate from numerical results within 2.5% and 4%, respectively.

Numerical investigations on the aerodynamic performance of wind turbine: Downwind versus upwind configuration

NASA Astrophysics Data System (ADS)

Zhou, Hu; Wan, Decheng

2015-03-01

Although the upwind configuration is more popular in the field of wind energy, the downwind one is a promising type for the offshore wind energy due to its special advantages. Different configurations have different aerodynamic performance and it is important to predict the performance of both downwind and upwind configurations accurately for designing and developing more reliable wind turbines. In this paper, a numerical investigation on the aerodynamic performance of National Renewable Energy Laboratory (NREL) phase VI wind turbine in downwind and upwind configurations is presented. The open source toolbox OpenFOAM coupled with arbitrary mesh interface (AMI) method is applied to tackle rotating problems of wind turbines. Two 3D numerical models of NREL phase VI wind turbine with downwind and upwind configurations under four typical working conditions of incoming wind velocities are set up for the study of different unsteady characteristics of the downwind and upwind configurations, respectively. Numerical results of wake vortex structure, time histories of thrust, pressure distribution on the blade and limiting streamlines which can be used to identify points of separation in a 3D flow are presented. It can be concluded that thrust reduction due to blade-tower interaction is small for upwind wind turbines but relatively large for downwind wind turbines and attention should be paid to the vibration at a certain frequency induced by the cyclic reduction for both configurations. The results and conclusions are helpful to analyze the different aerodynamic performance of wind turbines between downwind and upwind configurations, providing useful references for practical design of wind turbine.

Non Destructive Testing by active infrared thermography coupled with shearography under same optical heat excitation

NASA Astrophysics Data System (ADS)

Theroux, Louis-Daniel; Dumoulin, Jean; Maldague, Xavier

2014-05-01

As infrastructures are aging, the evaluation of their health is becoming crucial. To do so, numerous Non Destructive Testing (NDT) methods are available. Among them, thermal shearography and active infrared thermography represent two full field and contactless methods for surface inspection. The synchronized use of both methods presents multiples advantages. Most importantly, both NDT are based on different material properties. Thermography depend on the thermal properties and shearography on the mechanical properties. The cross-correlation of both methods result in a more accurate and exact detection of the defects. For real site application, the simultaneous use of both methods is simplified due to the fact that the excitation method (thermal) is the same. Active infrared thermography is the measure of the temperature by an infrared camera of a surface subjected to heat flux. Observation of the variation of temperature in function of time reveal the presence of defects. On the other hand, shearography is a measure of out-of-plane surface displacement. This displacement is caused by the application of a strain on the surface which (in our case) take the form of a temperature gradient inducing a thermal stress To measure the resulting out-of-plane displacement, shearography exploit the relation between the phase difference and the optical path length. The phase difference is measured by the observation of the interference between two coherent light beam projected on the surface. This interference is due to change in optical path length as the surface is deformed [1]. A series of experimentation have been conducted in laboratory with various sample of concrete reinforced with CFRP materials. Results obtained reveal that with both methods it was possible to detect defects in the gluing. An infrared lamp radiating was used as the active heat source. This is necessary if measurements with shearography are to be made during the heating process. A heating lamp in the visible spectrum would hinder the projected light beam since a laser with wavelength of 532 nm was used as the coherent light source. Experimentations were successful, but only with mitigated efficiency for shearography [2]. The thermal response was the fastest and it was possible to fully locate all defects. For shearography, the available equipment forced us to restrict the area of observation to only one defect at a time (roughly 100 cm²). Numerical models were designed based on the multiple sample tested in the experimental step of the study. Using the COMSOL© finite elements modeling software, numerous simulations yielded results in accordance with experimental data. Different types of defect could be modeled and showed that both shearography and thermography have different sensibility in function of the nature of the defect. Furthermore, analysis of the simulated results demonstrated a relation between the contrast evolution of the temperature and displacement field. In the near future, we expect to make several improvement to our experimental setup. As for the numerical model, some small disparities between the theoretical and experimental results still remain to be addressed. The numerical model could be improved but to do so it requires to raise the shearographic measurements sampling rate close to the one used for infrared thermography. Once this issue will be resolved, it will be possible to use experimental data to refine the numerical model. So, accurate models will be helpful to optimize the overall efficiency of the coupling of thermal shearography and active infrared thermography for in situ NDT application. References [1] Y.Y. Hung, C.Y. Liand, Image-shearing camera for direct measurement of surface strains, Applied Optics, Vol. 18, n°7, pages 1046-1051, 1979 [2] L-D. Théroux, J. Dumoulin, X. Maldague, Square heating applied to shearography and active infrared thermography measurements coupling: form feasibility test in laboratory to numerical study of pultruded CFRP plates glued on concrete specimen, STRAIN journal, in press

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations. Chapter 1

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sjoegreen, B.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Passive synthetic aperture radar imaging of ground moving targets

NASA Astrophysics Data System (ADS)

Wacks, Steven; Yazici, Birsen

2012-05-01

In this paper we present a method for imaging ground moving targets using passive synthetic aperture radar. A passive radar imaging system uses small, mobile receivers that do not radiate any energy. For these reasons, passive imaging systems result in signicant cost, manufacturing, and stealth advantages. The received signals are obtained by multiple airborne receivers collecting scattered waves due to illuminating sources of opportunity such as commercial television, radio, and cell phone towers. We describe a novel forward model and a corresponding ltered-backprojection type image reconstruction method combined with entropy optimization. Our method determines the location and velocity of multiple targets moving at dierent velocities. Furthermore, it can accommodate arbitrary imaging geometries. we present numerical simulations to verify the imaging method.

