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Sample records for advanced numerical methods

  1. Analytical and numerical methods; advanced computer concepts

    SciTech Connect

    Lax, P D

    1991-03-01

    This past year, two projects have been completed and a new is under way. First, in joint work with R. Kohn, we developed a numerical algorithm to study the blowup of solutions to equations with certain similarity transformations. In the second project, the adaptive mesh refinement code of Berger and Colella for shock hydrodynamic calculations has been parallelized and numerical studies using two different shared memory machines have been done. My current effort is towards the development of Cartesian mesh methods to solve pdes with complicated geometries. Most of the coming year will be spent on this project, which is joint work with Prof. Randy Leveque at the University of Washington in Seattle.

  2. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

    Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A

    2010-01-01

    Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge

  3. Numerical modeling of spray combustion with an advanced VOF method

    NASA Technical Reports Server (NTRS)

    Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul

    1995-01-01

    This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.

  4. Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

    DOE PAGES

    Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.

    2000-01-01

    In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less

  5. Advanced numerical methods and software approaches for semiconductor device simulation

    SciTech Connect

    CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.

    2000-03-23

    In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.

  6. Numerical approximation of a nonlinear delay-advance functional differential equation by a finite element method

    NASA Astrophysics Data System (ADS)

    Teodoro, M. F.

    2012-09-01

    We are particularly interested in the numerical solution of the functional differential equations with symmetric delay and advance. In this work, we consider a nonlinear forward-backward equation, the Fitz Hugh-Nagumo equation. It is presented a scheme which extends the algorithm introduced in [1]. A computational method using Newton's method, finite element method and method of steps is developped.

  7. Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound

    PubMed Central

    Borazjani, Iman; Westerdale, John; McMahon, Eileen M.; Rajaraman, Prathish K.; Heys, Jeffrey J.

    2013-01-01

    The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics. PMID:23690874

  8. BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

    NASA Astrophysics Data System (ADS)

    Katsaounis, T. D.

    2005-02-01

    The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using

  9. Numerical Evaluation of Fluid Mixing Phenomena in Boiling Water Reactor Using Advanced Interface Tracking Method

    NASA Astrophysics Data System (ADS)

    Yoshida, Hiroyuki; Takase, Kazuyuki

    Thermal-hydraulic design of the current boiling water reactor (BWR) is performed with the subchannel analysis codes which incorporated the correlations based on empirical results including actual-size tests. Then, for the Innovative Water Reactor for Flexible Fuel Cycle (FLWR) core, an actual size test of an embodiment of its design is required to confirm or modify such correlations. In this situation, development of a method that enables the thermal-hydraulic design of nuclear reactors without these actual size tests is desired, because these tests take a long time and entail great cost. For this reason, we developed an advanced thermal-hydraulic design method for FLWRs using innovative two-phase flow simulation technology. In this study, a detailed Two-Phase Flow simulation code using advanced Interface Tracking method: TPFIT is developed to calculate the detailed information of the two-phase flow. In this paper, firstly, we tried to verify the TPFIT code by comparing it with the existing 2-channel air-water mixing experimental results. Secondary, the TPFIT code was applied to simulation of steam-water two-phase flow in a model of two subchannels of a current BWRs and FLWRs rod bundle. The fluid mixing was observed at a gap between the subchannels. The existing two-phase flow correlation for fluid mixing is evaluated using detailed numerical simulation data. This data indicates that pressure difference between fluid channels is responsible for the fluid mixing, and thus the effects of the time average pressure difference and fluctuations must be incorporated in the two-phase flow correlation for fluid mixing. When inlet quality ratio of subchannels is relatively large, it is understood that evaluation precision of the existing two-phase flow correlations for fluid mixing are relatively low.

  10. Advanced numerical methods for three dimensional two-phase flow calculations

    SciTech Connect

    Toumi, I.; Caruge, D.

    1997-07-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.

  11. Advanced Magnetic Materials Methods and Numerical Models for Fluidization in Microgravity and Hypogravity

    NASA Technical Reports Server (NTRS)

    Atwater, James; Wheeler, Richard, Jr.; Akse, James; Jovanovic, Goran; Reed, Brian

    2013-01-01

    To support long-duration manned missions in space such as a permanent lunar base, Mars transit, or Mars Surface Mission, improved methods for the treatment of solid wastes, particularly methods that recover valuable resources, are needed. The ability to operate under microgravity and hypogravity conditions is essential to meet this objective. The utilization of magnetic forces to manipulate granular magnetic media has provided the means to treat solid wastes under variable gravity conditions by filtration using a consolidated magnetic media bed followed by thermal processing of the solid wastes in a fluidized bed reactor. Non-uniform magnetic fields will produce a magnetic field gradient in a bed of magnetically susceptible media toward the distributor plate of a fluidized bed reactor. A correctly oriented magnetic field gradient will generate a downward direct force on magnetic media that can substitute for gravitational force in microgravity, or which may augment low levels of gravity, such as on the Moon or Mars. This approach is termed Gradient Magnetically Assisted Fluidization (G-MAFB), in which the magnitude of the force on the fluidized media depends upon the intensity of the magnetic field (H), the intensity of the field gradient (dH/dz), and the magnetic susceptibility of the media. Fluidized beds based on the G-MAFB process can operate in any gravitational environment by tuning the magnetic field appropriately. Magnetic materials and methods have been developed that enable G-MAFB operation under variable gravity conditions.

  12. Advancing Efficient All-Electron Electronic Structure Methods Based on Numeric Atom-Centered Orbitals for Energy Related Materials

    NASA Astrophysics Data System (ADS)

    Blum, Volker

    This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.

  13. Advanced numerical methods for the simulation of flows in heterogeneous porous media and their application to parallel computing

    SciTech Connect

    Rame, M.

    1990-01-01

    Flows in highly heterogeneous porous media arise in a variety of processes including enhanced oil recovery, in situ bioremediation of underground contaminants, transport in underground aquifers and transport through biological membranes. The common denominator of these processes is the transport (and possibly reaction) of a multi-component fluid in several phases. A new numerical methodology for the analysis of flows in heterogeneous porous media is presented. Cases of miscible and immiscible displacement are simulated to investigate the influence of the local heterogeneities on the flow paths. This numerical scheme allows for a fine description of the flowing medium and the concentration and saturation distributions thus generated show low numerical dispersion. If the size of the area of interest is a square of a thousand feet per side, geological information on the porous medium can be incorporated to a length scale of about one to two feet. The technique here introduced, Operator Splitting on Multiple Grids, solves the elliptic operators by a higher-order finite-element technique on a coarse grid that proves efficient and accurate in incorporating different scales of heterogeneities. This coarse solution is interpolated to a fine grid by a splines-under-tension technique. The equations for the conservation of species are solved on this fine grid (of approximately half a million cells) by a finite-difference technique yielding numerical dispersions of less than ten feet. Cases presented herein involve a single phase miscible flow, and liquid-phase immiscible displacements. Cases are presented for model distributions of physical properties and for porosity and permeability data taken from a real reservoir. Techniques for the extension of the methods to compressible flow situations and compositional simulations are discussed.

  14. Towards Direct Numerical Simulation of mass and energy fluxes at the soil-atmospheric interface with advanced Lattice Boltzmann methods

    NASA Astrophysics Data System (ADS)

    Wang, Ying; Krafczyk, Manfred; Geier, Martin; Schönherr, Martin

    2014-05-01

    The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on many scales and are dominated by multi-component and multi-phase mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation has only started to be taken into account using simplified macroscopic models. As the flow field over the soil can be safely considered as turbulent, it would be natural to study the detailed transient flow dynamics by means of Large Eddy Simulation (LES [1]) where the three-dimensional flow field is resolved down to the laminar sub-layer. Yet this requires very fine resolved meshes allowing a grid resolution of at least one order of magnitude below the typical grain diameter of the soil under consideration. In order to gain reliable turbulence statistics, up to several hundred eddy turnover times have to be simulated which adds up to several seconds of real time. Yet, the time scale of the receding saturated water front dynamics in the soil is on the order of hours. Thus we are faced with the task of solving a transient turbulent flow problem including the advection-diffusion of water vapour over the soil-atmospheric interface represented by a realistic tomographic reconstruction of a real porous medium taken from laboratory probes. Our flow solver is based on the Lattice Boltzmann method (LBM) [2] which has been extended by a Cumulant approach similar to the one described in [3,4] to minimize the spurious coupling between the degrees of freedom in previous LBM approaches and can be used as an implicit LES turbulence model due to its low numerical dissipation and increased stability at high Reynolds numbers. The kernel has been integrated into the research code Virtualfluids [5] and delivers up to 30% of the

  15. Advances in numerical and applied mathematics

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)

    1986-01-01

    This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

  16. Brush seal numerical simulation: Concepts and advances

    NASA Technical Reports Server (NTRS)

    Braun, M. J.; Kudriavtsev, V. V.

    1994-01-01

    The development of the brush seal is considered to be most promising among the advanced type seals that are presently in use in the high speed turbomachinery. The brush is usually mounted on the stationary portions of the engine and has direct contact with the rotating element, in the process of limiting the 'unwanted' leakage flows between stages, or various engine cavities. This type of sealing technology is providing high (in comparison with conventional seals) pressure drops due mainly to the high packing density (around 100 bristles/sq mm), and brush compliance with the rotor motions. In the design of modern aerospace turbomachinery leakage flows between the stages must be minimal, thus contributing to the higher efficiency of the engine. Use of the brush seal instead of the labyrinth seal reduces the leakage flow by one order of magnitude. Brush seals also have been found to enhance dynamic performance, cost less, and are lighter than labyrinth seals. Even though industrial brush seals have been successfully developed through extensive experimentation, there is no comprehensive numerical methodology for the design or prediction of their performance. The existing analytical/numerical approaches are based on bulk flow models and do not allow the investigation of the effects of brush morphology (bristle arrangement), or brushes arrangement (number of brushes, spacing between them), on the pressure drops and flow leakage. An increase in the brush seal efficiency is clearly a complex problem that is closely related to the brush geometry and arrangement, and can be solved most likely only by means of a numerically distributed model.

  17. Brush seal numerical simulation: Concepts and advances

    NASA Astrophysics Data System (ADS)

    Braun, M. J.; Kudriavtsev, V. V.

    1994-07-01

    The development of the brush seal is considered to be most promising among the advanced type seals that are presently in use in the high speed turbomachinery. The brush is usually mounted on the stationary portions of the engine and has direct contact with the rotating element, in the process of limiting the 'unwanted' leakage flows between stages, or various engine cavities. This type of sealing technology is providing high (in comparison with conventional seals) pressure drops due mainly to the high packing density (around 100 bristles/sq mm), and brush compliance with the rotor motions. In the design of modern aerospace turbomachinery leakage flows between the stages must be minimal, thus contributing to the higher efficiency of the engine. Use of the brush seal instead of the labyrinth seal reduces the leakage flow by one order of magnitude. Brush seals also have been found to enhance dynamic performance, cost less, and are lighter than labyrinth seals. Even though industrial brush seals have been successfully developed through extensive experimentation, there is no comprehensive numerical methodology for the design or prediction of their performance. The existing analytical/numerical approaches are based on bulk flow models and do not allow the investigation of the effects of brush morphology (bristle arrangement), or brushes arrangement (number of brushes, spacing between them), on the pressure drops and flow leakage. An increase in the brush seal efficiency is clearly a complex problem that is closely related to the brush geometry and arrangement, and can be solved most likely only by means of a numerically distributed model.

  18. Numerical methods for molecular dynamics

    SciTech Connect

    Skeel, R.D.

    1991-01-01

    This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.

  19. Numerical methods for multibody systems

    NASA Technical Reports Server (NTRS)

    Glowinski, Roland; Nasser, Mahmoud G.

    1994-01-01

    This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.

  20. Some recent advances in the numerical solution of differential equations

    NASA Astrophysics Data System (ADS)

    D'Ambrosio, Raffaele

    2016-06-01

    The purpose of the talk is the presentation of some recent advances in the numerical solution of differential equations, with special emphasis to reaction-diffusion problems, Hamiltonian problems and ordinary differential equations with discontinuous right-hand side. As a special case, in this short paper we focus on the solution of reaction-diffusion problems by means of special purpose numerical methods particularly adapted to the problem: indeed, following a problem oriented approach, we propose a modified method of lines based on the employ of finite differences shaped on the qualitative behavior of the solutions. Constructive issues and a brief analysis are presented, together with some numerical experiments showing the effectiveness of the approach and a comparison with existing solvers.

  1. RELAP-7 Numerical Stabilization: Entropy Viscosity Method

    SciTech Connect

    R. A. Berry; M. O. Delchini; J. Ragusa

    2014-06-01

    The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.

  2. Numerical methods for engine-airframe integration

    SciTech Connect

    Murthy, S.N.B.; Paynter, G.C.

    1986-01-01

    Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.

  3. Advanced Numerical Model for Irradiated Concrete

    SciTech Connect

    Giorla, Alain B.

    2015-03-01

    In this report, we establish a numerical model for concrete exposed to irradiation to address these three critical points. The model accounts for creep in the cement paste and its coupling with damage, temperature and relative humidity. The shift in failure mode with the loading rate is also properly represented. The numerical model for creep has been validated and calibrated against different experiments in the literature [Wittmann, 1970, Le Roy, 1995]. Results from a simplified model are shown to showcase the ability of numerical homogenization to simulate irradiation effects in concrete. In future works, the complete model will be applied to the analysis of the irradiation experiments of Elleuch et al. [1972] and Kelly et al. [1969]. This requires a careful examination of the experimental environmental conditions as in both cases certain critical information are missing, including the relative humidity history. A sensitivity analysis will be conducted to provide lower and upper bounds of the concrete expansion under irradiation, and check if the scatter in the simulated results matches the one found in experiments. The numerical and experimental results will be compared in terms of expansion and loss of mechanical stiffness and strength. Both effects should be captured accordingly by the model to validate it. Once the model has been validated on these two experiments, it can be applied to simulate concrete from nuclear power plants. To do so, the materials used in these concrete must be as well characterized as possible. The main parameters required are the mechanical properties of each constituent in the concrete (aggregates, cement paste), namely the elastic modulus, the creep properties, the tensile and compressive strength, the thermal expansion coefficient, and the drying shrinkage. These can be either measured experimentally, estimated from the initial composition in the case of cement paste, or back-calculated from mechanical tests on concrete. If some

  4. Numerical analysis of the V-Y shaped advancement flap.

    PubMed

    Remache, D; Chambert, J; Pauchot, J; Jacquet, E

    2015-10-01

    The V-Y advancement flap is a usual technique for the closure of skin defects. A triangular flap is incised adjacent to a skin defect of rectangular shape. As the flap is advanced to close the initial defect, two smaller defects in the shape of a parallelogram are formed with respect to a reflection symmetry. The height of the defects depends on the apex angle of the flap and the closure efforts are related to the defects height. Andrades et al. 2005 have performed a geometrical analysis of the V-Y flap technique in order to reach a compromise between the flap size and the defects width. However, the geometrical approach does not consider the mechanical properties of the skin. The present analysis based on the finite element method is proposed as a complement to the geometrical one. This analysis aims to highlight the major role of the skin elasticity for a full analysis of the V-Y advancement flap. Furthermore, the study of this technique shows that closing at the flap apex seems mechanically the most interesting step. Thus different strategies of defect closure at the flap apex stemming from surgeon's know-how have been tested by numerical simulations. PMID:26342442

  5. Advanced Numerical Modeling of Turbulent Atmospheric Flows

    NASA Astrophysics Data System (ADS)

    Kühnlein, Christian; Dörnbrack, Andreas; Gerz, Thomas

    The present chapter introduces the method of computational simulation to predict and study turbulent atmospheric flows. This includes a description of the fundamental approach to computational simulation and the practical implementation using the technique of large-eddy simulation. In addition, selected contributions from IPA scientists to computational model development and various examples for applications are given. These examples include homogeneous turbulence, convective boundary layers, heated forest canopy, buoyant thermals, and large-scale flows with baroclinic wave instability.

  6. Advances in Numerical Boundary Conditions for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.

    1997-01-01

    Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

  7. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    SciTech Connect

    Klein, R I; Stone, J M

    2007-11-20

    We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.

  8. 25 Years of Self-organized Criticality: Numerical Detection Methods

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

  9. Preface to advances in numerical simulation of plasmas

    NASA Astrophysics Data System (ADS)

    Parker, Scott E.; Chacon, Luis

    2016-10-01

    This Journal of Computational Physics Special Issue, titled "Advances in Numerical Simulation of Plasmas," presents a snapshot of the international state of the art in the field of computational plasma physics. The articles herein are a subset of the topics presented as invited talks at the 24th International Conference on the Numerical Simulation of Plasmas (ICNSP), August 12-14, 2015 in Golden, Colorado. The choice of papers was highly selective. The ICNSP is held every other year and is the premier scientific meeting in the field of computational plasma physics.

  10. a Numerical Method for Turbulent Combustion Problems

    NASA Astrophysics Data System (ADS)

    Song, Yu.

    This dissertation presents a random numerical method which combines a random vortex method and a random choice method. With the assumption of incompressibility, the equations governing the fluid motion can be uncoupled from the equations governing the chemical reaction. A hybrid random vortex method is used for solving Navier -Stokes equation which governs the fluid motion. Combustion process is governed by reaction-diffusion system for the conservation of energy and the various chemical species participating in reaction. A random choice method is used for the modeling reaction-diffusion equations. The random choice method is tested and the numerical solutions are compared with the results by either the other numerical methods or exact solutions, good improvement and agreement have been obtained. For physical problem in two or more space dimensions, extension of the random choice method requires splitting the source terms into an x-sweep followed by a y-sweep. The splitting of the source term is also examined for an equation with an exact solution. The combustion model is applied to the problem of combustion in a circular cylinder with cylinder heated or kept cold. The flame profiles are obtained and effect of the turbulent is observed. The method is also applied to the ignition of a Bunsen burner. The correct modeling of mixing layer at the edge of the burner is found important in this application. Flame propagation profiles are obtained and have good agreement with experiments.

  11. A numerical method of detecting singularity

    NASA Technical Reports Server (NTRS)

    Laporte, M.; Vignes, J.

    1978-01-01

    A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.

  12. Recent advances in two-phase flow numerics

    SciTech Connect

    Mahaffy, J.H.; Macian, R.

    1997-07-01

    The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.

  13. Numerical Methods in Polarized Line Formation Theory

    NASA Astrophysics Data System (ADS)

    Nagendra, K. N.; Sampoorna, M.

    2009-06-01

    We review some numerical methods and provide benchmark solutions for the polarized line formation theory with partial redistribution (PRD) in the presence of magnetic fields. The transfer equation remains non-axisymmetric when written in the `Stokes vector basis'. It is relatively easier to develop numerical methods to solve the transfer equation for axisymmetric radiation fields. Therefore for non-axisymmetric problems it would be necessary to expand the azimuthal dependence of the scattering redistribution matrices in a Fourier series. The transfer equation in this so called `reduced form' becomes axisymmetric in the Fourier domain in which it is solved, and the reduced intensity is then transformed into the Stokes vector basis in real space. The advantage is that the reduced problem lends itself to be solved by appropriately organized PALI (Polarized Approximate Lambda Iteration) methods. We first dwell upon a frequency by frequency method (PALI7) that uses non-domain based PRD for the Hanle scattering problem, and then compare it with a core-wing method (PALI6) that uses a domain based PRD. The PALI methods use operator perturbation and involve construction of a suitable procedure to evaluate an `iterated source vector correction'. Another important component of PALI methods is the `Formal Solver' (for example Feautrier, short characteristic, DELOPAR etc.). The PALI methods are extremely fast on a computer and require very small memory. Finally, we present a simple perturbation method to solve the Hanle-Zeeman line formation problem in arbitrary strength magnetic fields.

  14. Advanced epidemiologic and analytical methods.

    PubMed

    Albanese, E

    2016-01-01

    Observational studies are indispensable for etiologic research, and are key to test life-course hypotheses and improve our understanding of neurologic diseases that have long induction and latency periods. In recent years a plethora of advanced design and analytic techniques have been developed to strengthen the robustness and ultimately the validity of the results of observational studies, and to address their inherent proneness to bias. It is the responsibility of clinicians and researchers to critically appraise and appropriately contextualize the findings of the exponentially expanding scientific literature. This critical appraisal should be rooted in a thorough understanding of advanced epidemiologic methods and techniques commonly used to formulate and test relevant hypotheses and to keep bias at bay. PMID:27637951

  15. Numerical methods: Analytical benchmarking in transport theory

    SciTech Connect

    Ganapol, B.D. )

    1988-01-01

    Numerical methods applied to reactor technology have reached a high degree of maturity. Certainly one- and two-dimensional neutron transport calculations have become routine, with several programs available on personal computer and the most widely used programs adapted to workstation and minicomputer computational environments. With the introduction of massive parallelism and as experience with multitasking increases, even more improvement in the development of transport algorithms can be expected. Benchmarking an algorithm is usually not a very pleasant experience for the code developer. Proper algorithmic verification by benchmarking involves the following considerations: (1) conservation of particles, (2) confirmation of intuitive physical behavior, and (3) reproduction of analytical benchmark results. By using today's computational advantages, new basic numerical methods have been developed that allow a wider class of benchmark problems to be considered.

  16. Hyperbolic conservation laws and numerical methods

    NASA Technical Reports Server (NTRS)

    Leveque, Randall J.

    1990-01-01

    The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

  17. Numerical methods for molecular dynamics. Progress report

    SciTech Connect

    Skeel, R.D.

    1991-12-31

    This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.

  18. Numerical analysis method for linear induction machines.

    NASA Technical Reports Server (NTRS)

    Elliott, D. G.

    1972-01-01

    A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.

  19. Numerical methods for finding stationary gravitational solutions

    NASA Astrophysics Data System (ADS)

    Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson

    2016-07-01

    The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.

  20. Numerical solution methods for viscoelastic orthotropic materials

    NASA Technical Reports Server (NTRS)

    Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

    1988-01-01

    Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

  1. Advanced numerics for multi-dimensional fluid flow calculations

    SciTech Connect

    Vanka, S.P.

    1984-04-01

    In recent years, there has been a growing interest in the development and use of mathematical models for the simulation of fluid flow, heat transfer and combustion processes in engineering equipment. The equations representing the multi-dimensional transport of mass, momenta and species are numerically solved by finite-difference or finite-element techniques. However despite the multiude of differencing schemes and solution algorithms, and the advancement of computing power, the calculation of multi-dimensional flows, especially three-dimensional flows, remains a mammoth task. The following discussion is concerned with the author's recent work on the construction of accurate discretization schemes for the partial derivatives, and the efficient solution of the set of nonlinear algebraic equations resulting after discretization. The present work has been jointly supported by the Ramjet Engine Division of the Wright Patterson Air Force Base, Ohio, and the NASA Lewis Research Center.

  2. Advanced numerics for multi-dimensional fluid flow calculations

    NASA Technical Reports Server (NTRS)

    Vanka, S. P.

    1984-01-01

    In recent years, there has been a growing interest in the development and use of mathematical models for the simulation of fluid flow, heat transfer and combustion processes in engineering equipment. The equations representing the multi-dimensional transport of mass, momenta and species are numerically solved by finite-difference or finite-element techniques. However despite the multiude of differencing schemes and solution algorithms, and the advancement of computing power, the calculation of multi-dimensional flows, especially three-dimensional flows, remains a mammoth task. The following discussion is concerned with the author's recent work on the construction of accurate discretization schemes for the partial derivatives, and the efficient solution of the set of nonlinear algebraic equations resulting after discretization. The present work has been jointly supported by the Ramjet Engine Division of the Wright Patterson Air Force Base, Ohio, and the NASA Lewis Research Center.

  3. Recent advances in numerical analysis of structural eigenvalue problems

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1973-01-01

    A wide range of eigenvalue problems encountered in practical structural engineering analyses is defined, in which the structures are assumed to be discretized by any suitable technique such as the finite-element method. A review of the usual numerical procedures for the solution of such eigenvalue problems is presented and is followed by an extensive account of recently developed eigenproblem solution procedures. Particular emphasis is placed on the new numerical algorithms and associated computer programs based on the Sturm sequence method. Eigenvalue algorithms developed for efficient solution of natural frequency and buckling problems of structures are presented, as well as some eigenvalue procedures formulated in connection with the solution of quadratic matrix equations associated with free vibration analysis of structures. A new algorithm is described for natural frequency analysis of damped structural systems.

  4. Numerical methods for problems in computational aeroacoustics

    NASA Astrophysics Data System (ADS)

    Mead, Jodi Lorraine

    1998-12-01

    A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev

  5. Numerical manifold method based on the method of weighted residuals

    NASA Astrophysics Data System (ADS)

    Li, S.; Cheng, Y.; Wu, Y.-F.

    2005-05-01

    Usually, the governing equations of the numerical manifold method (NMM) are derived from the minimum potential energy principle. For many applied problems it is difficult to derive in general outset the functional forms of the governing equations. This obviously strongly restricts the implementation of the minimum potential energy principle or other variational principles in NMM. In fact, the governing equations of NMM can be derived from a more general method of weighted residuals. By choosing suitable weight functions, the derivation of the governing equations of the NMM from the weighted residual method leads to the same result as that derived from the minimum potential energy principle. This is demonstrated in the paper by deriving the governing equations of the NMM for linear elasticity problems, and also for Laplace's equation for which the governing equations of the NMM cannot be derived from the minimum potential energy principle. The performance of the method is illustrated by three numerical examples.

  6. Advanced diagnostic methods in avionics

    NASA Astrophysics Data System (ADS)

    Popyack, Leonard Joseph, Jr.

    Advanced diagnostic systems facilitate further enhancement of reliability and safety of modern aircraft. Unlike classical reliability analyses, addressing specific classes of systems or devices, this research is aimed at the development of methods for assessment of the individual reliability characteristics of particular system components subjected to their unique histories of operational conditions and exposure to adverse environmental factors. Individual reliability characteristics are crucial for the implementation of the most efficient maintenance practice of flight-critical system components, known as "condition-based maintenance." The dissertation presents hardware and software aspects of a computer-based system, Time-Stress Monitoring Device, developed to record, store, and analyze raw data characterizing operational and environmental conditions and performance of electro-mechanical flight control system components and aircraft electronics (avionics). Availability of this data facilitates formulation and solution of such diagnostic problems as estimation of the probability of failure and life expectancy of particular components, failure detection, identification, and prediction. Statistical aspects of system diagnostics are considered. Particular diagnostic procedures utilizing cluster analysis, Bayes' technique, and regression analysis are formulated. Laboratory and simulation experiment that verify the obtained results are provided.

  7. Recent numerical and algorithmic advances within the volume tracking framework for modeling interfacial flows

    DOE PAGES

    François, Marianne M.

    2015-05-28

    A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented. The volume tracking method, also known as the volume-of-fluid method has become an established numerical approach to model and simulate interfacial flows. Its advantage is its strict mass conservation. However, because the interface is not explicitly tracked but captured via the material volume fraction on a fixed mesh, accurate estimation of the interface position, its geometric properties and modeling of interfacial physics in the volume tracking framework remain difficult. Several improvements have been made over the last decade to address these challenges.more » In this study, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted.« less

  8. Recent numerical and algorithmic advances within the volume tracking framework for modeling interfacial flows

    SciTech Connect

    François, Marianne M.

    2015-05-28

    A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented. The volume tracking method, also known as the volume-of-fluid method has become an established numerical approach to model and simulate interfacial flows. Its advantage is its strict mass conservation. However, because the interface is not explicitly tracked but captured via the material volume fraction on a fixed mesh, accurate estimation of the interface position, its geometric properties and modeling of interfacial physics in the volume tracking framework remain difficult. Several improvements have been made over the last decade to address these challenges. In this study, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted.

  9. Advanced surface paneling method for subsonic and supersonic flow

    NASA Technical Reports Server (NTRS)

    Erickson, L. L.; Johnson, F. T.; Ehlers, F. E.

    1976-01-01

    Numerical results illustrating the capabilities of an advanced aerodynamic surface paneling method are presented. The method is applicable to both subsonic and supersonic flow, as represented by linearized potential flow theory. The method is based on linearly varying sources and quadratically varying doublets which are distributed over flat or curved panels. These panels are applied to the true surface geometry of arbitrarily shaped three dimensional aerodynamic configurations.

  10. Numerical Methods for Forward and Inverse Problems in Discontinuous Media

    SciTech Connect

    Chartier, Timothy P.

    2011-03-08

    The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.

  11. Advanced reliability methods - A review

    NASA Astrophysics Data System (ADS)

    Forsyth, David S.

    2016-02-01

    There are a number of challenges to the current practices for Probability of Detection (POD) assessment. Some Nondestructive Testing (NDT) methods, especially those that are image-based, may not provide a simple relationship between a scalar NDT response and a damage size. Some damage types are not easily characterized by a single scalar metric. Other sensing paradigms, such as structural health monitoring, could theoretically replace NDT but require a POD estimate. And the cost of performing large empirical studies to estimate POD can be prohibitive. The response of the research community has been to develop new methods that can be used to generate the same information, POD, in a form that can be used by engineering designers. This paper will highlight approaches to image-based data and complex defects, Model Assisted POD estimation, and Bayesian methods for combining information. This paper will also review the relationship of the POD estimate, confidence bounds, tolerance bounds, and risk assessment.

  12. Numerical matrix method for quantum periodic potentials

    NASA Astrophysics Data System (ADS)

    Le Vot, Felipe; Meléndez, Juan J.; Yuste, Santos B.

    2016-06-01

    A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, a KP solid containing a surface, and a KP solid under an external field. A short list of additional problems that can be solved with this procedure is presented.

  13. Numerical methods in Markov chain modeling

    NASA Technical Reports Server (NTRS)

    Philippe, Bernard; Saad, Youcef; Stewart, William J.

    1989-01-01

    Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

  14. Interpolation Method Needed for Numerical Uncertainty

    NASA Technical Reports Server (NTRS)

    Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.

    2014-01-01

    Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

  15. Advanced Fine Particulate Characterization Methods

    SciTech Connect

    Steven Benson; Lingbu Kong; Alexander Azenkeng; Jason Laumb; Robert Jensen; Edwin Olson; Jill MacKenzie; A.M. Rokanuzzaman

    2007-01-31

    The characterization and control of emissions from combustion sources are of significant importance in improving local and regional air quality. Such emissions include fine particulate matter, organic carbon compounds, and NO{sub x} and SO{sub 2} gases, along with mercury and other toxic metals. This project involved four activities including Further Development of Analytical Techniques for PM{sub 10} and PM{sub 2.5} Characterization and Source Apportionment and Management, Organic Carbonaceous Particulate and Metal Speciation for Source Apportionment Studies, Quantum Modeling, and High-Potassium Carbon Production with Biomass-Coal Blending. The key accomplishments included the development of improved automated methods to characterize the inorganic and organic components particulate matter. The methods involved the use of scanning electron microscopy and x-ray microanalysis for the inorganic fraction and a combination of extractive methods combined with near-edge x-ray absorption fine structure to characterize the organic fraction. These methods have direction application for source apportionment studies of PM because they provide detailed inorganic analysis along with total organic and elemental carbon (OC/EC) quantification. Quantum modeling using density functional theory (DFT) calculations was used to further elucidate a recently developed mechanistic model for mercury speciation in coal combustion systems and interactions on activated carbon. Reaction energies, enthalpies, free energies and binding energies of Hg species to the prototype molecules were derived from the data obtained in these calculations. Bimolecular rate constants for the various elementary steps in the mechanism have been estimated using the hard-sphere collision theory approximation, and the results seem to indicate that extremely fast kinetics could be involved in these surface reactions. Activated carbon was produced from a blend of lignite coal from the Center Mine in North Dakota and

  16. Free Radical Addition Polymerization Kinetics without Steady-State Approximations: A Numerical Analysis for the Polymer, Physical, or Advanced Organic Chemistry Course

    ERIC Educational Resources Information Center

    Iler, H. Darrell; Brown, Amber; Landis, Amanda; Schimke, Greg; Peters, George

    2014-01-01

    A numerical analysis of the free radical addition polymerization system is described that provides those teaching polymer, physical, or advanced organic chemistry courses the opportunity to introduce students to numerical methods in the context of a simple but mathematically stiff chemical kinetic system. Numerical analysis can lead students to an…

  17. Recent advances in lattice Boltzmann methods

    SciTech Connect

    Chen, S.; Doolen, G.D.; He, X.; Nie, X.; Zhang, R.

    1998-12-31

    In this paper, the authors briefly present the basic principles of lattice Boltzmann method and summarize recent advances of the method, including the application of the lattice Boltzmann method for fluid flows in MEMS and simulation of the multiphase mixing and turbulence.

  18. Numerical analysis of the orthogonal descent method

    SciTech Connect

    Shokov, V.A.; Shchepakin, M.B.

    1994-11-01

    The author of the orthogonal descent method has been testing it since 1977. The results of these tests have only strengthened the need for further analysis and development of orthogonal descent algorithms for various classes of convex programming problems. Systematic testing of orthogonal descent algorithms and comparison of test results with other nondifferentiable optimization methods was conducted at TsEMI RAN in 1991-1992 using the results.

  19. Numerical simulation of the boat growth method

    NASA Astrophysics Data System (ADS)

    Oda, K.; Saito, T.; Nishihama, J.; Ishihara, T.

    1989-09-01

    This paper presents a three-dimensional mathematical model for thermal convection in molten metals, which is applicable to the heat transfer phenomena in a boat-shaped crucibles. The governing equations are solved using an extended version, developed by Saito et al. (1986), of the Amsden and Harlow (1968) simplified marker and cell method. It is shown that the following parameters must be incorporated for an accurate simulation of melt growth: (1) the radiative heat transfer in the furnace, (2) the complex crucible configuration, (3) the melt flow, and (4) the solid-liquid interface shape. The velocity and temperature distribution calculated from this model are compared with the results of previous studies.

  20. Numerical methods for analyzing electromagnetic scattering

    NASA Technical Reports Server (NTRS)

    Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.

    1985-01-01

    Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.

  1. Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

    PubMed

    Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

    2016-09-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record

  2. Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

    PubMed Central

    2016-01-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

  3. Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

    PubMed

    Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

    2016-09-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record PMID:26913930

  4. Advanced analysis methods in particle physics

    SciTech Connect

    Bhat, Pushpalatha C.; /Fermilab

    2010-10-01

    Each generation of high energy physics experiments is grander in scale than the previous - more powerful, more complex and more demanding in terms of data handling and analysis. The spectacular performance of the Tevatron and the beginning of operations of the Large Hadron Collider, have placed us at the threshold of a new era in particle physics. The discovery of the Higgs boson or another agent of electroweak symmetry breaking and evidence of new physics may be just around the corner. The greatest challenge in these pursuits is to extract the extremely rare signals, if any, from huge backgrounds arising from known physics processes. The use of advanced analysis techniques is crucial in achieving this goal. In this review, I discuss the concepts of optimal analysis, some important advanced analysis methods and a few examples. The judicious use of these advanced methods should enable new discoveries and produce results with better precision, robustness and clarity.

  5. Numerical solution of integral-algebraic equations for multistep methods

    NASA Astrophysics Data System (ADS)

    Budnikova, O. S.; Bulatov, M. V.

    2012-05-01

    Systems of Volterra linear integral equations with identically singular matrices in the principal part (called integral-algebraic equations) are examined. Multistep methods for the numerical solution of a selected class of such systems are proposed and justified.

  6. Cost estimating methods for advanced space systems

    NASA Technical Reports Server (NTRS)

    Cyr, Kelley

    1988-01-01

    The development of parametric cost estimating methods for advanced space systems in the conceptual design phase is discussed. The process of identifying variables which drive cost and the relationship between weight and cost are discussed. A theoretical model of cost is developed and tested using a historical data base of research and development projects.

  7. An advanced probabilistic structural analysis method for implicit performance functions

    NASA Technical Reports Server (NTRS)

    Wu, Y.-T.; Millwater, H. R.; Cruse, T. A.

    1989-01-01

    In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.

  8. A numerical classical flutter analysis of advanced propellers

    NASA Technical Reports Server (NTRS)

    Srivastava, R.; Reddy, T. S. R.; Mehmed, O.

    1992-01-01

    A three-dimensional Euler solver is coupled with a three-dimensional structural dynamics model to investigate flutter of propfans. An implicit-explicit hybrid scheme is used to reduce computational time for the solution of Euler equations. The aeroelastic equations are formulated in normal modes and are solved for flutter in frequency domain. The required generalized forces are obtained using a pulse response method. Computations show that the instability is dominated by the second mode frequency as was observed in experiment.

  9. Numerical Modeling and Inverse Scattering in Nondestructive Testing: Recent Applications and Advances

    NASA Astrophysics Data System (ADS)

    Marklein, R.; Langenberg, K. J.; Mayer, K.; Shlivinski, A.; Miao, J.; Zimmer, A.; Müller, W.; Schmitz, V.; Kohl, C.; Mletzko, U.

    2005-04-01

    This paper presents recent advances and future challenges of the application of different numerical modeling tools and linear and nonlinear inversion algorithms in ultrasonics and electromagnetics applied in NDE. The inversion methods considered in the presented work vary from linear schemes, e.g. SAFT/InASAFT and Diffraction Tomography/FT-SAFT, to nonlinear schemes, e.g. the Contrast Source Inversion. Inversion results are presented and compared for modeled and measured ultrasonic and electromagnetic data to locate voids and cracks as well as to locate aluminum tendon ducts in concrete, which is a typical GPR problem. Finite Integration Technique (FIT) and Domain Integral Equation (DIE) solvers are used as modeling tools.

  10. Asymptotic-induced numerical methods for conservation laws

    NASA Technical Reports Server (NTRS)

    Garbey, Marc; Scroggs, Jeffrey S.

    1990-01-01

    Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

  11. EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY

    SciTech Connect

    FRANCOIS, MARIANNE M.; DENDY, EDWARD D.; LOWRIE, ROBERT B.; LIVESCU, DANIEL; STEINKAMP, MICHAEL J.

    2007-01-11

    The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.

  12. Parallel processing numerical method for confined vortex dynamics and applications

    NASA Astrophysics Data System (ADS)

    Bistrian, Diana Alina

    2013-10-01

    This paper explores a combined analytical and numerical technique to investigate the hydrodynamic instability of confined swirling flows, with application to vortex rope dynamics in a Francis turbine diffuser, in condition of sophisticated boundary constraints. We present a new approach based on the method of orthogonal decomposition in the Hilbert space, implemented with a spectral descriptor scheme in discrete space. A parallel implementation of the numerical scheme is conducted reducing the computational time compared to other techniques.

  13. Numeric Modified Adomian Decomposition Method for Power System Simulations

    SciTech Connect

    Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth

    2016-01-01

    This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.

  14. Evolving excised black holes with TVD numerical methods

    NASA Astrophysics Data System (ADS)

    Neilsen, David

    2003-04-01

    Total Variation Diminishing (TVD) numerical methods have improved stability properties for nonlinear differential equations, and are widely used in computational fluid dynamics. While Einstein's equations are not genuinely nonlinear, these methods may be advantageous for solving the Einstein equations in specific instances, such as evolving fluid spacetimes and black holes with excision. Using a Frittelli-Reula formulation of the Einstein equations, I will present results of 1-D and 3-D black hole evolutions, and compare the performance of TVD methods with other numerical approaches.

