Advanced numerical methods in mesh generation and mesh adaptation
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
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.
Advanced numerical methods and software approaches for semiconductor device simulation
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.
Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation
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
2011-07-28
nonequilibrium. For example, the plasma transport may transition between rarefied and continuum flow , requiring appropriate models for each case through...AFRL-AFOSR-UK-TR-2011-0023 Advanced Physical Models and Numerical Methods for High Enthalpy and Plasma Flows Applied to Hypersonics...2010 4. TITLE AND SUBTITLE Advanced Physical Models and Numerical Methods for High Enthalpy and Plasma Flows Applied to Hypersonics 5a
Advanced Numerical Methods for Computing Statistical Quantities of Interest
2014-07-10
coefficients , forcing terms, and initial conditions was analyzed. The input data were assumed to depend on a finite number of random variables . Unlike...89, 2012, 1269-1280. We considered the Musiela equation of forward rates; this is a hyperbolic stochastic partial differential equation . A weak...ZHANG AND M. GUNZBURGER, Error analysis of stochastic collocation method for parabolic partial differential equations with random input data; SIAM Journal
Borazjani, Iman; Westerdale, John; McMahon, Eileen M; Rajaraman, Prathish K; Heys, Jeffrey J; Belohlavek, Marek
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.
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
Advanced Numerical methods for F. E. Simulation of Metal Forming Processes
NASA Astrophysics Data System (ADS)
Chenot, Jean-Loup; Bernacki, Marc; Fourment, Lionel; Ducloux, Richard
2010-06-01
The classical scientific basis for finite element modeling of metal forming processes is first recalled. Several developments in advanced topics are summarized: adaptive and anisotropic remeshing, parallel solving, multi material deformation. More recent researches in numerical analysis are outlined, including multi grid and multi mesh methods, mainly devoted to decrease computation time, automatic optimization method for faster and more effective design of forming processes. The link of forming simulation and structural computations is considered with emphasis on the necessity to predict the final mechanical properties. Finally a brief account of computation at the micro scale level is given.
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
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.
Advanced numerical methods for three dimensional two-phase flow calculations
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.
Recent advances in methods for numerical solution of O.D.E. initial value problems
NASA Technical Reports Server (NTRS)
Bui, T. D.; Oppenheim, A. K.; Pratt, D. T.
1984-01-01
In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.
Advanced Numerical Methods for Computing Statistical Quantities of Interest from Solutions of SPDES
2012-01-19
and tested our method. Figure 1 presents a comparison of the solution of (5) obtained by a Monte- Carlo method and that of (6) using a stochastic...2 0 .3 0 .4 0.4 0.4 0.5 0 .5 0 .6 0 .6 0.6 0.6 0 .7 0.70 .7 0 .8 0.8 0 .9 x y Isotherms, Monte Carlo method, number of samples=200 0 0.2 0.4 0.6 0.8 0...of the solution of (5) obtained by a Monte- Carlo method (top) and that of (6) using a stochastic collocation method with fewer samples (bottom
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Weizhong; Yoshida, Hiroyuki; Ose, Yasuo; Ohnuki, Akira; Akimoto, Hajime; Hotta, Akitoshi; Fujimura, Ken
In relation to the design of an innovative FLexible-fuel-cycle Water Reactor (FLWR), investigation of thermal-hydraulic performance in tight-lattice rod bundles of the FLWR is being carried out at Japan Atomic Energy Agency (JAEA). The FLWR core adopts a tight triangular lattice arrangement with about 1 mm gap clearance between adjacent fuel rods. In view of importance of accurate prediction of cross flow between subchannels in the evaluation of the boiling transition (BT) in the FLWR core, this study presents a statistical evaluation of numerical simulation results obtained by a detailed two-phase flow simulation code, TPFIT, which employs an advanced interface tracking method. In order to clarify mechanisms of cross flow in such tight lattice rod bundles, the TPFIT is applied to simulate water-steam two-phase flow in two modeled subchannels. Attention is focused on instantaneous fluctuation characteristics of cross flow. With the calculation of correlation coefficients between differential pressure and gas/liquid mixing coefficients, time scales of cross flow are evaluated, and effects of mixing section length, flow pattern and gap spacing on correlation coefficients are investigated. Differences in mechanism between gas and liquid cross flows are pointed out.