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

Discontinuous Galerkin Methods and High-Speed Turbulent Flows

NASA Astrophysics Data System (ADS)

Atak, Muhammed; Larsson, Johan; Munz, Claus-Dieter

2014-11-01

Discontinuous Galerkin methods gain increasing importance within the CFD community as they combine arbitrary high order of accuracy in complex geometries with parallel efficiency. Particularly the discontinuous Galerkin spectral element method (DGSEM) is a promising candidate for both the direct numerical simulation (DNS) and large eddy simulation (LES) of turbulent flows due to its excellent scaling attributes. In this talk, we present a DNS of a compressible turbulent boundary layer along a flat plate at a free-stream Mach number of M = 2.67 and assess the computational efficiency of the DGSEM at performing high-fidelity simulations of both transitional and turbulent boundary layers. We compare the accuracy of the results as well as the computational performance to results using a high order finite difference method.

A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

NASA Astrophysics Data System (ADS)

Wu, Keyi; Li, Jinglai

2016-09-01

In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter y. The performance parameter y is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of y. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithms, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo methods.

Using well casing as an electrical source to monitor hydraulic fracture fluid injection

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

Wilt, Michael; Nieuwenhuis, Greg; MacLennan, Kris

2016-03-09

The depth to surface resistivity (DSR) method transmits current from a source located in a cased or openhole well to a distant surface return electrode while electric field measurements are made at the surface over the target of interest. This paper presents both numerical modelling results and measured data from a hydraulic fracturing field test where conductive water was injected into a resistive shale reservoir during a hydraulic fracturing operation. Modelling experiments show that anomalies due to hydraulic fracturing are small but measureable with highly sensitive sensor technology. The field measurements confirm the model results,showing that measured differences in themore » surface fields due to hydraulic fracturing have been detected above the noise floor. Our results show that the DSR method is sensitive to the injection of frac fluids; they are detectable above the noise floor in a commercially active hydraulic fracturing operation, and therefore this method can be used for monitoring fracture fluid movement.« less

Survey and analysis of research on supersonic drag-due-to-lift minimization with recommendations for wing design

NASA Technical Reports Server (NTRS)

Carlson, Harry W.; Mann, Michael J.

1992-01-01

A survey of research on drag-due-to-lift minimization at supersonic speeds, including a study of the effectiveness of current design and analysis methods was conducted. The results show that a linearized theory analysis with estimated attainable thrust and vortex force effects can predict with reasonable accuracy the lifting efficiency of flat wings. Significantly better wing performance can be achieved through the use of twist and camber. Although linearized theory methods tend to overestimate the amount of twist and camber required for a given application and provide an overly optimistic performance prediction, these deficiencies can be overcome by implementation of recently developed empirical corrections. Numerous examples of the correlation of experiment and theory are presented to demonstrate the applicability and limitations of linearized theory methods with and without empirical corrections. The use of an Euler code for the estimation of aerodynamic characteristics of a twisted and cambered wing and its application to design by iteration are discussed.

Study on Damage Evaluation and Machinability of UD-CFRP for the Orthogonal Cutting Operation Using Scanning Acoustic Microscopy and the Finite Element Method.

PubMed

Wang, Dongyao; He, Xiaodong; Xu, Zhonghai; Jiao, Weicheng; Yang, Fan; Jiang, Long; Li, Linlin; Liu, Wenbo; Wang, Rongguo

2017-02-20

Owing to high specific strength and designability, unidirectional carbon fiber reinforced polymer (UD-CFRP) has been utilized in numerous fields to replace conventional metal materials. Post machining processes are always required for UD-CFRP to achieve dimensional tolerance and assembly specifications. Due to inhomogeneity and anisotropy, UD-CFRP differs greatly from metal materials in machining and failure mechanism. To improve the efficiency and avoid machining-induced damage, this paper undertook to study the correlations between cutting parameters, fiber orientation angle, cutting forces, and cutting-induced damage for UD-CFRP laminate. Scanning acoustic microscopy (SAM) was employed and one-/two-dimensional damage factors were then created to quantitatively characterize the damage of the laminate workpieces. According to the 3D Hashin's criteria a numerical model was further proposed in terms of the finite element method (FEM). A good agreement between simulation and experimental results was validated for the prediction and structural optimization of the UD-CFRP.

The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2004-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.

Study on Damage Evaluation and Machinability of UD-CFRP for the Orthogonal Cutting Operation Using Scanning Acoustic Microscopy and the Finite Element Method

PubMed Central

Wang, Dongyao; He, Xiaodong; Xu, Zhonghai; Jiao, Weicheng; Yang, Fan; Jiang, Long; Li, Linlin; Liu, Wenbo; Wang, Rongguo

2017-01-01

Owing to high specific strength and designability, unidirectional carbon fiber reinforced polymer (UD-CFRP) has been utilized in numerous fields to replace conventional metal materials. Post machining processes are always required for UD-CFRP to achieve dimensional tolerance and assembly specifications. Due to inhomogeneity and anisotropy, UD-CFRP differs greatly from metal materials in machining and failure mechanism. To improve the efficiency and avoid machining-induced damage, this paper undertook to study the correlations between cutting parameters, fiber orientation angle, cutting forces, and cutting-induced damage for UD-CFRP laminate. Scanning acoustic microscopy (SAM) was employed and one-/two-dimensional damage factors were then created to quantitatively characterize the damage of the laminate workpieces. According to the 3D Hashin’s criteria a numerical model was further proposed in terms of the finite element method (FEM). A good agreement between simulation and experimental results was validated for the prediction and structural optimization of the UD-CFRP. PMID:28772565

Multitemperature compaction model of a magma melt in the asthenosphere: A numerical approach

NASA Astrophysics Data System (ADS)

Pak, V. V.