  15. Editorial: Latest methods and advances in biotechnology.

    PubMed

    Lee, Sang Yup; Jungbauer, Alois

    2014-01-01

    The latest "Biotech Methods and Advances" special issue of Biotechnology Journal continues the BTJ tradition of featuring the latest breakthroughs in biotechnology. The special issue is edited by our Editors-in-Chief, Prof. Sang Yup Lee and Prof. Alois Jungbauer and covers a wide array of topics in biotechnology, including the perennial favorite workhorses of the biotech industry, Chinese hamster ovary (CHO) cell and Escherichia coli.

  16. Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation

    SciTech Connect

    Ismail, M. S.

    2010-09-30

    The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.

  17. A numerical method for solving singular De`s

    SciTech Connect

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  18. Investigating Convergence Patterns for Numerical Methods Using Data Analysis

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    2013-01-01

    The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

  19. Advanced electromagnetic methods for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Balanis, Constantine A.; El-Sharawy, El-Budawy; Hashemi-Yeganeh, Shahrokh; Aberle, James T.; Birtcher, Craig R.

    1991-01-01

    The Advanced Helicopter Electromagnetics is centered on issues that advance technology related to helicopter electromagnetics. Progress was made on three major topics: composite materials; precipitation static corona discharge; and antenna technology. In composite materials, the research has focused on the measurements of their electrical properties, and the modeling of material discontinuities and their effect on the radiation pattern of antennas mounted on or near material surfaces. The electrical properties were used to model antenna performance when mounted on composite materials. Since helicopter platforms include several antenna systems at VHF and UHF bands, measuring techniques are being explored that can be used to measure the properties at these bands. The effort on corona discharge and precipitation static was directed toward the development of a new two dimensional Voltage Finite Difference Time Domain computer program. Results indicate the feasibility of using potentials for simulating electromagnetic problems in the cases where potentials become primary sources. In antenna technology the focus was on Polarization Diverse Conformal Microstrip Antennas, Cavity Backed Slot Antennas, and Varactor Tuned Circular Patch Antennas. Numerical codes were developed for the analysis of two probe fed rectangular and circular microstrip patch antennas fed by resistive and reactive power divider networks.

  20. Simulation methods for advanced scientific computing

    SciTech Connect

    Booth, T.E.; Carlson, J.A.; Forster, R.A.

    1998-11-01

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objective of the project was to create effective new algorithms for solving N-body problems by computer simulation. The authors concentrated on developing advanced classical and quantum Monte Carlo techniques. For simulations of phase transitions in classical systems, they produced a framework generalizing the famous Swendsen-Wang cluster algorithms for Ising and Potts models. For spin-glass-like problems, they demonstrated the effectiveness of an extension of the multicanonical method for the two-dimensional, random bond Ising model. For quantum mechanical systems, they generated a new method to compute the ground-state energy of systems of interacting electrons. They also improved methods to compute excited states when the diffusion quantum Monte Carlo method is used and to compute longer time dynamics when the stationary phase quantum Monte Carlo method is used.

  1. Comparison of methods for numerical calculation of continuum damping

    SciTech Connect

    Bowden, G. W.; Hole, M. J.; Dennis, G. R.; Könies, A.; Gorelenkov, N. N.

    2014-05-15

    Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly, in the case of the toroidicity-induced shear Alfvén eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.

  2. Random element method for numerical modeling of diffusional processes

    NASA Technical Reports Server (NTRS)

    Ghoniem, A. F.; Oppenheim, A. K.

    1982-01-01

    The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

  3. Advanced Bayesian Method for Planetary Surface Navigation

    NASA Technical Reports Server (NTRS)

    Center, Julian

    2015-01-01

    Autonomous Exploration, Inc., has developed an advanced Bayesian statistical inference method that leverages current computing technology to produce a highly accurate surface navigation system. The method combines dense stereo vision and high-speed optical flow to implement visual odometry (VO) to track faster rover movements. The Bayesian VO technique improves performance by using all image information rather than corner features only. The method determines what can be learned from each image pixel and weighs the information accordingly. This capability improves performance in shadowed areas that yield only low-contrast images. The error characteristics of the visual processing are complementary to those of a low-cost inertial measurement unit (IMU), so the combination of the two capabilities provides highly accurate navigation. The method increases NASA mission productivity by enabling faster rover speed and accuracy. On Earth, the technology will permit operation of robots and autonomous vehicles in areas where the Global Positioning System (GPS) is degraded or unavailable.

  4. Recent advances in analytical methods for mycotoxins.

    PubMed

    Gilbert, J

    1993-01-01

    Recent advances in analytical methods are reviewed using the examples of aflatoxins and trichothecene mycotoxins. The most dramatic advances are seen as being those based on immunological principles utilized for aflatoxins to produce simple screening methods and for rapid specific clean-up. The possibilities of automation using immunoaffinity columns is described. In contrast for the trichothecenes immunological methods have not had the same general impact. Post-column derivatization using bromine or iodine to enhance fluorescence for HPLC detection of aflatoxins has become widely employed and there are similar possibilities for improved HPLC detection for trichothecenes using electrochemical or trichothecene-specific post-column reactions. There have been improvements in the use of more rapid and specific clean-up methods for trichothecenes, whilst HPLC and GC remain equally favoured for the end-determination. More sophisticated instrumental techniques such as mass spectrometry (LC/MS, MS/MS) and supercritical fluid chromatography (SFC/MS) have been demonstrated to have potential for application to mycotoxin analysis, but have not as yet made much general impact.

  5. Prandtl's Equations: Numerical Results about Singularity Formation and a New Numerical Method

    NASA Astrophysics Data System (ADS)

    Puppo, Gabriella

    1990-01-01

    In this work, new numerical results about singularity formation for unsteady Prandtl's equations are presented. Extensive computations with a Lax Wendroff scheme for the impulsively started circular cylinder show that the gradient of the velocity becomes infinite in a finite time. The accuracy and the simplicity of the Lax Wendroff scheme allow us to couple the resolution given by second order accuracy in space with the detail of an extremely fine grid. Thus, while these computations confirm previous results about singularity formation (Van Dommelen and Shen, Cebeci, Wang), they differ in other respects. In fact the peak in the velocity gradient appears to be located upstream of the region of reversed flow and away from the zero vorticity line. Some analytic arguments are also presented to support these conclusions, independently of the computations. In the second part of this work another new numerical method to solve the unsteady Prandtl equations is proposed. This numerical scheme derives from Chorin's Vortex Sheet method. The equations are also solved with operator splitting, but, unlike Chorin's, this scheme is deterministic. This feature is achieved using a Lagrangian particle formulation for the convective step and solving the diffusion step with finite differences on an Eulerian mesh. Finally, a numerical convergence proof is presented.

  6. Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

    SciTech Connect

    Cai, Wei

    2014-05-15

    Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.

  7. Advanced Analysis Methods in High Energy Physics

    SciTech Connect

    Pushpalatha C. Bhat

    2001-10-03

    During the coming decade, high energy physics experiments at the Fermilab Tevatron and around the globe will use very sophisticated equipment to record unprecedented amounts of data in the hope of making major discoveries that may unravel some of Nature's deepest mysteries. The discovery of the Higgs boson and signals of new physics may be around the corner. The use of advanced analysis techniques will be crucial in achieving these goals. The author discusses some of the novel methods of analysis that could prove to be particularly valuable for finding evidence of any new physics, for improving precision measurements and for exploring parameter spaces of theoretical models.

  8. COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

    SciTech Connect

    Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov

    2011-08-10

    Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the

  9. Numerical methods for aerothermodynamic design of hypersonic space transport vehicles

    NASA Astrophysics Data System (ADS)

    Wanie, K. M.; Brenneis, A.; Eberle, A.; Heiss, S.

    1993-04-01

    The requirement of the design process of hypersonic vehicles to predict flow past entire configurations with wings, fins, flaps, and propulsion system represents one of the major challenges for aerothermodynamics. In this context computational fluid dynamics has come up as a powerful tool to support the experimental work. A couple of numerical methods developed at MBB designed to fulfill the needs of the design process are described. The governing equations and fundamental details of the solution methods are shortly reviewed. Results are given for both geometrically simple test cases and realistic hypersonic configurations. Since there is still a considerable lack of experience for hypersonic flow calculations an extensive testing and verification is essential. This verification is done by comparison of results with experimental data and other numerical methods. The results presented prove that the methods used are robust, flexible, and accurate enough to fulfill the strong needs of the design process.

  10. A general numerical method to solve for dislocation configurations

    NASA Astrophysics Data System (ADS)

    Xin, X. J.; Wagoner, R. H.; Daehn, G. S.

    1999-08-01

    The shape of a mechanically equilibrated dislocation line is of considerable interest in the study of plastic deformation of metals and alloys. A general numerical method for finding such configurations in arbitrary stress fields has been developed. Analogous to the finite-element method (FEM), a general dislocation line is approximated by a series of straight segments (elements) bounded by nodes. The equilibrium configuration is found by minimizing the system energy with respect to nodal positions using a Newton-Raphson procedure. This approach, termed the finite-segment method (FSM), confers several advantages relative to segment-based, explicit formulations. The utility, generality, and robustness of the FSM is demonstrated by analyzing the Orowan bypass mechanism and a model of dislocation generation and equilibration at misfitting particles. Energy differences from previous analytical methods based on simple loop shapes are significant, up to 80 pct. Explicit expressions for the coordinate transformations, energies, and forces required for numerical implementation are presented.

  11. A gyrokinetic continuum code based on the numerical Lie transform (NLT) method

    NASA Astrophysics Data System (ADS)

    Ye, Lei; Xu, Yingfeng; Xiao, Xiaotao; Dai, Zongliang; Wang, Shaojie

    2016-07-01

    In this work, we report a novel gyrokinetic simulation method named numerical Lie transform (NLT), which depends on a new physical model derived from the I-transform theory. In this model, the perturbed motion of a particle is decoupled from the unperturbed motion. Due to this property, the unperturbed orbit can be computed in advance and saved as numerical tables for real-time computation. A 4D tensor B-spline interpolation module is developed and applied with the semi-Lagrangian scheme to avoid operator splitting. The NLT code is verified by the Rosenbluth-Hinton test and the linear ITG Cyclone test.

  12. A novel numerical method for radiation exchange in granular medium

    NASA Astrophysics Data System (ADS)

    Dayal, Ram; Gambaryan-Roisman, Tatiana

    2016-11-01

    A very simple numerical method is developed to determine the inter-particle radiation heat transfer in a granular powder bed. The method is completely independent of coordinate system and does not require any domain discretization. The solution procedure does not involve any matrix inversion, thus making it suitable candidate for radiation heat transfer problems involving large number of interacting surfaces, especially granular powder beds.

  13. Comparison of Two Numerical Methods for Computing Fractal Dimensions

    NASA Astrophysics Data System (ADS)

    Shiozawa, Yui; Miller, Bruce; Rouet, Jean-Louis

    2012-10-01

    From cosmology to economics, the examples of fractals can be found virtually everywhere. However, since few fractals permit the analytical evaluation of generalized fractal dimensions or R'enyi dimensions, the search for effective numerical methods is inevitable. In this project two promising numerical methods for obtaining generalized fractal dimensions, based on the distribution of distances within a set, are examined. They can be applied, in principle, to any set even if no closed-form expression is available. The biggest advantage of these methods is their ability to generate a spectrum of generalized dimensions almost simultaneously. It should be noted that this feature is essential to the analysis of multifractals. As a test of their effectiveness, here the methods were applied to the generalized Cantor set and the multiplicative binomial process. The generalized dimensions of both sets can be readily derived analytically, thus enabling the accuracy of the numerical methods to be verified. Here we will present a comparison of the analytical results and the predictions of the methods. We will show that, while they are effective, care must be taken in their interpretation.

  14. Singularity Preserving Numerical Methods for Boundary Integral Equations

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki (Principal Investigator)

    1996-01-01

    In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

  15. 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.

  16. Advances in plant gene silencing methods.

    PubMed

    Pandey, Prachi; Senthil-Kumar, Muthappa; Mysore, Kirankumar S

    2015-01-01

    Understanding molecular mechanisms of transcriptional and posttranscriptional gene silencing pathways in plants over the past decades has led to development of tools and methods for silencing a target gene in various plant species. In this review chapter, both the recent understanding of molecular basis of gene silencing pathways and advances in various widely used gene silencing methods are compiled. We also discuss the salient features of the different methods like RNA interference (RNAi) and virus-induced gene silencing (VIGS) and highlight their advantages and disadvantages. Gene silencing technology is constantly progressing as reflected by rapidly emerging new methods. A succinct discussion on the recently developed methods like microRNA-mediated virus-induced gene silencing (MIR-VIGS) and microRNA-induced gene silencing (MIGS) is also provided. One major bottleneck in gene silencing approaches has been the associated off-target silencing. The other hurdle has been the lack of a universal approach that can be applied to all plants. For example, we face hurdles like incompatibility of VIGS vectors with the host and inability to use MIGS for plant species which are not easily transformable. However, the overwhelming research in this direction reflects the scope for overcoming the short comings of gene silencing technology.

  17. Numerical Polynomial Homotopy Continuation Method and String Vacua

    DOE PAGES

    Mehta, Dhagash

    2011-01-01

    Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

  18. Numerical analysis of Weyl's method for integrating boundary layer equations

    NASA Technical Reports Server (NTRS)

    Najfeld, I.

    1982-01-01

    A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.

  19. Computational methods for aerodynamic design using numerical optimization

    NASA Technical Reports Server (NTRS)

    Peeters, M. F.

    1983-01-01

    Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.

  20. Projected discrete ordinates methods for numerical transport problems

    SciTech Connect

    Larsen, E.W.

    1985-01-01

    A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

  1. A numerical method to study the dynamics of capillary fluid systems

    NASA Astrophysics Data System (ADS)

    Herrada, M. A.; Montanero, J. M.

    2016-02-01

    We propose a numerical approach to study both the nonlinear dynamics and linear stability of capillary fluid systems. In the nonlinear analysis, the time-dependent fluid region is mapped onto a fixed numerical domain through a coordinate transformation. The hydrodynamic equations are spatially discretized with the Chebyshev spectral collocation technique, while an implicit time advancement is performed using second-order backward finite differences. The resulting algebraic equations are solved with the iterative Newton-Raphson technique. The most novel aspect of the method is the fact that the elements of the Jacobian of the discretized system of equations are symbolic functions calculated before running the simulation. These functions are evaluated numerically in the Newton-Raphson iterations to find the solution at each time step, which reduces considerably the computing time. Besides, this numerical procedure can be easily adapted to solve the eigenvalue problem which determines the linear global modes of the capillary system. Therefore, both the nonlinear dynamics and the linear stability analysis can be conducted with essentially the same algorithm. We validate this numerical approach by studying the dynamics of a liquid bridge close to its minimum volume stability limit. The results are virtually the same as those obtained with other methods. The proposed approach proves to be much more computationally efficient than those other methods. Finally, we show the versatility of the method by calculating the linear global modes of a gravitational jet.

  2. Advancing MODFLOW Applying the Derived Vector Space Method

    NASA Astrophysics Data System (ADS)

    Herrera, G. S.; Herrera, I.; Lemus-García, M.; Hernandez-Garcia, G. D.

    2015-12-01

    The most effective domain decomposition methods (DDM) are non-overlapping DDMs. Recently a new approach, the DVS-framework, based on an innovative discretization method that uses a non-overlapping system of nodes (the derived-nodes), was introduced and developed by I. Herrera et al. [1, 2]. Using the DVS-approach a group of four algorithms, referred to as the 'DVS-algorithms', which fulfill the DDM-paradigm (i.e. the solution of global problems is obtained by resolution of local problems exclusively) has been derived. Such procedures are applicable to any boundary-value problem, or system of such equations, for which a standard discretization method is available and then software with a high degree of parallelization can be constructed. In a parallel talk, in this AGU Fall Meeting, Ismael Herrera will introduce the general DVS methodology. The application of the DVS-algorithms has been demonstrated in the solution of several boundary values problems of interest in Geophysics. Numerical examples for a single-equation, for the cases of symmetric, non-symmetric and indefinite problems were demonstrated before [1,2]. For these problems DVS-algorithms exhibited significantly improved numerical performance with respect to standard versions of DDM algorithms. In view of these results our research group is in the process of applying the DVS method to a widely used simulator for the first time, here we present the advances of the application of this method for the parallelization of MODFLOW. Efficiency results for a group of tests will be presented. References [1] I. Herrera, L.M. de la Cruz and A. Rosas-Medina. Non overlapping discretization methods for partial differential equations, Numer Meth Part D E, (2013). [2] Herrera, I., & Contreras Iván "An Innovative Tool for Effectively Applying Highly Parallelized Software To Problems of Elasticity". Geofísica Internacional, 2015 (In press)

  3. Fast and stable numerical method for neuronal modelling

    NASA Astrophysics Data System (ADS)

    Hashemi, Soheil; Abdolali, Ali

    2016-11-01

    Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.

  4. Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method

    NASA Technical Reports Server (NTRS)

    Spalart, P. R.

    1986-01-01

    A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.

  5. Fast numerical treatment of nonlinear wave equations by spectral methods

    SciTech Connect

    Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.

    2011-02-15

    A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.

  6. Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

    SciTech Connect

    Safta, Cosmin; Najm, Habib N.; Phipps, Eric Todd

    2014-09-01

    Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.

  7. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

    NASA Astrophysics Data System (ADS)

    Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

    2015-05-01

    We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

  8. Integrated numerical methods for hypersonic aircraft cooling systems analysis

    NASA Technical Reports Server (NTRS)

    Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.

    1992-01-01

    Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.

  9. Numerical simulation of thermal discharge based on FVM method

    NASA Astrophysics Data System (ADS)

    Yu, Yunli; Wang, Deguan; Wang, Zhigang; Lai, Xijun

    2006-01-01

    A two-dimensional numerical model is proposed to simulate the thermal discharge from a power plant in Jiangsu Province. The equations in the model consist of two-dimensional non-steady shallow water equations and thermal waste transport equations. Finite volume method (FVM) is used to discretize the shallow water equations, and flux difference splitting (FDS) scheme is applied. The calculated area with the same temperature increment shows the effect of thermal discharge on sea water. A comparison between simulated results and the experimental data shows good agreement. It indicates that this method can give high precision in the heat transfer simulation in coastal areas.

  10. Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer

    SciTech Connect

    Lucas, D.S.

    2004-10-03

    This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.

  11. Optimization methods and silicon solar cell numerical models

    NASA Technical Reports Server (NTRS)

    Girardini, K.; Jacobsen, S. E.

    1986-01-01

    An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

  12. Numerical methods for the Poisson-Fermi equation in electrolytes

    NASA Astrophysics Data System (ADS)

    Liu, Jinn-Liang

    2013-08-01

    The Poisson-Fermi equation proposed by Bazant, Storey, and Kornyshev [Phys. Rev. Lett. 106 (2011) 046102] for ionic liquids is applied to and numerically studied for electrolytes and biological ion channels in three-dimensional space. This is a fourth-order nonlinear PDE that deals with both steric and correlation effects of all ions and solvent molecules involved in a model system. The Fermi distribution follows from classical lattice models of configurational entropy of finite size ions and solvent molecules and hence prevents the long and outstanding problem of unphysical divergence predicted by the Gouy-Chapman model at large potentials due to the Boltzmann distribution of point charges. The equation reduces to Poisson-Boltzmann if the correlation length vanishes. A simplified matched interface and boundary method exhibiting optimal convergence is first developed for this equation by using a gramicidin A channel model that illustrates challenging issues associated with the geometric singularities of molecular surfaces of channel proteins in realistic 3D simulations. Various numerical methods then follow to tackle a range of numerical problems concerning the fourth-order term, nonlinearity, stability, efficiency, and effectiveness. The most significant feature of the Poisson-Fermi equation, namely, its inclusion of steric and correlation effects, is demonstrated by showing good agreement with Monte Carlo simulation data for a charged wall model and an L type calcium channel model.

  13. Numerical integration of population models satisfying conservation laws: NSFD methods.

    PubMed

    Mickens, Ronald E

    2007-10-01

    Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models.

  14. Ductile damage prediction in metal forming processes: Advanced modeling and numerical simulation

    NASA Astrophysics Data System (ADS)

    Saanouni, K.

    2013-05-01

    This paper describes the needs required in modern virtual metal forming including both sheet and bulk metal forming of mechanical components. These concern the advanced modeling of thermo-mechanical behavior including the multiphysical phenomena and their interaction or strong coupling, as well as the associated numerical aspects using fully adaptive simulation strategies. First a survey of advanced constitutive equations accounting for the main thermomechanical phenomena as the thermo-elasto-plastic finite strains with isotropic and kinematic hardenings fully coupled with ductile damage will be presented. Only the macroscopic phenomenological approach with state variables (monoscale approach) will be discussed in the general framework of the rational thermodynamics for generalized micromorphic continua. The micro-macro (multi-scales approach) in the framework of polycrystalline inelasticity is not presented here for the sake of shortness but will be presented during the oral presentation. The main numerical aspects related to the resolution of the associated initial and boundary value problem will be outlined. A fully adaptive numerical methodology will be briefly described and some numerical examples will be given in order to show the high predictive capabilities of this adaptive methodology for virtual metal forming simulations.

  15. Advanced fault diagnosis methods in molecular networks.

    PubMed

    Habibi, Iman; Emamian, Effat S; Abdi, Ali

    2014-01-01

    Analysis of the failure of cell signaling networks is an important topic in systems biology and has applications in target discovery and drug development. In this paper, some advanced methods for fault diagnosis in signaling networks are developed and then applied to a caspase network and an SHP2 network. The goal is to understand how, and to what extent, the dysfunction of molecules in a network contributes to the failure of the entire network. Network dysfunction (failure) is defined as failure to produce the expected outputs in response to the input signals. Vulnerability level of a molecule is defined as the probability of the network failure, when the molecule is dysfunctional. In this study, a method to calculate the vulnerability level of single molecules for different combinations of input signals is developed. Furthermore, a more complex yet biologically meaningful method for calculating the multi-fault vulnerability levels is suggested, in which two or more molecules are simultaneously dysfunctional. Finally, a method is developed for fault diagnosis of networks based on a ternary logic model, which considers three activity levels for a molecule instead of the previously published binary logic model, and provides equations for the vulnerabilities of molecules in a ternary framework. Multi-fault analysis shows that the pairs of molecules with high vulnerability typically include a highly vulnerable molecule identified by the single fault analysis. The ternary fault analysis for the caspase network shows that predictions obtained using the more complex ternary model are about the same as the predictions of the simpler binary approach. This study suggests that by increasing the number of activity levels the complexity of the model grows; however, the predictive power of the ternary model does not appear to be increased proportionally.

  16. Numerous Numerals.

    ERIC Educational Resources Information Center

    Henle, James M.

    This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…

  17. The numerical methods for the fluid flow of UCMCWS

    SciTech Connect

    Zhang Wenfu; Li Hui; Zhu Shuquan; Wang Zuna

    1997-12-31

    As an alternative for diesel oil for internal combustion engines, the fluid flow state of Ultra Clean Micronized Coal-Water Slurry (UCMCWS) in mini pipe and nozzle of a diesel engine must be known. In the laboratory three kinds of UCMCWS have been made with coal containing less than 0.8% ash, viscosity less than 600 mPa.s and concentration between 50% and 56%. Because the UCMCWS is a non-Newtonian fluid, there are no analytical resolution for pipe flow, especially in inlet and outlet sections. In this case using the numerical methods to research the flow state of UCMCWS is a useful method. Using the method of finite element, the flow state of UCMCWS in inlet and outlet sections (similar to a nozzle) have been studied. The distribution of velocity at different pressures of UCMCWS in outlet and inlet sections have been obtained. The result of the numerical methods is the efficient base for the pipe and nozzle design.

  18. Advanced Electromagnetic Methods for Aerospace Vehicles

    NASA Technical Reports Server (NTRS)

    Balanis, Constantine A.; Polycarpou, Anastasis; Birtcher, Craig R.; Georgakopoulos, Stavros; Han, Dong-Ho; Ballas, Gerasimos

    1999-01-01

    The imminent destructive threats of Lightning on helicopters and other airborne systems has always been a topic of great interest to this research grant. Previously, the lightning induced currents on the surface of the fuselage and its interior were predicted using the finite-difference time-domain (FDTD) method as well as the NEC code. The limitations of both methods, as applied to lightning, were identified and extensively discussed in the last meeting. After a thorough investigation of the capabilities of the FDTD, it was decided to incorporate into the numerical method a subcell model to accurately represent current diffusion through conducting materials of high conductivity and finite thickness. Because of the complexity of the model, its validity will be first tested for a one-dimensional FDTD problem. Although results are not available yet, the theory and formulation of the subcell model are presented and discussed here to a certain degree. Besides lightning induced currents in the interior of an aircraft, penetration of electromagnetic fields through apertures (e.g., windows and cracks) could also be devastating for the navigation equipment, electronics, and communications systems in general. The main focus of this study is understanding and quantifying field penetration through apertures. The simulation is done using the FDTD method and the predictions are compared with measurements and moment method solutions obtained from the NASA Langley Research Center. Cavity-backed slot (CBS) antennas or slot antennas in general have many applications in aircraft-satellite type of communications. These can be flushmounted on the surface of the fuselage and, therefore, they retain the aerodynamic shape of the aircraft. In the past, input impedance and radiation patterns of CBS antennas were computed using a hybrid FEM/MoM code. The analysis is now extended to coupling between two identical slot antennas mounted on the same structure. The predictions are performed

  19. Advanced electromagnetic methods for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Balanis, Constantine A.; Choi, Jachoon; El-Sharawy, El-Budawy; Hashemi-Yeganeh, Shahrokh; Birtcher, Craig R.

    1990-01-01

    High- and low-frequency methods to analyze various radiation elements located on aerospace vehicles with combinations of conducting, nonconducting, and energy absorbing surfaces and interfaces. The focus was on developing fundamental concepts, techniques, and algorithms which would remove some of the present limitations in predicting radiation characteristics of antennas on complex aerospace vehicles. In order to accomplish this, the following subjects were examined: (1) the development of techniques for rigorous analysis of surface discontinuities of metallic and nonmetallic surfaces using the equivalent surface impedance concept and Green's function; (2) the effects of anisotropic material on antenna radiation patterns through the use of an equivalent surface impedance concept which is incorporated into the existing numerical electromagnetics computer codes; and (3) the fundamental concepts of precipitation static (P-Static), such as formulations and analytical models. A computer code was used to model the P-Static process on a simple structure. Measurement techniques were also developed to characterized the electrical properties at microwave frequencies. Samples of typical materials used in airframes were tested and the results are included.

  20. Numerical Analysis of a Finite Element/Volume Penalty Method

    NASA Astrophysics Data System (ADS)

    Maury, Bertrand

    The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.

  1. Numerical methods for high-dimensional probability density function equations

    NASA Astrophysics Data System (ADS)

    Cho, H.; Venturi, D.; Karniadakis, G. E.

    2016-01-01

    In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

  2. Calculation of free-fall trajectories using numerical optimization methods.

    NASA Technical Reports Server (NTRS)

    Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.

    1972-01-01

    An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.

  3. Advanced continuous cultivation methods for systems microbiology.

    PubMed

    Adamberg, Kaarel; Valgepea, Kaspar; Vilu, Raivo

    2015-09-01

    Increasing the throughput of systems biology-based experimental characterization of in silico-designed strains has great potential for accelerating the development of cell factories. For this, analysis of metabolism in the steady state is essential as only this enables the unequivocal definition of the physiological state of cells, which is needed for the complete description and in silico reconstruction of their phenotypes. In this review, we show that for a systems microbiology approach, high-resolution characterization of metabolism in the steady state--growth space analysis (GSA)--can be achieved by using advanced continuous cultivation methods termed changestats. In changestats, an environmental parameter is continuously changed at a constant rate within one experiment whilst maintaining cells in the physiological steady state similar to chemostats. This increases the resolution and throughput of GSA compared with chemostats, and, moreover, enables following of the dynamics of metabolism and detection of metabolic switch-points and optimal growth conditions. We also describe the concept, challenge and necessary criteria of the systematic analysis of steady-state metabolism. Finally, we propose that such systematic characterization of the steady-state growth space of cells using changestats has value not only for fundamental studies of metabolism, but also for systems biology-based metabolic engineering of cell factories.

  4. Advanced electromagnetic methods for aerospace vehicles

    NASA Astrophysics Data System (ADS)

    Balanis, Constantine A.; Sun, Weimin; El-Sharawy, El-Budawy; Aberle, James T.; Birtcher, Craig R.; Peng, Jian; Tirkas, Panayiotis A.; Kokotoff, David; Zavosh, Frank

    1993-06-01

    The Advanced Helicopter Electromagnetics (AHE) Industrial Associates Program has continuously progressed with its research effort focused on subjects identified and recommended by the Advisory Task Force of the program. The research activities in this reporting period have been steered toward practical helicopter electromagnetic problems, such as HF antenna problems and antenna efficiencies, recommended by the AHE members at the annual conference held at Arizona State University on 28-29 Oct. 1992 and the last biannual meeting held at the Boeing Helicopter on 19-20 May 1993. The main topics addressed include the following: Composite Materials and Antenna Technology. The research work on each topic is closely tied with the AHE Consortium members' interests. Significant progress in each subject is reported. Special attention in the area of Composite Materials has been given to the following: modeling of material discontinuity and their effects on towel-bar antenna patterns; guidelines for composite material modeling by using the Green's function approach in the NEC code; measurements of towel-bar antennas grounded with a partially material-coated plate; development of 3-D volume mesh generator for modeling thick and volumetric dielectrics by using FD-TD method; FDTD modeling of horn antennas with composite E-plane walls; and antenna efficiency analysis for a horn antenna loaded with composite dielectric materials.

  5. Advanced electromagnetic methods for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Balanis, Constantine A.; Sun, Weimin; El-Sharawy, El-Budawy; Aberle, James T.; Birtcher, Craig R.; Peng, Jian; Tirkas, Panayiotis A.; Kokotoff, David; Zavosh, Frank

    1993-01-01

    The Advanced Helicopter Electromagnetics (AHE) Industrial Associates Program has continuously progressed with its research effort focused on subjects identified and recommended by the Advisory Task Force of the program. The research activities in this reporting period have been steered toward practical helicopter electromagnetic problems, such as HF antenna problems and antenna efficiencies, recommended by the AHE members at the annual conference held at Arizona State University on 28-29 Oct. 1992 and the last biannual meeting held at the Boeing Helicopter on 19-20 May 1993. The main topics addressed include the following: Composite Materials and Antenna Technology. The research work on each topic is closely tied with the AHE Consortium members' interests. Significant progress in each subject is reported. Special attention in the area of Composite Materials has been given to the following: modeling of material discontinuity and their effects on towel-bar antenna patterns; guidelines for composite material modeling by using the Green's function approach in the NEC code; measurements of towel-bar antennas grounded with a partially material-coated plate; development of 3-D volume mesh generator for modeling thick and volumetric dielectrics by using FD-TD method; FDTD modeling of horn antennas with composite E-plane walls; and antenna efficiency analysis for a horn antenna loaded with composite dielectric materials.

  6. Advanced electromagnetic methods for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Balanis, Constantine A.; Sun, Weimin; El-Sharawy, El-Budawy; Aberle, James T.; Birtcher, Craig R.; Peng, Jian; Tirkas, Panayiotis A.; Andrew, William V.; Kokotoff, David; Zavosh, Frank

    1993-01-01

    The Advanced Helicopter Electromagnetics (AHE) Industrial Associates Program has fruitfully completed its fourth year. Under the support of the AHE members and the joint effort of the research team, new and significant progress has been achieved in the year. Following the recommendations by the Advisory Task Force, the research effort is placed on more practical helicopter electromagnetic problems, such as HF antennas, composite materials, and antenna efficiencies. In this annual report, the main topics to be addressed include composite materials and antenna technology. The research work on each topic has been driven by the AHE consortium members' interests and needs. The remarkable achievements and progresses in each subject is reported respectively in individual sections of the report. The work in the area of composite materials includes: modeling of low conductivity composite materials by using Green's function approach; guidelines for composite material modeling by using the Green's function approach in the NEC code; development of 3-D volume mesh generator for modeling thick and volumetric dielectrics by using FD-TD method; modeling antenna elements mounted on a composite Comanche tail stabilizer; and antenna pattern control and efficiency estimate for a horn antenna loaded with composite dielectric materials.

  7. A Collocation Method for Numerical Solutions of Coupled Burgers' Equations

    NASA Astrophysics Data System (ADS)

    Mittal, R. C.; Tripathi, A.

    2014-09-01

    In this paper, we propose a collocation-based numerical scheme to obtain approximate solutions of coupled Burgers' equations. The scheme employs collocation of modified cubic B-spline functions. We have used modified cubic B-spline functions for unknown dependent variables u, v, and their derivatives w.r.t. space variable x. Collocation forms of the partial differential equations result in systems of first-order ordinary differential equations (ODEs). In this scheme, we did not use any transformation or linearization method to handle nonlinearity. The obtained system of ODEs has been solved by strong stability preserving the Runge-Kutta method. The proposed scheme needs less storage space and execution time. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed scheme. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. The scheme is simple as well as easy to implement. The scheme provides approximate solutions not only at the grid points, but also at any point in the solution range.

  8. Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer

    SciTech Connect

    D. S. Lucas

    2004-10-01

    A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.

  9. A numerical method for solving the Vlasov equation

    NASA Technical Reports Server (NTRS)

    Satofuka, N.

    1982-01-01

    A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.

  10. Numerical solution of fractionally damped beam by homotopy perturbation method

    NASA Astrophysics Data System (ADS)

    Behera, Diptiranjan; Chakraverty, Snehashish

    2013-06-01

    This paper investigates the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order. The Homotopy Perturbation Method (HPM) is used to obtain the dynamic response. Unit step function response is considered for the analysis. The obtained results are depicted in various plots. From the results obtained it is interesting to note that by increasing the order of the fractional derivative the beam suffers less oscillation. Similar observations have also been made by keeping the order of the fractional derivative constant and varying the damping ratios. Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan [Appl. Math. Mech. 28, 219 (2007)] to show the effectiveness and validation of this method.

  11. Multigrid methods for numerical simulation of laminar diffusion flames

    NASA Technical Reports Server (NTRS)

    Liu, C.; Liu, Z.; Mccormick, S.

    1993-01-01

    This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

  12. Numerical Methods and Simulations of Complex Multiphase Flows

    NASA Astrophysics Data System (ADS)

    Brady, Peter

    Multiphase flows are an important part of many natural and technological phenomena such as ocean-air coupling (which is important for climate modeling) and the atomization of liquid fuel jets in combustion engines. The unique challenges of multiphase flow often make analytical solutions to the governing equations impossible and experimental investigations very difficult. Thus, high-fidelity numerical simulations can play a pivotal role in understanding these systems. This dissertation describes numerical methods developed for complex multiphase flows and the simulations performed using these methods. First, the issue of multiphase code verification is addressed. Code verification answers the question "Is this code solving the equations correctly?" The method of manufactured solutions (MMS) is a procedure for generating exact benchmark solutions which can test the most general capabilities of a code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented, using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. Guidelines for the use of the MMS to help locate coding mistakes are also detailed. Three multiphase systems are then investigated: (1) the thermocapillary motion of three-dimensional and axisymmetric drops in a confined apparatus, (2) the flow of two immiscible fluids completely filling an enclosed cylinder and driven by the rotation of the bottom endwall, and (3) the atomization of a single drop subjected to a high shear turbulent flow. The systems are simulated numerically by solving the full multiphase Navier-Stokes equations coupled to the various equations of state and a level set interface tracking scheme based on the refined level set grid method. The codes have been parallelized using MPI in order to take advantage of today's very large parallel computational

  13. Numerical methods for assessment of the ship's pollutant emissions

    NASA Astrophysics Data System (ADS)

    Jenaru, A.; Acomi, N.

    2016-08-01

    The maritime transportation sector constitutes a source of atmospheric pollution. To avoid or minimize ships pollutant emissions the first step is to assess them. Two methods of estimation of the ships’ emissions are proposed in this paper. These methods prove their utility for shipboard and shore based management personnel from the practical perspective. The methods were demonstrated for a product tanker vessel where a permanent monitoring system for the pollutant emissions has previously been fitted. The values of the polluting agents from the exhaust gas were determined for the ship from the shipyard delivery and were used as starting point. Based on these values, the paper aimed at numerical assessing of ship's emissions in order to determine the ways for avoiding environmental pollution: the analytical method of determining the concentrations of the exhaust gas components, by using computation program MathCAD, and the graphical method of determining the concentrations of the exhaust gas components, using variation diagrams of the parameters, where the results of the on board measurements were introduced, following the application of pertinent correction factors. The results should be regarded as a supporting tool during the decision making process linked to the reduction of ship's pollutant emissions.

  14. Asymmetric MRI magnet design using a hybrid numerical method.

    PubMed

    Zhao, H; Crozier, S; Doddrell, D M

    1999-12-01

    This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries.

  15. Numerical study of Alfvén eigenmodes in the Experimental Advanced Superconducting Tokamak

    SciTech Connect

    Hu, Youjun; Li, Guoqiang; Yang, Wenjun; Zhou, Deng; Ren, Qilong; Gorelenkov, N. N.; Cai, Huishan

    2014-05-15

    Alfvén eigenmodes in up-down asymmetric tokamak equilibria are studied by a new magnetohydrodynamic eigenvalue code. The code is verified with the NOVA code for the Solovév equilibrium and then is used to study Alfvén eigenmodes in a up-down asymmetric equilibrium of the Experimental Advanced Superconducting Tokamak. The frequency and mode structure of toroidicity-induced Alfvén eigenmodes are calculated. It is demonstrated numerically that up-down asymmetry induces phase variation in the eigenfunction across the major radius on the midplane.

  16. Simulation studies of the impact of advanced observing systems on numerical weather prediction

    NASA Technical Reports Server (NTRS)

    Atlas, R.; Kalnay, E.; Susskind, J.; Reuter, D.; Baker, W. E.; Halem, M.

    1984-01-01

    To study the potential impact of advanced passive sounders and lidar temperature, pressure, humidity, and wind observing systems on large-scale numerical weather prediction, a series of realistic simulation studies between the European Center for medium-range weather forecasts, the National Meteorological Center, and the Goddard Laboratory for Atmospheric Sciences is conducted. The project attempts to avoid the unrealistic character of earlier simulation studies. The previous simulation studies and real-data impact tests are reviewed and the design of the current simulation system is described. Consideration is given to the simulation of observations of space-based sounding systems.

  17. A method for improving time-stepping numerics

    NASA Astrophysics Data System (ADS)

    Williams, P. D.

    2012-04-01

    In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.

  18. Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

    NASA Technical Reports Server (NTRS)

    Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark

    2002-01-01

    Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

  19. Unsaturated Shear Strength and Numerical Analysis Methods for Unsaturated Soils

    NASA Astrophysics Data System (ADS)

    Kim, D.; Kim, G.; Kim, D.; Baek, H.; Kang, S.

    2011-12-01

    The angles of shearing resistance(φb) and internal friction(φ') appear to be identical in low suction range, but the angle of shearing resistance shows non-linearity as suction increases. In most numerical analysis however, a fixed value for the angle of shearing resistance is applied even in low suction range for practical reasons, often leading to a false conclusion. In this study, a numerical analysis has been undertaken employing the estimated shear strength curve of unsaturated soils from the residual water content of SWCC proposed by Vanapalli et al.(1996). The result was also compared with that from a fixed value of φb. It is suggested that, in case it is difficult to measure the unsaturated shear strength curve through the triaxial soil tests, the estimated shear strength curve using the residual water content can be a useful alternative. This result was applied for analyzing the slope stablity of unsaturated soils. The effects of a continuous rainfall on slope stability were analyzed using a commercial program "SLOPE/W", with the coupled infiltration analysis program "SEEP/W" from the GEO-SLOPE International Ltd. The results show that, prior to the infiltration by the intensive rainfall, the safety factors using the estimated shear strength curve were substantially higher than that from the fixed value of φb at all time points. After the intensive infiltration, both methods showed a similar behavior.

  20. Space-time adaptive numerical methods for geophysical applications.

    PubMed

    Castro, C E; Käser, M; Toro, E F

    2009-11-28

    In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost. PMID:19840984

  1. Numerical method of characteristics for one-dimensional blood flow

    NASA Astrophysics Data System (ADS)

    Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.

    2015-08-01

    Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.

  2. A mathematical model and numerical method for thermoelectric DNA sequencing

    NASA Astrophysics Data System (ADS)

    Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong

    2014-05-01

    Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.

  3. Numerical optimization method for packing regular convex polygons

    NASA Astrophysics Data System (ADS)

    Galiev, Sh. I.; Lisafina, M. S.

    2016-08-01

    An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.

  4. Recent advances in numerical simulation and control of asymmetric flows around slender bodies

    NASA Technical Reports Server (NTRS)

    Kandil, Osama A.; Wong, Tin-Chee; Sharaf, Hazem H.; Liu, C. H.

    1992-01-01

    The problems of asymmetric flow around slender bodies and its control are formulated using the unsteady, compressible, thin-layer or full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. The problem is numerically simulated for both locally-conical and three-dimensional flows. The numerical applications include studies of the effects of relative incidence, Mach number and Reynolds number on the flow asymmetry. For the control of flow asymmetry, the numerical simulation cover passive and active control methods. For the passive control, the effectiveness of vertical fins placed in the leeward plane of geometric symmetry and side strakes with different orientations is studied. For the active control, the effectiveness of normal and tangential flow injection and surface heating and a combination of these methods is studied.

  5. Why Video? How Technology Advances Method

    ERIC Educational Resources Information Center

    Downing, Martin J., Jr.

    2008-01-01

    This paper reports on the use of video to enhance qualitative research. Advances in technology have improved our ability to capture lived experiences through visual means. I reflect on my previous work with individuals living with HIV/AIDS, the results of which are described in another paper, to evaluate the effectiveness of video as a medium that…

  6. a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms

    NASA Astrophysics Data System (ADS)

    Beale, D. G.; Lee, S. W.

    1996-05-01

    A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].

  7. Introduction to finite-difference methods for numerical fluid dynamics

    SciTech Connect

    Scannapieco, E.; Harlow, F.H.

    1995-09-01

    This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.

  8. Numerical Improvement of The Three-dimensional Boundary Element Method

    NASA Astrophysics Data System (ADS)

    Ortiz-Aleman, C.; Gil-Zepeda, A.; Sánchez-Sesma, F. J.; Luzon-Martinez, F.

    2001-12-01

    Boundary element methods have been applied to calculate the seismic response of various types of geological structures. Dimensionality reduction and a relatively easy fulfillment of radiation conditions at infinity are recognized advantages over domain approaches. Indirect Boundary Element Method (IBEM) formulations give rise to large systems of equations, and the considerable amount of operations required for solving them suggest the possibility of getting some benefit from exploitation of sparsity patterns. In this article, a brief study on the structure of the linear systems derived from the IBEM method is carried out. Applicability of a matrix static condensation algorithm to the inversion of the IBEM coefficient matrix is explored, in order to optimize the numerical burden of such method. Seismic response of a 3-D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzon (1995), was computed and comparisons on time consumption and memory allocation are established. An alternative way to deal with those linear systems is the use of threshold criteria for the truncation of the coefficient matrix, which implies the solution of sparse approximations instead of the original full IBEM systems (Ortiz-Aleman et al., 1998). Performance of this optimized approach is evaluated on its application to the case of a three-dimensional alluvial basin with irregular shape. Transfer functions were calculated for the frequency range from 0 to 1.25 Hz. Inversion of linear systems by using this algorithm lead to significant saving on computer time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.

  9. Advances in Analytical and Numerical Dispersion Modeling of Pollutants Releasing from an Area-source

    NASA Astrophysics Data System (ADS)

    Nimmatoori, Praneeth

    The air quality near agricultural activities such as tilling, plowing, harvesting, and manure application is of main concern because they release fine particulate matter into the atmosphere. These releases are modeled as area-sources in the air quality modeling research. None of the currently available dispersion models relate and incorporate physical characteristics and meteorological conditions for modeling the dispersion and deposition of particulates emitting from such area-sources. This knowledge gap was addressed by developing the advanced analytical and numerical methods for modeling the dispersion of particulate matter. The development, application, and evaluation of new dispersion modeling methods are discussed in detail in this dissertation. In the analytical modeling, a ground-level area source analytical dispersion model known as particulate matter deposition -- PMD was developed for predicting the concentrations of different particle sizes. Both the particle dynamics (particle physical characteristics) and meteorological conditions which have significant effect on the dispersion of particulates were related and incorporated in the PMD model using the formulations of particle gravitational settling and dry deposition velocities. The modeled particle size concentrations of the PMD model were evaluated statistically after applying it to particulates released from a biosolid applied agricultural field. The evaluation of the PMD model using the statistical criteria concluded effective and successful inclusion of dry deposition theory for modeling particulate matter concentrations. A comprehensive review of analytical area-source dispersion models, which do not account for dry deposition and treat pollutants as gases, was conducted and determined three models -- the Shear, the Parker, and the Smith. A statistical evaluation of these dispersion models was conducted after applying them to two different field data sets and the statistical results concluded that

  10. A survey of numerical methods for shock physics applications

    SciTech Connect

    Hertel, E.S. Jr.

    1997-10-01

    Hydrocodes or more accurately, shock physics analysis packages, have been widely used in the US Department of Energy (DOE) laboratories and elsewhere around the world for over 30 years. Initial applications included weapons effects studies where the pressure levels were high enough to disregard the material strength, hence the term hydrocode. Over the last 30 years, Sandia has worked extensively to develop and apply advanced hydrocodes to armor/anti-armor interactions, warhead design, high explosive initiation, and nuclear weapon safety issues. The needs of the DOE have changed over the last 30 years, especially over the last decade. A much stronger emphasis is currently placed on the details of material deformation and high explosive initiation phenomena. The hydrocodes of 30 years ago have now evolved into sophisticated analysis tools that can replace testing in some situations and complement it in all situations. A brief history of the development of hydrocodes in the US will be given. The author also discusses and compares the four principal methods in use today for the solution of the conservation equations of mass, momentum, and energy for shock physics applications. The techniques discussed are the Eulerian methods currently employed by the Sandia multi-dimensional shock physics analysis package known as CTH; the element based Lagrangian method currently used by codes like DYNA; the element free Lagrangian method (also known as smooth particle hydrodynamics) used by codes like the Los Alamos code SPHINX; and the Arbitrary Lagrangian Eulerian methods used by codes like the Lawrence Livermore code CALE or the Sandia code ALEGRA.

  11. Advanced Numerical-Algebraic Thinking: Constructing the Concept of Covariation as a Prelude to the Concept of Function

    ERIC Educational Resources Information Center

    Hitt, Fernando; Morasse, Christian

    2009-01-01

    Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

  12. Advanced electromagnetic methods for aerospace vehicles

    NASA Technical Reports Server (NTRS)

    Balanis, Constantine A.; Sun, Weimin; El-Sharawy, El-Budawy; Aberle, James T.; Birtcher, Craig R.; Peng, Jian; Tirkas, Panayiotis A.

    1992-01-01

    The Advanced Helicopter Electromagnetics (AHE) Industrial Associates Program continues its research on variety of main topics identified and recommended by the Advisory Task Force of the program. The research activities center on issues that advance technology related to helicopter electromagnetics. While most of the topics are a continuation of previous works, special effort has been focused on some of the areas due to recommendations from the last annual conference. The main topics addressed in this report are: composite materials, and antenna technology. The area of composite materials continues getting special attention in this period. The research has focused on: (1) measurements of the electrical properties of low-conductivity materials; (2) modeling of material discontinuity and their effects on the scattering patterns; (3) preliminary analysis on interaction of electromagnetic fields with multi-layered graphite fiberglass plates; and (4) finite difference time domain (FDTD) modeling of fields penetration through composite panels of a helicopter.

  13. Method and apparatus for advancing tethers

    DOEpatents

    Zollinger, W.T.

    1998-06-02

    A tether puller for advancing a tether through a channel may include a bellows assembly having a leading end fixedly attached to the tether at a first position and a trailing end fixedly attached to the tether at a second position so that the leading and trailing ends of the bellows assembly are located a substantially fixed distance apart. The bellows assembly includes a plurality of independently inflatable elements each of which may be separately inflated to an extended position and deflated to a retracted position. Each of the independently inflatable elements expands radially and axially upon inflation. An inflation system connected to the independently inflatable elements inflates and deflates selected ones of the independently inflatable elements to cause the bellows assembly to apply a tractive force to the tether and advance it in the channel. 9 figs.

  14. Method and apparatus for advancing tethers

    DOEpatents

    Zollinger, W. Thor

    1998-01-01

    A tether puller for advancing a tether through a channel may include a bellows assembly having a leading end fixedly attached to the tether at a first position and a trailing end fixedly attached to the tether at a second position so that the leading and trailing ends of the bellows assembly are located a substantially fixed distance apart. The bellows assembly includes a plurality of independently inflatable elements each of which may be separately inflated to an extended position and deflated to a retracted position. Each of the independently inflatable elements expands radially and axially upon inflation. An inflation system connected to the independently inflatable elements inflates and deflates selected ones of the independently inflatable elements to cause the bellows assembly to apply a tractive force to the tether and advance it in the channel.

  15. A new nonlocal thermodynamical equilibrium radiative transfer method for cool stars. Method and numerical implementation

    NASA Astrophysics Data System (ADS)

    Lambert, J.; Josselin, E.; Ryde, N.; Faure, A.

    2015-08-01

    Context. The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to handle large-scale systems, such as molecular spectra emerging from, for example, cool stellar atmospheres. Aims: Our objective is to develop a new method, which aims to circumvent these problems, using nonstationary numerical techniques and taking advantage of parallel computers. Methods: The technique we develop may be seen as a generalization of the coupled escape probability method. It solves the statistical equilibrium equations in all layers of a discretized model simultaneously. The numerical scheme adopted is based on the generalized minimum residual method. Results: The code has already been applied to the special case of the water spectrum in a red supergiant stellar atmosphere. This demonstrates the fast convergence of this method, and opens the way to a wide variety of astrophysical problems.

  16. Numerical methods for determining interstitial oxygen in silicon

    SciTech Connect

    Stevenson, J.O.; Medernach, J.W.

    1995-01-01

    The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.

  17. Advanced methods of structural and trajectory analysis for transport aircraft

    NASA Technical Reports Server (NTRS)

    Ardema, Mark D.

    1995-01-01

    This report summarizes the efforts in two areas: (1) development of advanced methods of structural weight estimation, and (2) development of advanced methods of trajectory optimization. The majority of the effort was spent in the structural weight area. A draft of 'Analytical Fuselage and Wing Weight Estimation of Transport Aircraft', resulting from this research, is included as an appendix.

  18. Simplified method for numerical modeling of fiber lasers.

    PubMed

    Shtyrina, O V; Yarutkina, I A; Fedoruk, M P

    2014-12-29

    A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.

  19. Numerical Weather Predictions Evaluation Using Spatial Verification Methods

    NASA Astrophysics Data System (ADS)

    Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.

    2014-12-01

    During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain-­-Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is co­financed by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007-­-2013).

  20. Numerical methods for portfolio selection with bounded constraints

    NASA Astrophysics Data System (ADS)

    Yin, G.; Jin, Hanqing; Jin, Zhuo

    2009-11-01

    This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.

  1. Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs

    NASA Astrophysics Data System (ADS)

    Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

    2016-06-01

    In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.

  2. Numerical approach for the voloxidation process of an advanced spent fuel conditioning process (ACP)

    SciTech Connect

    Park, Byung Heung; Jeong, Sang Mun; Seo, Chung-Seok

    2007-07-01

    A voloxidation process is adopted as the first step of an advanced spent fuel conditioning process in order to prepare the SF oxide to be reduced in the following electrolytic reduction process. A semi-batch type voloxidizer was devised to transform a SF pellet into powder. In this work, a simple reactor model was developed for the purpose of correlating a gas phase flow rate with an operation time as a numerical approach. With an assumption that a solid phase and a gas phase are homogeneous in a reactor, a reaction rate for an oxidation was introduced into a mass balance equation. The developed equation can describe a change of an outlet's oxygen concentration including such a case that a gas flow is not sufficient enough to continue a reaction at its maximum reaction rate. (authors)

  3. Full Wave Simulation of Integrated Circuits Using Hybrid Numerical Methods

    NASA Astrophysics Data System (ADS)

    Tan, Jilin

    Transmission lines play an important role in digital electronics, and in microwave and millimeter-wave circuits. Analysis, modeling, and design of transmission lines are critical to the development of the circuitry in the chip, subsystem, and system levels. In the past several decays, at the EM modeling level, the quasi-static approximation has been widely used due to its great simplicity. As the clock rates increase, the inter-connect effects such as signal delay, distortion, dispersion, reflection, and crosstalk, limit the performance of microwave systems. Meanwhile, the quasi-static approach loses its validity for some complex system structures. Since the successful system design of the PCB, MCM, and the chip packaging, rely very much on the computer aided EM level modeling and simulation, many new methods have been developed, such as the full wave approach, to guarantee the successful design. Many difficulties exist in the rigorous EM level analysis. Some of these include the difficulties in describing the behavior of the conductors with finite thickness and finite conductivity, the field singularity, and the arbitrary multilayered multi-transmission lines structures. This dissertation concentrates on the full wave study of the multi-conductor transmission lines with finite conductivity and finite thickness buried in an arbitrary lossy multilayered environment. Two general approaches have been developed. The first one is the integral equation method in which the dyadic Green's function for arbitrary layered media has been correctly formulated and has been tested both analytically and numerically. By applying this method, the double layered high dielectric permitivitty problem and the heavy dielectrical lossy problem in multilayered media in the CMOS circuit design have been solved. The second approach is the edge element method. In this study, the correct functional for the two dimensional propagation problem has been successfully constructed in a rigorous way

  4. Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods

    ERIC Educational Resources Information Center

    Maase, Eric L.; High, Karen A.

    2008-01-01

    "Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

  5. Advanced particulate matter control apparatus and methods

    DOEpatents

    Miller, Stanley J.; Zhuang, Ye; Almlie, Jay C.

    2012-01-10

    Apparatus and methods for collection and removal of particulate matter, including fine particulate matter, from a gas stream, comprising a unique combination of high collection efficiency and ultralow pressure drop across the filter. The apparatus and method utilize simultaneous electrostatic precipitation and membrane filtration of a particular pore size, wherein electrostatic collection and filtration occur on the same surface.

  6. The role of numerical simulation for the development of an advanced HIFU system

    NASA Astrophysics Data System (ADS)

    Okita, Kohei; Narumi, Ryuta; Azuma, Takashi; Takagi, Shu; Matumoto, Yoichiro

    2014-10-01

    High-intensity focused ultrasound (HIFU) has been used clinically and is under clinical trials to treat various diseases. An advanced HIFU system employs ultrasound techniques for guidance during HIFU treatment instead of magnetic resonance imaging in current HIFU systems. A HIFU beam imaging for monitoring the HIFU beam and a localized motion imaging for treatment validation of tissue are introduced briefly as the real-time ultrasound monitoring techniques. Numerical simulations have a great impact on the development of real-time ultrasound monitoring as well as the improvement of the safety and efficacy of treatment in advanced HIFU systems. A HIFU simulator was developed to reproduce ultrasound propagation through the body in consideration of the elasticity of tissue, and was validated by comparison with in vitro experiments in which the ultrasound emitted from the phased-array transducer propagates through the acrylic plate acting as a bone phantom. As the result, the defocus and distortion of the ultrasound propagating through the acrylic plate in the simulation quantitatively agree with that in the experimental results. Therefore, the HIFU simulator accurately reproduces the ultrasound propagation through the medium whose shape and physical properties are well known. In addition, it is experimentally confirmed that simulation-assisted focus control of the phased-array transducer enables efficient assignment of the focus to the target. Simulation-assisted focus control can contribute to design of transducers and treatment planning.

  7. NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.

    SciTech Connect

    LUCCIO, A.; D'IMPERIO, N.; MALITSKY, N.

    2005-09-12

    Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.

  8. Indentation Methods in Advanced Materials Research Introduction

    SciTech Connect

    Pharr, George Mathews; Cheng, Yang-Tse; Hutchings, Ian; Sakai, Mototsugu; Moody, Neville; Sundararajan, G.; Swain, Michael V.

    2009-01-01

    Since its commercialization early in the 20th century, indentation testing has played a key role in the development of new materials and understanding their mechanical behavior. Progr3ess in the field has relied on a close marriage between research in the mechanical behavior of materials and contact mechanics. The seminal work of Hertz laid the foundations for bringing these two together, with his contributions still widely utilized today in examining elastic behavior and the physics of fracture. Later, the pioneering work of Tabor, as published in his classic text 'The Hardness of Metals', exapdned this understanding to address the complexities of plasticity. Enormous progress in the field has been achieved in the last decade, made possible both by advances in instrumentation, for example, load and depth-sensing indentation and scanning electron microscopy (SEM) and transmission electron microscopy (TEM) based in situ testing, as well as improved modeling capabilities that use computationally intensive techniques such as finite element analysis and molecular dynamics simulation. The purpose of this special focus issue is to present recent state of the art developments in the field.

  9. Advanced spectral methods for climatic time series

    USGS Publications Warehouse

    Ghil, M.; Allen, M.R.; Dettinger, M.D.; Ide, K.; Kondrashov, D.; Mann, M.E.; Robertson, A.W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.

    2002-01-01

    The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal- to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.

  10. Numerical divergence effects of equivalence theory in the nodal expansion method

    SciTech Connect

    Zika, M.R.; Downar, T.J. )

    1993-11-01

    Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible.

  11. Advances in methods for deepwater TLP installations

    SciTech Connect

    Wybro, P.G.

    1995-10-01

    This paper describes a method suitable for installing deepwater TLP structures in water depths beyond 3,000 ft. An overview is presented of previous TLP installation, wherein an evaluation is made of the various methods and their suitability to deepwater applications. A novel method for installation of deepwater TLP`s is described. This method of installation is most suitable for deepwater and/or large TLP structures, but can also be used in moderate water depth as well. The tendon installation method utilizes the so-called Platform Arrestor Concept (PAC), wherein tendon sections are transported by barges to site, and assembled vertically using a dynamically position crane vessel. The tendons are transferred to the platform where they are hung off until there are a full complement of tendons. The hull lock off operation is performed on all tendons simultaneously, avoiding dangerous platform resonant behavior. The installation calls for relatively simple installation equipment, and also enables the use of simple tendon tie-off equipment, such as a single piece nut.

  12. SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS

    NASA Technical Reports Server (NTRS)

    Frisch, H. P.

    1994-01-01

    SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any

  13. Numerical Analysis on the Vortex Pattern and Flux Particle Dispersion in KR Method Using MPS Method

    NASA Astrophysics Data System (ADS)

    Hirata, N.; Xu, Y.; Anzai, K.

    2015-06-01

    The mechanically-stirring vessel is widely used in many fields, such as chemical reactor, bioreactor, and metallurgy, etc. The type of vortex mode that formed during impeller stirring has great effect on stirring efficiency, chemical reacting rate and air entrapment. Many efforts have been made to numerically simulate the fluid flow in the stirring vessel with classical Eulerian method. However, it is difficult to directly investigate the vortex mode and flux particle dispersion. Therefore, moving particle semi-implicit (MPS) method, which is based on Lagrangian method, is applied to simulate the fluid flow in a KR method in this practice. Top height and bottom heights of vortex surface in a steady state under several rotation speed was taken as key parameters to compare the results of numerical and published results. Flux particle dispersion behaviour under a rotation speed range from 80 to 480 rpm was also compared with the past study. The result shows that the numerical calculation has high consistency with experimental results. It is confirmed that the calculation using MPS method well reflected the vortex mode and flux particle dispersion in a mechanically-stirring vessel.

  14. High Order Numerical Methods for the Investigation of the Two Dimensional Richtmyer-Meshkov Instability

    SciTech Connect

    Don, W-S; Gotllieb, D; Shu, C-W; Jameson, L

    2001-11-26

    For flows that contain significant structure, high order schemes offer large advantages over low order schemes. Fundamentally, the reason comes from the truncation error of the differencing operators. If one examines carefully the expression for the truncation error, one will see that for a fixed computational cost that the error can be made much smaller by increasing the numerical order than by increasing the number of grid points. One can readily derive the following expression which holds for systems dominated by hyperbolic effects and advanced explicitly in time: flops = const * p{sup 2} * k{sup (d+1)(p+1)/p}/E{sup (d+1)/p} where flops denotes floating point operations, p denotes numerical order, d denotes spatial dimension, where E denotes the truncation error of the difference operator, and where k denotes the Fourier wavenumber. For flows that contain structure, such as turbulent flows or any calculation where, say, vortices are present, there will be significant energy in the high values of k. Thus, one can see that the rate of growth of the flops is very different for different values of p. Further, the constant in front of the expression is also very different. With a low order scheme, one quickly reaches the limit of the computer. With the high order scheme, one can obtain far more modes before the limit of the computer is reached. Here we examine the application of spectral methods and the Weighted Essentially Non-Oscillatory (WENO) scheme to the Richtmyer-Meshkov Instability. We show the intricate structure that these high order schemes can calculate and we show that the two methods, though very different, converge to the same numerical solution indicating that the numerical solution is very likely physically correct.

  15. Advanced method for making vitreous waste forms

    SciTech Connect

    Pope, J.M.; Harrison, D.E.

    1980-01-01

    A process is described for making waste glass that circumvents the problems of dissolving nuclear waste in molten glass at high temperatures. Because the reactive mixing process is independent of the inherent viscosity of the melt, any glass composition can be prepared with equal facility. Separation of the mixing and melting operations permits novel glass fabrication methods to be employed.

  16. Adaptive Numerical Dissipation Controls for High Order Methods

    NASA Technical Reports Server (NTRS)

    Yee, Helen C.; Sjogreen, B.; Sandham, N. D.; Mansour, Nagi (Technical Monitor)

    2001-01-01

    A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.

  17. Cost estimating methods for advanced space systems

    NASA Technical Reports Server (NTRS)

    Cyr, Kelley

    1988-01-01

    Parametric cost estimating methods for space systems in the conceptual design phase are developed. The approach is to identify variables that drive cost such as weight, quantity, development culture, design inheritance, and time. The relationship between weight and cost is examined in detail. A theoretical model of cost is developed and tested statistically against a historical data base of major research and development programs. It is concluded that the technique presented is sound, but that it must be refined in order to produce acceptable cost estimates.

  18. A numerical method for solving partial differential algebraic equations

    NASA Astrophysics Data System (ADS)

    Diep, Nguyen Khac; Chistyakov, V. F.

    2013-06-01

    Linear systems of partial differential equations with constant coefficient matrices are considered. The matrices multiplying the derivatives of the sought vector function are assumed to be singular. The structure of solutions to such systems is examined. The numerical solution of initialboundary value problems for such equations by applying implicit difference schemes is discussed.

  19. Advances in organometallic synthesis with mechanochemical methods.

    PubMed

    Rightmire, Nicholas R; Hanusa, Timothy P

    2016-02-14

    Solvent-based syntheses have long been normative in all areas of chemistry, although mechanochemical methods (specifically grinding and milling) have been used to good effect for decades in organic, and to a lesser but growing extent, inorganic coordination chemistry. Organometallic synthesis, in contrast, represents a relatively underdeveloped area for mechanochemical research, and the potential benefits are considerable. From access to new classes of unsolvated complexes, to control over stoichiometries that have not been observed in solution routes, mechanochemical (or 'M-chem') approaches have much to offer the synthetic chemist. It has already become clear that removing the solvent from an organometallic reaction can change reaction pathways considerably, so that prediction of the outcome is not always straightforward. This Perspective reviews recent developments in the field, and describes equipment that can be used in organometallic synthesis. Synthetic chemists are encouraged to add mechanochemical methods to their repertoire in the search for new and highly reactive metal complexes and novel types of organometallic transformations.

  20. Advancements in Research Synthesis Methods: From a Methodologically Inclusive Perspective

    ERIC Educational Resources Information Center

    Suri, Harsh; Clarke, David

    2009-01-01

    The dominant literature on research synthesis methods has positivist and neo-positivist origins. In recent years, the landscape of research synthesis methods has changed rapidly to become inclusive. This article highlights methodologically inclusive advancements in research synthesis methods. Attention is drawn to insights from interpretive,…

  1. Current methods and advances in bone densitometry

    NASA Technical Reports Server (NTRS)

    Guglielmi, G.; Gluer, C. C.; Majumdar, S.; Blunt, B. A.; Genant, H. K.

    1995-01-01

    Bone mass is the primary, although not the only, determinant of fracture. Over the past few years a number of noninvasive techniques have been developed to more sensitively quantitate bone mass. These include single and dual photon absorptiometry (SPA and DPA), single and dual X-ray absorptiometry (SXA and DXA) and quantitative computed tomography (QCT). While differing in anatomic sites measured and in their estimates of precision, accuracy, and fracture discrimination, all of these methods provide clinically useful measurements of skeletal status. It is the intent of this review to discuss the pros and cons of these techniques and to present the new applications of ultrasound (US) and magnetic resonance (MRI) in the detection and management of osteoporosis.

  2. Method and ethics in advancing jury research.

    PubMed

    Robertshaw, P

    1998-10-01

    In this article the contemporary problems of the jury and jury research are considered. This is timely, in view of the current Home Office Consultation Paper on the future of, and alternatives to, the jury in serious fraud trials, to which the author has submitted representations on its jury aspects. The research position is dominated by the prohibitions in the Contempt of Court Act 1981. The types of indirect research on jury deliberation which have been achieved within this stricture are outlined. In the USA, direct research of the jury is possible but, for historical reasons, it has been in television documentaries that direct observation of the deliberation process has been achieved. The first issue is discussed and the problems of inauthenticity, 'the observer effect', and of existential invalidity in 'mock' or 'shadow' juries are noted. Finally, the kinds of issues that could be addressed if licensed jury deliberation research was legalized, are proposed. It is also suggested that there are methods available to transcend the problems associated with American direct research. PMID:9808945

  3. Cost estimating methods for advanced space systems

    NASA Technical Reports Server (NTRS)

    Cyr, Kelley

    1994-01-01

    NASA is responsible for developing much of the nation's future space technology. Cost estimates for new programs are required early in the planning process so that decisions can be made accurately. Because of the long lead times required to develop space hardware, the cost estimates are frequently required 10 to 15 years before the program delivers hardware. The system design in conceptual phases of a program is usually only vaguely defined and the technology used is so often state-of-the-art or beyond. These factors combine to make cost estimating for conceptual programs very challenging. This paper describes an effort to develop parametric cost estimating methods for space systems in the conceptual design phase. The approach is to identify variables that drive cost such as weight, quantity, development culture, design inheritance and time. The nature of the relationships between the driver variables and cost will be discussed. In particular, the relationship between weight and cost will be examined in detail. A theoretical model of cost will be developed and tested statistically against a historical database of major research and development projects.

  4. Advanced Fuzzy Potential Field Method for Mobile Robot Obstacle Avoidance

    PubMed Central

    Park, Jong-Wook; Kwak, Hwan-Joo; Kang, Young-Chang; Kim, Dong W.

    2016-01-01

    An advanced fuzzy potential field method for mobile robot obstacle avoidance is proposed. The potential field method primarily deals with the repulsive forces surrounding obstacles, while fuzzy control logic focuses on fuzzy rules that handle linguistic variables and describe the knowledge of experts. The design of a fuzzy controller—advanced fuzzy potential field method (AFPFM)—that models and enhances the conventional potential field method is proposed and discussed. This study also examines the rule-explosion problem of conventional fuzzy logic and assesses the performance of our proposed AFPFM through simulations carried out using a mobile robot. PMID:27123001

  5. Advanced Fuzzy Potential Field Method for Mobile Robot Obstacle Avoidance.

    PubMed

    Park, Jong-Wook; Kwak, Hwan-Joo; Kang, Young-Chang; Kim, Dong W

    2016-01-01

    An advanced fuzzy potential field method for mobile robot obstacle avoidance is proposed. The potential field method primarily deals with the repulsive forces surrounding obstacles, while fuzzy control logic focuses on fuzzy rules that handle linguistic variables and describe the knowledge of experts. The design of a fuzzy controller--advanced fuzzy potential field method (AFPFM)--that models and enhances the conventional potential field method is proposed and discussed. This study also examines the rule-explosion problem of conventional fuzzy logic and assesses the performance of our proposed AFPFM through simulations carried out using a mobile robot. PMID:27123001

  6. An Improved Numerical Integration Method for Springback Predictions

    NASA Astrophysics Data System (ADS)

    Ibrahim, R.; Smith, L. M.; Golovashchenko, Sergey F.

    2011-08-01

    In this investigation, the focus is on the springback of steel sheets in V-die air bending. A full replication to a numerical integration algorithm presented rigorously in [1] to predict the springback in air bending was performed and confirmed successfully. Algorithm alteration and extensions were proposed here. The altered approach used in solving the moment equation numerically resulted in springback values much closer to the trend presented by the experimental data, Although investigation here extended to use a more realistic work-hardening model, the differences in the springback values obtained by both hardening models were almost negligible. The algorithm was extended to be applied on thin sheets down to 0.8 mm. Results show that this extension is possible as verified by FEA and other published experiments on TRIP steel sheets.

  7. Methods, Software and Tools for Three Numerical Applications. Final report

    SciTech Connect

    E. R. Jessup

    2000-03-01

    This is a report of the results of the authors work supported by DOE contract DE-FG03-97ER25325. They proposed to study three numerical problems. They are: (1) the extension of the PMESC parallel programming library; (2) the development of algorithms and software for certain generalized eigenvalue and singular value (SVD) problems, and (3) the application of techniques of linear algebra to an information retrieval technique known as latent semantic indexing (LSI).

  8. Algorithms for the Fractional Calculus: A Selection of Numerical Methods

    NASA Technical Reports Server (NTRS)

    Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.

    2003-01-01

    Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

  9. Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

    ERIC Educational Resources Information Center

    Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

    2016-01-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

  10. Finite strip method combined with other numerical methods for the analysis of plates

    NASA Astrophysics Data System (ADS)

    Cheung, M. S.; Li, Wenchang

    1992-09-01

    Finite plate strips are combined with finite elements or boundary elements in the analysis of rectangular plates with some minor irregularities such as openings, skew edges, etc. The plate is divided into regular and irregular regions. The regular region is analyzed by the finite strip method while the irregular one is analyzed by the finite element or boundary element method. A special transition element and strip are developed in order to connect the both regions. Numerical examples will show the accuracy and efficiency of this combined analysis.

  11. Numerical methods for a general class of porous medium equations

    SciTech Connect

    Rose, M. E.

    1980-03-01

    The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.

  12. Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods

    NASA Technical Reports Server (NTRS)

    Wu, S. T.

    1988-01-01

    Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.

  13. Advanced Ablative Insulators and Methods of Making Them

    NASA Technical Reports Server (NTRS)

    Congdon, William M.

    2005-01-01

    Advanced ablative (more specifically, charring) materials that provide temporary protection against high temperatures, and advanced methods of designing and manufacturing insulators based on these materials, are undergoing development. These materials and methods were conceived in an effort to replace the traditional thermal-protection systems (TPSs) of re-entry spacecraft with robust, lightweight, better-performing TPSs that can be designed and manufactured more rapidly and at lower cost. These materials and methods could also be used to make improved TPSs for general aerospace, military, and industrial applications.

  14. Strategy to Promote Active Learning of an Advanced Research Method

    ERIC Educational Resources Information Center

    McDermott, Hilary J.; Dovey, Terence M.

    2013-01-01

    Research methods courses aim to equip students with the knowledge and skills required for research yet seldom include practical aspects of assessment. This reflective practitioner report describes and evaluates an innovative approach to teaching and assessing advanced qualitative research methods to final-year psychology undergraduate students. An…

  15. Advanced Numerical Imaging Procedure Accounting for Non-Ideal Effects in GPR Scenarios

    NASA Astrophysics Data System (ADS)

    Comite, Davide; Galli, Alessandro; Catapano, Ilaria; Soldovieri, Francesco

    2015-04-01

    advanced implementation have also been tested by introducing 'errors' on the knowledge of the background medium permittivity, by simulating the presence of one or more layers, and by choosing different models of the surface roughness. The impact of these issues on the performance of both the conventional procedure and the advanced one will be extensively highlighted and discussed at the conference. [1] G. Valerio et al., "GPR detectability of rocks in a Martian-like shallow subsoil: A numerical approach," Plan. Sp. Sci., vol. 62, pp. 31-40, 2012. [2] A. Galli et al., "3D imaging of buried dielectric targets with a tomographic microwave approach applied to GPR synthetic data," Int. J. Antennas Propag., art. ID 610389, 10 pp., 2013 [3] F. Soldovieri et al., "A linear inverse scattering algorithm for realistic GPR applications," Near Surface Geophysics, 5 (1), pp. 29-42, 2007.

  16. Projection methods for the numerical solution of Markov chain models

    NASA Technical Reports Server (NTRS)

    Saad, Youcef

    1989-01-01

    Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

  17. Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM

    SciTech Connect

    Ding, Ning Zhang, Yang Xiao, Delong Wu, Jiming Huang, Jun Yin, Li Sun, Shunkai Xue, Chuang Dai, Zihuan Ning, Cheng Shu, Xiaojian Wang, Jianguo Li, Hua

    2014-12-15

    Fast Z-pinch has produced the most powerful X-ray radiation source in laboratory and also shows the possibility to drive inertial confinement fusion (ICF). Recent advances in wire-array Z-pinch researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper. A typical wire array Z-pinch process has three phases: wire plasma formation and ablation, implosion and the MRT instability development, stagnation and radiation. A mass injection model with azimuthal modulation coefficient is used to describe the wire initiation, and the dynamics of ablated plasmas of wire-array Z-pinches in (r, θ) geometry is numerically studied. In the implosion phase, a two-dimensional(r, z) three temperature radiation MHD code MARED has been developed to investigate the development of the Magneto-Rayleigh-Taylor(MRT) instability. We also analyze the implosion modes of nested wire-array and find that the inner wire-array is hardly affected before the impaction of the outer wire-array. While the plasma accelerated to high speed in the implosion stage stagnates on the axis, abundant x-ray radiation is produced. The energy spectrum of the radiation and the production mechanism are investigated. The computational x-ray pulse shows a reasonable agreement with the experimental result. We also suggest that using alloyed wire-arrays can increase multi-keV K-shell yield by decreasing the opacity of K-shell lines. In addition, we use a detailed circuit model to study the energy coupling between the generator and the Z-pinch implosion. Recently, we are concentrating on the problems of Z-pinch driven ICF, such as dynamic hohlraum and capsule implosions. Our numerical investigations on the interaction of wire-array Z-pinches on foam convertors show qualitative agreements with experimental results on the “Qiangguang I” facility. An integrated two-dimensional simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire

  18. Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM

    NASA Astrophysics Data System (ADS)

    Ding, Ning; Zhang, Yang; Xiao, Delong; Wu, Jiming; Huang, Jun; Yin, Li; Sun, Shunkai; Xue, Chuang; Dai, Zihuan; Ning, Cheng; Shu, Xiaojian; Wang, Jianguo; Li, Hua

    2014-12-01

    Fast Z-pinch has produced the most powerful X-ray radiation source in laboratory and also shows the possibility to drive inertial confinement fusion (ICF). Recent advances in wire-array Z-pinch researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper. A typical wire array Z-pinch process has three phases: wire plasma formation and ablation, implosion and the MRT instability development, stagnation and radiation. A mass injection model with azimuthal modulation coefficient is used to describe the wire initiation, and the dynamics of ablated plasmas of wire-array Z-pinches in (r, θ) geometry is numerically studied. In the implosion phase, a two-dimensional(r, z) three temperature radiation MHD code MARED has been developed to investigate the development of the Magneto-Rayleigh-Taylor(MRT) instability. We also analyze the implosion modes of nested wire-array and find that the inner wire-array is hardly affected before the impaction of the outer wire-array. While the plasma accelerated to high speed in the implosion stage stagnates on the axis, abundant x-ray radiation is produced. The energy spectrum of the radiation and the production mechanism are investigated. The computational x-ray pulse shows a reasonable agreement with the experimental result. We also suggest that using alloyed wire-arrays can increase multi-keV K-shell yield by decreasing the opacity of K-shell lines. In addition, we use a detailed circuit model to study the energy coupling between the generator and the Z-pinch implosion. Recently, we are concentrating on the problems of Z-pinch driven ICF, such as dynamic hohlraum and capsule implosions. Our numerical investigations on the interaction of wire-array Z-pinches on foam convertors show qualitative agreements with experimental results on the "Qiangguang I" facility. An integrated two-dimensional simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire

  19. Numerical conformal mapping methods for exterior and doubly connected regions

    SciTech Connect

    DeLillo, T.K.; Pfaltzgraff, J.A.

    1996-12-31

    Methods are presented and analyzed for approximating the conformal map from the exterior of the disk to the exterior a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. We show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.

  20. An introduction to nonlinear programming. IV - Numerical methods for constrained minimization

    NASA Technical Reports Server (NTRS)

    Sorenson, H. W.; Koble, H. M.

    1976-01-01

    An overview is presented of the numerical solution of constrained minimization problems. Attention is given to both primal and indirect (linear programs and unconstrained minimizations) methods of solution.

  1. A Primer In Advanced Fatigue Life Prediction Methods

    NASA Technical Reports Server (NTRS)

    Halford, Gary R.

    2000-01-01

    Metal fatigue has plagued structural components for centuries, and it remains a critical durability issue in today's aerospace hardware. This is true despite vastly improved and advanced materials, increased mechanistic understanding, and development of accurate structural analysis and advanced fatigue life prediction tools. Each advance is quickly taken advantage of to produce safer, more reliable more cost effective, and better performing products. In other words, as the envelop is expanded, components are then designed to operate just as close to the newly expanded envelop as they were to the initial one. The problem is perennial. The economic importance of addressing structural durability issues early in the design process is emphasized. Tradeoffs with performance, cost, and legislated restrictions are pointed out. Several aspects of structural durability of advanced systems, advanced materials and advanced fatigue life prediction methods are presented. Specific items include the basic elements of durability analysis, conventional designs, barriers to be overcome for advanced systems, high-temperature life prediction for both creep-fatigue and thermomechanical fatigue, mean stress effects, multiaxial stress-strain states, and cumulative fatigue damage accumulation assessment.

  2. Numerical methods for simulating blood flow at macro, micro, and multi scales.

    PubMed

    Imai, Yohsuke; Omori, Toshihiro; Shimogonya, Yuji; Yamaguchi, Takami; Ishikawa, Takuji

    2016-07-26

    In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow.

  3. Analysis of free turbulent shear flows by numerical methods

    NASA Technical Reports Server (NTRS)

    Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.