2007-09-01

A numerical compaction model of a fluid in a viscous skeleton is developed with regard for a phase transition. The temperatures of phases are different. The solution is found by the method of asymptotic expansion relative to the incompressible variant, which removes a number of computational problems related to the weak compressibility of the skeleton. For each approximation, the problem is solved by the finite element method. The process of 2-D compaction of a magmatic melt in the asthenosphere under a fault zone is examined for one-and two-temperature cases. The magmatic flow concentrates in this region due to a lower pore pressure. Higher temperature magma entering from lower levels causes a local heating of the skeleton and intense melting of its fusible component. In the two-temperature model, a magma concentration anomaly develops under the fault zone. The fundamental limitations substantially complicating the corresponding calculations within the framework of a one-temperature model are pointed out and the necessity of applying a multitemperature variant is substantiated.

An improved coupled-states approximation including the nearest neighbor Coriolis couplings for diatom-diatom inelastic collision

NASA Astrophysics Data System (ADS)

Yang, Dongzheng; Hu, Xixi; Zhang, Dong H.; Xie, Daiqian

2018-02-01

Solving the time-independent close coupling equations of a diatom-diatom inelastic collision system by using the rigorous close-coupling approach is numerically difficult because of its expensive matrix manipulation. The coupled-states approximation decouples the centrifugal matrix by neglecting the important Coriolis couplings completely. In this work, a new approximation method based on the coupled-states approximation is presented and applied to time-independent quantum dynamic calculations. This approach only considers the most important Coriolis coupling with the nearest neighbors and ignores weaker Coriolis couplings with farther K channels. As a result, it reduces the computational costs without a significant loss of accuracy. Numerical tests for para-H2+ortho-H2 and para-H2+HD inelastic collision were carried out and the results showed that the improved method dramatically reduces the errors due to the neglect of the Coriolis couplings in the coupled-states approximation. This strategy should be useful in quantum dynamics of other systems.

Two-dimensional water acoustic waveguide based on pressure compensation method

NASA Astrophysics Data System (ADS)

Zheng, Mingye; Chen, Yi; Liu, Xiaoning; Hu, Gengkai

2018-02-01

A two-dimensional (2D) waveguide is a basic facility for experiment measurement due to a much more simplified wave field pattern than that in free space. A waveguide for airborne sound is easily achieved with almost any solid plates. However, the design of a 2D water acoustic waveguide is still challenging because of unavailable solids with a sufficient large impedance difference from water. In this work, a new method of constructing a 2D water acoustic waveguide is proposed based on pressure compensation and has been verified by numerical simulation. A prototype of the water acoustic waveguide is fabricated and complemented by an acoustic pressure scanning system; the measured scattered pressure fields by air and aluminum cylinders both agree quite well with numerical simulations. Most acoustic pressure fields within a frequency range 7 kHz-15 kHz can be measured in this waveguide when the required scanning region is smaller than the aluminum plate area (1800 mm × 800 mm).

Glycerol dehydration of native and diabetic animal tissues studied by THz-TDS and NMR methods

PubMed Central

Smolyanskaya, O. A.; Schelkanova, I. J.; Kulya, M. S.; Odlyanitskiy, E. L.; Goryachev, I. S.; Tcypkin, A. N.; Grachev, Ya. V.; Toropova, Ya. G.; Tuchin, V. V.

2018-01-01

The optical clearing method has been widely used for different spectral ranges where it provides tissue transparency. In this work, we observed the enhanced penetration of the terahertz waves inside biological samples (skin, kidney, and cornea) treated with glycerol solutions inducing changes of optical and dielectric properties. It was supported by the observed trend of free-to-bound water ratio measured by the nuclear magnetic resonance (NMR) method. The terahertz clearing efficiency was found to be less for diabetic samples than for normal ones. Results of the numerical simulation proved that pulse deformation is due to bigger penetration depth caused by the reduction of absorption and refraction at optical clearing. PMID:29541513

Investigation of p-type depletion doping for InGaN/GaN-based light-emitting diodes

NASA Astrophysics Data System (ADS)

Zhang, Yiping; Zhang, Zi-Hui; Tan, Swee Tiam; Hernandez-Martinez, Pedro Ludwig; Zhu, Binbin; Lu, Shunpeng; Kang, Xue Jun; Sun, Xiao Wei; Demir, Hilmi Volkan

2017-01-01

Due to the limitation of the hole injection, p-type doping is essential to improve the performance of InGaN/GaN multiple quantum well light-emitting diodes (LEDs). In this work, we propose and show a depletion-region Mg-doping method. Here we systematically analyze the effectiveness of different Mg-doping profiles ranging from the electron blocking layer to the active region. Numerical computations show that the Mg-doping decreases the valence band barrier for holes and thus enhances the hole transportation. The proposed depletion-region Mg-doping approach also increases the barrier height for electrons, which leads to a reduced electron overflow, while increasing the hole concentration in the p-GaN layer. Experimentally measured external quantum efficiency indicates that Mg-doping position is vitally important. The doping in or adjacent to the quantum well degrades the LED performance due to Mg diffusion, increasing the corresponding nonradiative recombination, which is well supported by the measured carrier lifetimes. The experimental results are well numerically reproduced by modifying the nonradiative recombination lifetimes, which further validate the effectiveness of our approach.