    1973-01-01

    Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

  4. Advanced stress analysis methods applicable to turbine engine structures

    NASA Technical Reports Server (NTRS)

    Pian, T. H. H.

    1985-01-01

    Advanced stress analysis methods applicable to turbine engine structures are investigated. Constructions of special elements which containing traction-free circular boundaries are investigated. New versions of mixed variational principle and version of hybrid stress elements are formulated. A method is established for suppression of kinematic deformation modes. semiLoof plate and shell elements are constructed by assumed stress hybrid method. An elastic-plastic analysis is conducted by viscoplasticity theory using the mechanical subelement model.

  5. Feasibility study of the numerical integration of shell equations using the field method

    NASA Technical Reports Server (NTRS)

    Cohen, G. A.

    1973-01-01

    The field method is developed for arbitrary open branch domains subjected to general linear boundary conditions. Although closed branches are within the scope of the method, they are not treated here. The numerical feasibility of the method has been demonstrated by implementing it in a computer program for the linear static analysis of open branch shells of revolution under asymmetric loads. For such problems the field method eliminates the well-known numerical problem of long subintervals associated with the rapid growth of extraneous solutions. Also, the method appears to execute significantly faster than other numerical integration methods.

  6. Using MACSYMA to drive numerical methods to computer radiation integrals

    SciTech Connect

    Clark, B.A.

    1986-01-01

    Because the emission of thermal radiation is characterized by the Planck emission spectrum, a multigroup solution of the thermal-radiation transport equation demands the calculation of definite integrals of the Planck spectrum. In the past, many approximate methods have been used with varying degrees of accuracy and efficiency. This paper describes how a symbolic algebra package, in this case MACSYMA is used to develop new methods for accurately and efficiently evaluating multigroup Planck integrals. The advantage of using a symbolic algebra package is that the job of developing the new methods is accomplished more efficiently.

  7. Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

    SciTech Connect

    Duez, Matthew D.; Liu, Yuk Tung; Shapiro, Stuart L.; Stephens, Branson C.

    2005-07-15

    Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the Baumgarte-Shapiro-Shibata-Nakamura equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code's ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.

  8. Numerical Stability and Convergence of Approximate Methods for Conservation Laws

    NASA Astrophysics Data System (ADS)

    Galkin, V. A.

    We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.

  9. A numerical method for eigenvalue problems in modeling liquid crystals

    SciTech Connect

    Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A.; Calvetti, D.

    1996-12-31

    Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.

  10. Advanced digital methods for solid propellant burning rate determination

    NASA Astrophysics Data System (ADS)

    Jones, Daniel A.

    The work presented here is a study of a digital method for determining the combustion bomb burning rate of a fuel-rich gas generator propellant sample using the ultrasonic pulse-echo technique. The advanced digital method, which places user defined limits on the search for the ultrasonic echo from the burning surface, is computationally faster than the previous cross correlation method, and is able to analyze data for this class of propellant that the previous cross correlation data reduction method could not. For the conditions investigated, the best fit burning rate law at 800 psi from the ultrasonic technique and advanced cross correlation method is within 3 percent of an independent analysis of the same data, and is within 5 percent of the best fit burning rate law found from parallel research of the same propellant in a motor configuration.

  11. Recent advances in optical measurement methods in physics and chemistry

    SciTech Connect

    Gerardo, J.B.

    1985-01-01

    Progress being made in the development of new scientific measurement tools based on optics and the scientific advances made possible by these new tools is impressive. In some instances, new optical-based measurement methods have made new scientific studies possible, while in other instances they have offered an improved method for performing these studies, e.g., better signal-to-noise ratio, increased data acquisition rate, remote analysis, reduced perturbation to the physical or chemical system being studied, etc. Many of these advances were made possible by advances in laser technology - spectral purity, spectral brightness, tunability, ultrashort pulse width, amplitude stability, etc. - while others were made possible by improved optical components - single-made fibers, modulators, detectors, wavelength multiplexes, etc. Attention is limited to just a few of many such accomplishments made recently at Sandia. 17 references, 16 figures.

  12. Advanced Methods for the Solution of Differential Equations.

    ERIC Educational Resources Information Center

    Goldstein, Marvin E.; Braun, Willis H.

    This is a textbook, originally developed for scientists and engineers, which stresses the actual solutions of practical problems. Theorems are precisely stated, but the proofs are generally omitted. Sample contents include first-order equations, equations in the complex plane, irregular singular points, and numerical methods. A more recent idea,…

  13. 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.

  14. Improved numerical methods for turbulent viscous recirculating flows

    NASA Technical Reports Server (NTRS)

    Turan, A.; Vandoormaal, J. P.

    1988-01-01

    The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

  15. Numerical solution of 2D-vector tomography problem using the method of approximate inverse

    NASA Astrophysics Data System (ADS)

    Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

    2016-08-01

    We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

  16. 7 CFR 27.92 - Method of payment; advance deposit.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Method of payment; advance deposit. 27.92 Section 27.92 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE COMMODITY STANDARDS AND STANDARD...

  17. METHODS ADVANCEMENT FOR MILK ANALYSIS: THE MAMA STUDY

    EPA Science Inventory

    The Methods Advancement for Milk Analysis (MAMA) study was designed by US EPA and CDC investigators to provide data to support the technological and study design needs of the proposed National Children=s Study (NCS). The NCS is a multi-Agency-sponsored study, authorized under the...

  18. Numerical experiments with a parallel conjugate gradient method

    SciTech Connect

    Oppe, T.C.; Kincaid, D.R.

    1987-04-01

    A parallel version of the conjugate gradient method introduced by Seager is implemented using various Cray multitasking tools. The parallel algorithm is used to solve a model partial differential equation on the unit square for various mesh sizes. Speed-up factors are given, and the effects of bank conflicts are noted. 8 refs., 10 figs.

  19. Evaluating numerical ODE/DAE methods, algorithms and software

    NASA Astrophysics Data System (ADS)

    Soderlind, Gustaf; Wang, Lina

    2006-01-01

    Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to DASPK and RADAU5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.

  20. Advanced propulsion for LEO-Moon transport. 1: A method for evaluating advanced propulsion performance

    NASA Technical Reports Server (NTRS)

    Stern, Martin O.

    1992-01-01

    This report describes a study to evaluate the benefits of advanced propulsion technologies for transporting materials between low Earth orbit and the Moon. A relatively conventional reference transportation system, and several other systems, each of which includes one advanced technology component, are compared in terms of how well they perform a chosen mission objective. The evaluation method is based on a pairwise life-cycle cost comparison of each of the advanced systems with the reference system. Somewhat novel and economically important features of the procedure are the inclusion not only of mass payback ratios based on Earth launch costs, but also of repair and capital acquisition costs, and of adjustments in the latter to reflect the technological maturity of the advanced technologies. The required input information is developed by panels of experts. The overall scope and approach of the study are presented in the introduction. The bulk of the paper describes the evaluation method; the reference system and an advanced transportation system, including a spinning tether in an eccentric Earth orbit, are used to illustrate it.

  1. Sound graphs: a numerical data analysis method for the blind.

    PubMed

    Mansur, D L; Blattner, M M; Joy, K I

    1985-06-01

    A system for the creation of computer-generated sound patterns of two-dimensional line graphs is described. The objectives of the system are to provide the blind with a means of understanding line graphs in the holistic manner used by those with sight. A continuously varying pitch is used to represent motion in the x direction. To test the feasibility of using sound to represent graphs, a prototype system was developed and human factors experimenters were performed. Fourteen subjects were used to compare the tactile-graph methods normally used by the blind to these new sound graphs. It was discovered that mathematical concepts such as symmetry, monotonicity, and the slopes of lines could be determined quickly using sound. Even better performance may be expected with additional training. The flexibility, speed, cost-effectiveness, and greater measure of independence provided the blind or sight-impaired using these methods was demonstrated. PMID:2932516

  2. Numerical Modeling of Tsunami Bore Attenuation and Extreme Hydrodynamic Impact Forces Using the SPH Method

    NASA Astrophysics Data System (ADS)

    Piche, Steffanie

    Understanding the impact of coastal forests on the propagation of rapidly advancing onshore tsunami bores is difficult due to complexity of this phenomenon and the large amount of parameters which must be considered. The research presented in the thesis focuses on understanding the protective effect of the coastal forest on the forces generated by the tsunami and its ability to reduce the propagation and velocity of the incoming tsunami bore. Concern for this method of protecting the coast from tsunamis is based on the effectiveness of the forest and its ability to withstand the impact forces caused by both the bore and the debris carried along by it. The devastation caused by the tsunami has been investigated in recent examples such as the 2011 Tohoku Tsunami in Japan and the Indian Ocean Tsunami which occurred in 2004. This research examines the reduction of the spatial extent of the tsunami bore inundation and runup due to the presence of the coastal forest, and attempts to quantify the impact forces induced by the tsunami bores and debris impact on the structures. This research work was performed using a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method which is a single-phase three-dimensional model. The simulations performed in this study were separated into three sections. The first section focused on the reduction of the extent of the tsunami inundation and the magnitude of the bore velocity by the coastal forest. This section included the analysis of the hydrodynamic forces acting on the individual trees. The second section involved the numerical modeling of some of the physical laboratory experiments performed by researchers at the University of Ottawa, in cooperation with colleagues from the Ocean, Coastal and River Engineering Lab at the National Research Council, Ottawa, in an attempt to validate the movement and impact forces of floating driftwood on a column. The final section modeled the movement and impact of floating debris

  3. Extremal polynomials and methods of optimization of numerical algorithms

    SciTech Connect

    Lebedev, V I

    2004-10-31

    Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.

  4. Advances and future directions of research on spectral methods

    NASA Technical Reports Server (NTRS)

    Patera, A. T.

    1986-01-01

    Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

  5. Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.

    PubMed

    Liu, Jinn-Liang; Eisenberg, Bob

    2015-07-01

    Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are

  6. Fully Coupled Simulation of Cosmic Reionization. I. Numerical Methods and Tests

    NASA Astrophysics Data System (ADS)

    Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.

    2015-01-01

    We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ~(100 Mpc)3 cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 32003 Eulerian grid cells and dark matter particles.

  7. Fully coupled simulation of cosmic reionization. I. numerical methods and tests

    DOE PAGES

    Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.

    2015-01-09

    Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use tomore » advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.« less

  8. Fully coupled simulation of cosmic reionization. I. numerical methods and tests

    SciTech Connect

    Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.

    2015-01-09

    Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.

  9. FULLY COUPLED SIMULATION OF COSMIC REIONIZATION. I. NUMERICAL METHODS AND TESTS

    SciTech Connect

    Norman, Michael L.; So, Geoffrey C.; Reynolds, Daniel R.; Harkness, Robert P.; Wise, John H.

    2015-01-01

    We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ∼(100 Mpc){sup 3} cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200{sup 3} Eulerian grid cells and dark matter particles.

  10. Numerical simulation of fluid-structure interactions with stabilized finite element method

    NASA Astrophysics Data System (ADS)

    Sváček, Petr

    2016-03-01

    This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.

  11. Design of braided composite tubes by numerical analysis method

    SciTech Connect

    Hamada, Hiroyuki; Fujita, Akihiro; Maekawa, Zenichiro; Nakai, Asami; Yokoyama, Atsushi

    1995-11-01

    Conventional composite laminates have very poor strength through thickness and as a result are limited in their application for structural parts with complex shape. In this paper, the design for braided composite tube was proposed. The concept of analysis model which involved from micro model to macro model was presented. This method was applied to predict bending rigidity and initial fracture stress under bending load of the braided tube. The proposed analytical procedure can be included as a unit in CAE system for braided composites.

  12. Numerical simulation of electromagnetic acoustic transducers using distributed point source method.

    PubMed

    Eskandarzade, M; Kundu, T; Liebeaux, N; Placko, D; Mobadersani, F

    2010-05-01

    In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.

  13. Advanced material modelling in numerical simulation of primary acetabular press-fit cup stability.

    PubMed

    Souffrant, R; Zietz, C; Fritsche, A; Kluess, D; Mittelmeier, W; Bader, R

    2012-01-01

    Primary stability of artificial acetabular cups, used for total hip arthroplasty, is required for the subsequent osteointegration and good long-term clinical results of the implant. Although closed-cell polymer foams represent an adequate bone substitute in experimental studies investigating primary stability, correct numerical modelling of this material depends on the parameter selection. Material parameters necessary for crushable foam plasticity behaviour were originated from numerical simulations matched with experimental tests of the polymethacrylimide raw material. Experimental primary stability tests of acetabular press-fit cups consisting of static shell assembly with consecutively pull-out and lever-out testing were subsequently simulated using finite element analysis. Identified and optimised parameters allowed the accurate numerical reproduction of the raw material tests. Correlation between experimental tests and the numerical simulation of primary implant stability depended on the value of interference fit. However, the validated material model provides the opportunity for subsequent parametric numerical studies.

  14. Advances of vibrational spectroscopic methods in phytomics and bioanalysis.

    PubMed

    Huck, Christian W

    2014-01-01

    During the last couple of years great advances in vibrational spectroscopy including near-infrared (NIR), mid-infrared (MIR), attenuated total reflection (ATR) and imaging and also mapping techniques could be achieved. On the other hand spectral treatment features have improved dramatically allowing filtering out relevant information from spectral data much more efficiently and providing new insights into the biochemical composition. These advances offer new possible quality control strategies in phytomics and enable to get deeper insights into biochemical background in terms of medicinal relevant questions. It is the aim of the present article pointing out the technical and methodological advancements in the NIR and MIR field and to demonstrate the individual methods efficiency by discussing distinct selected applications.

  15. Two Different Methods for Numerical Solution of the Modified Burgers' Equation

    PubMed Central

    Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi

    2014-01-01

    A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. PMID:25162064

  16. Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces

    NASA Technical Reports Server (NTRS)

    Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John

    2011-01-01

    Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

  17. Numerical computation of sapphire crystal growth using heat exchanger method

    NASA Astrophysics Data System (ADS)

    Lu, Chung-Wei; Chen, Jyh-Chen

    2001-05-01

    The finite element software FIDAP is employed to study the temperature and velocity distribution and the interface shape during a large sapphire crystal growth process using a heat exchanger method (HEM). In the present study, the energy input to the crucible by the radiation and convection inside the furnace and the energy output through the heat exchanger is modeled by the convection boundary conditions. The effects of the various growth parameters are studied. It is found that the contact angle is obtuse before the solid-melt interface touches the sidewall of the crucible. Therefore, hot spots always appear in this process. The maximum convexity decreases significantly when the cooling-zone radius (RC) increases. The maximum convexity also decreases significantly as the combined convection coefficient inside the furnace (hI) decreases.

  18. Transforming Mean and Osculating Elements Using Numerical Methods

    NASA Technical Reports Server (NTRS)

    Ely, Todd A.

    2010-01-01

    Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order

  19. Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs

    SciTech Connect

    X. Frank Xu

    2010-03-30

    Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory of MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will

  20. Numerical solution of multi-dimensional compressible reactive flow using a parallel wavelet adaptive multi-resolution method

    NASA Astrophysics Data System (ADS)

    Grenga, Temistocle

    The aim of this research is to further develop a dynamically adaptive algorithm based on wavelets that is able to solve efficiently multi-dimensional compressible reactive flow problems. This work demonstrates the great potential for the method to perform direct numerical simulation (DNS) of combustion with detailed chemistry and multi-component diffusion. In particular, it addresses the performance obtained using a massive parallel implementation and demonstrates important savings in memory storage and computational time over conventional methods. In addition, fully-resolved simulations of challenging three dimensional problems involving mixing and combustion processes are performed. These problems are particularly challenging due to their strong multiscale characteristics. For these solutions, it is necessary to combine the advanced numerical techniques applied to modern computational resources.

  1. Advances in nucleic acid-based detection methods.

    PubMed Central

    Wolcott, M J

    1992-01-01

    Laboratory techniques based on nucleic acid methods have increased in popularity over the last decade with clinical microbiologists and other laboratory scientists who are concerned with the diagnosis of infectious agents. This increase in popularity is a result primarily of advances made in nucleic acid amplification and detection techniques. Polymerase chain reaction, the original nucleic acid amplification technique, changed the way many people viewed and used nucleic acid techniques in clinical settings. After the potential of polymerase chain reaction became apparent, other methods of nucleic acid amplification and detection were developed. These alternative nucleic acid amplification methods may become serious contenders for application to routine laboratory analyses. This review presents some background information on nucleic acid analyses that might be used in clinical and anatomical laboratories and describes some recent advances in the amplification and detection of nucleic acids. PMID:1423216

  2. Fracture Toughness in Advanced Monolithic Ceramics - SEPB Versus SEVENB Methods

    NASA Technical Reports Server (NTRS)

    Choi, S. R.; Gyekenyesi, J. P.

    2005-01-01

    Fracture toughness of a total of 13 advanced monolithic ceramics including silicon nitrides, silicon carbide, aluminas, and glass ceramic was determined at ambient temperature by using both single edge precracked beam (SEPB) and single edge v-notched beam (SEVNB) methods. Relatively good agreement in fracture toughness between the two methods was observed for advanced ceramics with flat R-curves; whereas, poor agreement in fracture toughness was seen for materials with rising R-curves. The discrepancy in fracture toughness between the two methods was due to stable crack growth with crack closure forces acting in the wake region of cracks even in SEVNB test specimens. The effect of discrepancy in fracture toughness was analyzed in terms of microstructural feature (grain size and shape), toughening exponent, and stable crack growth determined using back-face strain gaging.

  3. Science-Based Approach for Advancing Marine and Hydrokinetic Energy: Integrating Numerical Simulations with Experiments

    NASA Astrophysics Data System (ADS)

    Sotiropoulos, F.; Kang, S.; Chamorro, L. P.; Hill, C.

    2011-12-01

    The field of MHK energy is still in its infancy lagging approximately a decade or more behind the technology and development progress made in wind energy engineering. Marine environments are characterized by complex topography and three-dimensional (3D) turbulent flows, which can greatly affect the performance and structural integrity of MHK devices and impact the Levelized Cost of Energy (LCoE). Since the deployment of multi-turbine arrays is envisioned for field applications, turbine-to-turbine interactions and turbine-bathymetry interactions need to be understood and properly modeled so that MHK arrays can be optimized on a site specific basis. Furthermore, turbulence induced by MHK turbines alters and interacts with the nearby ecosystem and could potentially impact aquatic habitats. Increased turbulence in the wake of MHK devices can also change the shear stress imposed on the bed ultimately affecting the sediment transport and suspension processes in the wake of these structures. Such effects, however, remain today largely unexplored. In this work a science-based approach integrating state-of-the-art experimentation with high-resolution computational fluid dynamics is proposed as a powerful strategy for optimizing the performance of MHK devices and assessing environmental impacts. A novel numerical framework is developed for carrying out Large-Eddy Simulation (LES) in arbitrarily complex domains with embedded MHK devices. The model is able to resolve the geometrical complexity of real-life MHK devices using the Curvilinear Immersed Boundary (CURVIB) method along with a wall model for handling the flow near solid surfaces. Calculations are carried out for an axial flow hydrokinetic turbine mounted on the bed of rectangular open channel on a grid with nearly 200 million grid nodes. The approach flow corresponds to fully developed turbulent open channel flow and is obtained from a separate LES calculation. The specific case corresponds to that studied

  4. IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.

    SciTech Connect

    Tidwell, Vincent Carroll; Sue Tillery; Phillip King

    2008-09-01

    A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field application

  5. Genomic DNA microextraction: a method to screen numerous samples.

    PubMed

    Ramírez-Solis, R; Rivera-Pérez, J; Wallace, J D; Wims, M; Zheng, H; Bradley, A

    1992-03-01

    Many experimental designs require the analysis of genomic DNA from a large number of samples. Although the polymerase chain reaction (PCR) can be used, the Southern blot is preferred for many assays because of its inherent reliability. The rapid acceptance of PCR, despite a significant rate of false positive/negative results, is partly due to the disadvantages of the sample preparation process for Southern blot analysis. We have devised a rapid protocol to extract high-molecular-weight genomic DNA from a large number of samples. It involves the use of a single 96-well tissue culture dish to carry out all the steps of the sample preparation. This, coupled with the use of a multichannel pipette, facilitates the simultaneous analysis of multiple samples. The procedure may be automated since no centrifugation, mixing, or transferring of the samples is necessary. The method has been used to screen embryonic stem cell clones for the presence of targeted mutations at the Hox-2.6 locus and to obtain data from human blood.

  6. Numerical methods on some structured matrix algebra problems

    SciTech Connect

    Jessup, E.R.

    1996-06-01

    This proposal concerned the design, analysis, and implementation of serial and parallel algorithms for certain structured matrix algebra problems. It emphasized large order problems and so focused on methods that can be implemented efficiently on distributed-memory MIMD multiprocessors. Such machines supply the computing power and extensive memory demanded by the large order problems. We proposed to examine three classes of matrix algebra problems: the symmetric and nonsymmetric eigenvalue problems (especially the tridiagonal cases) and the solution of linear systems with specially structured coefficient matrices. As all of these are of practical interest, a major goal of this work was to translate our research in linear algebra into useful tools for use by the computational scientists interested in these and related applications. Thus, in addition to software specific to the linear algebra problems, we proposed to produce a programming paradigm and library to aid in the design and implementation of programs for distributed-memory MIMD computers. We now report on our progress on each of the problems and on the programming tools.

  7. A comparative study of divergence cleaning methods of magnetic field in the solar coronal numerical simulation

    NASA Astrophysics Data System (ADS)

    Feng, Xueshang; Zhang, Man

    2016-03-01

    This paper presents a comparative study of divergence cleaning methods of magnetic field in the solar coronal three-dimensional numerical simulation. For such purpose, the diffusive method, projection method, generalized Lagrange multiplier method and constrained-transport method are used. All these methods are combined with a finite-volume scheme based on a six-component grid system in spherical coordinates. In order to see the performance between the four divergence cleaning methods, solar coronal numerical simulation for Carrington rotation 2056 has been studied. Numerical results show that the average relative divergence error is around 10^{-4.5} for the constrained-transport method, while about 10^{-3.1}- 10^{-3.6} for the other three methods. Although there exist some differences in the average relative divergence errors for the four employed methods, our tests show they can all produce basic structured solar wind.

  8. Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels

    NASA Astrophysics Data System (ADS)

    Liu, Jinn-Liang; Eisenberg, Bob

    2015-07-01

    Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca2 + may cause more unstable discrete Ca2 + fluxes than that of monovalent Na+. Two different methods—called the SMIB and multiscale methods—are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are

  9. Advanced stress analysis methods applicable to turbine engine structures

    NASA Technical Reports Server (NTRS)

    Pian, Theodore H. H.

    1991-01-01

    The following tasks on the study of advanced stress analysis methods applicable to turbine engine structures are described: (1) constructions of special elements which contain traction-free circular boundaries; (2) formulation of new version of mixed variational principles and new version of hybrid stress elements; (3) establishment of methods for suppression of kinematic deformation modes; (4) construction of semiLoof plate and shell elements by assumed stress hybrid method; and (5) elastic-plastic analysis by viscoplasticity theory using the mechanical subelement model.

  10. Improved method of HIPOT testing of advanced ignition system product

    SciTech Connect

    Baker, P.C.

    1992-04-01

    A new method of high potential (HIPOT) testing of advanced ignition system (AIS) product was developed. The new incorporated using a silver-filled RTV silicone as the electrodes of the HIPOT tester instead of the preformed, semi-rigid aluminum electrodes of the current tester. Initial results indicate that the developed method was more sensitive to the testing requirements of the HIPOT test. A patent for the combination of the material used and the method of testing developed was attempted but was withdrawn following a patent search by the US Patent Office.

  11. Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics

    NASA Technical Reports Server (NTRS)

    Stowers, S. T.; Bass, J. M.; Oden, J. T.

    1993-01-01

    A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.

  12. BWR Full Integral Simulation Test (FIST) Program. TRAC-BWR model development. Volume 1. Numerical methods

    SciTech Connect

    Heck, C.L.; Andersen, J.G.M.

    1985-11-01

    A complete technical basis for implementation of the 3-D fast numerics in TRACB04 is presented. The 3-D fast numerics is a generalization of the predictor/corrector method previously developed for the 1-D components in TRACB. 20 figs.

  13. A study of numerical methods for hyperbolic conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.; Yee, H. C.

    1988-01-01

    The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

  14. Laboratory and numerical evaluation of borehole methods for subsurface horizontal flow characterization.

    SciTech Connect

    Pedler, William H. (Radon Abatement Systems, Inc., Golden, CO); Jepsen, Richard Alan (Sandia National Laboratories, Carlsbad, NM)

    2003-08-01

    The requirement to accurately measure subsurface groundwater flow at contaminated sites, as part of a time and cost effective remediation program, has spawned a variety of flow evaluation technologies. Validation of the accuracy and knowledge regarding the limitations of these technologies are critical for data quality and application confidence. Leading the way in the effort to validate and better understand these methodologies, the US Army Environmental Center has funded a multi-year program to compare and evaluate all viable horizontal flow measurement technologies. This multi-year program has included a field comparison phase, an application of selected methods as part of an integrated site characterization program phase, and most recently, a laboratory and numerical simulator phase. As part of this most recent phase, numerical modeling predictions and laboratory measurements were made in a simulated fracture borehole set-up within a controlled flow simulator. The scanning colloidal borescope flowmeter (SCBFM) and advanced hydrophysical logging (NxHpL{trademark}) tool were used to measure velocities and flow rate in a simulated fractured borehole in the flow simulator. Particle tracking and mass flux measurements were observed and recorded under a range of flow conditions in the simulator. Numerical models were developed to aid in the design of the flow simulator and predict the flow conditions inside the borehole. Results demonstrated that the flow simulator allowed for predictable, easily controlled, and stable flow rates both inside and outside the well. The measurement tools agreed well with each other over a wide range of flow conditions. The model results demonstrate that the Scanning Colloidal Borescope did not interfere with the flow in the borehole in any of the tests. The model is capable of predicting flow conditions and agreed well with the measurements and observations in the flow simulator and borehole. Both laboratory and model results showed a

  15. Conservation properties of numerical integration methods for systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Rosenbaum, J. S.

    1976-01-01

    If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

  16. A fifth order implicit method for the numerical solution of differential-algebraic equations

    NASA Astrophysics Data System (ADS)

    Skvortsov, L. M.

    2015-06-01

    An implicit two-step Runge-Kutta method of fifth order is proposed for the numerical solution of differential and differential-algebraic equations. The location of nodes in this method makes it possible to estimate the values of higher derivatives at the initial and terminal points of an integration step. Consequently, the proposed method can be regarded as a finite-difference analog of the Obrechkoff method. Numerical results, some of which are presented in this paper, show that our method preserves its order while solving stiff equations and equations of indices two and three. This is the main advantage of the proposed method as compared with the available ones.

  17. A numerical method for approximating antenna surfaces defined by discrete surface points

    NASA Technical Reports Server (NTRS)

    Lee, R. Q.; Acosta, R.

    1985-01-01

    A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

  18. Novel Methods for 3D Numerical Simulation of Meteor Radar Reflections

    NASA Astrophysics Data System (ADS)

    Räbinä, J.; Mönkölä, S.; Rossi, T.; Markkanen, J.; Gritsevich, M.; Muinonen, K.

    2016-08-01

    We model the radar reflections in a three-dimensional space as time-harmonic electromagnetic scattering from plasmatic obstacles. We introduce two novel methods for numerical simulation of meteor radar reflections.

  19. A review of recent advances in numerical simulations of microscale fuel processor for hydrogen production

    NASA Astrophysics Data System (ADS)

    Holladay, J. D.; Wang, Y.

    2015-05-01

    Microscale (<5 W) reformers for hydrogen production have been investigated for over a decade. These devices are intended to provide hydrogen for small fuel cells. Due to the reformer's small size, numerical simulations are critical to understand heat and mass transfer phenomena occurring in the systems and help guide the further improvements. This paper reviews the development of the numerical codes and details the reaction equations used. The majority of the devices utilized methanol as the fuel due to methanol's low reforming temperature and high conversion, although, there are several methane fueled systems. The increased computational power and more complex codes have led to improved accuracy of numerical simulations. Initial models focused on the reformer, while more recently, the simulations began including other unit operations such as vaporizers, inlet manifolds, and combustors. These codes are critical for developing the next generation systems. The systems reviewed included plate reactors, microchannel reactors, and annulus reactors for both wash-coated and packed bed systems.

  20. On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1980-01-01

    New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

  1. Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

    NASA Astrophysics Data System (ADS)

    Artichowicz, Wojciech; Prybytak, Dzmitry

    2015-12-01

    In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

  2. Advances in Statistical Methods for Substance Abuse Prevention Research

    PubMed Central

    MacKinnon, David P.; Lockwood, Chondra M.

    2010-01-01

    The paper describes advances in statistical methods for prevention research with a particular focus on substance abuse prevention. Standard analysis methods are extended to the typical research designs and characteristics of the data collected in prevention research. Prevention research often includes longitudinal measurement, clustering of data in units such as schools or clinics, missing data, and categorical as well as continuous outcome variables. Statistical methods to handle these features of prevention data are outlined. Developments in mediation, moderation, and implementation analysis allow for the extraction of more detailed information from a prevention study. Advancements in the interpretation of prevention research results include more widespread calculation of effect size and statistical power, the use of confidence intervals as well as hypothesis testing, detailed causal analysis of research findings, and meta-analysis. The increased availability of statistical software has contributed greatly to the use of new methods in prevention research. It is likely that the Internet will continue to stimulate the development and application of new methods. PMID:12940467

  3. A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

    SciTech Connect

    Marxen, Olaf; Magin, Thierry E.; Shaqfeh, Eric S.G.; Iaccarino, Gianluca

    2013-12-15

    A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as well as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.

  4. CNC Turning Center Advanced Operations. Computer Numerical Control Operator/Programmer. 444-332.

    ERIC Educational Resources Information Center

    Skowronski, Steven D.; Tatum, Kenneth

    This student guide provides materials for a course designed to introduce the student to the operations and functions of a two-axis computer numerical control (CNC) turning center. The course consists of seven units. Unit 1 presents course expectations and syllabus, covers safety precautions, and describes the CNC turning center components, CNC…

  5. Evaluation of Advanced Stirling Convertor Net Heat Input Correlation Methods Using a Thermal Standard

    NASA Technical Reports Server (NTRS)

    Briggs, Maxwell H.; Schifer, Nicholas A.

    2012-01-01

    The U.S. Department of Energy (DOE) and Lockheed Martin Space Systems Company (LMSSC) have been developing the Advanced Stirling Radioisotope Generator (ASRG) for use as a power system for space science missions. This generator would use two high-efficiency Advanced Stirling Convertors (ASCs), developed by Sunpower Inc. and NASA Glenn Research Center (GRC). The ASCs convert thermal energy from a radioisotope heat source into electricity. As part of ground testing of these ASCs, different operating conditions are used to simulate expected mission conditions. These conditions require achieving a particular operating frequency, hot end and cold end temperatures, and specified electrical power output for a given net heat input. In an effort to improve net heat input predictions, numerous tasks have been performed which provided a more accurate value for net heat input into the ASCs, including testing validation hardware, known as the Thermal Standard, to provide a direct comparison to numerical and empirical models used to predict convertor net heat input. This validation hardware provided a comparison for scrutinizing and improving empirical correlations and numerical models of ASC-E2 net heat input. This hardware simulated the characteristics of an ASC-E2 convertor in both an operating and non-operating mode. This paper describes the Thermal Standard testing and the conclusions of the validation effort applied to the empirical correlation methods used by the Radioisotope Power System (RPS) team at NASA Glenn.

  6. Numerical methods in vehicle system dynamics: state of the art and current developments

    NASA Astrophysics Data System (ADS)

    Arnold, M.; Burgermeister, B.; Führer, C.; Hippmann, G.; Rill, G.

    2011-07-01

    Robust and efficient numerical methods are an essential prerequisite for the computer-based dynamical analysis of engineering systems. In vehicle system dynamics, the methods and software tools from multibody system dynamics provide the integration platform for the analysis, simulation and optimisation of the complex dynamical behaviour of vehicles and vehicle components and their interaction with hydraulic components, electronical devices and control structures. Based on the principles of classical mechanics, the modelling of vehicles and their components results in nonlinear systems of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) of moderate dimension that describe the dynamical behaviour in the frequency range required and with a level of detail being characteristic of vehicle system dynamics. Most practical problems in this field may be transformed to generic problems of numerical mathematics like systems of nonlinear equations in the (quasi-)static analysis and explicit ODEs or DAEs with a typical semi-explicit structure in the dynamical analysis. This transformation to mathematical standard problems allows to use sophisticated, freely available numerical software that is based on well approved numerical methods like the Newton-Raphson iteration for nonlinear equations or Runge-Kutta and linear multistep methods for ODE/DAE time integration. Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics. In the present paper, we follow this framework and start with some modelling aspects being relevant from the numerical viewpoint. The focus of the paper is on numerical methods for static and dynamic problems, including software issues and a discussion which method fits best for which class of problems. Adaptive components in state-of-the-art numerical software like stepsize and order control in time integration are

  7. Time-optimal control of the race car: a numerical method to emulate the ideal driver

    NASA Astrophysics Data System (ADS)

    Kelly, D. P.; Sharp, R. S.

    2010-12-01

    A numerical method for the time-optimal control of the race car is presented. The method is then used to perform the role of the driver in numerical simulations of manoeuvres at the limit of race car performance. The method does not attempt to model the driver but rather replaces the driver with methods normally associated with numerical optimal control. The method simultaneously finds the optimal driven line and the driver control inputs (steer, throttle and brake) to drive this line in minimum time. In principle, the method is capable of operation with arbitrarily complex vehicle models as it requires only limited access to the vehicle model state vector. It also requires solution of the differential equation representing the vehicle model in only the forward time direction and is hence capable of simulating the full vehicle transient response.

  8. Numerical method for estimating the size of chaotic regions of phase space

    SciTech Connect

    Henyey, F.S.; Pomphrey, N.

    1987-10-01

    A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs. (LSP)

  9. A method for investigating the mechanical properties of intracoronary stents using finite element numerical simulation.

    PubMed

    Tan, L B; Webb, D C; Kormi, K; Al-Hassani, S T

    2001-03-01

    The proliferation of stent designs poses difficult problems to clinicians, who have to learn the relative merits of all stents to ensure optimal selection for each lesion, and also to regulatory authorities who have the dilemma of preventing the inappropriate marketing of substandard stents while not denying patients the benefits of advanced technology. Of the major factors influencing long-term results, those of patency and restenosis are being actively studied whereas the mechanical characteristics of devices influencing the technical results of stenting remain under-investigated. Each different stent design has its own particular features. A robust method for the independent objective comparison of the mechanical performance of each design is required. To do this by experimental measurement alone may be prohibitively expensive. A less costly option is to combine computer analysis, employing the standard numerical technique of the finite element method (FEM), with targeted experimental measurements of the specific mechanical behaviour of stents. In this paper the FEM technique is used to investigate the structural behaviour of two different stent geometries: Freedom stent geometry and Palmaz-Schatz (P-S) stent geometry. The effects of altering the stent geometry, the stent wire diameter and contact with (and material properties of) a hard eccentric intravascular lesion (simulating a calcified plaque) on stent mechanical performance were investigated. Increasing the wire diameter and the arterial elastic modulus by 150% results in the need to increase the balloon pressure to expand the stent by 10-fold. Increasing the number of circumferential convolutions increases the pressure required to initiate radial expansion of mounted stents. An incompressible plaque impinging on the mid portion of a stent causes a gross distortion of the Freedom stent and an hour-glass deformity in the P-S stent. These findings are of relevance for future comparative studies of the

  10. A numerical technique for calculation of the noise of high-speed propellers with advanced blade geometry

    NASA Technical Reports Server (NTRS)

    Nystrom, P. A.; Farassat, F.

    1980-01-01

    A numerical technique and computer program were developed for the prediction of the noise of propellers with advanced geometry. The blade upper and lower surfaces are described by a curvilinear coordinate system, which was also used to divide the blade surfaces into panels. Two different acoustic formulations in the time domain were used to improve the speed and efficiency of the noise calculations: an acoustic formualtion with the Doppler factor singularity for panels moving at subsonic speeds and the collapsing sphere formulation for panels moving at transonic or supersonic speeds. This second formulation involves a sphere which is centered at the observer position and whose radius decreases at the speed of sound. The acoustic equation consisted of integrals over the curve of intersection for both the sphere and the panels on the blade. Algorithms used in some parts of the computer program are discussed. Comparisons with measured acoustic data for two model high speed propellers with advanced geometry are also presented.

  11. A review of recent advances of numerical simulations of microscale fuel processors for hydrogen production

    SciTech Connect

    Holladay, Jamelyn D.; Wang, Yong

    2015-05-01

    Microscale (<5W) reformers for hydrogen production have been investigated for over a decade. These devices are intended to provide hydrogen for small fuel cells. Due to the reformer’s small size, numerical simulations are critical to understand heat and mass transfer phenomena occurring in the systems. This paper reviews the development of the numerical codes and details the reaction equations used. The majority of the devices utilized methanol as the fuel due to methanol’s low reforming temperature and high conversion, although, there are several methane fueled systems. As computational power has decreased in cost and increased in availability, the codes increased in complexity and accuracy. Initial models focused on the reformer, while more recently, the simulations began including other unit operations such as vaporizers, inlet manifolds, and combustors. These codes are critical for developing the next generation systems. The systems reviewed included, plate reactors, microchannel reactors, annulus reactors, wash-coated, packed bed systems.

  12. Novel glass inspection method for advanced photomask blanks

    NASA Astrophysics Data System (ADS)

    Tanabe, Masaru; Kikuchi, Toshiharu; Hashimoto, Masahiro; Ohkubo, Yasushi

    2007-05-01

    Recently, extremely-high-quality-quartz substrates have been demanded for advancing ArF-lithography. HOYA has developed a novel inspection method for interior defects as well as surface defects. The total internal reflection of the substrate is employed to produce an ideal dark field illumination. The novel inspection method can detect a "nano-pit" of 12nm-EDS, the Equivalent of the Diameter of a Sphere (EDS). It will meet the sensitivity for 32nm node and beyond. Moreover, a type of unique defect is detected, which induces Serious Transmittance Error for Arf-LiTHography. We call it the "STEALTH" defect. It is a killer defect in wafer printing; but it cannot be detected with any conventional inspection in the mask-making process so far. In this paper, the performance of the novel inspection method for quartz substrates and the investigation of "STEALTH" are reported.

  13. Advanced reactor physics methods for heterogeneous reactor cores

    NASA Astrophysics Data System (ADS)

    Thompson, Steven A.

    To maintain the economic viability of nuclear power the industry has begun to emphasize maximizing the efficiency and output of existing nuclear power plants by using longer fuel cycles, stretch power uprates, shorter outage lengths, mixed-oxide (MOX) fuel and more aggressive operating strategies. In order to accommodate these changes, while still satisfying the peaking factor and power envelope requirements necessary to maintain safe operation, more complexity in commercial core designs have been implemented, such as an increase in the number of sub-batches and an increase in the use of both discrete and integral burnable poisons. A consequence of the increased complexity of core designs, as well as the use of MOX fuel, is an increase in the neutronic heterogeneity of the core. Such heterogeneous cores introduce challenges for the current methods that are used for reactor analysis. New methods must be developed to address these deficiencies while still maintaining the computational efficiency of existing reactor analysis methods. In this thesis, advanced core design methodologies are developed to be able to adequately analyze the highly heterogeneous core designs which are currently in use in commercial power reactors. These methodological improvements are being pursued with the goal of not sacrificing the computational efficiency which core designers require. More specifically, the PSU nodal code NEM is being updated to include an SP3 solution option, an advanced transverse leakage option, and a semi-analytical NEM solution option.

  14. Mathematical model and its fast numerical method for the tumor growth.

    PubMed

    Lee, Hyun Geun; Kim, Yangjin; Kim, Junseok

    2015-12-01

    In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions. PMID:26775855

  15. Review of numerical methods for simulation of the aortic root: Present and future directions

    NASA Astrophysics Data System (ADS)

    Mohammadi, Hossein; Cartier, Raymond; Mongrain, Rosaire

    2016-05-01

    Heart valvular disease is still one of the main causes of mortality and morbidity in develop countries. Numerical modeling has gained considerable attention in studying hemodynamic conditions associated with valve abnormalities. Simulating the large displacement of the valve in the course of the cardiac cycle needs a well-suited numerical method to capture the natural biomechanical phenomena which happens in the valve. The paper aims to review the principal progress of the numerical approaches for studying the hemodynamic of the aortic valve. In addition, the future directions of the current approaches as well as their potential clinical applications are discussed.

  16. A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

    NASA Technical Reports Server (NTRS)

    Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

    1992-01-01

    The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

  17. Numerical solution of differential-algebraic equations using the spline collocation-variation method

    NASA Astrophysics Data System (ADS)

    Bulatov, M. V.; Rakhvalov, N. P.; Solovarova, L. S.

    2013-03-01

    Numerical methods for solving initial value problems for differential-algebraic equations are proposed. The approximate solution is represented as a continuous vector spline whose coefficients are found using the collocation conditions stated for a subgrid with the number of collocation points less than the degree of the spline and the minimality condition for the norm of this spline in the corresponding spaces. Numerical results for some model problems are presented.

  18. Numerical solution of hybrid fuzzy differential equations using improved predictor-corrector method

    NASA Astrophysics Data System (ADS)

    Kim, Hyunsoo; Sakthivel, Rathinasamy

    2012-10-01

    The hybrid fuzzy differential equations have a wide range of applications in science and engineering. This paper considers numerical solution for hybrid fuzzy differential equations. The improved predictor-corrector method is adapted and modified for solving the hybrid fuzzy differential equations. The proposed algorithm is illustrated by numerical examples and the results obtained using the scheme presented here agree well with the analytical solutions. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated calculations of algorithm.

  19. Review: Advances in delta-subsidence research using satellite methods

    NASA Astrophysics Data System (ADS)

    Higgins, Stephanie A.

    2016-05-01

    Most of the world's major river deltas are sinking relative to local sea level. The effects of subsidence can include aquifer salinization, infrastructure damage, increased vulnerability to flooding and storm surges, and permanent inundation of low-lying land. Consequently, determining the relative importance of natural vs. anthropogenic pressures in driving delta subsidence is a topic of ongoing research. This article presents a review of knowledge with respect to delta surface-elevation loss. The field is rapidly advancing due to applications of space-based techniques: InSAR (interferometric synthetic aperture radar), GPS (global positioning system), and satellite ocean altimetry. These techniques have shed new light on a variety of subsidence processes, including tectonics, isostatic adjustment, and the spatial and temporal variability of sediment compaction. They also confirm that subsidence associated with fluid extraction can outpace sea-level rise by up to two orders of magnitude, resulting in effective sea-level rise that is one-hundred times faster than the global average rate. In coming years, space-based and airborne instruments will be critical in providing near-real-time monitoring to facilitate management decisions in sinking deltas. However, ground-based observations continue to be necessary for generating complete measurements of surface-elevation change. Numerical modeling should seek to simulate couplings between subsidence processes for greater predictive power.

  20. Numerical simulation of stratified shear flow using a higher order Taylor series expansion method

    SciTech Connect

    Iwashige, Kengo; Ikeda, Takashi

    1995-09-01

    A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.

  1. Numerical implementation of the method of fictitious domains for elliptic equations

    NASA Astrophysics Data System (ADS)

    Temirbekov, Almas N.

    2016-08-01

    In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.

  2. A study of numerical methods for hyperbolic conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.; Yee, H. C.

    1990-01-01

    In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.

  3. Non-standard numerical methods applied to subsurface biobarrier formation models in porous media.

    PubMed

    Chen, B M; Kojouharov, H V

    1999-07-01

    Biofilm forming microbes have complex effects on the flow properties of natural porous media. Subsurface biofilms have the potential for the formation of biobarriers to inhibit contaminant migration in groundwater. Another example of beneficial microbial effects is the biotransformation of organic contaminants to less harmful forms, thereby providing an in situ method for treatment of contaminated groundwater supplies. Mathematical models that describe contaminant transport with biodegradation involve a set of coupled convection-dispersion equations with non-linear reactions. The reactive solute transport equation is one for which numerical solution procedures continue to exhibit significant limitations for certain problems of groundwater hydrology interest. Accurate numerical simulations are crucial to the development of contaminant remediation strategies. A new numerical method is developed for simulation of reactive bacterial transport in porous media. The non-standard numerical approach is based on the ideas of the 'exact' time-stepping scheme. It leads to solutions free from the numerical instabilities that arise from incorrect modeling of derivatives and reaction terms. Applications to different biofilm models are examined and numerical results are presented to demonstrate the performance of the proposed new method.

  4. Numerical Simulation of High Velocity Impact Phenomenon by the Distinct Element Method (dem)

    NASA Astrophysics Data System (ADS)

    Tsukahara, Y.; Matsuo, A.; Tanaka, K.

    2007-12-01

    Continuous-DEM (Distinct Element Method) for impact analysis is proposed in this paper. Continuous-DEM is based on DEM (Distinct Element Method) and the idea of the continuum theory. Numerical simulations of impacts between SUS 304 projectile and concrete target has been performed using the proposed method. The results agreed quantitatively with the impedance matching method. Experimental elastic-plastic behavior with compression and rarefaction wave under plate impact was also qualitatively reproduced, matching the result by AUTODYN®.

  5. Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.

    PubMed

    Yuan, Lijun; Lu, Ya Yan

    2013-05-20

    Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.

  6. Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.

    PubMed

    Yuan, Lijun; Lu, Ya Yan

    2013-05-20

    Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime. PMID:23736417

  7. Method for the numerical integration of equations of perturbed satellite motion in problems of space geodesy

    NASA Astrophysics Data System (ADS)

    Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.

    A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.

  8. Advanced Techniques for Seismic Protection of Historical Buildings: Experimental and Numerical Approach

    SciTech Connect

    Mazzolani, Federico M.

    2008-07-08

    The seismic protection of historical and monumental buildings, namely dating back from the ancient age up to the 20th Century, is being looked at with greater and greater interest, above all in the Euro-Mediterranean area, its cultural heritage being strongly susceptible to undergo severe damage or even collapse due to earthquake. The cultural importance of historical and monumental constructions limits, in many cases, the possibility to upgrade them from the seismic point of view, due to the fear of using intervention techniques which could have detrimental effects on their cultural value. Consequently, a great interest is growing in the development of sustainable methodologies for the use of Reversible Mixed Technologies (RMTs) in the seismic protection of the existing constructions. RMTs, in fact, are conceived for exploiting the peculiarities of innovative materials and special devices, and they allow ease of removal when necessary. This paper deals with the experimental and numerical studies, framed within the EC PROHITECH research project, on the application of RMTs to the historical and monumental constructions mainly belonging to the cultural heritage of the Euro-Mediterranean area. The experimental tests and the numerical analyses are carried out at five different levels, namely full scale models, large scale models, sub-systems, devices, materials and elements.

  9. Methods and systems for advanced spaceport information management

    NASA Technical Reports Server (NTRS)

    Fussell, Ronald M. (Inventor); Ely, Donald W. (Inventor); Meier, Gary M. (Inventor); Halpin, Paul C. (Inventor); Meade, Phillip T. (Inventor); Jacobson, Craig A. (Inventor); Blackwell-Thompson, Charlie (Inventor)

    2007-01-01

    Advanced spaceport information management methods and systems are disclosed. In one embodiment, a method includes coupling a test system to the payload and transmitting one or more test signals that emulate an anticipated condition from the test system to the payload. One or more responsive signals are received from the payload into the test system and are analyzed to determine whether one or more of the responsive signals comprises an anomalous signal. At least one of the steps of transmitting, receiving, analyzing and determining includes transmitting at least one of the test signals and the responsive signals via a communications link from a payload processing facility to a remotely located facility. In one particular embodiment, the communications link is an Internet link from a payload processing facility to a remotely located facility (e.g. a launch facility, university, etc.).

  10. Methods and Systems for Advanced Spaceport Information Management

    NASA Technical Reports Server (NTRS)

    Fussell, Ronald M. (Inventor); Ely, Donald W. (Inventor); Meier, Gary M. (Inventor); Halpin, Paul C. (Inventor); Meade, Phillip T. (Inventor); Jacobson, Craig A. (Inventor); Blackwell-Thompson, Charlie (Inventor)

    2007-01-01

    Advanced spaceport information management methods and systems are disclosed. In one embodiment, a method includes coupling a test system to the payload and transmitting one or more test signals that emulate an anticipated condition from the test system to the payload. One or more responsive signals are received from the payload into the test system and are analyzed to determine whether one or more of the responsive signals comprises an anomalous signal. At least one of the steps of transmitting, receiving, analyzing and determining includes transmitting at least one of the test signals and the responsive signals via a communications link from a payload processing facility to a remotely located facility. In one particular embodiment, the communications link is an Internet link from a payload processing facility to a remotely located facility (e.g. a launch facility, university, etc.).

  11. Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

    SciTech Connect

    Hykes, J. M.; Ferrer, R. M.

    2013-07-01

    The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

  12. Numerical Study on Crossflow Printed Circuit Heat Exchanger for Advanced Small Modular Reactors

    SciTech Connect

    Yoon, Su-Jong; Sabharwall, Piyush; Kim, Eung-Soo

    2014-03-01

    Various fluids such as water, gases (helium), molten salts (FLiNaK, FLiBe) and liquid metal (sodium) are used as a coolant of advanced small modular reactors (SMRs). The printed circuit heat exchanger (PCHE) has been adopted as the intermediate and/or secondary heat exchanger of SMR systems because this heat exchanger is compact and effective. The size and cost of PCHE can be changed by the coolant type of each SMR. In this study, the crossflow PCHE analysis code for advanced small modular reactor has been developed for the thermal design and cost estimation of the heat exchanger. The analytical solution of single pass, both unmixed fluids crossflow heat exchanger model was employed to calculate a two dimensional temperature profile of a crossflow PCHE. The analytical solution of crossflow heat exchanger was simply implemented by using built in function of the MATLAB program. The effect of fluid property uncertainty on the calculation results was evaluated. In addition, the effect of heat transfer correlations on the calculated temperature profile was analyzed by taking into account possible combinations of primary and secondary coolants in the SMR systems. Size and cost of heat exchanger were evaluated for the given temperature requirement of each SMR.

  13. Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

    PubMed Central

    Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly

    2016-01-01

    This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.

  14. Numerical modelling of the groundwater inflow to an advancing open pit mine: Kolahdarvazeh pit, Central Iran.

    PubMed

    Bahrami, Saeed; Doulati Ardejani, Faramarz; Aslani, Soheyla; Baafi, Ernest

    2014-12-01

    The groundwater inflow into a mine during its life and after ceasing operations is one of the most important concerns of the mining industry. This paper presents a hydrogeological assessment of the Irankuh Zn-Pb mine at 20 km south of Esfahan and 1 km northeast of Abnil in west-Central Iran. During mine excavation, the upper impervious bed of a confined aquifer was broken and water at high-pressure flowed into an open pit mine associated with the Kolahdarvazeh deposit. The inflow rates were 6.7 and 1.4 m(3)/s at the maximum and minimum quantities, respectively. Permeability, storage coefficient, thickness and initial head of the fully saturated confined aquifer were 3.5 × 10(-4) m/s, 0.2, 30 m and 60 m, respectively. The hydraulic heads as a function of time were monitored at four observation wells in the vicinity of the pit over 19 weeks and at an observation well near a test well over 21 h. In addition, by measuring the rate of pumping out from the pit sump, at a constant head (usually equal to height of the pit floor), the real inflow rates to the pit were monitored. The main innovations of this work were to make comparison between numerical modelling using a finite element software called SEEP/W and actual data related to inflow and extend the applicability of the numerical model. This model was further used to estimate the hydraulic heads at the observation wells around the pit over 19 weeks during mining operations. Data from a pump-out test and observation wells were used for model calibration and verification. In order to evaluate the model efficiency, the modelling results of inflow quantity and hydraulic heads were compared to those from analytical solutions, as well as the field data. The mean percent error in relation to field data for the inflow quantity was 0.108. It varied between 1.16 and 1.46 for hydraulic head predictions, which are much lower values than the mean percent errors resulted from the analytical solutions (from 1.8 to 5

  15. Numerical modelling of the groundwater inflow to an advancing open pit mine: Kolahdarvazeh pit, Central Iran.

    PubMed

    Bahrami, Saeed; Doulati Ardejani, Faramarz; Aslani, Soheyla; Baafi, Ernest

    2014-12-01

    The groundwater inflow into a mine during its life and after ceasing operations is one of the most important concerns of the mining industry. This paper presents a hydrogeological assessment of the Irankuh Zn-Pb mine at 20 km south of Esfahan and 1 km northeast of Abnil in west-Central Iran. During mine excavation, the upper impervious bed of a confined aquifer was broken and water at high-pressure flowed into an open pit mine associated with the Kolahdarvazeh deposit. The inflow rates were 6.7 and 1.4 m(3)/s at the maximum and minimum quantities, respectively. Permeability, storage coefficient, thickness and initial head of the fully saturated confined aquifer were 3.5 × 10(-4) m/s, 0.2, 30 m and 60 m, respectively. The hydraulic heads as a function of time were monitored at four observation wells in the vicinity of the pit over 19 weeks and at an observation well near a test well over 21 h. In addition, by measuring the rate of pumping out from the pit sump, at a constant head (usually equal to height of the pit floor), the real inflow rates to the pit were monitored. The main innovations of this work were to make comparison between numerical modelling using a finite element software called SEEP/W and actual data related to inflow and extend the applicability of the numerical model. This model was further used to estimate the hydraulic heads at the observation wells around the pit over 19 weeks during mining operations. Data from a pump-out test and observation wells were used for model calibration and verification. In order to evaluate the model efficiency, the modelling results of inflow quantity and hydraulic heads were compared to those from analytical solutions, as well as the field data. The mean percent error in relation to field data for the inflow quantity was 0.108. It varied between 1.16 and 1.46 for hydraulic head predictions, which are much lower values than the mean percent errors resulted from the analytical solutions (from 1.8 to 5

  16. 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

  17. Evaluation of Temperature Gradient in Advanced Automated Directional Solidification Furnace (AADSF) by Numerical Simulation

    NASA Technical Reports Server (NTRS)

    Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

    1996-01-01

    A numerical model of heat transfer using combined conduction, radiation and convection in AADSF was used to evaluate temperature gradients in the vicinity of the crystal/melt interface for variety of hot and cold zone set point temperatures specifically for the growth of mercury cadmium telluride (MCT). Reverse usage of hot and cold zones was simulated to aid the choice of proper orientation of crystal/melt interface regarding residual acceleration vector without actual change of furnace location on board the orbiter. It appears that an additional booster heater will be extremely helpful to ensure desired temperature gradient when hot and cold zones are reversed. Further efforts are required to investigate advantages/disadvantages of symmetrical furnace design (i.e. with similar length of hot and cold zones).

  18. Advanced friction simulation of standardized friction tests: a numerical and experimental demonstrator

    NASA Astrophysics Data System (ADS)

    Hol, J.; Wiebenga, J. H.; Hörning, M.; Dietrich, F.; Dane, C.

    2016-08-01

    For the characterization of friction conditions under sheet metal forming process conditions, different friction test set-ups are being used in industry. However, different friction tests and test set-ups are known to result in scattering friction results. In this work, the TriboForm software is utilized to numerically model the frictional behavior. The simulated coefficients of friction are experimentally validated using friction results from a standardized strip drawing friction test set-up. The experimental and simulation results of the friction behavior show a good overall agreement. This demonstrates that the TriboForm software enables simulating friction conditions for varying tribology conditions, i.e. resulting in a generally applicable approach for friction characterization under industrial sheet metal forming process conditions.

  19. Numerical simulation of the reactive flow in advanced (HSR) combustors using KIVA-2

    NASA Technical Reports Server (NTRS)

    Winowich, Nicholas S.

    1991-01-01

    Recent work has been done with the goal of establishing ultralow emission aircraft gas turbine combustors. A significant portion of the effort is the development of three dimensional computational combustor models. The KIVA-II computer code which is based on the Implicit Continuous Eulerian Difference mesh Arbitrary Lagrangian Eulerian (ICED-ALE) numerical scheme is one of the codes selected by NASA to achieve these goals. This report involves a simulation of jet injection through slanted slots within the Rich burn/Quick quench/Lean burn (RQL) baseline experimental rig. The RQL combustor distinguishes three regions of combustion. This work specifically focuses on modeling the quick quench mixer region in which secondary injection air is introduced radially through 12 equally spaced slots around the mixer circumference. Steady state solutions are achieved with modifications to the KIVA-II program. Work currently underway will evaluate thermal mixing as a function of injection air velocity and angle of inclination of the slots.

  20. Development of a numerical method for the prediction of turbulent flows in dump diffusers

    NASA Astrophysics Data System (ADS)

    Ando, Yasunori; Kawai, Masafumi; Sato, Yukinori; Toh, Hidemi

    1987-01-01

    In order to obtain an effective tool to design dump diffusers for gas turbine combustors, a finite-volume numerical calculation method has been developed for the solution of two-dimensional/axisymmetric incompressible steady Navier-Stokes equation in general curvilinear coordinate system. This method was applied to the calculations of turbulent flows in a two-dimensional dump diffuser with uniform and distorted inlet velocity profiles as well as an annular dump diffuser with uniform inlet velocity profile, and the calculated results were compared with experimental data. The numerical results showed a good agreement with experimental data in case of both inlet velocity profiles; eventually, the numerical method was confirmed to be an effective tool for the development of dump diffusers which can predict the flow pattern, velocity distribution and the pressure loss.

  1. A method for generating numerical pilot opinion ratings using the optimal pilot model

    NASA Technical Reports Server (NTRS)

    Hess, R. A.

    1976-01-01

    A method for generating numerical pilot opinion ratings using the optimal pilot model is introduced. The method is contained in a rating hypothesis which states that the numerical rating which a human pilot assigns to a specific vehicle and task can be directly related to the numerical value of the index of performance resulting from the optimal pilot modeling procedure as applied to that vehicle and task. The hypothesis is tested using the data from four piloted simulations. The results indicate that the hypothesis is reasonable, but that the predictive capability of the method is a strong function of the accuracy of the pilot model itself. This accuracy is, in turn, dependent upon the parameters which define the optimal modeling problem. A procedure for specifying the parameters for the optimal pilot model in the absence of experimental data is suggested.

  2. A numerical method for determining highly precise electron energy distribution functions from Langmuir probe characteristics

    SciTech Connect

    Bang, Jin-Young; Chung, Chin-Wook

    2010-12-15

    Electron energy distribution functions (EEDFs) were determined from probe characteristics using a numerical ac superimposed method with a distortion correction of high derivative terms by varying amplitude of a sinusoidal perturbation voltage superimposed onto the dc sweep voltage, depending on the related electron energy. Low amplitude perturbation applied around the plasma potential represented the low energy peak of the EEDF exactly, and high amplitude perturbation applied around the floating potential was effective to suppress noise or distortion of the probe characteristic, which is fatal to the tail electron distribution. When a small random noise was imposed over the stabilized prove characteristic, the numerical differentiation method was not suitable to determine the EEDF, while the numerical ac superimposed method was able to obtain a highly precise EEDF.

  3. A numerical investigation on the efficiency of range extending systems using Advanced Vehicle Simulator

    NASA Astrophysics Data System (ADS)

    Varnhagen, Scott; Same, Adam; Remillard, Jesse; Park, Jae Wan

    2011-03-01

    Series plug-in hybrid electric vehicles of varying engine configuration and battery capacity are modeled using Advanced Vehicle Simulator (ADVISOR). The performance of these vehicles is analyzed on the bases of energy consumption and greenhouse gas emissions on the tank-to-wheel and well-to-wheel paths. Both city and highway driving conditions are considered during the simulation. When simulated on the well-to-wheel path, it is shown that the range extender with a Wankel rotary engine consumes less energy and emits fewer greenhouse gases compared to the other systems with reciprocating engines during many driving cycles. The rotary engine has a higher power-to-weight ratio and lower noise, vibration and harshness compared to conventional reciprocating engines, although performs less efficiently. The benefits of a Wankel engine make it an attractive option for use as a range extender in a plug-in hybrid electric vehicle.

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

    PubMed

    Ling, Hong; Luo, Ercang; Dai, Wei

    2006-12-22

    Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy. PMID:16996099

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

    PubMed

    Ling, Hong; Luo, Ercang; Dai, Wei

    2006-12-22

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

  6. Recent advances in computational structural reliability analysis methods

    NASA Technical Reports Server (NTRS)

    Thacker, Ben H.; Wu, Y.-T.; Millwater, Harry R.; Torng, Tony Y.; Riha, David S.

    1993-01-01

    The goal of structural reliability analysis is to determine the probability that the structure will adequately perform its intended function when operating under the given environmental conditions. Thus, the notion of reliability admits the possibility of failure. Given the fact that many different modes of failure are usually possible, achievement of this goal is a formidable task, especially for large, complex structural systems. The traditional (deterministic) design methodology attempts to assure reliability by the application of safety factors and conservative assumptions. However, the safety factor approach lacks a quantitative basis in that the level of reliability is never known and usually results in overly conservative designs because of compounding conservatisms. Furthermore, problem parameters that control the reliability are not identified, nor their importance evaluated. A summary of recent advances in computational structural reliability assessment is presented. A significant level of activity in the research and development community was seen recently, much of which was directed towards the prediction of failure probabilities for single mode failures. The focus is to present some early results and demonstrations of advanced reliability methods applied to structural system problems. This includes structures that can fail as a result of multiple component failures (e.g., a redundant truss), or structural components that may fail due to multiple interacting failure modes (e.g., excessive deflection, resonate vibration, or creep rupture). From these results, some observations and recommendations are made with regard to future research needs.

  7. Advanced superposition methods for high speed turbopump vibration analysis

    NASA Technical Reports Server (NTRS)

    Nielson, C. E.; Campany, A. D.

    1981-01-01

    The small, high pressure Mark 48 liquid hydrogen turbopump was analyzed and dynamically tested to determine the cause of high speed vibration at an operating speed of 92,400 rpm. This approaches the design point operating speed of 95,000 rpm. The initial dynamic analysis in the design stage and subsequent further analysis of the rotor only dynamics failed to predict the vibration characteristics found during testing. An advanced procedure for dynamics analysis was used in this investigation. The procedure involves developing accurate dynamic models of the rotor assembly and casing assembly by finite element analysis. The dynamically instrumented assemblies are independently rap tested to verify the analytical models. The verified models are then combined by modal superposition techniques to develop a completed turbopump model where dynamic characteristics are determined. The results of the dynamic testing and analysis obtained are presented and methods of moving the high speed vibration characteristics to speeds above the operating range are recommended. Recommendations for use of these advanced dynamic analysis procedures during initial design phases are given.

  8. A numerical method of tracing a vortical axis along local topological axis line

    NASA Astrophysics Data System (ADS)

    Nakayama, Katsuyuki; Hasegawa, Hideki

    2016-06-01

    A new numerical method is presented to trace or identify a vortical axis in flow, which is based on Galilean invariant flow topology. We focus on the local flow topology specified by the eigenvalues and eigenvectors of the velocity gradient tensor, and extract the axis component from its flow trajectory. Eigen-vortical-axis line is defined from the eigenvector of the real eigenvalue of the velocity gradient tensor where the tensor has the conjugate complex eigenvalues. This numerical method integrates the eigen-vortical-axis line and traces a vortical axis in terms of the invariant flow topology, which enables to investigate the feature of the topology-based vortical axis.

  9. Exploration of Advanced Probabilistic and Stochastic Design Methods

    NASA Technical Reports Server (NTRS)

    Mavris, Dimitri N.

    2003-01-01

    The primary objective of the three year research effort was to explore advanced, non-deterministic aerospace system design methods that may have relevance to designers and analysts. The research pursued emerging areas in design methodology and leverage current fundamental research in the area of design decision-making, probabilistic modeling, and optimization. The specific focus of the three year investigation was oriented toward methods to identify and analyze emerging aircraft technologies in a consistent and complete manner, and to explore means to make optimal decisions based on this knowledge in a probabilistic environment. The research efforts were classified into two main areas. First, Task A of the grant has had the objective of conducting research into the relative merits of possible approaches that account for both multiple criteria and uncertainty in design decision-making. In particular, in the final year of research, the focus was on the comparison and contrasting between three methods researched. Specifically, these three are the Joint Probabilistic Decision-Making (JPDM) technique, Physical Programming, and Dempster-Shafer (D-S) theory. The next element of the research, as contained in Task B, was focused upon exploration of the Technology Identification, Evaluation, and Selection (TIES) methodology developed at ASDL, especially with regards to identification of research needs in the baseline method through implementation exercises. The end result of Task B was the documentation of the evolution of the method with time and a technology transfer to the sponsor regarding the method, such that an initial capability for execution could be obtained by the sponsor. Specifically, the results of year 3 efforts were the creation of a detailed tutorial for implementing the TIES method. Within the tutorial package, templates and detailed examples were created for learning and understanding the details of each step. For both research tasks, sample files and

  10. Advance in methods studying the pharmacokinetics of polyphenols.

    PubMed

    Santos, Ana C; Costa, G; Veiga, F; Figueiredo, I V; Batista, M T; Ribeiro, António J

    2014-01-01

    Significant advances have been achieved during the past decade concerning the metabolism of polyphenol compounds in vitro, but scarce data has been presented about what really happens in vivo. Many studies on polyphenols to date have focused on the bioactivity of one specific molecule in aglycone form, often at supraphysiological doses, whereas foods contain complex, often poorly characterized mixtures with multiple additive or interfering activities. Whereas most studies up to the middle-late 1990s measured total aglycones in plasma and urine, after chemical or enzymatic deconjugation, or both, several recent works now report the polyphenol conjugate composition of plasma, urine, feces and/or tissues, after the administration of pure polyphenols or polyphenol-rich matrices. HPLC methods with electrochemical, mass spectrometric and fluorescence detection have adequate sensitivity. LC/UV-Vis methods have also been widely reported, but they are much less sensitive. Compared with electro-chemical and fluorescence detection, MS can quantify analytes without chromatographic separation, which leads to high throughput, presenting itself as the best choice to date. Regarding the experimental model to monitor the bioavailability of phenolic compounds, most published studies are based on human and animal models, with the majority using rodents, primates and recently the nematode Caenorhabditis elegans. This review focuses on the fundamentals of pharmacokinetic methods from the last 15 years and how the results are evaluated and validated. The types of analytical methods, animal models and biological matrices were used to better elucidate pharmacokinetics of polyphenols.

  11. Numerical methods for large-scale, time-dependent partial differential equations

    NASA Technical Reports Server (NTRS)

    Turkel, E.

    1979-01-01

    A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

  12. A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology

    NASA Astrophysics Data System (ADS)

    Brewin, Leo

    2015-10-01

    Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method.

  13. Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates.

    PubMed

    Ritter, André

    2014-10-20

    The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields. In this work, a modification of the shifted angular spectrum method is presented. It allows a further reduction of the spatial sampling rate for certain wave fields. We calculate the benefit of this method for spherical waves. Additionally, a working implementation is presented showing the example of a spherical wave propagating through a circular aperture. PMID:25401659

  14. A numerical method for the stress analysis of stiffened-shell structures under nonuniform temperature distributions

    NASA Technical Reports Server (NTRS)

    Heldenfels, Richard R

    1951-01-01

    A numerical method is presented for the stress analysis of stiffened-shell structures of arbitrary cross section under nonuniform temperature distributions. The method is based on a previously published procedure that is extended to include temperature effects and multicell construction. The application of the method to practical problems is discussed and an illustrative analysis is presented of a two-cell box beam under the combined action of vertical loads and a nonuniform temperature distribution.

  15. Comparative Assessment of Advanced Gay Hydrate Production Methods

    SciTech Connect

    M. D. White; B. P. McGrail; S. K. Wurstner

    2009-06-30

    Displacing natural gas and petroleum with carbon dioxide is a proven technology for producing conventional geologic hydrocarbon reservoirs, and producing additional yields from abandoned or partially produced petroleum reservoirs. Extending this concept to natural gas hydrate production offers the potential to enhance gas hydrate recovery with concomitant permanent geologic sequestration. Numerical simulation was used to assess a suite of carbon dioxide injection techniques for producing gas hydrates from a variety of geologic deposit types. Secondary hydrate formation was found to inhibit contact of the injected CO{sub 2} regardless of injectate phase state, thus diminishing the exchange rate due to pore clogging and hydrate zone bypass of the injected fluids. Additional work is needed to develop methods of artificially introducing high-permeability pathways in gas hydrate zones if injection of CO{sub 2} in either gas, liquid, or micro-emulsion form is to be more effective in enhancing gas hydrate production rates.

  16. Advancing predictive models for particulate formation in turbulent flames via massively parallel direct numerical simulations

    PubMed Central

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-01-01

    Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs. PMID:25024412

  17. A review on recent advances in numerical modelling of bone cutting.

    PubMed

    Marco, Miguel; Rodríguez-Millán, Marcos; Santiuste, Carlos; Giner, Eugenio; Henar Miguélez, María

    2015-04-01

    Common practice of surgical treatments in orthopaedics and traumatology involves cutting processes of bone. These operations introduce risk of thermo-mechanical damage, since the threshold of critical temperature producing thermal osteonecrosis is very low. Therefore, it is important to develop predictive tools capable of simulating accurately the increase of temperature during bone cutting, being the modelling of these processes still a challenge. In addition, the prediction of cutting forces and mechanical damage is also important during machining operations. As the accuracy of simulations depends greatly on the proper choice of the thermo-mechanical properties, an essential part of the numerical model is the constitutive behaviour of the bone tissue, which is considered in different ways in the literature. This paper focuses on the review of the main contributions in modelling of bone cutting with special attention to the bone mechanical behaviour. The aim is to give the reader a complete vision of the approaches commonly presented in the literature in order to help in the development of accurate models for bone cutting. PMID:25676359

  18. Advancing predictive models for particulate formation in turbulent flames via massively parallel direct numerical simulations.

    PubMed

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-08-13

    Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs.

  19. Advancing predictive models for particulate formation in turbulent flames via massively parallel direct numerical simulations.

    PubMed

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-08-13

    Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs. PMID:25024412

  20. Advanced Motion Compensation Methods for Intravital Optical Microscopy.

    PubMed

    Vinegoni, Claudio; Lee, Sungon; Feruglio, Paolo Fumene; Weissleder, Ralph

    2014-03-01

    Intravital microscopy has emerged in the recent decade as an indispensible imaging modality for the study of the micro-dynamics of biological processes in live animals. Technical advancements in imaging techniques and hardware components, combined with the development of novel targeted probes and new mice models, have enabled us to address long-standing questions in several biology areas such as oncology, cell biology, immunology and neuroscience. As the instrument resolution has increased, physiological motion activities have become a major obstacle that prevents imaging live animals at resolutions analogue to the ones obtained in vitro. Motion compensation techniques aim at reducing this gap and can effectively increase the in vivo resolution. This paper provides a technical review of some of the latest developments in motion compensation methods, providing organ specific solutions.

  1. Advanced Motion Compensation Methods for Intravital Optical Microscopy

    PubMed Central

    Vinegoni, Claudio; Lee, Sungon; Feruglio, Paolo Fumene; Weissleder, Ralph

    2013-01-01

    Intravital microscopy has emerged in the recent decade as an indispensible imaging modality for the study of the micro-dynamics of biological processes in live animals. Technical advancements in imaging techniques and hardware components, combined with the development of novel targeted probes and new mice models, have enabled us to address long-standing questions in several biology areas such as oncology, cell biology, immunology and neuroscience. As the instrument resolution has increased, physiological motion activities have become a major obstacle that prevents imaging live animals at resolutions analogue to the ones obtained in vitro. Motion compensation techniques aim at reducing this gap and can effectively increase the in vivo resolution. This paper provides a technical review of some of the latest developments in motion compensation methods, providing organ specific solutions. PMID:24273405

  2. Numerical evaluation of longitudinal motions of Wigley hulls advancing in waves by using Bessho form translating-pulsating source Green'S function

    NASA Astrophysics Data System (ADS)

    Xiao, Wenbin; Dong, Wencai

    2016-06-01

    In the framework of 3D potential flow theory, Bessho form translating-pulsating source Green's function in frequency domain is chosen as the integral kernel in this study and hybrid source-and-dipole distribution model of the boundary element method is applied to directly solve the velocity potential for advancing ship in regular waves. Numerical characteristics of the Green function show that the contribution of local-flow components to velocity potential is concentrated at the nearby source point area and the wave component dominates the magnitude of velocity potential in the far field. Two kinds of mathematical models, with or without local-flow components taken into account, are adopted to numerically calculate the longitudinal motions of Wigley hulls, which demonstrates the applicability of translating-pulsating source Green's function method for various ship forms. In addition, the mesh analysis of discrete surface is carried out from the perspective of ship-form characteristics. The study shows that the longitudinal motion results by the simplified model are somewhat greater than the experimental data in the resonant zone, and the model can be used as an effective tool to predict ship seakeeping properties. However, translating-pulsating source Green function method is only appropriate for the qualitative analysis of motion response in waves if the ship geometrical shape fails to satisfy the slender-body assumption.

  3. Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

    NASA Astrophysics Data System (ADS)

    Takahashi, Ryohei; Mamori, Hiroya; Yamamoto, Makoto

    2016-02-01

    A numerical method for simulating gas-liquid-solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas-liquid two-phase problem, and the latter is a gas-liquid-solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.

  4. Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations

    SciTech Connect

    Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg

    2007-08-10

    In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.

  5. Advanced electrochemical methods for characterizing the performance of organic coatings

    NASA Astrophysics Data System (ADS)

    Upadhyay, Vinod

    Advanced electrochemical techniques such as electrochemical impedance spectroscopy (EIS), electrochemical noise method (ENM) and coulometry as tools to study and extract information about the coating system is the focus of this thesis. This thesis explored three areas of research. In all the three research areas, advanced electrochemical techniques were used to extract information and understand the coating system. The first area was to use EIS and coulometric technique for extracting information using AC-DC-AC method. It was examined whether the total charge passing through the coating during the DC polarization step of AC-DC-AC determines coating failure. An almost constant total amount of charge transfer was required by the coating before it failed and was independent of the applied DC polarization. The second area focused in this thesis was to investigate if embedded sensors in coatings are sensitive enough to monitor changes in environmental conditions and to locate defects in coatings by electrochemical means. Influence of topcoat on embedded sensor performance was also studied. It was observed that the embedded sensors can distinguish varying environmental conditions and locate defects in coatings. Topcoat could influence measurements made using embedded sensors and the choice of topcoat could be very important in the successful use of embedded sensors. The third area of research of this thesis work was to examine systematically polymer-structure coating property relationships using electrochemical impedance spectroscopy. It was observed that the polymer modifications could alter the electrochemical properties of the coating films. Moreover, it was also observed that by cyclic wet-dry capacitance measurement using aqueous electrolyte and ionic liquid, ranking of the stability of organic polymer films could be performed.

  6. Finite element method for optimal guidance of an advanced launch vehicle

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

    1992-01-01

    A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

  7. Advanced Methods for Aircraft Engine Thrust and Noise Benefits: Nozzle-Inlet Flow Analysis

    NASA Technical Reports Server (NTRS)

    Morgan, Morris H., III; Gilinsky, Mikhail M.

    2004-01-01

    In this project on the first stage (2000-Ol), we continued to develop the previous joint research between the Fluid Mechanics and Acoustics Laboratory (FM&AL) at Hampton University (HU) and the Jet Noise Team (JNT) at the NASA Langley Research Center (NASA LaRC). At the second stage (2001-03), FM&AL team concentrated its efforts on solving of problems of interest to Glenn Research Center (NASA GRC), especially in the field of propulsion system enhancement. The NASA GRC R&D Directorate and LaRC Hyper-X Program specialists in a hypersonic technology jointly with the FM&AL staff conducted research on a wide region of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analyses for advanced aircraft and rocket engines. The last year the Hampton University School of Engineering & Technology was awarded the NASA grant, for creation of the Aeropropulsion Center, and the FM&AL is a key team of the project fulfillment responsible for research in Aeropropulsion and Acoustics (Pillar I). This work is supported by joint research between the NASA GRC/ FM&AL and the Institute of Mechanics at Moscow State University (IMMSU) in Russia under a CRDF grant. The main areas of current scientific interest of the FM&AL include an investigation of the proposed and patented advanced methods for aircraft engine thrust and noise benefits. This is the main subject of our other projects, of which one is presented. The last year we concentrated our efforts to analyze three main problems: (a) new effective methods fuel injection into the flow stream in air-breathing engines; (b) new re-circulation method for mixing, heat transfer and combustion enhancement in propulsion systems and domestic industry application; (c) covexity flow The research is focused on a wide regime of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analyses for advanced aircraft and rocket engines (see, for

  8. A numerical investigation of the finite element method in compressible primitive variable Navier-Stokes flow

    NASA Technical Reports Server (NTRS)

    Cook, C. H.

    1977-01-01

    The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.

  9. Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory

    NASA Technical Reports Server (NTRS)

    Ramos, J. I.

    1987-01-01

    A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.

  10. A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

    NASA Astrophysics Data System (ADS)

    Witte, J. H.; Reisinger, C.

    2010-09-01

    We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

  11. Termination of the MRI via parasitic instabilities in core-collapse supernovae: influence of numerical methods

    NASA Astrophysics Data System (ADS)

    Rembiasz, T.; Obergaulinger, M.; Cerdá-Durán, P.; Aloy, M. Á.; Müller, E.

    2016-05-01

    We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in threedimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerical convergence can be achieved even at relatively low grid resolutions if high-order reconstruction methods are used.

  12. Time-Space Decoupled Explicit Method for Fast Numerical Simulation of Tsunami Propagation

    NASA Astrophysics Data System (ADS)

    Guo, Anxin; Xiao, Shengchao; Li, Hui

    2015-02-01

    This study presents a novel explicit numerical scheme for simulating tsunami propagation using the exact solution of the wave equations. The objective of this study is to develop a fast and stable numerical scheme by decoupling the wave equation in both the time and space domains. First, the finite difference scheme of the shallow-water equations for tsunami simulation are briefly introduced. The time-space decoupled explicit method based on the exact solution of the wave equation is given for the simulation of tsunami propagation without including frequency dispersive effects. Then, to consider wave dispersion, the second-order accurate numerical scheme to solve the shallow-water equations, which mimics the physical frequency dispersion with numerical dispersion, is derived. Lastly, the computation efficiency and the accuracy of the two types of numerical schemes are investigated by the 2004 Indonesia tsunami and the solution of the Boussinesq equation for a tsunami with Gaussian hump over both uniform and varying water depths. The simulation results indicate that the proposed numerical scheme can achieve a fast and stable tsunami propagation simulation while maintaining computation accuracy.