Physico-Chemical Alternatives in Lignocellulosic Materials in Relation to the Kind of Component for Fermenting Purposes

PubMed Central

Coz, Alberto; Llano, Tamara; Cifrián, Eva; Viguri, Javier; Maican, Edmond; Sixta, Herbert

2016-01-01

The complete bioconversion of the carbohydrate fraction is of great importance for a lignocellulosic-based biorefinery. However, due to the structure of the lignocellulosic materials, and depending basically on the main parameters within the pretreatment steps, numerous byproducts are generated and they act as inhibitors in the fermentation operations. In this sense, the impact of inhibitory compounds derived from lignocellulosic materials is one of the major challenges for a sustainable biomass-to-biofuel and -bioproduct industry. In order to minimise the negative effects of these compounds, numerous methodologies have been tested including physical, chemical, and biological processes. The main physical and chemical treatments have been studied in this work in relation to the lignocellulosic material and the inhibitor in order to point out the best mechanisms for fermenting purposes. In addition, special attention has been made in the case of lignocellulosic hydrolysates obtained by chemical processes with SO2, due to the complex matrix of these materials and the increase in these methodologies in future biorefinery markets. Recommendations of different detoxification methods have been given. PMID:28773700

Surface plasticity: theory and computation

NASA Astrophysics Data System (ADS)

Esmaeili, A.; Steinmann, P.; Javili, A.

2017-11-01

Surfaces of solids behave differently from the bulk due to different atomic rearrangements and processes such as oxidation or aging. Such behavior can become markedly dominant at the nanoscale due to the large ratio of surface area to bulk volume. The surface elasticity theory (Gurtin and Murdoch in Arch Ration Mech Anal 57(4):291-323, 1975) has proven to be a powerful strategy to capture the size-dependent response of nano-materials. While the surface elasticity theory is well-established to date, surface plasticity still remains elusive and poorly understood. The objective of this contribution is to establish a thermodynamically consistent surface elastoplasticity theory for finite deformations. A phenomenological isotropic plasticity model for the surface is developed based on the postulated elastoplastic multiplicative decomposition of the surface superficial deformation gradient. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and the consistent elastoplastic tangent of the surface contribution is derived. Finally, a series of numerical examples provide further insight into the problem and elucidate the key features of the proposed theory.

Numerical analysis of the change in skin color due to ecchymosis and petechiae generated by cupping: a pilot study.

PubMed

Kim, Soo-Byeong; Lee, Yong-Heum

2014-12-01

Cupping is one of the various treatment methods used in traditional oriental medicine. Cupping is also used as a diagnostic method and it may cause skin hyperpigmentation. Quantitative measurements and analysis of changes in skin color due to cupping are critical. The purpose of this study is to suggest an optical technique to visualize and identify changes in skin color due to cupping. We suggest the following analysis methods: digital color spaces [red, green, and blue (RGB) and L∗a∗b], the Erythema Index (E.I.), and the Melanin Index (M.I.). For experiments, we selected and stimulated 10 acupoints at 80 kilopascals (kPa) per minute. The RGB and L∗a∗b color spaces were observed to be decreased (p < 0.05) after cupping. The E.I. and M.I. were observed to be increased significantly (p < 0.05) after cupping. To assess various changes in skin color, we observed the changes for 72 hours. We also obtained the color changes by using the recovery pattern during the recovery period (p < 0.01). We propose that this method can be useful for visual identification and as a way to improve the identification of skin color changes. Copyright © 2014. Published by Elsevier B.V.

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

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.

Accuracy of Time Integration Approaches for Stiff Magnetohydrodynamics Problems

NASA Astrophysics Data System (ADS)

Knoll, D. A.; Chacon, L.

2003-10-01

The simulation of complex physical processes with multiple time scales presents a continuing challenge to the computational plasma physisist due to the co-existence of fast and slow time scales. Within computational plasma physics, practitioners have developed and used linearized methods, semi-implicit methods, and time splitting in an attempt to tackle such problems. All of these methods are understood to generate numerical error. We are currently developing algorithms which remove such error for MHD problems [1,2]. These methods do not rely on linearization or time splitting. We are also attempting to analyze the errors introduced by existing ``implicit'' methods using modified equation analysis (MEA) [3]. In this presentation we will briefly cover the major findings in [3]. We will then extend this work further into MHD. This analysis will be augmented with numerical experiments with the hope of gaining insight, particularly into how these errors accumulate over many time steps. [1] L. Chacon,. D.A. Knoll, J.M. Finn, J. Comput. Phys., vol. 178, pp. 15-36 (2002) [2] L. Chacon and D.A. Knoll, J. Comput. Phys., vol. 188, pp. 573-592 (2003) [3] D.A. Knoll , L. Chacon, L.G. Margolin, V.A. Mousseau, J. Comput. Phys., vol. 185, pp. 583-611 (2003)

Large-Eddy Simulation of Waked Turbines in a Scaled Wind Farm Facility

NASA Astrophysics Data System (ADS)

Wang, J.; McLean, D.; Campagnolo, F.; Yu, T.; Bottasso, C. L.