  13. Numerical method for the solution of large systems of differential equations of the boundary layer type

    NASA Technical Reports Server (NTRS)

    Green, M. J.; Nachtsheim, P. R.

    1972-01-01

    A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

  14. Numerical Simulations of Optical Turbulence Using an Advanced Atmospheric Prediction Model: Implications for Adaptive Optics Design

    NASA Astrophysics Data System (ADS)

    Alliss, R.

    2014-09-01

    Optical turbulence (OT) acts to distort light in the atmosphere, degrading imagery from astronomical telescopes and reducing the data quality of optical imaging and communication links. Some of the degradation due to turbulence can be corrected by adaptive optics. However, the severity of optical turbulence, and thus the amount of correction required, is largely dependent upon the turbulence at the location of interest. Therefore, it is vital to understand the climatology of optical turbulence at such locations. In many cases, it is impractical and expensive to setup instrumentation to characterize the climatology of OT, so numerical simulations become a less expensive and convenient alternative. The strength of OT is characterized by the refractive index structure function Cn2, which in turn is used to calculate atmospheric seeing parameters. While attempts have been made to characterize Cn2 using empirical models, Cn2 can be calculated more directly from Numerical Weather Prediction (NWP) simulations using pressure, temperature, thermal stability, vertical wind shear, turbulent Prandtl number, and turbulence kinetic energy (TKE). In this work we use the Weather Research and Forecast (WRF) NWP model to generate Cn2 climatologies in the planetary boundary layer and free atmosphere, allowing for both point-to-point and ground-to-space seeing estimates of the Fried Coherence length (ro) and other seeing parameters. Simulations are performed using a multi-node linux cluster using the Intel chip architecture. The WRF model is configured to run at 1km horizontal resolution and centered on the Mauna Loa Observatory (MLO) of the Big Island. The vertical resolution varies from 25 meters in the boundary layer to 500 meters in the stratosphere. The model top is 20 km. The Mellor-Yamada-Janjic (MYJ) TKE scheme has been modified to diagnose the turbulent Prandtl number as a function of the Richardson number, following observations by Kondo and others. This modification

  15. Advancing Satellite-Based Flood Prediction in Complex Terrain Using High-Resolution Numerical Weather Prediction

    NASA Astrophysics Data System (ADS)

    Zhang, X.; Anagnostou, E. N.; Nikolopoulos, E. I.; Bartsotas, N. S.

    2015-12-01

    Floods constitute one of the most significant and frequent natural hazard in mountainous regions. Satellite-based precipitation products offer in many cases the only available source of QPE. However, satellite-based QPE over complex terrain suffer from significant bias that limits their applicability for hydrologic modeling. In this work we investigate the potential of a new correction procedure, which involves the use of high-resolution numerical weather prediction (NWP) model simulations to adjust satellite QPE. Adjustment is based on the pdf matching of satellite and NWP (used as reference) precipitation distribution. The impact of correction procedure on simulating the hydrologic response is examined for 15 storm events that generated floods over the mountainous Upper Adige region of Northern Italy. Atmospheric simulations were performed at 1-km resolution from a state-of-the-art atmospheric model (RAMS/ICLAMS). The proposed error correction procedure was then applied on the widely used TRMM 3B42 satellite precipitation product and the evaluation of the correction was based on independent in situ precipitation measurements from a dense rain gauge network (1 gauge / 70 km2) available in the study area. Satellite QPE, before and after correction, are used to simulate flood response using ARFFS (Adige River Flood Forecasting System), a semi-distributed hydrologic model, which is used for operational flood forecasting in the region. Results showed that bias in satellite QPE before correction was significant and had a tremendous impact on the simulation of flood peak, however the correction procedure was able to reduce bias in QPE and therefore improve considerably the simulated flood hydrograph.

  16. Advanced Hydraulic Tomography Analysis Strategies--A Numerical Study based on Field Observations

    NASA Astrophysics Data System (ADS)

    Tso, C. M.; Yeh, T. J.

    2013-12-01

    This report presents a discussion on some of the unexplored issues pertaining to the application of hydraulic tomography to interpret pumping test data collected in the field. Using numerical experiments, we probe at a few new strategies to analyze pumping test results for multi-layer aquifers. First of all, we study the averaging of heads over packer intervals of a wellbore. How does the length of the packers reduce the resolution of the estimated hydraulic conductivity (K) field? Next we investigate the effect of using hard data (a.k.a. primary information or K measurements) conditioning on the estimated K field. Does the conditioning constrain the solution better and if so, by how much? Then we examine the effect of initial guess of K field on the inversion results. Currently, our hydraulic tomography approach (SSLE (Yeh and Liu (2000) and SimSLE (Xiang et al. (2009)) assumes a homogeneous K field as initial guess by default. What if we use a random field as initial guess? What about assigning different zones in the domain and designate different homogenous initial guess values to each of them? Finally, updating and storing the covariance matrix heavily consumes computation time during the inversion process and can sometimes be prohibiting when solving large problems. In fact, it is often the most time-consuming part of the hydraulic tomography analysis. We study the effects on the hydraulic tomography results of (1) whether updating the covariance matrix after each iteration and (2) whether storing the full matrix or diagonal terms only. The investigation outlined above will shed light on the development of more effective and reliable hydraulic tomography analysis practices and algorithms.

  17. An Experimental Comparison of Two Methods Of Teaching Numerical Control Manual Programming Concepts; Visual Media Versus Hands-On Equipment.

    ERIC Educational Resources Information Center

    Biekert, Russell

    Accompanying the rapid changes in technology has been a greater dependence on automation and numerical control, which has resulted in the need to find ways of preparing programers for industrial machines using numerical control. To compare the hands-on equipment method and a visual media method of teaching numerical control, an experimental and a…

  18. Numerical Investigation of a Cascaded Longitudinal Space-Charge Amplifier at the Fermilab's Advanced Superconducting Test Accelerator

    SciTech Connect

    Halavanau, A.; Piot, P.

    2015-06-01

    In a cascaded longitudinal space-charge amplifier (LSCA), initial density noise in a relativistic e-beam is amplified via the interplay of longitudinal space charge forces and properly located dispersive sections. This type of amplification process was shown to potentially result in large final density modulations [1] compatible with the production of broadband electromagnetic radiation. The technique was recently demonstrated in the optical domain [2]. In this paper we investigate, via numerical simulations, the performances of a cascaded LSCA beamline at the Fermilab’s Advanced Superconducting Test Accelerator (ASTA). We especially explore the properties of the produced broadband radiation. Our studies have been conducted with a grid-less three-dimensional space-charge algorithm.

  19. Numerical simulation of rip-raps with the distinct element method

    NASA Astrophysics Data System (ADS)

    Mittelbach, Livia

    2013-06-01

    and costal shores. They have to resist hydraulic loads such as ship and wind induced waves, tidal and ship induced currents, tidal varying water levels and storm surges. The numerical modelling of rip-rap revetments is undertaken by using the Distinct Element Method in three dimensions. With the DEM rip-rap stones can be modelled as autonomous objects with any degrees of freedom. Typical shapes of stones are formed by using clumped spherical particles. A method for the generation of the rip-rap stones based on geometrical and probabilistic parameters has been developed in order to generate stones with a realistic size and mass distribution. The DEM program is coupled with a computational fluid dynamics program to account for the influence of the hydraulic loads on the rip-rap stones. The acting forces can be simulated realistically for waves, currents and tidal varying water levels. Field measurements and model tests serve as validation for the numerical model. Physical model tests are carried out in a hydraulic flume with an instrumented rip-rap section for the calibration of the numerical stones material parameters. The behaviour of the particles depends on properties such as density, friction coefficient, normal and shear stiffness as well as the accuracy of the numerical representation of the rip-rap stones. Influences on the accuracy of the modelling of rip-raps with regard to the variation of these parameters are examined by comparing the results of the physical flume tests and numerical model.

  20. Methods for numerical study of tube bundle vibrations in cross-flows

    NASA Astrophysics Data System (ADS)

    Longatte, E.; Bendjeddou, Z.; Souli, M.

    2003-11-01

    In many industrial applications, mechanical structures like heat exchanger tube bundles are subjected to complex flows causing possible vibrations and damage. Part of fluid forces are coupled with tube motion and the so-called fluid-elastic forces can affect the structure dynamic behaviour generating possible instabilities and leading to possible short term failures through high amplitude vibrations. Most classical fluid force identification methods rely on structure response experimental measurements associated with convenient data processes. Owing to recent improvements in Computational Fluid Dynamics, numerical simulation of flow-induced vibrations is now practicable for industrial purposes. The present paper is devoted to the numerical identification of fluid-elastic effects affecting tube bundle motion in presence of fluid at rest and one-phase cross-flows. What is the numerical process? When fluid-elastic effects are not significant and are restricted to added mass effects, there is no strong coupling between structure and fluid motions. The structure displacement is not supposed to affect flow patterns. Thus it is possible to solve flow and structure problems separately by using a fixed nonmoving mesh for the fluid dynamic computation. Power spectral density and time record of lift and drag forces acting on tube bundles can be computed numerically by using an unsteady fluid computation involving for example a large Eddy simulation. Fluid force spectra or time record can then be introduced as inlet conditions into the structure code providing the tube dynamic response generated by flow. Such a computation is not possible in presence of strong flow structure coupling. When fluid-elastic effects cannot be neglected, in presence of tube bundles subjected to cross-flows for example, a coupling between flow and structure computations is required. Appropriate numerical methods are investigated in the present work. The purpose is to be able to provide a numerical

  1. Interactive Computing With a Programmable Calculator; Student Experimentations in Numerical Methods.

    ERIC Educational Resources Information Center

    Gerald, Curtis F.

    Programable desk calculators can provide students with personal experience in the use of numerical methods. Courses at California Polytechnic State University at San Luis Obispo use the Compucorp Model 025 Educator Experiences with it as a teaching device for solving non-linear equations and differential equations show that students can by-pass…

  2. Abstract Applets: A Method for Integrating Numerical Problem Solving into the Undergraduate Physics Curriculum

    SciTech Connect

    Peskin, Michael E

    2003-02-13

    In upper-division undergraduate physics courses, it is desirable to give numerical problem-solving exercises integrated naturally into weekly problem sets. I explain a method for doing this that makes use of the built-in class structure of the Java programming language. I also supply a Java class library that can assist instructors in writing programs of this type.

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

    NASA Astrophysics Data System (ADS)

    Song, Haiming; Zhang, Qi; Zhang, Ran

    2015-10-01

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

  4. TRANSPORT OF REACTING SOLUTES SUBJECT TO A MOVING DISSOLUTION BOUNDARY: NUMERICAL METHODS AND SOLUTIONS.

    USGS Publications Warehouse

    Willis, Catherine; Rubin, Jacob

    1987-01-01

    In this paper we consider examples of chemistry-affected transport processes in porous media. A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters.

  5. Numerical Simulation of Parachute Inflation Process Using AN Overset Deforming Grids Method

    NASA Astrophysics Data System (ADS)

    Xia, Jian; Tian, Shuling; Wu, Yizhao

    A numerical method for the simulation of parachute inflation process is presented in this paper. The unsteady compressible N-S equations are fully coupled with MSD (Mass Spring Damper) structure model and integrated forward in time. The CFD solver is based on an unstructured finite volume algorithm and the preconditioning technique is applied to alleviate the stiffness caused by low Mach number. The Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity. The whole system (fluid equations and structural model equations) is marched implicitly in time using a dual time stepping method. An overset deforming grids method is adopted in this paper to deal with the very large domain deformation during the parachute inflation process. Finally numerical test is performed to validate the robustness of this method.

  6. Software system for numerical simulation of minor gas constituents lidar sensing by the differential absorption method

    NASA Astrophysics Data System (ADS)

    Bochkovskii, D. A.; Matvienko, G. G.; Romanovskii, O. A.; Kharchenko, O. V.; Yakovlev, S. V.

    2014-11-01

    This paper reports the development of LIDAS (LIdar Differential Absorption Sensing) program-algorithmic system for laser remote sensing of minor gas constituents (MGCs) of the atmosphere by the differential absorption method (DIAL). The system includes modules for the search of wavelengths informative for laser gas analysis by the differential absorption method, for numerical simulation of lidar sensing of atmospheric MGCs, and for calculation of errors of methodical, atmospheric, spectral, and instrumental origin. Lidar sensing of gas constituents by the differential absorption method as applied to problems of sensing of atmospheric MGCs is simulated numerically. Results of experiments on remote sensing of gas constituents of the atmosphere with the use of RO laser are presented.

  7. L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography

    NASA Astrophysics Data System (ADS)

    Chen, Xueli; Yang, Defu; Zhang, Qitan; Liang, Jimin

    2014-05-01

    Even though bioluminescence tomography (BLT) exhibits significant potential and wide applications in macroscopic imaging of small animals in vivo, the inverse reconstruction is still a tough problem that has plagued researchers in a related area. The ill-posedness of inverse reconstruction arises from insufficient measurements and modeling errors, so that the inverse reconstruction cannot be solved directly. In this study, an l1/2 regularization based numerical method was developed for effective reconstruction of BLT. In the method, the inverse reconstruction of BLT was constrained into an l1/2 regularization problem, and then the weighted interior-point algorithm (WIPA) was applied to solve the problem through transforming it into obtaining the solution of a series of l1 regularizers. The feasibility and effectiveness of the proposed method were demonstrated with numerical simulations on a digital mouse. Stability verification experiments further illustrated the robustness of the proposed method for different levels of Gaussian noise.

  8. Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

    PubMed Central

    Jun, Ding; Song, Chen; Wei-Bin, Wen; Shao-Ming, Luo; Xia, Huang

    2014-01-01

    A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method. PMID:24883403

  9. An iterative analytic—numerical method for scattering from a target buried beneath a rough surface

    NASA Astrophysics Data System (ADS)

    Xu, Run-Wen; Guo, Li-Xin; Wang, Rui

    2014-11-01

    An efficiently iterative analytical—numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.

  10. Recent advances in high-performance modeling of plasma-based acceleration using the full PIC method

    NASA Astrophysics Data System (ADS)

    Vay, J.-L.; Lehe, R.; Vincenti, H.; Godfrey, B. B.; Haber, I.; Lee, P.

    2016-09-01

    Numerical simulations have been critical in the recent rapid developments of plasma-based acceleration concepts. Among the various available numerical techniques, the particle-in-cell (PIC) approach is the method of choice for self-consistent simulations from first principles. The fundamentals of the PIC method were established decades ago, but improvements or variations are continuously being proposed. We report on several recent advances in PIC-related algorithms that are of interest for application to plasma-based accelerators, including (a) detailed analysis of the numerical Cherenkov instability and its remediation for the modeling of plasma accelerators in laboratory and Lorentz boosted frames, (b) analytic pseudo-spectral electromagnetic solvers in Cartesian and cylindrical (with azimuthal modes decomposition) geometries, and (c) novel analysis of Maxwell's solvers' stencil variation and truncation, in application to domain decomposition strategies and implementation of perfectly matched layers in high-order and pseudo-spectral solvers.

  11. Numerical study of three-parameter matrix eigenvalue problem by Rayleigh quotient method

    NASA Astrophysics Data System (ADS)

    Bora, Niranjan; Baruah, Arun Kumar

    2016-06-01

    In this paper, an attempt is done to find approximate eigenvalues and the corresponding eigenvectors of three-parameter matrix eigenvalue problem by extending Rayleigh Quotient Iteration Method (RQIM), which is generally used to solve generalized eigenvalue problems of the form Ax = λBx. Convergence criteria of RQIM will be derived in terms of matrix 2-norm. We will test the computational efficiency of the Method analytically with the help of numerical examples. All calculations are done in MATLAB software.

  12. Applications of numerical optimization methods to helicopter design problems: A survey

    NASA Technical Reports Server (NTRS)

    Miura, H.

    1984-01-01

    A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.

  13. Analysis of the water film behavior and its breakup on profile using experimental and numerical methods

    NASA Astrophysics Data System (ADS)

    Muzik, Tomas; Safarik, Pavel; Tucek, Antonín

    2014-08-01

    This paper deals with the description of water film behaviour on the airfoil NACA0012 using experimental and numerical methods. Properties of the water film on the profile and its breakup into droplets behind the profile are investigated in the aerodynamic tunnel and using CFD methods. The characteristic parameters of the water film, like its thickness and shape for different flow modes are described. Hereafter are described droplets drifted by the air, which water film is broken behind the profile.

  14. Numerical simulation of dynamic processes in biomechanics using the grid-characteristic method

    NASA Astrophysics Data System (ADS)

    Beklemysheva, K. A.; Vasyukov, A. V.; Petrov, I. B.

    2015-08-01

    Results of the numerical simulation of mechanical processes occurring in biological tissues under dynamic actions are presented. The grid-characteristic method on unstructured grids is used to solve the system of equations of mechanics of deformable solids; this method takes into account the characteristic properties of the constitutive system of partial differential equations and produces adequate algorithms on interfaces between media and on the boundaries of integration domains.

  15. Advanced statistical methods for the definition of new staging models.

    PubMed

    Kates, Ronald; Schmitt, Manfred; Harbeck, Nadia

    2003-01-01

    Adequate staging procedures are the prerequisite for individualized therapy concepts in cancer, particularly in the adjuvant setting. Molecular staging markers tend to characterize specific, fundamental disease processes to a greater extent than conventional staging markers. At the biological level, the course of the disease will almost certainly involve interactions between multiple underlying processes. Since new therapeutic strategies tend to target specific processes as well, their impact will also involve interactions. Hence, assessment of the prognostic impact of new markers and their utilization for prediction of response to therapy will require increasingly sophisticated statistical tools that are capable of detecting and modeling complicated interactions. Because they are designed to model arbitrary interactions, neural networks offer a promising approach to improved staging. However, the typical clinical data environment poses severe challenges to high-performance survival modeling using neural nets, particularly the key problem of maintaining good generalization. Nonetheless, it turns out that by using newly developed methods to minimize unnecessary complexity in the neural network representation of disease course, it is possible to obtain models with high predictive performance. This performance has been validated on both simulated and real patient data sets. There are important applications for design of studies involving targeted therapy concepts and for identification of the improvement in decision support resulting from new staging markers. In this article, advantages of advanced statistical methods such as neural networks for definition of new staging models will be illustrated using breast cancer as an example.

  16. A numerical method for DNS/LES of turbulent reacting flows

    SciTech Connect

    Doom, Jeff; Hou, Yucheng; Mahesh, Krishnan

    2007-09-10

    A spatially non-dissipative, implicit numerical method to simulate turbulent reacting flows over a range of Mach numbers, is described. The compressible Navier-Stokes equations are rescaled so that the zero Mach number equations are discretely recovered in the limit of zero Mach number. The dependent variables are co-located in space, and thermodynamic variables are staggered from velocity in time. The algorithm discretely conserves kinetic energy in the incompressible, inviscid, non-reacting limit. The chemical source terms are implicit in time to allow for stiff chemical mechanisms. The algorithm is readily extended to complex chemical mechanisms. Numerical examples using both simple and complex chemical mechanisms are presented.

  17. Direct numerical simulations of a reacting turbulent mixing layer by a pseudospectral-spectral element method

    NASA Technical Reports Server (NTRS)

    Mcmurtry, Patrick A.; Givi, Peyman

    1992-01-01

    An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.

  18. Numerical radiative transfer with state-of-the-art iterative methods made easy

    NASA Astrophysics Data System (ADS)

    Lambert, Julien; Paletou, Frédéric; Josselin, Eric; Glorian, Jean-Michel

    2016-01-01

    This article presents an on-line tool and its accompanying software resources for the numerical solution of basic radiation transfer out of local thermodynamic equilibrium (LTE). State-of-the-art stationary iterative methods such as Accelerated Λ-iteration and Gauss-Seidel schemes, using a short characteristics-based formal solver are used. We also comment on typical numerical experiments associated to the basic non-LTE radiation problem. These resources are intended for the largest use and benefit, in support to more classical radiation transfer lectures usually given at the Master level.

  19. Numerical Viscous Flow Analysis of an Advanced Semispan Diamond-Wing Model at High-Life Conditions

    NASA Technical Reports Server (NTRS)

    Ghaffari, F.; Biedron, R. T.; Luckring, J. M.

    2002-01-01

    Turbulent Navier-Stokes computational results are presented for an advanced diamond wing semispan model at low speed, high-lift conditions. The numerical results are obtained in support of a wind-tunnel test that was conducted in the National Transonic Facility (NTF) at the NASA Langley Research Center. The model incorporated a generic fuselage and was mounted on the tunnel sidewall using a constant width standoff. The analyses include: (1) the numerical simulation of the NTF empty, tunnel flow characteristics; (2) semispan high-lift model with the standoff in the tunnel environment; (3) semispan high-lift model with the standoff and viscous sidewall in free air; and (4) semispan high-lift model without the standoff in free air. The computations were performed at conditions that correspond to a nominal approach and landing configuration. The wing surface pressure distributions computed for the model in both the tunnel and in free air agreed well with the corresponding experimental data and they both indicated small increments due to the wall interference effects. However, the wall interference effects were found to be more pronounced in the total measured and the computed lift, drag and pitching moment due to standard induced up-flow effects. Although the magnitudes of the computed forces and moment were slightly off compared to the measured data, the increments due the wall interference effects were predicted well. The numerical predictions are also presented on the combined effects of the tunnel sidewall boundary layer and the standoff geometry on the fuselage fore-body pressure distributions and the resulting impact on the overall configuration longitudinal aerodynamic characteristics.

  20. Numerical solution of optimal control problems using multiple-interval integral Gegenbauer pseudospectral methods

    NASA Astrophysics Data System (ADS)

    Tang, Xiaojun

    2016-04-01

    The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.

  1. Numerical Simulation of Supercavitating Flows using a Viscous-Potential Method

    NASA Astrophysics Data System (ADS)

    Kim, Ji-Hye; Ahn, Byoung-Kwon

    2015-12-01

    A numerical method was developed to predict the supercavity around axi-symmetric bodies. Employing potential flow, the proposed method computes the cavity shape and drag force, which are the important features of practical concern for supercavitating objects. A method to calculate the frictional drag acting on the wetted body surface was implemented, which is called the viscous-potential method. The results revealed details of the drag curve appearing in the course of an increase in speed and cavity growth. In addition, the supercavity and drag features of the actual shape of the supercavitating torpedo were investigated according to the different depth conditions.

  2. OpenGeoSys: Performance-Oriented Computational Methods for Numerical Modeling of Flow in Large Hydrogeological Systems

    NASA Astrophysics Data System (ADS)

    Naumov, D.; Fischer, T.; Böttcher, N.; Watanabe, N.; Walther, M.; Rink, K.; Bilke, L.; Shao, H.; Kolditz, O.

    2014-12-01

    OpenGeoSys (OGS) is a scientific open source code for numerical simulation of thermo-hydro-mechanical-chemical processes in porous and fractured media. Its basic concept is to provide a flexible numerical framework for solving multi-field problems for applications in geoscience and hydrology as e.g. for CO2 storage applications, geothermal power plant forecast simulation, salt water intrusion, water resources management, etc. Advances in computational mathematics have revolutionized the variety and nature of the problems that can be addressed by environmental scientists and engineers nowadays and an intensive code development in the last years enables in the meantime the solutions of much larger numerical problems and applications. However, solving environmental processes along the water cycle at large scales, like for complete catchment or reservoirs, stays computationally still a challenging task. Therefore, we started a new OGS code development with focus on execution speed and parallelization. In the new version, a local data structure concept improves the instruction and data cache performance by a tight bundling of data with an element-wise numerical integration loop. Dedicated analysis methods enable the investigation of memory-access patterns in the local and global assembler routines, which leads to further data structure optimization for an additional performance gain. The concept is presented together with a technical code analysis of the recent development and a large case study including transient flow simulation in the unsaturated / saturated zone of the Thuringian Syncline, Germany. The analysis is performed on a high-resolution mesh (up to 50M elements) with embedded fault structures.

  3. A constrained-gradient method to control divergence errors in numerical MHD

    NASA Astrophysics Data System (ADS)

    Hopkins, Philip F.

    2016-10-01

    In numerical magnetohydrodynamics (MHD), a major challenge is maintaining nabla \\cdot {B}=0. Constrained transport (CT) schemes achieve this but have been restricted to specific methods. For more general (meshless, moving-mesh, ALE) methods, `divergence-cleaning' schemes reduce the nabla \\cdot {B} errors; however they can still be significant and can lead to systematic errors which converge away slowly. We propose a new constrained gradient (CG) scheme which augments these with a projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. Unlike `locally divergence free' methods, this actually minimizes the numerically unstable nabla \\cdot {B} terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare various test problems. Compared to cleaning schemes, our CG method reduces the maximum nabla \\cdot {B} errors by ˜1-3 orders of magnitude (˜2-5 dex below typical errors if no nabla \\cdot {B} cleaning is used). By preventing large nabla \\cdot {B} at discontinuities, this eliminates systematic errors at jumps. Our CG results are comparable to CT methods; for practical purposes, the nabla \\cdot {B} errors are eliminated. The cost is modest, ˜30 per cent of the hydro algorithm, and the CG correction can be implemented in a range of numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a range of problems where using only Powell or `8-wave' cleaning can produce order-of-magnitude errors.

  4. Nonlinear evolution of cylindrical gravitational waves: Numerical method and physical aspects

    NASA Astrophysics Data System (ADS)

    Celestino, Juliana; de Oliveira, H. P.; Rodrigues, E. L.

    2016-05-01

    General cylindrical waves are the simplest axisymmetrical gravitational waves that contain both + and × modes of polarization. In this paper, we have studied the evolution of general cylindrical gravitational waves in the realm of the characteristic scheme with a numerical code based on the Galerkin-Collocation method. The investigation consists of the numerical realization of concepts such as Bondi mass and the news functions adapted to cylindrical symmetry. The Bondi mass decays due to the presence of the news functions associated with both polarization modes. We have interpreted each polarization mode as channels from which mass is extracted. Under this perspective, we have presented the enhancement effect of the polarization mode + due to the nonlinear interaction with the mode ×. After discussing the role of matter in cylindrical symmetry, we have extended the numerical code to include electromagnetic fields.

  5. A wavelet-optimized, very high order adaptive grid and order numerical method

    NASA Technical Reports Server (NTRS)

    Jameson, Leland

    1996-01-01

    Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.

  6. Numerical solution of the time dependent neutron transport equation by the method of the characteristics

    SciTech Connect

    Talamo, Alberto

    2013-05-01

    This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

  7. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

    DOE PAGES

    Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; Beerli, Peter; Zeng, Xiankui; Lu, Dan; Tao, Yuezan

    2016-02-05

    Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamicmore » integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.« less

  8. Estimation of region of attraction for polynomial nonlinear systems: a numerical method.

    PubMed

    Khodadadi, Larissa; Samadi, Behzad; Khaloozadeh, Hamid

    2014-01-01

    This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.

  9. A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Calise, Anthony J.; Bless, Robert R.; Leung, Martin

    1989-01-01

    A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

  10. Advanced methods for time-varying effective connectivity estimation in memory processes.

    PubMed

    Astolfi, L; Toppi, J; Wood, G; Kober, S; Risetti, M; Macchiusi, L; Salinari, S; Babiloni, F; Mattia, D

    2013-01-01

    Memory processes are based on large cortical networks characterized by non-stationary properties and time scales which represent a limitation to the traditional connectivity estimation methods. The recent development of connectivity approaches able to consistently describe the temporal evolution of large dimension connectivity networks, in a fully multivariate way, represents a tool that can be used to extract novel information about the processes at the basis of memory functions. In this paper, we applied such advanced approach in combination with the use of state-of-the-art graph theory indexes, computed on the connectivity networks estimated from high density electroencephalographic (EEG) data recorded in a group of healthy adults during the Sternberg Task. The results show how this approach is able to return a characterization of the main phases of the investigated memory task which is also sensitive to the increased length of the numerical string to be memorized. PMID:24110342

  11. Numerical Modeling for Hole-Edge Cracking of Advanced High-Strength Steels (AHSS) Components in the Static Bend Test

    NASA Astrophysics Data System (ADS)

    Kim, Hyunok; Mohr, William; Yang, Yu-Ping; Zelenak, Paul; Kimchi, Menachem

    2011-08-01

    Numerical modeling of local formability, such as hole-edge cracking and shear fracture in bending of AHSS, is one of the challenging issues for simulation engineers for prediction and evaluation of stamping and crash performance of materials. This is because continuum-mechanics-based finite element method (FEM) modeling requires additional input data, "failure criteria" to predict the local formability limit of materials, in addition to the material flow stress data input for simulation. This paper presents a numerical modeling approach for predicting hole-edge failures during static bend tests of AHSS structures. A local-strain-based failure criterion and a stress-triaxiality-based failure criterion were developed and implemented in LS-DYNA simulation code to predict hole-edge failures in component bend tests. The holes were prepared using two different methods: mechanical punching and water-jet cutting. In the component bend tests, the water-jet trimmed hole showed delayed fracture at the hole-edges, while the mechanical punched hole showed early fracture as the bending angle increased. In comparing the numerical modeling and test results, the load-displacement curve, the displacement at the onset of cracking, and the final crack shape/length were used. Both failure criteria also enable the numerical model to differentiate between the local formability limit of mechanical-punched and water-jet-trimmed holes. The failure criteria and static bend test developed here are useful to evaluate the local formability limit at a structural component level for automotive crash tests.

  12. Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains

    NASA Astrophysics Data System (ADS)

    Fukuchi, Tsugio

    2014-06-01

    The finite difference method (FDM) based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.

  13. Underwater Photosynthesis of Submerged Plants – Recent Advances and Methods

    PubMed Central

    Pedersen, Ole; Colmer, Timothy D.; Sand-Jensen, Kaj

    2013-01-01

    We describe the general background and the recent advances in research on underwater photosynthesis of leaf segments, whole communities, and plant dominated aquatic ecosystems and present contemporary methods tailor made to quantify photosynthesis and carbon fixation under water. The majority of studies of aquatic photosynthesis have been carried out with detached leaves or thalli and this selectiveness influences the perception of the regulation of aquatic photosynthesis. We thus recommend assessing the influence of inorganic carbon and temperature on natural aquatic communities of variable density in addition to studying detached leaves in the scenarios of rising CO2 and temperature. Moreover, a growing number of researchers are interested in tolerance of terrestrial plants during flooding as torrential rains sometimes result in overland floods that inundate terrestrial plants. We propose to undertake studies to elucidate the importance of leaf acclimation of terrestrial plants to facilitate gas exchange and light utilization under water as these acclimations influence underwater photosynthesis as well as internal aeration of plant tissues during submergence. PMID:23734154

  14. Quantifying hydrate solidification front advancing using method of characteristics

    NASA Astrophysics Data System (ADS)

    You, Kehua; DiCarlo, David; Flemings, Peter B.

    2015-10-01

    We develop a one-dimensional analytical solution based on the method of characteristics to explore hydrate formation from gas injection into brine-saturated sediments within the hydrate stability zone. Our solution includes fully coupled multiphase and multicomponent flow and the associated advective transport in a homogeneous system. Our solution shows that hydrate saturation is controlled by the initial thermodynamic state of the system and changed by the gas fractional flow. Hydrate saturation in gas-rich systems can be estimated by 1-cl0/cle when Darcy flow dominates, where cl0 is the initial mass fraction of salt in brine, and cle is the mass fraction of salt in brine at three-phase (gas, liquid, and hydrate) equilibrium. Hydrate saturation is constant, gas saturation and gas flux decrease, and liquid saturation and liquid flux increase with the distance from the gas inlet to the hydrate solidification front. The total gas and liquid flux is constant from the gas inlet to the hydrate solidification front and decreases abruptly at the hydrate solidification front due to gas inclusion into the hydrate phase. The advancing velocity of the hydrate solidification front decreases with hydrate saturation at a fixed gas inflow rate. This analytical solution illuminates how hydrate is formed by gas injection (methane, CO2, ethane, propane) at both the laboratory and field scales.

  15. Regenerative medicine: advances in new methods and technologies.

    PubMed

    Park, Dong-Hyuk; Eve, David J

    2009-11-01

    The articles published in the journal Cell Transplantation - The Regenerative Medicine Journal over the last two years reveal the recent and future cutting-edge research in the fields of regenerative and transplantation medicine. 437 articles were published from 2007 to 2008, a 17% increase compared to the 373 articles in 2006-2007. Neuroscience was still the most common section in both the number of articles and the percentage of all manuscripts published. The increasing interest and rapid advance in bioengineering technology is highlighted by tissue engineering and bioartificial organs being ranked second again. For a similar reason, the methods and new technologies section increased significantly compared to the last period. Articles focusing on the transplantation of stem cell lineages encompassed almost 20% of all articles published. By contrast, the non-stem cell transplantation group which is made up primarily of islet cells, followed by biomaterials and fetal neural tissue, etc. comprised less than 15%. Transplantation of cells pre-treated with medicine or gene transfection to prolong graft survival or promote differentiation into the needed phenotype, was prevalent in the transplantation articles regardless of the kind of cells used. Meanwhile, the majority of non-transplantation-based articles were related to new devices for various purposes, characterization of unknown cells, medicines, cell preparation and/or optimization for transplantation (e.g. isolation and culture), and disease pathology.

  16. Advanced diagnostic methods in oral and maxillofacial pathology. Part II: immunohistochemical and immunofluorescent methods.

    PubMed

    Jordan, Richard C K; Daniels, Troy E; Greenspan, John S; Regezi, Joseph A

    2002-01-01

    The practice of pathology is currently undergoing significant change, in large part due to advances in the analysis of DNA, RNA, and proteins in tissues. These advances have permitted improved biologic insights into many developmental, inflammatory, metabolic, infectious, and neoplastic diseases. Moreover, molecular analysis has also led to improvements in the accuracy of disease diagnosis and classification. It is likely that, in the future, these methods will increasingly enter into the day-to-day diagnosis and management of patients. The pathologist will continue to play a fundamental role in diagnosis and will likely be in a pivotal position to guide the implementation and interpretation of these tests as they move from the research laboratory into diagnostic pathology. The purpose of this 2-part series is to provide an overview of the principles and applications of current molecular biologic and immunologic tests. In Part I, the biologic fundamentals of DNA, RNA, and proteins and methods that are currently available or likely to become available to the pathologist in the next several years for their isolation and analysis in tissue biopsies were discussed. In Part II, advances in immunohistochemistry and immunofluorescence methods and their application to modern diagnostic pathology are reviewed. PMID:11805778

  17. A Class of TVD Type Combined Numerical Scheme for MHD Equations With a Survey About Numerical Methods in Solar Wind Simulations

    NASA Astrophysics Data System (ADS)

    Feng, Xueshang; Wu, S. T.; Wei, Fengsi; Fan, Quanlin

    2003-04-01

    It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made.

  18. A Fourier collocation time domain method for numerically solving Maxwell's equations

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1991-01-01

    A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

  19. Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods

    NASA Astrophysics Data System (ADS)

    Biryukov, V. A.; Miryakha, V. A.; Petrov, I. B.; Khokhlov, N. I.

    2016-06-01

    For wave propagation in heterogeneous media, we compare numerical results produced by grid-characteristic methods on structured rectangular and unstructured triangular meshes and by a discontinuous Galerkin method on unstructured triangular meshes as applied to the linear system of elasticity equations in the context of direct seismic exploration with an anticlinal trap model. It is shown that the resulting synthetic seismograms are in reasonable quantitative agreement. The grid-characteristic method on structured meshes requires more nodes for approximating curved boundaries, but it has a higher computation speed, which makes it preferable for the given class of problems.

  20. A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

    NASA Technical Reports Server (NTRS)

    Schneider, Harold

    1959-01-01

    This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

  1. A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

    SciTech Connect

    Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin

    2015-06-05

    The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

  2. A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

    DOE PAGES

    Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin

    2015-06-05

    The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less

  3. Development and Applications of Advanced Electronic Structure Methods

    NASA Astrophysics Data System (ADS)

    Bell, Franziska

    This dissertation contributes to three different areas in electronic structure theory. The first part of this thesis advances the fundamentals of orbital active spaces. Orbital active spaces are not only essential in multi-reference approaches, but have also become of interest in single-reference methods as they allow otherwise intractably large systems to be studied. However, despite their great importance, the optimal choice and, more importantly, their physical significance are still not fully understood. In order to address this problem, we studied the higher-order singular value decomposition (HOSVD) in the context of electronic structure methods. We were able to gain a physical understanding of the resulting orbitals and proved a connection to unrelaxed natural orbitals in the case of Moller-Plesset perturbation theory to second order (MP2). In the quest to find the optimal choice of the active space, we proposed a HOSVD for energy-weighted integrals, which yielded the fastest convergence in MP2 correlation energy for small- to medium-sized active spaces to date, and is also potentially transferable to coupled-cluster theory. In the second part, we studied monomeric and dimeric glycerol radical cations and their photo-induced dissociation in collaboration with Prof. Leone and his group. Understanding the mechanistic details involved in these processes are essential for further studies on the combustion of glycerol and carbohydrates. To our surprise, we found that in most cases, the experimentally observed appearance energies arise from the separation of product fragments from one another rather than rearrangement to products. The final chapters of this work focus on the development, assessment, and application of the spin-flip method, which is a single-reference approach, but capable of describing multi-reference problems. Systems exhibiting multi-reference character, which arises from the (near-) degeneracy of orbital energies, are amongst the most

  4. Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

    NASA Technical Reports Server (NTRS)

    Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.

    1997-01-01

    A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

  5. The global extrapolation of numerical methods for computing concentration profiles in percutaneous drug absorption.

    PubMed

    Twizell, E H

    1989-01-01

    A family of numerical methods is developed and analyzed for the numerical solution of the parabolic partial differential equation together with the associated initial and boundary conditions, which arise in a mathematical model of the transient stage of percutaneous drug absorption. Two global extrapolation procedures are described, the first in time only, the second in both space and time, for improving the accuracy of the computed concentration profiles. The behaviours of two members of the family of methods, before and after extrapolation, are examined by repeating a number of experiments reported in the literature. Modifications to the algorithms, which are necessary in computing concentration profiles after the ointment is removed at the steady state, are outlined.

  6. A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

    NASA Astrophysics Data System (ADS)

    Delgado-Vences, Francisco; Flandoli, Franco

    2016-08-01

    We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.

  7. Effects of numerical methods on comparisons between experiments and simulations of shock-accelerated mixing.

    SciTech Connect

    Rider, William; Kamm, J. R.; Tomkins, C. D.; Zoldi, C. A.; Prestridge, K. P.; Marr-Lyon, M.; Rightley, P. M.; Benjamin, R. F.

    2002-01-01

    We consider the detailed structures of mixing flows for Richtmyer-Meshkov experiments of Prestridge et al. [PRE 00] and Tomkins et al. [TOM 01] and examine the most recent measurements from the experimental apparatus. Numerical simulations of these experiments are performed with three different versions of high resolution finite volume Godunov methods. We compare experimental data with simulations for configurations of one and two diffuse cylinders of SF{sub 6} in air using integral measures as well as fractal analysis and continuous wavelet transforms. The details of the initial conditions have a significant effect on the computed results, especially in the case of the double cylinder. Additionally, these comparisons reveal sensitive dependence of the computed solution on the numerical method.

  8. One-level prediction-A numerical method for estimating undiscovered metal endowment

    USGS Publications Warehouse

    McCammon, R.B.; Kork, J.O.