2017-05-01

The aim of this paper is to present the numerical simulation of waked scaled wind turbines operating in a boundary layer wind tunnel. The simulation uses a LES-lifting-line numerical model. An immersed boundary method in conjunction with an adequate wall model is used to represent the effects of both the wind turbine nacelle and tower, which are shown to have a considerable effect on the wake behavior. Multi-airfoil data calibrated at different Reynolds numbers are used to account for the lift and drag characteristics at the low and varying Reynolds conditions encountered in the experiments. The present study focuses on low turbulence inflow conditions and inflow non-uniformity due to wind tunnel characteristics, while higher turbulence conditions are considered in a separate study. The numerical model is validated by using experimental data obtained during test campaigns conducted with the scaled wind farm facility. The simulation and experimental results are compared in terms of power capture, rotor thrust, downstream velocity profiles and turbulence intensity.

Experimental and Numerical Investigation on Micro-Bending of AISI 304 Sheet Metal Using a Low Power Nanosecond Laser

NASA Astrophysics Data System (ADS)

Paramasivan, K.; Das, Sandip; Marimuthu, Sundar; Misra, Dipten

2018-06-01

The aim of this experimental study is to identify and characterize the response related to the effects of process parameters in terms of bending angle for micro-bending of AISI 304 sheet using a low power Nd:YVO4 laser source. Numerical simulation is also carried out through a coupled thermo-mechanical formulation with finite element method using COMSOL MULTIPHYSICS. The developed numerical simulation indicates that bending is caused by temperature gradient mechanism in the present investigation involving laser micro-bending. The results of experiment indicate that bending angle increases with laser power, number of irradiations, and decreases with increase in scanning speed. Moreover, average bending angle increases with number of laser passes and edge effect, defined in terms of relative variation of bending angle (RBAV), decreases monotonically with the number of laser scans. The substrate is damaged over a width of about 80 μm due to the high temperatures experienced during laser forming at a low scanning speed.

Cylindrical and spherical Akhmediev breather and freak waves in ultracold neutral plasmas

NASA Astrophysics Data System (ADS)

El-Tantawy, S. A.; El-Awady, E. I.

2018-01-01

The properties of cylindrical and spherical ion-acoustic breathers Akhmediev breather and freak waves in strongly coupled ultracold neutral plasmas (UNPs), whose constituents are inertial strongly coupled ions and weakly coupled Maxwellian electrons, are investigated numerically. Using the derivative expansion method, the basic set of fluid equations is reduced to a nonplanar (cylindrical and spherical)/modified nonlinear Schrödinger equation (mNLSE). The analytical solutions of the mNLSE were not possible until now, so their numerical solutions are obtained using the finite difference scheme with the help of the Dirichlet boundary conditions. Moreover, the criteria for the existence and propagation of breathers are discussed in detail. The geometrical effects due to the cylindrical and spherical geometries on the breather profile are studied numerically. It is found that the propagation of the ion-acoustic breathers in one-dimensional planar and nonplanar geometries is very different. Finally, our results may help to manipulate matter breathers experimentally in UNPs.

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego

2012-03-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel Lagrangian Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical formulation, which ensures a consistent numerical discretization temporally and spatially for arbitrary χ/χ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.

Numerical Analysis of Transient Temperature Response of Soap Film

NASA Astrophysics Data System (ADS)

Tanaka, Seiichi; Tatesaku, Akihiro; Dantsuka, Yuki; Fujiwara, Seiji; Kunimine, Kanji

2015-11-01

Measurements of thermophysical properties of thin liquid films are important to understand interfacial phenomena due to film structures composed of amphiphilic molecules in soap film, phospholipid bilayer of biological cell and emulsion. A transient hot-wire technique for liquid films less than 1 \\upmu m thick such as soap film has been proposed to measure the thermal conductivity and diffusivity simultaneously. Two-dimensional heat conduction equations for a solid cylinder with a liquid film have been solved numerically. The temperature of a thin wire with liquid film increases steeply with its own heat generation. The feasibility of this technique is verified through numerical experiments for various thermal conductivities, diffusivities, and film thicknesses. Calculated results indicate that the increase in the volumetric average temperature of the thin wire sufficiently varies with the change of thermal conductivity and diffusivity of the soap film. Therefore, the temperature characteristics could be utilized to evaluate both the thermal conductivity and diffusivity using the Gauss-Newton method.

Numerical prediction of kinetic model for enzymatic hydrolysis of cellulose using DAE-QMOM approach

NASA Astrophysics Data System (ADS)

Jamil, N. M.; Wang, Q.

2016-06-01

Bioethanol production from lignocellulosic biomass consists of three fundamental processes; pre-treatment, enzymatic hydrolysis, and fermentation. In enzymatic hydrolysis phase, the enzymes break the cellulose chains into sugar in the form of cellobiose or glucose. A currently proposed kinetic model for enzymatic hydrolysis of cellulose that uses population balance equation (PBE) mechanism was studied. The complexity of the model due to integrodifferential equations makes it difficult to find the analytical solution. Therefore, we solved the full model of PBE numerically by using DAE-QMOM approach. The computation was carried out using MATLAB software. The numerical results were compared to the asymptotic solution developed in the author's previous paper and the results of Griggs et al. Besides confirming the findings were consistent with those references, some significant characteristics were also captured. The PBE model for enzymatic hydrolysis process can be solved using DAE-QMOM method. Also, an improved understanding of the physical insights of the model was achieved.

Rigorous numerical modeling of scattering-type scanning near-field optical microscopy and spectroscopy

NASA Astrophysics Data System (ADS)

Chen, Xinzhong; Lo, Chiu Fan Bowen; Zheng, William; Hu, Hai; Dai, Qing; Liu, Mengkun

2017-11-01

Over the last decade, scattering-type scanning near-field optical microscopy and spectroscopy have been widely used in nano-photonics and material research due to their fine spatial resolution and broad spectral range. A number of simplified analytical models have been proposed to quantitatively understand the tip-scattered near-field signal. However, a rigorous interpretation of the experimental results is still lacking at this stage. Numerical modelings, on the other hand, are mostly done by simulating the local electric field slightly above the sample surface, which only qualitatively represents the near-field signal rendered by the tip-sample interaction. In this work, we performed a more comprehensive numerical simulation which is based on realistic experimental parameters and signal extraction procedures. By directly comparing to the experiments as well as other simulation efforts, our methods offer a more accurate quantitative description of the near-field signal, paving the way for future studies of complex systems at the nanoscale.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media.

PubMed

Voinovich, Peter; Merlen, Alain

2005-12-01

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.

Methodology trends on gamma and electron radiation damage simulation studies in solids under high fluency irradiation environments

NASA Astrophysics Data System (ADS)

Cruz Inclán, Carlos M.; González Lazo, Eduardo; Rodríguez Rodríguez, Arturo; Guzmán Martínez, Fernando; Abreu Alfonso, Yamiel; Piñera Hernández, Ibrahin; Leyva Fabelo, Antonio

2017-09-01

The present work deals with the numerical simulation of gamma and electron radiation damage processes under high brightness and radiation particle fluency on regard to two new radiation induced atom displacement processes, which concern with both, the Monte Carlo Method based numerical simulation of the occurrence of atom displacement process as a result of gamma and electron interactions and transport in a solid matrix and the atom displacement threshold energies calculated by Molecular Dynamic methodologies. The two new radiation damage processes here considered in the framework of high brightness and particle fluency irradiation conditions are: 1) The radiation induced atom displacement processes due to a single primary knockout atom excitation in a defective target crystal matrix increasing its defect concentrations (vacancies, interstitials and Frenkel pairs) as a result of a severe and progressive material radiation damage and 2) The occurrence of atom displacements related to multiple primary knockout atom excitations for the same or different atomic species in an perfect target crystal matrix due to subsequent electron elastic atomic scattering in the same atomic neighborhood during a crystal lattice relaxation time. In the present work a review numeral simulation attempts of these two new radiation damage processes are presented, starting from the former developed algorithms and codes for Monte Carlo simulation of atom displacements induced by electron and gamma in

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media

NASA Astrophysics Data System (ADS)

Voinovich, Peter; Merlen, Alain

2005-12-01

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Hathwar, Raghuraj; Saraniti, Marco; Goodnick, Stephen M.

2016-07-01

We report on a new numerical approach for multi-band drift within the context of full band Monte Carlo (FBMC) simulation and apply this to Si and InAs nanowires. The approach is based on the solution of the Krieger and Iafrate (KI) equations [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)], which gives the probability of carriers undergoing interband transitions subject to an applied electric field. The KI equations are based on the solution of the time-dependent Schrödinger equation, and previous solutions of these equations have used Runge-Kutta (RK) methods to numerically solve the KI equations. This approach made the solution of the KI equations numerically expensive and was therefore only applied to a small part of the Brillouin zone (BZ). Here we discuss an alternate approach to the solution of the KI equations using the Magnus expansion (also known as "exponential perturbation theory"). This method is more accurate than the RK method as the solution lies on the exponential map and shares important qualitative properties with the exact solution such as the preservation of the unitary character of the time evolution operator. The solution of the KI equations is then incorporated through a modified FBMC free-flight drift routine and applied throughout the nanowire BZ. The importance of the multi-band drift model is then demonstrated for the case of Si and InAs nanowires by simulating a uniform field FBMC and analyzing the average carrier energies and carrier populations under high electric fields. Numerical simulations show that the average energy of the carriers under high electric field is significantly higher when multi-band drift is taken into consideration, due to the interband transitions allowing carriers to achieve higher energies.

Numerical investigation of the effects of channel geometry on platelet activation and blood damage.

PubMed

Wu, Jingshu; Yun, B Min; Fallon, Anna M; Hanson, Stephen R; Aidun, Cyrus K; Yoganathan, Ajit P