    1992-01-01

    One-level prediction has been developed as a numerical method for estimating undiscovered metal endowment within large areas. The method is based on a presumed relationship between a numerical measure of geologic favorability and the spatial distribution of metal endowment. Metal endowment within an unexplored area for which the favorability measure is greater than a favorability threshold level is estimated to be proportional to the area of that unexplored portion. The constant of proportionality is the ratio of the discovered endowment found within a suitably chosen control region, which has been explored, to the area of that explored region. In addition to the estimate of undiscovered endowment, a measure of the error of the estimate is also calculated. One-level prediction has been used to estimate the undiscovered uranium endowment in the San Juan basin, New Mexico, U.S.A. A subroutine to perform the necessary calculations is included. ?? 1992 Oxford University Press.

  9. A numerical method to determine the steady state distribution of passive contaminant in generic ventilation systems.

    PubMed

    Li, Xianting; Shao, Xiaoliang; Ma, Xiaojun; Zhang, Yuanhui; Cai, Hao

    2011-08-15

    Ventilation system with air recirculation is designed to conserve energy, yet at the same time may result in transporting hazardous substance among different rooms in the same building, which is a concern in indoor air quality control. There is a lack of effective methods to predict indoor contaminant distribution primarily because of uncertainty of the contaminant concentration in supply air which in turn due to the mixing ratio of fresh and recirculation air. In this paper, a versatile numerical method to determine the pollutant distribution of ventilation system with recirculation at steady state is proposed based on typical ventilation systems with accessibility of supply air (ASA) and accessibility of contaminant source (ACS). The relationship is established between contaminant concentrations of supply air and return air in a ventilated room or zone. The concentrations of supply air and contaminant distribution in each room can be determined using such parameters as ASA and ACS. The proposed method is validated by both experimental data and numerical simulation result. The computing speed of the proposed method is compared with the iteration method. The comparisons between the proposed method and the lumped parameter model are also conducted. The advantages of the proposed method in terms of accuracy, speed and versatility make it advantageous to be applied in air quality control of complex ventilation systems with recirculation.

  10. A new numerical method for calculating extrema of received power for polarimetric SAR

    USGS Publications Warehouse

    Zhang, Y.; Zhang, Jiahua; Lu, Zhiming; Gong, W.

    2009-01-01

    A numerical method called cross-step iteration is proposed to calculate the maximal/minimal received power for polarized imagery based on a target's Kennaugh matrix. This method is much more efficient than the systematic method, which searches for the extrema of received power by varying the polarization ellipse angles of receiving and transmitting polarizations. It is also more advantageous than the Schuler method, which has been adopted by the PolSARPro package, because the cross-step iteration method requires less computation time and can derive both the maximal and minimal received powers, whereas the Schuler method is designed to work out only the maximal received power. The analytical model of received-power optimization indicates that the first eigenvalue of the Kennaugh matrix is the supremum of the maximal received power. The difference between these two parameters reflects the depolarization effect of the target's backscattering, which might be useful for target discrimination. ?? 2009 IEEE.

  11. Numerical Modeling of Six Historical Transoceanic Tsunami Events Using a Robust Finite Volume Method on GPUs

    NASA Astrophysics Data System (ADS)

    Jalali Farahani, R.; Li, S.; Mohammed, F.; Astill, S.; Williams, C. R.; Lee, R.; Wilson, P. S.; Srinvias, B.

    2014-12-01

    Six transoceanic historical tsunami events including Japan Tohoku tsunami (2011), Chile Maule tsunami (2010), Indian Ocean tsunami (2004), Japan Nankai tsunami (1946), Chile Valdivia tsunami (1960), and Alaska tsunami (1964) have been modeled using a 2D well-balanced shallow water numerical model. The model solves the nonlinear 2D shallow water equations using an upwind finite volume method and is shown in this study to be capable of modeling the tsunami waves and resulting inundations over complex topography and bathymetry. The finite volume method is capable of modeling the wetting and drying of the bed surface at the coastline with no numerical instabilities and the inundation is modeled by allowing the computational cells to dynamically change from dry to wet. The numerical model implements parallel computations on Graphics Processing Units (GPUs), which enables the model to implement detailed modeling of inundation of small-scale coastal regions in a short simulation time. The slip distribution and seismic moment of the six earthquake driven tsunami events are introduced to the model as the initial condition including coastal uplift and subsidence. Both local regions and far-field regions affected by these tsunami waves are numerically studied and the resulting run-up and tsunami inundations are compared with the recorded observation data provided by National Oceanic and Atmospheric Administration (NOAA) including coastal tide gauges and eyewitness observation data. The GPU-based finite volume model indicates accuracy and robustness as well as short simulation time that can be used for transoceanic tsunami waves modeling including real-time numerical modeling of tsunami events and their inland inundations.

  12. A numerical method for the dynamics of non-spherical cavitation bubbles

    NASA Technical Reports Server (NTRS)

    Lucca, G.; Prosperetti, A.

    1982-01-01

    A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered.

  13. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies

    NASA Astrophysics Data System (ADS)

    Khoromskaia, Venera; Khoromskij, Boris N.

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\\times n\\times n $ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\\times L\\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \\log L)$ scaling by the Ewald-type approaches.

  14. Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.

    SciTech Connect

    Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio

    2011-12-01

    This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).

  15. Numerical modelling of the nonlinear evolutionary equations on the basis of an inverse scattering method

    NASA Astrophysics Data System (ADS)

    Grigorov, Igor V.

    2009-12-01

    In article the algorithm of numerical modelling of the nonlinear equation of Korteweg-de Vrieze which generates nonlinear algorithm of digital processing of signals is considered. For realisation of the specified algorithm it is offered to use a inverse scattering method (ISM). Algorithms of direct and return spectral problems, and also problems of evolution of the spectral data are in detail considered. Results of modelling are resulted.

  16. AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L(2) OPTIMAL MASS TRANSFER PROBLEM.

    PubMed

    Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen

    2010-01-01

    In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828

  17. AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*

    PubMed Central

    Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen

    2010-01-01

    In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828

  18. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    PubMed

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches. PMID:26016539

  19. Vine—A Numerical Code for Simulating Astrophysical Systems Using Particles. I. Description of the Physics and the Numerical Methods

    NASA Astrophysics Data System (ADS)

    Wetzstein, M.; Nelson, Andrew F.; Naab, T.; Burkert, A.

    2009-10-01

    We present a numerical code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is written in Fortran 95 and is designed to be versatile, flexible, and extensible, with modular options that can be selected either at the time the code is compiled or at run time through a text input file. We include a number of general purpose modules describing a variety of physical processes commonly required in the astrophysical community and we expect that the effort required to integrate additional or alternate modules into the code will be small. In its simplest form the code can evolve the dynamical trajectories of a set of particles in two or three dimensions using a module which implements either a Leapfrog or Runge-Kutta-Fehlberg integrator, selected by the user at compile time. The user may choose to allow the integrator to evolve the system using individual time steps for each particle or with a single, global time step for all. Particles may interact gravitationally as N-body particles, and all or any subset may also interact hydrodynamically, using the smoothed particle hydrodynamic (SPH) method by selecting the SPH module. A third particle species can be included with a module to model massive point particles which may accrete nearby SPH or N-body particles. Such particles may be used to model, e.g., stars in a molecular cloud. Free boundary conditions are implemented by default, and a module may be selected to include periodic boundary conditions. We use a binary "Press" tree to organize particles for rapid access in gravity and SPH calculations. Modules implementing an interface with special purpose "GRAPE" hardware may also be selected to accelerate the gravity calculations. If available, forces obtained from the GRAPE coprocessors may be transparently substituted for those obtained from the tree, or both tree and GRAPE may be used as a combination GRAPE/tree code. The code may be run without

  20. VINE-A NUMERICAL CODE FOR SIMULATING ASTROPHYSICAL SYSTEMS USING PARTICLES. I. DESCRIPTION OF THE PHYSICS AND THE NUMERICAL METHODS

    SciTech Connect

    Wetzstein, M.; Nelson, Andrew F.; Naab, T.; Burkert, A.

    2009-10-01

    We present a numerical code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is written in Fortran 95 and is designed to be versatile, flexible, and extensible, with modular options that can be selected either at the time the code is compiled or at run time through a text input file. We include a number of general purpose modules describing a variety of physical processes commonly required in the astrophysical community and we expect that the effort required to integrate additional or alternate modules into the code will be small. In its simplest form the code can evolve the dynamical trajectories of a set of particles in two or three dimensions using a module which implements either a Leapfrog or Runge-Kutta-Fehlberg integrator, selected by the user at compile time. The user may choose to allow the integrator to evolve the system using individual time steps for each particle or with a single, global time step for all. Particles may interact gravitationally as N-body particles, and all or any subset may also interact hydrodynamically, using the smoothed particle hydrodynamic (SPH) method by selecting the SPH module. A third particle species can be included with a module to model massive point particles which may accrete nearby SPH or N-body particles. Such particles may be used to model, e.g., stars in a molecular cloud. Free boundary conditions are implemented by default, and a module may be selected to include periodic boundary conditions. We use a binary 'Press' tree to organize particles for rapid access in gravity and SPH calculations. Modules implementing an interface with special purpose 'GRAPE' hardware may also be selected to accelerate the gravity calculations. If available, forces obtained from the GRAPE coprocessors may be transparently substituted for those obtained from the tree, or both tree and GRAPE may be used as a combination GRAPE/tree code. The code may be run without

  1. Bioinformatics Methods and Tools to Advance Clinical Care

    PubMed Central

    Lecroq, T.

    2015-01-01

    Summary Objectives To summarize excellent current research in the field of Bioinformatics and Translational Informatics with application in the health domain and clinical care. Method We provide a synopsis of the articles selected for the IMIA Yearbook 2015, from which we attempt to derive a synthetic overview of current and future activities in the field. As last year, a first step of selection was performed by querying MEDLINE with a list of MeSH descriptors completed by a list of terms adapted to the section. Each section editor has evaluated separately the set of 1,594 articles and the evaluation results were merged for retaining 15 articles for peer-review. Results The selection and evaluation process of this Yearbook’s section on Bioinformatics and Translational Informatics yielded four excellent articles regarding data management and genome medicine that are mainly tool-based papers. In the first article, the authors present PPISURV a tool for uncovering the role of specific genes in cancer survival outcome. The second article describes the classifier PredictSNP which combines six performing tools for predicting disease-related mutations. In the third article, by presenting a high-coverage map of the human proteome using high resolution mass spectrometry, the authors highlight the need for using mass spectrometry to complement genome annotation. The fourth article is also related to patient survival and decision support. The authors present datamining methods of large-scale datasets of past transplants. The objective is to identify chances of survival. Conclusions The current research activities still attest the continuous convergence of Bioinformatics and Medical Informatics, with a focus this year on dedicated tools and methods to advance clinical care. Indeed, there is a need for powerful tools for managing and interpreting complex, large-scale genomic and biological datasets, but also a need for user-friendly tools developed for the clinicians in their

  2. A numerical method for determining the strain rate intensity factor under plane strain conditions

    NASA Astrophysics Data System (ADS)

    Alexandrov, S.; Kuo, C.-Y.; Jeng, Y.-R.

    2016-07-01

    Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.

  3. Numerical Simulation of the Friction Stir Welding Process Using Coupled Eulerian Lagrangian Method

    NASA Astrophysics Data System (ADS)

    Iordache, M.; Badulescu, C.; Iacomi, D.; Nitu, E.; Ciuca, C.

    2016-08-01

    Friction Stir Welding (FSW) is a solid state joining process that relies on frictional heating and plastic deformation realized at the interaction between a non-consumable welding tool that rotates on the contact surfaces of the combined parts. The experiments are often time consuming and costly. To overcome these problems, numerical analysis has frequently been used in last years. Several simplified numerical models were designed to elucidate various aspects of the complex thermo-mechanical phenomena associated with FSW. This research investigates a thermo-mechanical finite element model based on Coupled Eulerian Lagrangian method to simulate the friction stir welding of the AA 6082-T6 alloy. Abaqus/cae software is used in order to simulate the welding stage of the Friction Stir Welding process. This paper presents the steps of the numerical simulation using the finite elements method, in order to evaluate the boundary conditions of the model and the geometry of the tools by using the Coupled Eulerian Lagrangian method.

  4. ADVANCED SEISMIC BASE ISOLATION METHODS FOR MODULAR REACTORS

    SciTech Connect

    E. Blanford; E. Keldrauk; M. Laufer; M. Mieler; J. Wei; B. Stojadinovic; P.F. Peterson

    2010-09-20

    Advanced technologies for structural design and construction have the potential for major impact not only on nuclear power plant construction time and cost, but also on the design process and on the safety, security and reliability of next generation of nuclear power plants. In future Generation IV (Gen IV) reactors, structural and seismic design should be much more closely integrated with the design of nuclear and industrial safety systems, physical security systems, and international safeguards systems. Overall reliability will be increased, through the use of replaceable and modular equipment, and through design to facilitate on-line monitoring, in-service inspection, maintenance, replacement, and decommissioning. Economics will also receive high design priority, through integrated engineering efforts to optimize building arrangements to minimize building heights and footprints. Finally, the licensing approach will be transformed by becoming increasingly performance based and technology neutral, using best-estimate simulation methods with uncertainty and margin quantification. In this context, two structural engineering technologies, seismic base isolation and modular steel-plate/concrete composite structural walls, are investigated. These technologies have major potential to (1) enable standardized reactor designs to be deployed across a wider range of sites, (2) reduce the impact of uncertainties related to site-specific seismic conditions, and (3) alleviate reactor equipment qualification requirements. For Gen IV reactors the potential for deliberate crashes of large aircraft must also be considered in design. This report concludes that base-isolated structures should be decoupled from the reactor external event exclusion system. As an example, a scoping analysis is performed for a rectangular, decoupled external event shell designed as a grillage. This report also reviews modular construction technology, particularly steel-plate/concrete construction using

  5. A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

  6. An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method.

    PubMed

    Xie, Lie-Jun; Zhou, Cai-Lian; Xu, Song

    2016-01-01

    In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. PMID:27462514

  7. Numerical study of a multigrid method with four smoothing methods for the incompressible Navier-Stokes equations in general coordinates

    NASA Technical Reports Server (NTRS)

    Zeng, S.; Wesseling, P.

    1993-01-01

    The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.

  8. Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

    NASA Astrophysics Data System (ADS)

    Azarnykh, Dmitrii; Litvinov, Sergey; Adams, Nikolaus A.

    2016-06-01

    A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.

  9. Numerical Methods in Atmospheric and Oceanic Modelling: The Andre J. Robert Memorial Volume

    NASA Astrophysics Data System (ADS)

    Rosmond, Tom

    Most people, even including some in the scientific community, do not realize how much the weather forecasts they use to guide the activities of their daily lives depend on very complex mathematics and numerical methods that are the basis of modern numerical weather prediction (NWP). André Robert (1929-1993), to whom Numerical Methods in Atmospheric and Oceanic Modelling is dedicated, had a career that contributed greatly to the growth of NWP and the role that the atmospheric computer models of NWP play in our society. There are probably no NWP models running anywhere in the world today that do not use numerical methods introduced by Robert, and those of us who work with and use these models everyday are indebted to him.The first two chapters of the volume are chronicles of Robert's life and career. The first is a 1987 interview by Harold Ritchie, one of Robert's many proteges and colleagues at the Canadian Atmospheric Environment Service. The interview traces Robert's life from his birth in New York to French Canadian parents, to his emigration to Quebec at an early age, his education and early employment, and his rise in stature as one of the preeminent research meteorologists of our time. An amusing anecdote he relates is his impression of weather forecasts while he was considering his first job as a meteorologist in the early 1950s. A newspaper of the time placed the weather forecast and daily horoscope side by side, and Robert regarded each to have a similar scientific basis. Thankfully he soon realized there was a difference between the two, and his subsequent career certainly confirmed the distinction.

  10. An efficient numerical method for computing dynamics of spin F = 2 Bose-Einstein condensates

    SciTech Connect

    Wang Hanquan

    2011-07-01

    In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross-Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose-Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose-Einstein condensates confined in a uniform/nonuniform magnetic field.

  11. Performance of Higher Order Campbell methods, Part I: review and numerical convergence study

    NASA Astrophysics Data System (ADS)

    Elter, Zs.; Bakkali, M.; Jammes, C.; Pázsit, I.

    2016-06-01

    This paper investigates, through numerical simulations, the performance of a signal analysis method by which a high temperature fission chamber can be used over a wide range of count rates. Results reported in a previous paper (Elter et al., 2015 [1]) indicated that the traditional Campbell method and the pulse mode cannot provide a sufficient overlap at medium count rates. Hence the use of the so-called Higher Order Campbell (HOC) methods is proposed and their performance is investigated. It is shown that the HOC methods can guarantee the linearity (i.e. correctness) of the neutron flux estimation over a wide count rate, even during transient conditions. The capabilities of these methods for suppressing parasitic noise (originating from various sources) are verified.

  12. A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map

    NASA Astrophysics Data System (ADS)

    Luque, Alejandro; Villanueva, Jordi

    2016-06-01

    We present a numerical method for computing initial conditions of Lagrangian quasi-periodic invariant tori of Hamiltonian systems and symplectic maps. Such initial conditions are found by solving, using the Newton method, a nonlinear system obtained by imposing suitable conditions on the frequency map. The basic tool is a newly developed methodology to perform the frequency analysis of a discrete quasi-periodic signal, allowing to compute frequencies and their derivatives with respect to parameters. Roughly speaking, this method consists in computing suitable weighted averages of the iterates of the signal and using the Richardson extrapolation method. The proposed approach performs with high accuracy at a moderate computational cost. We illustrate the method by considering a discrete FPU model and the vicinity of the point L4 in a RTBP.

  13. Numerical Analysis of Cold Spray Particles Impacting Behavior by the Eulerian Method: A Review

    NASA Astrophysics Data System (ADS)

    Li, W. Y.; Yang, K.; Yin, S.; Guo, X. P.

    2016-08-01

    Numerical simulations have been widely used to study particles impacting behavior in cold spraying. Among the used simulation methods, the Eulerian frame becomes increasingly attractive for its absence of mesh distortion which happens in the Lagrangian frame. It has been proved that particle deformation behaviors upon impacting calculated by the Eulerian method are well comparable to the experimental observations. In this review article, the literature on modeling particle impacting by the Eulerian method was summarized. In the second part, the Eulerian method was detailedly introduced. In the third part, the particle/substrate impacting behavior, and its influencing factors, i.e., mesh resolution, particle impacting velocity, preheating (particle or/and substrate) and oxide film, were summarized. Additionally, the prediction of critical velocity and residual stresses by using the Eulerian method was also discussed in detail. Finally, the current issues, problems and prospects existing in the Eulerian simulations of particle impacting were explored.

  14. The numerical solution of ordinary differential equations by the Taylor series method

    NASA Technical Reports Server (NTRS)

    Silver, A. H.; Sullivan, E.

    1973-01-01

    A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

  15. Multiscale numerical methods for passive advection-diffusion in incompressible turbulent flow fields

    NASA Astrophysics Data System (ADS)

    Lee, Yoonsang; Engquist, Bjorn

    2016-07-01

    We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the velocity fields in the Fourier space, which are similar to the decomposition in large eddy simulations. It also uses a hierarchy of local domains with different resolutions as in multigrid methods. The effective diffusivity from finer scale is used for the next coarser level computation and this process is repeated up to the coarsest scale of interest. The grids are only in local domains whose sizes decrease depending on the resolution level so that the overall computational complexity increases linearly as the number of different resolution grids increases. The method captures interactions between finer and coarser scales but has to sacrifice some of interactions between different scales. The proposed method is numerically tested with 2D examples including a successful approximation to a continuous spectrum flow.

  16. Numerical investigations of solving unsteady, incompressible, viscous fluid flow by finite element method

    NASA Astrophysics Data System (ADS)

    Hatanaka, K.; Hayashi, M.; Kawahara, M.

    A novel FEM scheme that is based on the fractional-step method for solving time-dependent, incompressible viscous flow is presented and employed in the solution of a free-surface flow. The equations are given in indicial notation, as well as in the summation convention for repeated indices. The numerical results obtained exhibit good stability without the specification of Neumann conditions, and are compared in tabular form with the solutions given by Laitone's (1960) approximation. The method is also applicable to problems with artificial, open boundaries.

  17. A numerical method of finding potentiometric titration end-points by use of approximative spline functions.

    PubMed

    Ren, K

    1990-07-01

    A new numerical method of determining potentiometric titration end-points is presented. It consists in calculating the coefficients of approximative spline functions describing the experimental data (e.m.f., volume of titrant added). The end-point (the inflection point of the curve) is determined by calculating zero points of the second derivative of the approximative spline function. This spline function, unlike rational spline functions, is free from oscillations and its course is largely independent of random errors in e.m.f. measurements. The proposed method is useful for direct analysis of titration data and especially as a basis for construction of microcomputer-controlled automatic titrators. PMID:18964999

  18. Development of Numerical Simulation Method for Compressible Gas-Liquid Two-Phase Flows

    NASA Astrophysics Data System (ADS)

    Tamura, Y.

    2015-12-01

    A numerical simulation method of compressible gas-liquid two-phase flow is developed for analyses of a cavitation bubble. Thermodynamic state of both phases is described with stiffened gas equation of state. Interface of two phases is captured by Level-Set method. As internal energy jump between two phases is critical for the stability of computation, total energy equation is modified so that inviscid flux of energy is smoothly connected across the interface. Detail of governing equations as well as their discretization is described followed by the result of one-dimensional simple example computation.

  19. A method for data handling numerical results in parallel OpenFOAM simulations

    SciTech Connect

    Anton, Alin; Muntean, Sebastian

    2015-12-31

    Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit{sup ®}[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.

  20. Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics

    NASA Astrophysics Data System (ADS)

    Burago, N. G.; Nikitin, I. S.; Yakushev, V. L.

    2016-06-01

    Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov-Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.

  1. Processing of alnico permanent magnets by advanced directional solidification methods

    DOE PAGES

    Zou, Min; Johnson, Francis; Zhang, Wanming; Zhao, Qi; Rutkowski, Stephen F.; Zhou, Lin; Kramer, Matthew J.

    2016-07-05

    Advanced directional solidification methods have been used to produce large (>15 cm length) castings of Alnico permanent magnets with highly oriented columnar microstructures. In combination with subsequent thermomagnetic and draw thermal treatment, this method was used to enable the high coercivity, high-Titanium Alnico composition of 39% Co, 29.5% Fe, 14% Ni, 7.5% Ti, 7% Al, 3% Cu (wt%) to have an intrinsic coercivity (Hci) of 2.0 kOe, a remanence (Br) of 10.2 kG, and an energy product (BH)max of 10.9 MGOe. These properties compare favorably to typical properties for the commercial Alnico 9. Directional solidification of higher Ti compositions yieldedmore » anisotropic columnar grained microstructures if high heat extraction rates through the mold surface of at least 200 kW/m2 were attained. This was achieved through the use of a thin walled (5 mm thick) high thermal conductivity SiC shell mold extracted from a molten Sn bath at a withdrawal rate of at least 200 mm/h. However, higher Ti compositions did not result in further increases in magnet performance. Images of the microstructures collected by scanning electron microscopy (SEM) reveal a majority α phase with inclusions of secondary αγ phase. Transmission electron microscopy (TEM) reveals that the α phase has a spinodally decomposed microstructure of FeCo-rich needles in a NiAl-rich matrix. In the 7.5% Ti composition the diameter distribution of the FeCo needles was bimodal with the majority having diameters of approximately 50 nm with a small fraction having diameters of approximately 10 nm. The needles formed a mosaic pattern and were elongated along one <001> crystal direction (parallel to the field used during magnetic annealing). Cu precipitates were observed between the needles. Regions of abnormal spinodal morphology appeared to correlate with secondary phase precipitates. The presence of these abnormalities did not prevent the material from displaying superior magnetic properties in the 7.5% Ti

  2. Processing of alnico permanent magnets by advanced directional solidification methods

    NASA Astrophysics Data System (ADS)

    Zou, Min; Johnson, Francis; Zhang, Wanming; Zhao, Qi; Rutkowski, Stephen F.; Zhou, Lin; Kramer, Matthew J.

    2016-12-01

    Advanced directional solidification methods have been used to produce large (>15 cm length) castings of Alnico permanent magnets with highly oriented columnar microstructures. In combination with subsequent thermomagnetic and draw thermal treatment, this method was used to enable the high coercivity, high-Titanium Alnico composition of 39% Co, 29.5% Fe, 14% Ni, 7.5% Ti, 7% Al, 3% Cu (wt%) to have an intrinsic coercivity (Hci) of 2.0 kOe, a remanence (Br) of 10.2 kG, and an energy product (BH)max of 10.9 MGOe. These properties compare favorably to typical properties for the commercial Alnico 9. Directional solidification of higher Ti compositions yielded anisotropic columnar grained microstructures if high heat extraction rates through the mold surface of at least 200 kW/m2 were attained. This was achieved through the use of a thin walled (5 mm thick) high thermal conductivity SiC shell mold extracted from a molten Sn bath at a withdrawal rate of at least 200 mm/h. However, higher Ti compositions did not result in further increases in magnet performance. Images of the microstructures collected by scanning electron microscopy (SEM) reveal a majority α phase with inclusions of secondary αγ phase. Transmission electron microscopy (TEM) reveals that the α phase has a spinodally decomposed microstructure of FeCo-rich needles in a NiAl-rich matrix. In the 7.5% Ti composition the diameter distribution of the FeCo needles was bimodal with the majority having diameters of approximately 50 nm with a small fraction having diameters of approximately 10 nm. The needles formed a mosaic pattern and were elongated along one <001> crystal direction (parallel to the field used during magnetic annealing). Cu precipitates were observed between the needles. Regions of abnormal spinodal morphology appeared to correlate with secondary phase precipitates. The presence of these abnormalities did not prevent the material from displaying superior magnetic properties in the 7.5% Ti

  3. MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS

    SciTech Connect

    Ciolek, Glenn E.; Roberge, Wayne G. E-mail: roberw@rpi.edu

    2013-05-01

    We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

  4. Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests

    NASA Astrophysics Data System (ADS)

    Ciolek, Glenn E.; Roberge, Wayne G.

    2013-05-01

    We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are Lt magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

  5. Numerical time dependent sheet cavitation simulations using a higher order panel method

    NASA Astrophysics Data System (ADS)

    Dekoninggans, H. J.

    1994-03-01

    This thesis deals with sheet cavitation. The investigation is aimed at profile design with respect to cavitation control. At present it is possible to predict the shape of cavities on an arbitrary two-dimensional profile in stationary flows. To compute the flow around an arbitrary profile, a higher order three-dimensional panel method program has been developed. The main algorithm used in this program is based on a special case of Green's theorem, called 'de Morino formulation'. This computer program (flow program) can calculate the potential on the body and the velocities at the surface of the body or in the flow field. A theoretical method is developed for time simulation of unsteady sheet cavitation. Numerical simulations of the flow around profiles and of cavitation have been carried out. The numerical results of the panel methods have been compared with other calculations of the two-dimensional flow around profiles and of three-dimensional flow around a sphere and a wing. Simulations of the growth of sheet cavitation on a foil have also been carried out. The conclusion is that higher order panel methods are more accurate than the zero order methods. Further refinement of the Kutta condition is required, however.

  6. Projected role of advanced computational aerodynamic methods at the Lockheed-Georgia company

    NASA Technical Reports Server (NTRS)

    Lores, M. E.

    1978-01-01

    Experience with advanced computational methods being used at the Lockheed-Georgia Company to aid in the evaluation and design of new and modified aircraft indicates that large and specialized computers will be needed to make advanced three-dimensional viscous aerodynamic computations practical. The Numerical Aerodynamic Simulation Facility should be used to provide a tool for designing better aerospace vehicles while at the same time reducing development costs by performing computations using Navier-Stokes equations solution algorithms and permitting less sophisticated but nevertheless complex calculations to be made efficiently. Configuration definition procedures and data output formats can probably best be defined in cooperation with industry, therefore, the computer should handle many remote terminals efficiently. The capability of transferring data to and from other computers needs to be provided. Because of the significant amount of input and output associated with 3-D viscous flow calculations and because of the exceedingly fast computation speed envisioned for the computer, special attention should be paid to providing rapid, diversified, and efficient input and output.

  7. Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory

    NASA Technical Reports Server (NTRS)

    Thomas, P. D.

    1979-01-01

    The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.

  8. 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.

  9. A Numerical Method for Integrating the Kinetic Equation of Coalescence and Breakup of Cloud Droplets.

    NASA Astrophysics Data System (ADS)

    Enukashvily, Isaac M.

    1980-11-01

    An extension of Bleck' method and of the method of moments is developed for the numerical integration of the kinetic equation of coalescence and breakup of cloud droplets. The number density function nk(x,t) in each separate cloud droplet packet between droplet mass grid points (xk,xk+1) is represented by an expansion in orthogonal polynomials with a given weighting function wk(x,k). The expansion coefficients describe the deviations of nk(x,t) from wk(x,k). In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved, and the problem of solving the kinetic equation is replaced by one of solving a set of coupled differential equations for the moments of the number density function nk(x,t). Equations for these moments in each droplet packet are derived. The method is tested against existing solutions of the coalescence equation. Numerical results are obtained when Bleck's uniform distribution hypothesis for nk(x,t) and Golovin's asymptotic solution of the coalescence equation is chosen for the, weighting function wk(x, k). A comparison between numerical results computed by Bleck's method and by the method of this study is made. It is shown that for the correct computation of the coalescence and breakup interactions between cloud droplet packets it is very important that the, approximation of the nk(x,t) between grid points (xk,xk+1) satisfies the conservation conditions for the number concentration, liquid water content and other moments of the cloud droplet packets. If these conservation conditions are provided, even the quasi-linear approximation of the nk(x,t) in comparison with Berry's six-point interpolation will give reasonable results which are very close to the existing analytic solutions.

  10. Efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates based on their characterizations

    SciTech Connect

    Bao, Weizhu; Chern, I-Liang; Zhang, Yanzhi

    2013-11-15

    In this paper, we propose efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates (BECs) with/without the Ioffe–Pritchard magnetic field B(x). When B(x)≠0, a numerical method is introduced to compute the ground states and it is also applied to study properties of ground states. Numerical results suggest that the densities of m{sub F}=±1 components in ground states are identical for any nonzero B(x). In particular, if B(x)≡B≠0 is a constant, the ground states satisfy the single-mode approximation. When B(x)≡0, efficient and simpler numerical methods are presented to solve the ground states of spin-1 BECs based on their ferromagnetic/antiferromagnetic characterizations. Numerical simulations show that our methods are more efficient than those in the literature. In addition, some conjectures are made from our numerical observations.

  11. A numerical method for generating rapidly rotating bipolytropic structures in equilibrium

    NASA Astrophysics Data System (ADS)

    Kadam, Kundan; Motl, Patrick M.; Frank, Juhan; Clayton, Geoffrey C.; Marcello, Dominic C.

    2016-10-01

    We demonstrate that rapidly rotating bipolytropic (composite polytropic) stars and toroidal discs can be obtained using Hachisu's self-consistent field technique. The core and the envelope in such a structure can have different polytropic indices and also different average molecular weights. The models converge for high T/|W| cases, where T is the kinetic energy and W is the gravitational energy of the system. The agreement between our numerical solutions with known analytical as well as previously calculated numerical results is excellent. We show that the uniform rotation lowers the maximum core mass fraction or the Schönberg-Chandrasekhar limit for a bipolytropic sequence. We also discuss the applications of this method to magnetic braking in low-mass stars with convective envelopes.

  12. Fourth-Order Method for Numerical Integration of Age- and Size-Structured Population Models

    SciTech Connect

    Iannelli, M; Kostova, T; Milner, F A

    2008-01-08

    In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.

  13. Numerical solution of flame sheet problems with and without multigrid methods

    NASA Technical Reports Server (NTRS)

    Douglas, Craig C.; Ern, Alexandre

    1993-01-01

    Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.

  14. Numerical simulation of dam-break problem using staggered finite volume method

    NASA Astrophysics Data System (ADS)

    Budiasih, L. K.; Wiryanto, L. H.

    2016-02-01

    A problem in a dam-break is when a wall separating two sides of water is removed. A shock wave occurs and propagates. The behavior of the wave is interesting to be investigated with respect to the water depth and its wave speed. The aim of this research is to model dam-break problem using the non-linear shallow water equations and solve them numerically using staggered finite volume method. The solution is used to simulate the dam-break on a wet bed. Our numerical solution will be compared to the analytical solution of shallow water equations for dam-break problem. The momentum non-conservative finite volume scheme on a staggered grid will give a good agreement for dam-break problem on a wet bed, for depth ratios greater than 0.25.

  15. A numerical method for computing three dimensional viscous supersonic flow fields about slender bodies

    NASA Technical Reports Server (NTRS)

    Walitt, L.; Trulio, J. G.

    1971-01-01

    A numerical method is presented for the calculation of steady, three-dimensional, viscous, compressible flow fields about slender bodies at angle of attack and at supersonic speeds. Approximations are introduced in modeling the flow in the longitudinal direction. Accordingly, the flow fields calculated with the program were computed with a model that permits viscous crossflow together with inviscid axial flow. An analysis of the errors introduced by such a treatment is presented. Numerical calculations were made and compared with experimental results for an ogive-cylinder and an airplane fuselage configuration. Generally, good agreement with experiment was obtained. However, boundary layer separation and body vortex positions differed from experimental locations on the ogive-cylinder, and the shock induced by the fuselage canopy was predicted at a slightly different location.

  16. Novel method of manufacturing hydrogen storage materials combining with numerical analysis based on discrete element method

    NASA Astrophysics Data System (ADS)

    Zhao, Xuzhe

    High efficiency hydrogen storage method is significant in development of fuel cell vehicle. Seeking for a high energy density material as the fuel becomes the key of wide spreading fuel cell vehicle. LiBH4 + MgH 2 system is a strong candidate due to their high hydrogen storage density and the reaction between them is reversible. However, LiBH4 + MgH 2 system usually requires the high temperature and hydrogen pressure for hydrogen release and uptake reaction. In order to reduce the requirements of this system, nanoengineering is the simple and efficient method to improve the thermodynamic properties and reduce kinetic barrier of reaction between LiBH4 and MgH2. Based on ab initio density functional theory (DFT) calculations, the previous study has indicated that the reaction between LiBH4 and MgH2 can take place at temperature near 200°C or below. However, the predictions have been shown to be inconsistent with many experiments. Therefore, it is the first time that our experiment using ball milling with aerosol spraying (BMAS) to prove the reaction between LiBH4 and MgH2 can happen during high energy ball milling at room temperature. Through this BMAS process we have found undoubtedly the formation of MgB 2 and LiH during ball milling of MgH2 while aerosol spraying of the LiBH4/THF solution. Aerosol nanoparticles from LiBH 4/THF solution leads to form Li2B12H12 during BMAS process. The Li2B12H12 formed then reacts with MgH2 in situ during ball milling to form MgB 2 and LiH. Discrete element modeling (DEM) is a useful tool to describe operation of various ball milling processes. EDEM is software based on DEM to predict power consumption, liner and media wear and mill output. In order to further improve the milling efficiency of BMAS process, EDEM is conducted to make analysis for complicated ball milling process. Milling speed and ball's filling ratio inside the canister as the variables are considered to determine the milling efficiency. The average and maximum

  17. Advanced Methods for Aircraft Engine Thrust and Noise Benefits: Nozzle-Inlet Flow Analysis

    NASA Technical Reports Server (NTRS)

    Morgan, Morris H.; Gilinsky, Mikhail M.

    2001-01-01

    Three connected sub-projects were conducted under reported project. Partially, these sub-projects are directed to solving the problems conducted by the HU/FM&AL under two other NASA grants. The fundamental idea uniting these projects is to use untraditional 3D corrugated nozzle designs and additional methods for exhaust jet noise reduction without essential thrust lost and even with thrust augmentation. Such additional approaches are: (1) to add some solid, fluid, or gas mass at discrete locations to the main supersonic gas stream to minimize the negative influence of strong shock waves forming in propulsion systems; this mass addition may be accompanied by heat addition to the main stream as a result of the fuel combustion or by cooling of this stream as a result of the liquid mass evaporation and boiling; (2) to use porous or permeable nozzles and additional shells at the nozzle exit for preliminary cooling of exhaust hot jet and pressure compensation for non-design conditions (so-called continuous ejector with small mass flow rate; and (3) to propose and analyze new effective methods fuel injection into flow stream in air-breathing engines. Note that all these problems were formulated based on detailed descriptions of the main experimental facts observed at NASA Glenn Research Center. Basically, the HU/FM&AL Team has been involved in joint research with the purpose of finding theoretical explanations for experimental facts and the creation of the accurate numerical simulation technique and prediction theory for solutions for current problems in propulsion systems solved by NASA and Navy agencies. The research is focused on a wide regime of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analysis for advanced aircraft and rocket engines. The F&AL Team uses analytical methods, numerical simulations, and possible experimental tests at the Hampton University campus. We will present some management activity

  18. A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation

    SciTech Connect

    Wu, Y.; Modest, M.F.; Haworth, D.C. . E-mail: dch12@psu.edu

    2007-05-01

    A high-order photon Monte Carlo method is developed to solve the radiative transfer equation. The statistical and discretization errors of the computed radiative heat flux and radiation source term are isolated and quantified. Up to sixth-order spatial accuracy is demonstrated for the radiative heat flux, and up to fourth-order accuracy for the radiation source term. This demonstrates the compatibility of the method with high-fidelity direct numerical simulation (DNS) for chemically reacting flows. The method is applied to address radiative heat transfer in a one-dimensional laminar premixed flame and a statistically one-dimensional turbulent premixed flame. Modifications of the flame structure with radiation are noted in both cases, and the effects of turbulence/radiation interactions on the local reaction zone structure are revealed for the turbulent flame. Computational issues in using a photon Monte Carlo method for DNS of turbulent reacting flows are discussed.

  19. Numerical solution of differential algebraic equations (DAEs) by mix-multistep method

    NASA Astrophysics Data System (ADS)

    Rahim, Yong Faezah; Suleiman, Mohamed; Ibrahim, Zarina Bibi

    2014-06-01

    Differential Algebraic Equations (DAEs) are regarded as stiff Ordinary Differential Equations (ODEs). Therefore they are solved using implicit method such as Backward Differentiation Formula (BDF) type of methods which require the use of Newton iteration which need much computational effort. However, not all of the ODEs in DAE system are stiff. In this paper, we describe a new technique for solving DAE, where the ODEs are treated as non-stiff at the start of the integration and putting the non-stiff ODEs into stiff subsystem should instability occurs. Adams type of method is used to solve the non-stiff part and BDF method for solving the stiff part. This strategy is shown to be competitive in terms of computational effort and accuracy. Numerical experiments are presented to validate its efficiency.

  20. Curvature-Based Method for Measuring Numerical Black-Hole Spins

    NASA Astrophysics Data System (ADS)

    Kelly, Bernard; Finch, Tehani; van Meter, James; Baker, John

    2015-04-01

    Accurate determination of spin magnitude and direction over time is crucial for the development of gravitational-wave templates that faithfully reflect the dynamics of generic comparable-mass black-hole binary mergers. We report on the development of a new method for measuring black-hole spins during numerical-relativity simulations of black-hole binary mergers. This method is based on the ``spin scalar,'' a complex scalar field derived from the Coulomb scalar of Beetle & Burko (2002). Our new method can be used to derive both spin magnitude and direction, and can be combined with other techniques, such as isolated-horizon methods. We present convergence studies, and demonstrations of behavior during precessing mergers of spinning black holes.

  1. Numerical method to compute acoustic scattering effect of a moving source.

    PubMed

    Song, Hao; Yi, Mingxu; Huang, Jun; Pan, Yalin; Liu, Dawei

    2016-01-01

    In this paper, the aerodynamic characteristic of a ducted tail rotor in hover has been numerically studied using CFD method. An analytical time domain formulation based on Ffowcs Williams-Hawkings (FW-H) equation is derived for the prediction of the acoustic velocity field and used as Neumann boundary condition on a rigid scattering surface. In order to predict the aerodynamic noise, a hybrid method combing computational aeroacoustics with an acoustic thin-body boundary element method has been proposed. The aerodynamic results and the calculated sound pressure levels (SPLs) are compared with the known method for validation. Simulation results show that the duct can change the value of SPLs and the sound directivity. Compared with the isolate tail rotor, the SPLs of the ducted tail rotor are smaller at certain azimuth. PMID:27610323

  2. Numerical method to compute acoustic scattering effect of a moving source.

    PubMed

    Song, Hao; Yi, Mingxu; Huang, Jun; Pan, Yalin; Liu, Dawei

    2016-01-01

    In this paper, the aerodynamic characteristic of a ducted tail rotor in hover has been numerically studied using CFD method. An analytical time domain formulation based on Ffowcs Williams-Hawkings (FW-H) equation is derived for the prediction of the acoustic velocity field and used as Neumann boundary condition on a rigid scattering surface. In order to predict the aerodynamic noise, a hybrid method combing computational aeroacoustics with an acoustic thin-body boundary element method has been proposed. The aerodynamic results and the calculated sound pressure levels (SPLs) are compared with the known method for validation. Simulation results show that the duct can change the value of SPLs and the sound directivity. Compared with the isolate tail rotor, the SPLs of the ducted tail rotor are smaller at certain azimuth.

  3. Comparison of numerical methods for 2D crystals under anisotropic surface free energy and through evolution

    NASA Astrophysics Data System (ADS)

    Lolla, Madhuri Udayanjani

    In this dissertation first, we compute the equilibrium shapes of 2D crystals under anisotropic surface free energies. An equilibrium shape minimizes the total surface free energy. The governing equation in polar coordinates is a nonlinear ordinary differential equation. Two numerical methods, finite difference and the finite element are used and compared. We investigate the accuracy, order of convergence and efficiency of the two methods in computing the equilibrium shapes. Secondly, we consider the surface of the crystal evolving under surface diffusion and compute the final shape in the evolution which is the equilibrium shape. The surface diffusion equation in polar coordinates is a time-dependent nonlinear 4th order partial differential equation. Again we apply the two methods finite difference and finite element. The results are observed at different stages of evolution of the crystal for the isotropy case. Then we compare the accuracy, order of convergence and efficiency of the two methods.

  4. A numerical method to optimize the design of a space inflatable membrane reflector

    NASA Astrophysics Data System (ADS)

    Bouzidi, Rabah; Lecieux, Yann

    2012-05-01

    A numerical method is proposed to optimize the design of a space inflatable membrane reflector. The initial geometry is expressed by polynomial series weighted by a set of shape parameters. The problem is formulated as a minimization of a cost function representing the difference between the effective shape of the reflector and a perfect parabolic surface. The minimization is performed using the Nelder-Mead method or downhill simplex method. The cost function is computed at each vertex of a simplex defined in the space of optimization parameters by solving direct problem thanks to a finite element method. The finite element model handles geometrical non-linearities and takes into account phenomena like membrane wrinkling and torus buckling which may affect the reflector shape when inflated.

  5. Application of the full approximation storage method to the numerical simulation of two-dimensional steady incompressible viscous multiphase flows

    NASA Astrophysics Data System (ADS)

    Thompson, C. P.; Lezeau, P.

    1998-11-01

    In recent years multigrid algorithms have been applied to increasingly difficult systems of partial differential equations and major improvements in both speed of convergence and robustness have been achieved. Problems involving several interacting fluids are of great interest in many industrial applications, especially in the process and petro-chemical sectors. However, the multifluid version of the Navier-Stokes equations is extremely complex and represents a challenge to advanced numerical algorithms. In this paper, we describe an extension of the full approximation storage (FAS) multigrid algorithm to the multifluid equations. A number of special issues had to be addressed. The first was the development of a customised, non-linear, coupled relaxation scheme for the smoothing step. Automatic differentiation was used to facilitate the coding of a robust, globally convergent quasi-Newton method. It was also necessary to use special inter-grid transfer operators to maintain the realisability of the solution. Algorithmic details are given and solutions for a series of test problems are compared with those from a widely validated, commercial code. The new approach has proved to be robust; it achieves convergence without resorting to specialised initialisation methods. Moreover, even though the rate of convergence is complex, the method has achieved very good reduction factors: typically five orders of magnitude in 50 cycles.

  6. WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

    NASA Astrophysics Data System (ADS)

    Crevoisier, David; Voltz, Marc

    2013-04-01

    To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute

  7. 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

  8. 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.

  9. A Numerical Method to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

    NASA Astrophysics Data System (ADS)

    Anda, E.; Chiappe, G.; Busser, C.; Davidovich, M.; Martins, G.; H-Meisner, F.; Dagotto, E.

    2008-03-01

    A numerical algorithm to study transport properties of highly correlated local structures is proposed. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's ideas of a logarithmic discretization of the representation of the Hamiltonian. LDECA's rapid convergence eliminates finite-size effects commonly present in the embedding cluster approximation (ECA) method. The physics associated with both one embedded dot and a string of two dots side-coupled to leads is discussed. In the former case, our results accurately agree with Bethe ansatz (BA) data, while in the latter, the results are framed in the conceptual background of a two-stage Kondo problem. A diagrammatic expansion provides the theoretical foundation for the method. It is argued that LDECA allows for the study of complex problems that are beyond the reach of currently available numerical methods.

  10. L{sub 1/2} regularization based numerical method for effective reconstruction of bioluminescence tomography

    SciTech Connect

    Chen, Xueli E-mail: jimleung@mail.xidian.edu.cn; Yang, Defu; Zhang, Qitan; Liang, Jimin E-mail: jimleung@mail.xidian.edu.cn

    2014-05-14

    Even though bioluminescence tomography (BLT) exhibits significant potential and wide applications in macroscopic imaging of small animals in vivo, the inverse reconstruction is still a tough problem that has plagued researchers in a related area. The ill-posedness of inverse reconstruction arises from insufficient measurements and modeling errors, so that the inverse reconstruction cannot be solved directly. In this study, an l{sub 1/2} regularization based numerical method was developed for effective reconstruction of BLT. In the method, the inverse reconstruction of BLT was constrained into an l{sub 1/2} regularization problem, and then the weighted interior-point algorithm (WIPA) was applied to solve the problem through transforming it into obtaining the solution of a series of l{sub 1} regularizers. The feasibility and effectiveness of the proposed method were demonstrated with numerical simulations on a digital mouse. Stability verification experiments further illustrated the robustness of the proposed method for different levels of Gaussian noise.

  11. Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods

    PubMed Central

    Weichert, Frank; Walczak, Lars; Fisseler, Denis; Opfermann, Tobias; Münster, Raphael; Grunwald, Iris; Roth, Christian; Veith, Christian; Wagner, Mathias

    2013-01-01

    The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms. PMID:23662158

  12. A simple numerical method for snowmelt simulation based on the equation of heat energy.

    PubMed

    Stojković, Milan; Jaćimović, Nenad

    2016-01-01

    This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events. PMID:27054726

  13. Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods.

    PubMed

    Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K

    2016-08-01

    In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption. PMID:27505799

  14. A simple numerical method for snowmelt simulation based on the equation of heat energy.

    PubMed

    Stojković, Milan; Jaćimović, Nenad

    2016-01-01

    This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events.

  15. International Symposium on Numerical Methods in Engineering, 5th, Ecole Polytechnique Federale de Lausanne, Switzerland, Sept. 11-15, 1989, Proceedings. Volumes 1 & 2

    NASA Astrophysics Data System (ADS)

    Gruber, Ralph; Periaux, Jaques; Shaw, Richard Paul

    Recent advances in computational mechanics are discussed in reviews and reports. Topics addressed include spectral superpositions on finite elements for shear banding problems, strain-based finite plasticity, numerical simulation of hypersonic viscous continuum flow, constitutive laws in solid mechanics, dynamics problems, fracture mechanics and damage tolerance, composite plates and shells, contact and friction, metal forming and solidification, coupling problems, and adaptive FEMs. Consideration is given to chemical flows, convection problems, free boundaries and artificial boundary conditions, domain-decomposition and multigrid methods, combustion and thermal analysis, wave propagation, mixed and hybrid FEMs, integral-equation methods, optimization, software engineering, and vector and parallel computing.

  16. Two step hybrid methods of 7th and 8th order for the numerical integration of second order IVPs

    NASA Astrophysics Data System (ADS)

    Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.

    2016-06-01

    In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct two step hybrid methods with six and seven stages and seventh and eighth algebraic order. We apply the new methods on the numerical integration of several test problems.

  17. A Method for Increasing Elders' Use of Advance Directives.

    ERIC Educational Resources Information Center

    Luptak, Marilyn K.; Boult, Chad

    1994-01-01

    Studied effectiveness of intervention to help frail elders to record advance directives (ADs). In collaboration with physicians and lay volunteer, social worker provided information/counseling to elderly subjects, families, and proxies in series of visits to geriatric evaluation and management clinic. Seventy-one percent of subjects recorded ADs.…

  18. An Efficient Mesh for Wavefront Construction Methods and its Numerical Properties for Anisotropic Media

    NASA Astrophysics Data System (ADS)

    Lee, K.; Gibson, R. L.

    2002-12-01

    The wavefront construction method is an efficient way to model wave propagation in anisotropic media. This method is based on asymptotic ray theory, and it explicitly tracks the propagation of wavefronts through the earth model. The first step is to trace a fan of rays through the earth model, initializing the wavefront by constructing a mesh from the set of all ray points at a specified travel time. The wavefront is thus a mesh composed of quadrilateral cells defined by four neighboring rays. Rays are computed by kinematic ray tracing using Runge-Kutta methods. The basic geometry, or coordinate system, used to select the rays comprising the initial mesh has significant affects on the precision and performance of the numerical calculation. A common approach is to trace rays with regular increments in the azimuthal and declination takeoff angles. These two angles, along with travel time, define a ray coordinate system that is commonly used for implementations of conventional ray tracing for wavefront construction schemes. While the ray coordinate system is straightforward to implement and has been used extensively, it has some drawbacks (Gibson et al., 2002). The most important is that the derivatives of Cartesian coordinates on the ray with respect to the azimuthal takeoff angle vanish near the poles of the coordinate system, leading to potential numerical errors. Our implementation applies paraxial methods, and the poor estimates of derivatives can seriously degrade the performance of the algorithm. Also, specifying an initial ray field with even increments in takeoff angles leads to large concentrations of rays near the poles, which is numerically inefficient. To overcome these important limitations of the ray coordinate system, we apply a new mesh generation algorithm that utilizes a cubic gnomonic mesh. A cubic gnomonic mesh maps points chosen at regular intervals on the surface of a cube surrounding the source point to the focal sphere. In essence, the initial

  19. Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements

    NASA Astrophysics Data System (ADS)

    Ellmer, Matthias; Mayer-Gürr, Torsten

    2016-04-01

    Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability. When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer. Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy. We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.

  20. 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.

  1. A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations

    NASA Astrophysics Data System (ADS)

    Moghadam, Mahdi Esmaily; Vignon-Clementel, Irene E.; Figliola, Richard; Marsden, Alison L.; Modeling Of Congenital Hearts Alliance (Mocha) Investigators

    2013-07-01

    Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of backflow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D-0D interface.

  2. A New AMR Code for Relativistic Magnetohydrodynamics in Dynamical Specetimes: Numerical Method and Code Validation

    NASA Astrophysics Data System (ADS)

    Liu, Yuk Tung; Etienne, Zachariah; Shapiro, Stuart

    2011-04-01

    The Illinois relativity group has written and tested a new GRMHD code, which is compatible with adaptive-mesh refinement (AMR) provided by the widely-used Cactus/Carpet infrastructure. Our code solves the Einstein-Maxwell-MHD system of coupled equations in full 3+1 dimensions, evolving the metric via the BSSN formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential. The divergenceless constraint div(B) = 0 is enforced by the curl of the vector potential. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We will present numerical method and code validation tests for both Minkowski and curved spacetimes. The tests include magnetized shocks, nonlinear Alfven waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order.

  3. Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method.

    PubMed

    Wu, Fengyuan; Fan, Yunyun; Liang, Li; Wang, Chao

    2016-01-01

    This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures. PMID:27513661

  4. Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method

    PubMed Central

    Wu, Fengyuan; Fan, Yunyun; Liang, Li; Wang, Chao

    2016-01-01

    This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures. PMID:27513661

  5. Multibody Dynamics of Reconfigurable Space System Part II: (Contact Dynamics and Numerical Verification Method)

    NASA Astrophysics Data System (ADS)

    Takahashi, Takashi; Matunaga, Saburo

    In order to analyze dynamics of space systems, such as cluster satellite systems and the capturing process of damaged satellites, it is necessary to consider such space systems as reconfigurable multibody systems. In this paper, we discuss the numerical computation of the dynamics of the ground experiment system to simulate the capturing and berthing process of a satellite by a dual-manipulator on the flat floor as an example. We have previously discussed the efficient dynamics algorithm for reconfigurable multibody system with topological changes. However, the contact dynamics, which is one of the most difficult issues on our study, remains to be discussed. We introduce two types of the linear complementarity problem (LCP) concerned with contact dynamics. The difference between two types of the LCP is whether impacts can be considered. Dynamics systems with impacts and friction are non-conservation systems, moreover the LCP is not always solvable. Therefore we must check if the solutions of the numerical computation are correct, or how accurate those are. In this paper, we derive the method of numerical computation with guaranteed accuracy of the LCP for contact dynamics.

  6. An advanced synthetic eddy method for the computation of aerofoil-turbulence interaction noise

    NASA Astrophysics Data System (ADS)

    Kim, Jae Wook; Haeri, Sina

    2015-04-01

    This paper presents an advanced method to synthetically generate flow turbulence via an inflow boundary condition particularly designed for three-dimensional aeroacoustic simulations. The proposed method is virtually free of spurious noise that might arise from the synthetic turbulence, which enables a direct calculation of propagated sound waves from the source mechanism. The present work stemmed from one of the latest outcomes of synthetic eddy method (SEM) derived from a well-defined vector potential function creating a divergence-free velocity field with correct convection speeds of eddies, which in theory suppresses pressure fluctuations. In this paper, a substantial extension of the SEM is introduced and systematically optimised to create a realistic turbulence field based on von Kármán velocity spectra. The optimised SEM is then combined with a well-established sponge-layer technique to quietly inject the turbulent eddies into the domain from the upstream boundary, which results in a sufficiently clean acoustic field. Major advantages in the present approach are: a) that genuinely three-dimensional turbulence is generated; b) that various ways of parametrisation can be created to control/characterise the randomly distributed eddies; and, c) that its numerical implementation is efficient as the size of domain section through which the turbulent eddies should be passing can be adjusted and minimised. The performance and reliability of the proposed SEM are demonstrated by a three-dimensional simulation of aerofoil-turbulence interaction noise.

  7. 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.

  8. Two Approaches in the Lunar Libration Theory: Analytical vs. Numerical Methods

    NASA Astrophysics Data System (ADS)

    Petrova, Natalia; Zagidullin, Arthur; Nefediev, Yurii; Kosulin, Valerii

    2016-10-01

    Observation of the physical libration of the Moon and the celestial bodies is one of the astronomical methods to remotely evaluate the internal structure of a celestial body without using expensive space experiments. Review of the results obtained due to the physical libration study, is presented in the report.The main emphasis is placed on the description of successful lunar laser ranging for libration determination and on the methods of simulating the physical libration. As a result, estimation of the viscoelastic and dissipative properties of the lunar body, of the lunar core parameters were done. The core's existence was confirmed by the recent reprocessing of seismic data Apollo missions. Attention is paid to the physical interpretation of the phenomenon of free libration and methods of its determination.A significant part of the report is devoted to describing the practical application of the most accurate to date the analytical tables of lunar libration built by comprehensive analytical processing of residual differences obtained when comparing the long-term series of laser observations with numerical ephemeris DE421 [1].In general, the basic outline of the report reflects the effectiveness of two approaches in the libration theory - numerical and analytical solution. It is shown that the two approaches complement each other for the study of the Moon in different aspects: numerical approach provides high accuracy of the theory necessary for adequate treatment of modern high-accurate observations and the analytic approach allows you to see the essence of the various kind manifestations in the lunar rotation, predict and interpret the new effects in observations of physical libration [2].[1] Rambaux, N., J. G. Williams, 2011, The Moon's physical librations and determination of their free modes, Celest. Mech. Dyn. Astron., 109, 85–100.[2] Petrova N., A. Zagidullin, Yu. Nefediev. Analysis of long-periodic variations of lunar libration parameters on the basis

  9. A pressure-based high resolution numerical method for resistive MHD

    NASA Astrophysics Data System (ADS)

    Xisto, Carlos M.; Páscoa, José C.; Oliveira, Paulo J.

    2014-10-01

    In the paper we describe in detail a numerical method for the resistive magnetohydrodynamic (MHD) equations involving viscous flow and report the results of application to a number of typical MHD test cases. The method is of the finite volume type but mixes aspects of pressure-correction and density based solvers; the algorithm arrangement is patterned on the well-known PISO algorithm, which is a pressure method, while the flux computation makes use of the AUSM-MHD scheme, which originates from density based methods. Five groups of test cases are addressed to verify and validate the method. We start with two resistive MHD cases, namely the Shercliff and Hunt flow problems, which are intended to validate the method for low-speed resistive MHD flows. The remaining three test cases, namely the cloud-shock interaction, the MHD rotor and the MHD blast wave, are standard 2D ideal MHD problems that serve to validate the method under high-speed flow and complex interaction of MHD shocks. Finally, we demonstrate the method with a more complex application problem, and discuss results of simulation for a quasi-bi-dimensional self-field magnetoplasmadynamic (MPD) thruster, for which we study the effect of cathode length upon the electromagnetic nozzle performance.

  10. Mirror fluid method for numerical simulation of sedimentation of a solid particle in a Newtonian fluid.

    PubMed

    Yang, Chao; Mao, Zai-Sha

    2005-03-01

    The mirror fluid method is proposed for simulating solid-fluid two-phase flow. The whole computational domain is modeled as an Eulerian one for the fluid with a Lagrangian subdomain embedded in it. The boundary condition is enforced implicitly on solid-fluid surface segments by mirror relations. Thus, the total flow is solved in the one domain, in which the solid particle region is replaced with the virtual flow as the mirror image of outside flow. The mirror fluid method is implemented to compute the motion of a rigid spherical or elliptic particle in a Newtonian fluid for the purpose of method validation. The control volume formulation with the SIMPLE algorithm incorporated is used to solve the governing equations on a staggered grid in a two-dimensional coordinate system. A number of numerical experiments on falling particles are performed and the computational results are in good agreement with the reported experimental data.

  11. Numerical method to determine mechanical parameters of engineering design in rock masses.

    PubMed

    Xue, Ting-He; Xiang, Yi-Qiang; Guo, Fa-Zhong

    2004-07-01

    This paper proposes a new continuity model for engineering in rock masses and a new schematic method for reporting the engineering of rock continuity. This method can be used to evaluate the mechanics of every kind of medium; and is a new way to determine the mechanical parameters used in engineering design in rock masses. In the numerical simulation, the experimental parameters of intact rock were combined with the structural properties of field rock. The experimental results for orthogonally-jointed rock are given. The results included the curves of the stress-strain relationship of some rock masses, the curve of the relationship between the dimension Delta and the uniaxial pressure-resistant strength sc of these rock masses, and pictures of the destructive procedure of some rock masses in uniaxial or triaxial tests, etc. Application of the method to engineering design in rock masses showed the potential of its application to engineering practice.

  12. Acoustic attenuation logging using centroid frequency shift and amplitude ratio methods: A numerical study

    SciTech Connect

    Quan, Y.; Harris, J.M.; Chen, X.

    1994-12-31

    The centroid frequency shift method is proposed to estimate seismic attenuation from full waveform acoustic logs. This approach along with the amplitude ratio method is applied to investigate the attenuation properties of the P head wave in fluid-filled boreholes. The generalized reflection and transmission coefficients method is used to perform forward modeling. The authors suggest an empirical formula to describe the frequency-dependent geometrical spreading of the P-wave in a borehole. They simulate a more realistic borehole by including a mudcake and an invaded zone which are modeled by a large number of radially symmetric thin layers. The numerical tests show that this invaded zone exhibits very strong influence on the attenuation measurement.

  13. Broken wires diagnosis method numerical simulation based on smart cable structure

    NASA Astrophysics Data System (ADS)

    Li, Sheng; Zhou, Min; Yang, Yan

    2014-12-01

    The smart cable with embedded distributed fiber optical Bragg grating (FBG) sensors was chosen as the object to study a new diagnosis method about broken wires of the bridge cable. The diagnosis strategy based on cable force and stress distribution state of steel wires was put forward. By establishing the bridge-cable and cable-steel wires model, the broken wires sample database was simulated numerically. A method of the characterization cable state pattern which can both represent the degree and location of broken wires inside a cable was put forward. The training and predicting results of the sample database by the back propagation (BP) neural network showed that the proposed broken wires diagnosis method was feasible and expanded the broken wires diagnosis research area by using the smart cable which was used to be only representing cable force.

  14. A rapid numerical method for horizontal fluid flow in unsaturated soils

    NASA Astrophysics Data System (ADS)

    Kirby, J. M.

    1984-06-01

    A rapid numerical method for the horizontal flow of water is presented, based on the approximation for conductivity k = k0 exp (αψ). A simple expression for the velocity of flow is obtained, which produces accurate solutions to horizontal infiltration problems even with very large time and length steps. The method is compared with previous solutions, including the much studied Yolo light clay infiltration problems. These examples are used to demonstrate the accuracy and economy (in terms of the time and necessary computer power) of the solution. The method is accurate for any choice of length step, provided that the time step is below a certain limit which is related to the length step. An expression for estimating the maximum permissible time step is presented and its use demonstrated via one of the examples.

  15. An integrated data-directed numerical method for estimating the undiscovered mineral endowment in a region

    USGS Publications Warehouse

    McCammon, R.B.; Finch, W.I.; Kork, J.O.; Bridges, N.J.

    1994-01-01

    An integrated data-directed numerical method has been developed to estimate the undiscovered mineral endowment within a given area. The method has been used to estimate the undiscovered uranium endowment in the San Juan Basin, New Mexico, U.S.A. The favorability of uranium concentration was evaluated in each of 2,068 cells defined within the Basin. Favorability was based on the correlated similarity of the geologic characteristics of each cell to the geologic characteristics of five area-related deposit models. Estimates of the undiscovered endowment for each cell were categorized according to deposit type, depth, and cutoff grade. The method can be applied to any mineral or energy commodity provided that the data collected reflect discovered endowment. ?? 1994 Oxford University Press.

  16. Numerical method for accessing the universal scaling function for a multiparticle discrete time asymmetric exclusion process.

    PubMed

    Chia, Nicholas; Bundschuh, Ralf

    2005-11-01

    In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz's original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N--> infinity) of a single-particle discrete time system, even in the case of very small system sizes (N< or =22). This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP. PMID:16383588

  17. Numerical analysis of an H1-Galerkin mixed finite element method for time fractional telegraph equation.

    PubMed

    Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

    2014-01-01

    We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.

  18. Numerical sedimentation particle-size analysis using the Discrete Element Method

    NASA Astrophysics Data System (ADS)

    Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.

    2015-12-01

    Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.

  19. An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

    NASA Astrophysics Data System (ADS)

    Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

    2015-03-01

    We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

  20. Keeping the edge: an accurate numerical method to solve the stream power law

    NASA Astrophysics Data System (ADS)

    Campforts, B.; Govers, G.

    2015-12-01

    Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.

  1. Numerical spherical aberration correction method using spatial light modulator under deep-part fluorescence observation

    NASA Astrophysics Data System (ADS)

    Takiguchi, Yu; Takamoto, Hisayoshi; Kanada, Masamitsu; Inoue, Takashi; Matsumoto, Naoya; Terakawa, Susumu

    2014-03-01

    We have developed a confocal fluorescence laser scanning microscopy (CFLSM) incorporating a liquid crystal on silicon spatial light modulator (LCOS-SLM). To achieve high-resolution and high-contrast imaging for deeper part of the tissue with CFLSM, high numerical aperture objective lenses are required to tightly focus excitation light to meet Rayleigh limit(criterion) for the specimens. However, mismatch of refractive index at the boundary of interfacing materials, such as atmosphere, glass cover, and biological tissues, causes spherical aberration. Recently, we proposed a numerical method for correcting spherical aberration. In this method a pre-distorted wavefront pattern for aberration correction is calculated by ray tracing from a hypothetical focal point inside a specimen to the pupil plane. The resulting microscope can correct such spherical aberration. We observed 6.0μm fluorescent micro-beads dispersed three-dimensionally in agarose gel to confirm effectiveness of aberration correction. We reconstructed a three-dimensional image by taking 20 images by changing the depth with 1 μm interval and stacking them. It was apparent that the longitudinal/depth resolution was improved and that the intensity of fluorescence image was increased with aberration correction. While this method is applicable to other laser scanning microscopes, it has potential to enhance the signals for various super-resolution microscopic techniques, such as stimulated- emission-depletion (STED) fluorescence microscopy.

  2. Numerical analysis of an H1-Galerkin mixed finite element method for time fractional telegraph equation.

    PubMed

    Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

    2014-01-01

    We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

  3. Numerical improvement of the three-dimensional indirect boundary element method

    NASA Astrophysics Data System (ADS)

    Ortiz-Aleman, C.; Gil-Zepeda, S. A.; Luzon, F.; Sanchez-Sesma, F. J.

    2003-04-01

    In recent years, several numerical techniques for the estimation of the seismic response in complex geologic configurations have been developed. The flexibility and versatility of these techniques have increased along with the improvement of computational systems, and they altogether have allowed the study of 3D geometries to model several sedimentary basins around the world. In this article we study the structure of the linear systems derived from the Indirect Boundary Element Method (IBEM). We apply a LU-sparse decomposition solver to the inversion of the IBEM coefficient matrix in order to optimise the numerical burden of such method. As pointed out before, special emphasis is given to understanding the main features of ground motion in sedimentary basins. We compute the seismic response of a 3D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzón (1995), and we establish comparisons on time consumption and memory allocation. Inversion of linear systems by using this new algorithm lead us to a significant saving on CPU time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.

  4. Computation of Nonlinear Backscattering Using a High-Order Numerical Method

    NASA Technical Reports Server (NTRS)

    Fibich, G.; Ilan, B.; Tsynkov, S.

    2001-01-01

    The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

  5. A numerical study of unsteady cavitation on a hydrofoil by LES and URANS method

    NASA Astrophysics Data System (ADS)

    Li, Zi-ru; Zhang, Guang-ming; He, Wei; van Terwisga, Tom

    2015-12-01

    In this paper, the unsteady cavitation phenomena on a NACA0015 hydrofoil is numerically simulated by unsteady Reynolds-Averaged Navier-Stokes (URANS) method and Large Eddy Simulation (LES) in single-fluid approaches to multiphase modelling, respectively. It is observed that the large-scale structures and characteristic periodic shedding predicted by the URANS with the modified SST k-ω turbulence model show a good qualitative match with the experimental observations but with quantitative discrepancies, such as a different cavity length and volume, and a different location of shedding. Compared to the URANS results, the LES results reproduce more details of unsteady dynamics with an improved quantitative agreement.

  6. A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

    NASA Technical Reports Server (NTRS)

    Radhakrishnan, K.

    1984-01-01

    The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.

  7. A new numerical method for the simulation of three dimensional flow in a pipe

    NASA Technical Reports Server (NTRS)

    Leonard, A.; Wray, A.

    1982-01-01

    A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction.

  8. Numerical study of human vocal folds vibration using Immersed Finite Element Method

    NASA Astrophysics Data System (ADS)

    Wang, Xingshi; Zhang, Lucy; Krane, Michael

    2011-11-01

    The voice production procedure is a self-oscillating, fluid-structure interaction problem. In this study, the vocal folds vibration during phonation will be simulated by self-oscillated layered-structure vocal folds model, using Immersed Finite Element Method. With the numerical results, we will find out the vocal folds vibration pattern, and also show how the lung pressure, stiffness and geometry of vocal folds will affect the vocal folds vibration. With further analysis, we shall get better understanding of the dynamics of voice production. National Institute on Deafness and Other Communication Disorders.

  9. Families of third and fourth algebraic order trigonometrically fitted symplectic methods for the numerical integration of Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

    2007-11-01

    The numerical integration of Hamiltonian systems by symplectic and trigonometrically fitted (TF) symplectic method is considered in this work. We construct new trigonometrically fitted symplectic methods of third and fourth order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis.

  10. Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods

    NASA Astrophysics Data System (ADS)

    Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard

    2013-04-01

    Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme

  11. Numerical and structural aberrations in advanced neuroblastoma tumours by CGH analysis; survival correlates with chromosome 17 status

    PubMed Central

    Cunsolo, C Lo; Bicocchi, M P; Petti, A R; Tonini, G P

    2000-01-01

    Rapid tumour progression in neuroblastoma is associated with MYCN amplification, deletion of the short arm of chromosome 1 and gain of 17q. However, patients with advanced disease without MYCN amplification and/or 1p deletion have a very poor outcome too, which suggests other genetic defects may predict an unfavourable prognosis. We employed CGH to study 22 tumours of patients at stages 3 and 4 over one year of age (6 and 16 cases respectively). Patients were divided in groups (A) long-term survivors and (B) short-term survivors. CGH showed a total of 226 chromosome imbalances (110 in group A and 116 in group B). The neuroblastoma cells of long-term survivors showed a preponderance of numerical aberrations (54%vs 43%); particularly gains of entire chromosomes 1 (P< 0.03), 7 (P< 0.04) and 19 (P< 0.05). An extra copy of 17 was detected in 6/8 (75%) samples of group A and only 1/14 (7%) samples of group B (P< 0.002). Conversely, tumours of patients who died from disease progression displayed a higher frequency of structural abnormalities (43%vs 35%), including loss of 1p, 9p, 11q, 15q and 18q and gain of 12q, although the difference was not significant (P= 0.24). Unbalanced gain of 17q was detected in 8/14 (57%) tumours of group B and only 1/8 (13%) tumours of group A (P< 0.05). The peculiar genetic difference observed in the tumours of long and short-term survivors may have prognostic relevance. © 2000 Cancer Research Campaign PMID:11044353

  12. Comparison of advanced distillation control methods. First annual report

    SciTech Connect

    1996-11-01

    A detailed dynamic simulator of a propylene/propane (C3) splitter, which was bench-marked against industrial data, has been used to compare dual composition control performance for a diagonal PI controller and several advanced controllers. The advanced controllers considered are DMC, nonlinear process model based control, and articial neutral networks. Each controller was tuned based upon setpoint changes in the overhead product composition using 50% changes in the impurity levels. Overall, there was not a great deal of difference in controller performance based upon the setpoint and disturbance tests. Periodic step changes in feed composition were also used to compare controller performance. In this case, oscillatory variations of the product composition were observed and the variabilities of the DMC and nonlinear process model based controllers were substantially smaller than that of the PI controller. The sensitivity of each controller to the frequency of the periodic step changes in feed composition was also investigated.

  13. Comparison of advanced distillation control methods. First annual report

    SciTech Connect

    Riggs, J.B.

    1996-11-01

    A detailed dynamic simulator of a propylene/propane (C{sub 3}) splitter, which was bench-marked against industrial data, has been used to compare dual composition control performance for a diagonal PI controller and several advanced controllers. The advanced controllers considered are dynamic matrix control (DMC), nonlinear process model based control, and artificial neutral networks. Each controller was tuned based upon setpoint changes in the overhead product composition using 50% changes in the impurity levels. Overall, there was not a great deal of difference in controller performance based upon the setpoint and disturbance tests. Periodic step changes in feed composition were also used to compare controller performance. In this case, oscillatory variations of the product composition were observed and the variabilities of the DC and nonlinear process model based controllers were substantially smaller than that of the PI controller. The sensitivity of each controller to the frequency of the periodic step changes in feed composition was also investigated.

  14. Conceptual frameworks and methods for advancing invasion ecology.

    PubMed

    Heger, Tina; Pahl, Anna T; Botta-Dukát, Zoltan; Gherardi, Francesca; Hoppe, Christina; Hoste, Ivan; Jax, Kurt; Lindström, Leena; Boets, Pieter; Haider, Sylvia; Kollmann, Johannes; Wittmann, Meike J; Jeschke, Jonathan M

    2013-09-01

    Invasion ecology has much advanced since its early beginnings. Nevertheless, explanation, prediction, and management of biological invasions remain difficult. We argue that progress in invasion research can be accelerated by, first, pointing out difficulties this field is currently facing and, second, looking for measures to overcome them. We see basic and applied research in invasion ecology confronted with difficulties arising from (A) societal issues, e.g., disparate perceptions of invasive species; (B) the peculiarity of the invasion process, e.g., its complexity and context dependency; and (C) the scientific methodology, e.g., imprecise hypotheses. To overcome these difficulties, we propose three key measures: (1) a checklist for definitions to encourage explicit definitions; (2) implementation of a hierarchy of hypotheses (HoH), where general hypotheses branch into specific and precisely testable hypotheses; and (3) platforms for improved communication. These measures may significantly increase conceptual clarity and enhance communication, thus advancing invasion ecology.

  15. Exploring biomolecular dynamics and interactions using advanced sampling methods

    NASA Astrophysics Data System (ADS)

    Luitz, Manuel; Bomblies, Rainer; Ostermeir, Katja; Zacharias, Martin

    2015-08-01

    Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

  16. Advanced Methods for Aircraft Engine Thrust and Noise Benefits: Nozzle-Inlet Flow Analysis

    NASA Technical Reports Server (NTRS)

    Gilinsky, Mikhail; Morgan, Morris H.; Povitsky, Alex; Schkolnikov, Natalia; Njoroge, Norman; Coston, Calvin; Blankson, Isaiah M.

    2001-01-01

    The Fluid Mechanics and Acoustics Laboratory at Hampton University (HU/FM&AL) jointly with the NASA Glenn Research Center has conducted four connected subprojects under the reporting project. Basically, the HU/FM&AL Team has been involved in joint research with the purpose of theoretical explanation of experimental facts and creation of accurate numerical simulation techniques and prediction theory for solution of current problems in propulsion systems of interest to the NAVY and NASA agencies. This work is also supported by joint research between the NASA GRC and the Institute of Mechanics at Moscow State University (IM/MSU) in Russia under a CRDF grant. The research is focused on a wide regime of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analyses for advanced aircraft and rocket engines. The FM&AL Team uses analytical methods, numerical simulations and possible experimental tests at the Hampton University campus. The fundamental idea uniting these subprojects is to use nontraditional 3D corrugated and composite nozzle and inlet designs and additional methods for exhaust jet noise reduction without essential thrust loss and even with thrust augmentation. These subprojects are: (1) Aeroperformance and acoustics of Bluebell-shaped and Telescope-shaped designs; (2) An analysis of sharp-edged nozzle exit designs for effective fuel injection into the flow stream in air-breathing engines: triangular-round, diamond-round and other nozzles; (3) Measurement technique improvement for the HU Low Speed Wind Tunnel; a new course in the field of aerodynamics, teaching and training of HU students; experimental tests of Mobius-shaped screws: research and training; (4) Supersonic inlet shape optimization. The main outcomes during this reporting period are: (l) Publications: The AIAA Paper #00-3170 was presented at the 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 17-19 June, 2000, Huntsville, AL. The AIAA

  17. Training toward Advanced 3D Seismic Methods for CO2 Monitoring, Verification, and Accounting

    SciTech Connect

    Christopher Liner

    2012-05-31

    The objective of our work is graduate and undergraduate student training related to improved 3D seismic technology that addresses key challenges related to monitoring movement and containment of CO{sub 2}, specifically better quantification and sensitivity for mapping of caprock integrity, fractures, and other potential leakage pathways. We utilize data and results developed through previous DOE-funded CO{sub 2} characterization project (DE-FG26-06NT42734) at the Dickman Field of Ness County, KS. Dickman is a type locality for the geology that will be encountered for CO{sub 2} sequestration projects from northern Oklahoma across the U.S. midcontinent to Indiana and Illinois. Since its discovery in 1962, the Dickman Field has produced about 1.7 million barrels of oil from porous Mississippian carbonates with a small structural closure at about 4400 ft drilling depth. Project data includes 3.3 square miles of 3D seismic data, 142 wells, with log, some core, and oil/water production data available. Only two wells penetrate the deep saline aquifer. In a previous DOE-funded project, geological and seismic data were integrated to create a geological property model and a flow simulation grid. We believe that sequestration of CO{sub 2} will largely occur in areas of relatively flat geology and simple near surface, similar to Dickman. The challenge is not complex geology, but development of improved, lower-cost methods for detecting natural fractures and subtle faults. Our project used numerical simulation to test methods of gathering multicomponent, full azimuth data ideal for this purpose. Our specific objectives were to apply advanced seismic methods to aide in quantifying reservoir properties and lateral continuity of CO{sub 2} sequestration targets. The purpose of the current project is graduate and undergraduate student training related to improved 3D seismic technology that addresses key challenges related to monitoring movement and containment of CO{sub 2

  18. A numerical method for the calibration of in situ gamma ray spectroscopy systems.

    PubMed

    Dewey, S C; Whetstone, Z D; Kearfott, K J

    2010-05-01

    High purity germanium in situ gamma ray spectroscopy systems are typically calibrated using pre-calculated tables and empirical formulas to estimate the response of a detector to an exponentially distributed source in a soil matrix. Although this method is effective, it has estimated uncertainties of 10-15%, is limited to only a restricted set of measurement scenarios, and the approach only applies to an exponentially distributed source. In addition, the only soil parameters that can be varied are density and moisture content, while soil attenuation properties are fixed. This paper presents a more flexible method for performing such calibrations. For this new method, a three- or four-dimensional analytical expression is derived that is a combination of a theoretical equation and experimentally measured data. Numerical methods are used to integrate this expression, which approximates the response of a detector to a large variety of source distributions within any soil, concrete, or other matrix. The calculation method is flexible enough to allow for the variation of multiple parameters, including media attenuation properties and the measurement geometry. The method could easily be adapted to horizontally non-uniform sources as well. Detector responses are calculated analytically and Monte Carlo radiation transport simulations are used to verify the results. Results indicate that the method adds an uncertainty of only approximately 5% to the other uncertainties typically associated with the calibration of a detector system. PMID:20386196

  19. Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

    SciTech Connect

    Cobb, J.W.

    1995-02-01

    There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

  20. Methods and Applications for Advancing Distance Education Technologies: International Issues and Solutions

    ERIC Educational Resources Information Center

    Syed, Mahbubur Rahman, Ed.

    2009-01-01

    The emerging field of advanced distance education delivers academic courses across time and distance, allowing educators and students to participate in a convenient learning method. "Methods and Applications for Advancing Distance Education Technologies: International Issues and Solutions" demonstrates communication technologies, intelligent…