2011-02-01

Thromboembolic complications in Bileaflet mechanical heart valves (BMHVs) are believed to be due to the combination of high shear stresses and large recirculation regions. Relating blood damage to design geometry is therefore essential to ultimately optimize the design of BMHVs. The aim of this research is to quantitatively study the effect of 3D channel geometry on shear-induced platelet activation and aggregation, and to choose an appropriate blood damage index (BDI) model for future numerical simulations. The simulations in this study use a recently developed lattice-Boltzmann with external boundary force (LBM-EBF) method [Wu, J., and C. K. Aidun. Int. J. Numer. Method Fluids 62(7):765-783, 2010; Wu, J., and C. K. Aidun. Int. J. Multiphase flow 36:202-209, 2010]. The channel geometries and flow conditions are re-constructed from recent experiments by Fallon [The Development of a Novel in vitro Flow System to Evaluate Platelet Activation and Procoagulant Potential Induced by Bileaflet Mechanical Heart Valve Leakage Jets in School of Chemical and Biomolecular Engineering. Atlanta: Georgia Institute of Technology] and Fallon et al. [Ann. Biomed. Eng. 36(1):1]. The fluid flow is computed on a fixed regular 'lattice' using the LBM, and each platelet is mapped onto a Lagrangian frame moving continuously throughout the fluid domain. The two-way fluid-solid interactions are determined by the EBF method by enforcing a no-slip condition on the platelet surface. The motion and orientation of the platelet are obtained from Newtonian dynamics equations. The numerical results show that sharp corners or sudden shape transitions will increase blood damage. Fallon's experimental results were used as a basis for choosing the appropriate BDI model for use in future computational simulations of flow through BMHVs.

Separation of crack extension modes in orthotropic delamination models

NASA Technical Reports Server (NTRS)

Beuth, Jack L.

1995-01-01

In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict composite delamination. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode 1 and mode 2 energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, Delta. In this work, a method is presented for using the VCCT to extract Delta-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, Delta-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-tip fields is used to determine the explicit Delta dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Delta. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Delta-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The Delta-independent modes extracted using this technique can also serve as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Experimental and numerical study of the effects of a wall on the coalescence and collapse of bubble pairs

NASA Astrophysics Data System (ADS)

Han, Rui; Zhang, A.-Man; Li, Shuai; Zong, Zhi

2018-04-01

Two-bubble interaction is the most fundamental problem in multi-bubbles dynamics, which is crucial in many practical applications involving air-gun arrays and underwater explosions. In this paper, we experimentally and numerically investigate coalescence, collapse, and rebound of non-buoyant bubble pairs below a rigid wall. Two oscillating vapor bubbles with similar size are generated simultaneously near a rigid wall in axisymmetric configuration using the underwater electric discharge method, and the physical process is captured by a high-speed camera. Numerical simulations are conducted based on potential flow theory coupled with the boundary integral method. Our numerical results show excellent agreement with the experimental data until the splashing of the jet impact sets in. With different ranges of γbw (the dimensionless distance between the rigid wall and the nearest bubble center), the interaction between the coalesced bubble and the rigid wall is divided into three types, i.e., "weak," "intermediate," and "strong." As γbw decreases, the contact point of the two axial jets migrates toward the wall. In "strong interaction" cases, only an upward jet towards the upper rigid wall forms and a secondary jet with a larger width appears at the base of the first jet. The collapsing coalesced bubble in a toroidal form splits into many smaller bubbles due to the instabilities and presents as bubble clouds during the rebounding phase, which may lead to a weakened pressure wave because the focusing energy associated with the collapsing bubble is disintegrated.

Numerical study of the influence of geometrical characteristics of a vertical helical coil on a bubbly flow

NASA Astrophysics Data System (ADS)

Saffari, H.; Moosavi, R.

2014-11-01

In this article, turbulent single-phase and two-phase (air-water) bubbly fluid flows in a vertical helical coil are analyzed by using computational fluid dynamics (CFD). The effects of the pipe diameter, coil diameter, coil pitch, Reynolds number, and void fraction on the pressure loss, friction coefficient, and flow characteristics are investigated. The Eulerian-Eulerian model is used in this work to simulate the two-phase fluid flow. Three-dimensional governing equations of continuity, momentum, and energy are solved by using the finite volume method. The k- ɛ turbulence model is used to calculate turbulence fluctuations. The SIMPLE algorithm is employed to solve the velocity and pressure fields. Due to the effect of a secondary force in helical pipes, the friction coefficient is found to be higher in helical pipes than in straight pipes. The friction coefficient increases with an increase in the curvature, pipe diameter, and coil pitch and decreases with an increase in the coil diameter and void fraction. The close correlation between the numerical results obtained in this study and the numerical and empirical results of other researchers confirm the accuracy of the applied method. For void fractions up to 0.1, the numerical results indicate that the friction coefficient increases with increasing the pipe diameter and keeping the coil pitch and diameter constant and decreases with increasing the coil diameter. Finally, with an increase in the Reynolds number, the friction coefficient decreases, while the void fraction increases.

Development of a Chemically Reacting Flow Solver on the Graphic Processing Units

DTIC Science & Technology

2011-05-10

been implemented on the GPU by Schive et al. (2010). The outcome of their work is the GAMER code for astrophysical simulation. Thibault and...Euler equations at each cell. For simplification, consider the Euler equations in one dimension with no source terms; the discretized form of the...is known to be more diffusive than the other fluxes due to the large bound of the numerical signal velocities: b+, b-. 3.4 Time Marching Methods

Stress intensity and crack displacement for small edge cracks

NASA Technical Reports Server (NTRS)

Orange, Thomas W.

1988-01-01

The weight function method was used to derive stress intensity factors and crack mouth displacement coefficients for small edge cracks (less than 20 percent of the specimen width) in common fracture specimen configurations. Contact stresses due to point application of loads were found to be small but significant for three-point bending and insignificant for four-point bending. The results are compared with available equations and numerical solutions from the literature and with unpublished boundary collocation results.

Stretching a Curved Surface in a Viscous Fluid

NASA Astrophysics Data System (ADS)

Sajid, M.; N., Ali; T., Javed; Z., Abbas

2010-02-01

This work is concerned with the viscous flow due to a curved stretching sheet. The similarity solution of the problem is obtained numerically by a shooting method using the Runge-Kutta algorithm. The physical quantities of interest like the fluid velocity and skin friction coefficient are obtained and discussed under the influence of dimensionless curvature. It is evident from the results that dimensionless curvature causes an increase in boundary layer thickness and a decrease in the skin friction coefficient.

Stochastic Control and Numerical Methods with Applications to Communications. Game Theoretic/Subsolution to Importance Sampling for Rare Event Simulation

DTIC Science & Technology

2008-11-01

support to the value of the approach. 9. Scheduling and Control of Mobile Communications Networks with Randomly Time Varying Channels by Stability ...biological systems . Many examples arise in communications and queueing, due to the finite speed of signal transmission, the nonnegligible time required...without delays, the system state takes values in a subset of some finite -dimensional Euclidean space, and the control is a functional of the current

The role of fluid viscosity in an immersed granular collapse

NASA Astrophysics Data System (ADS)

Yang, Geng Chao; Kwok, Chung Yee; Sobral, Yuri Dumaresq

2017-06-01

Instabilities of immersed slopes and cliffs can lead to catastrophic events that involve a sudden release of huge soil mass. The scaled deposit height and runout distance are found to follow simple power laws when a granular column collapses on a horizontal plane. However, if the granular column is submerged in a fluid, the mobility of the granular collapse due to high inertia effects will be reduced by fluid-particle interactions. In this study, the effects of fluid viscosity on granular collapse is investigated qualitatively by adopting a numerical approach based on the coupled lattice Boltzmann method (LBM) and discrete element method (DEM). It is found that the granular collapse can be dramatically slowed down due to the presence of viscous fluids. For the considered granular configuration, when the fluid viscosity increases. the runout distance decreases and the final deposition shows a larger deposit angle.

Understanding a reference-free impedance method using collocated piezoelectric transducers

NASA Astrophysics Data System (ADS)

Kim, Eun Jin; Kim, Min Koo; Sohn, Hoon; Park, Hyun Woo

2010-03-01

A new concept of a reference-free impedance method, which does not require direct comparison with a baseline impedance signal, is proposed for damage detection in a plate-like structure. A single pair of piezoelectric (PZT) wafers collocated on both surfaces of a plate are utilized for extracting electro-mechanical signatures (EMS) associated with mode conversion due to damage. A numerical simulation is conducted to investigate the EMS of collocated PZT wafers in the frequency domain at the presence of damage through spectral element analysis. Then, the EMS due to mode conversion induced by damage are extracted using the signal decomposition technique based on the polarization characteristics of the collocated PZT wafers. The effects of the size and the location of damage on the decomposed EMS are investigated as well. Finally, the applicability of the decomposed EMS to the reference-free damage diagnosis is discussed.

Aerodynamic losses calculation of a turbine blade with film cooling with forward and backward injection by numerical method

NASA Astrophysics Data System (ADS)

Prajapati, Anil

Thermal efficiency and power output of gas turbines can be increased by increasing the turbine blade inlet temperature. However, the main problem is the durability of the turbine blade due to the thermal stress on it at high temperature. This has led to the development of film cooling technology, in which coolant is injected from a series of cooling holes made on the blade surface to form an insulating blanket over the blade surface. However, it has to pay the aerodynamic penalties due to the injection of coolant, which are not fully understood. Pressure loss coefficient is one of the easy and widely used parameters to determine the aerodynamic loss occurred on a turbine blade. The losses occurred on the turbine blade with forward injection and backward injection cooling are studied at a different blowing ratios by a numerical simulation, which shows that the loss is higher in the case of backward injection than in forward injection. Fan-shaped cooling holes are also considered to compare with the cylindrical holes. It is observed that the loss is increased due to the fan-shaped holes in the forward injection whereas there is not a substantial difference due to the fan-shaped holes in the backward injection. The aerodynamic loss due to the location of coolant injection is studied by using injection from the leading edge, pressure side, suction side and trailing edge respectively. The study is performed to determine the effect of incidence angles and coolant injection angles on the aerodynamic loss.

Multistatic synthetic aperture radar image formation.

PubMed

Krishnan, V; Swoboda, J; Yarman, C E; Yazici, B

2010-05-01

In this paper, we consider a multistatic synthetic aperture radar (SAR) imaging scenario where a swarm of airborne antennas, some of which are transmitting, receiving or both, are traversing arbitrary flight trajectories and transmitting arbitrary waveforms without any form of multiplexing. The received signal at each receiving antenna may be interfered by the scattered signal due to multiple transmitters and additive thermal noise at the receiver. In this scenario, standard bistatic SAR image reconstruction algorithms result in artifacts in reconstructed images due to these interferences. In this paper, we use microlocal analysis in a statistical setting to develop a filtered-backprojection (FBP) type analytic image formation method that suppresses artifacts due to interference while preserving the location and orientation of edges of the scene in the reconstructed image. Our FBP-type algorithm exploits the second-order statistics of the target and noise to suppress the artifacts due to interference in a mean-square sense. We present numerical simulations to demonstrate the performance of our multistatic SAR image formation algorithm with the FBP-type bistatic SAR image reconstruction algorithm. While we mainly focus on radar applications, our image formation method is also applicable to other problems arising in fields such as acoustic, geophysical and medical imaging.