Recent advances in numerical PDEs
NASA Astrophysics Data System (ADS)
Zuev, Julia Michelle
In this thesis, we investigate four neighboring topics, all in the general area of numerical methods for solving Partial Differential Equations (PDEs). Topic 1. Radial Basis Functions (RBF) are widely used for multi-dimensional interpolation of scattered data. This methodology offers smooth and accurate interpolants, which can be further refined, if necessary, by clustering nodes in select areas. We show, however, that local refinements with RBF (in a constant shape parameter [varepsilon] regime) may lead to the oscillatory errors associated with the Runge phenomenon (RP). RP is best known in the case of high-order polynomial interpolation, where its effects can be accurately predicted via Lebesgue constant L (which is based solely on the node distribution). We study the RP and the applicability of Lebesgue constant (as well as other error measures) in RBF interpolation. Mainly, we allow for a spatially variable shape parameter, and demonstrate how it can be used to suppress RP-like edge effects and to improve the overall stability and accuracy. Topic 2. Although not as versatile as RBFs, cubic splines are useful for interpolating grid-based data. In 2-D, we consider a patch representation via Hermite basis functions s i,j ( u, v ) = [Special characters omitted.] h mn H m ( u ) H n ( v ), as opposed to the standard bicubic representation. Stitching requirements for the rectangular non-equispaced grid yield a 2-D tridiagonal linear system AX = B, where X represents the unknown first derivatives. We discover that the standard methods for solving this NxM system do not take advantage of the spline-specific format of the matrix B. We develop an alternative approach using this specialization of the RHS, which allows us to pre-compute coefficients only once, instead of N times. MATLAB implementation of our fast 2-D cubic spline algorithm is provided. We confirm analytically and numerically that for large N ( N > 200), our method is at least 3 times faster than the
Introduction to Numerical Methods
Schoonover, Joseph A.
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
Kollias, Pavlos
2016-09-06
This the final report for the DE-SC0007096 - Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales - PI: Pavlos Kollias. The final report outline the main findings of the research conducted using the aforementioned award in the area of cloud research from the cloud scale (10-100 m) to the mesoscale (20-50 km).
Numerical methods for turbulent flow
NASA Technical Reports Server (NTRS)
Turner, James C., Jr.
1988-01-01
It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.
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
NASA Astrophysics Data System (ADS)
Mehrmann, Volker; Xu, Hongguo
2000-11-01
We study classical control problems like pole assignment, stabilization, linear quadratic control and H[infinity] control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.
Advanced Usability Evaluation Methods
2007-04-01
tracking in usability evaluation : A practitioner’s guide. In J. Hyönä, R. Radach, & H. Deubel. (Eds.), The mind’s eye: Cognitive and applied...Advanced Usability Evaluation Methods Terence S. Andre, Lt Col, USAF Margaret Schurig, Human Factors Design Specialist, The Boeing Co...TITLE AND SUBTITLE Advanced Usability Evaluation Methods 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT
A numerical method of regenerator
NASA Astrophysics Data System (ADS)
Zhu, Shaowei; Matsubara, Yoichi
2004-02-01
A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.
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.
Numerical relativity and spectral methods
NASA Astrophysics Data System (ADS)
Grandclement, P.
2016-12-01
The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.
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.
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.
Spectral Methods for Numerical Relativity.
Grandclément, Philippe; Novak, Jérôme
2009-01-01
Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.
Numerical methods used in fusion science numerical modeling
NASA Astrophysics Data System (ADS)
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
RELAP-7 Numerical Stabilization: Entropy Viscosity Method
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.
Advanced Numerical Model for Irradiated Concrete
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
Numerical analysis of the V-Y shaped advancement flap.
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.
Implicit Numerical Methods in Meteorology
NASA Technical Reports Server (NTRS)
Augenbaum, J.
1984-01-01
The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.
Numerical Methods For Chemically Reacting Flows
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1990-01-01
Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.
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.
Perception of numerical methods in rarefied gasdynamics
NASA Technical Reports Server (NTRS)
Bird, G. A.
1989-01-01
The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.
Advances in Adaptive Control Methods
NASA Technical Reports Server (NTRS)
Nguyen, Nhan
2009-01-01
This poster presentation describes recent advances in adaptive control technology developed by NASA. Optimal Control Modification is a novel adaptive law that can improve performance and robustness of adaptive control systems. A new technique has been developed to provide an analytical method for computing time delay stability margin for adaptive control systems.
Editorial: biotech methods and advances.
Jungbauer, Alois
2013-01-01
This annual Methods and Advances Special Issue of Biotechnology Journal contains a selection of cutting-edge research and review articles with a particular emphasis on vertical process understanding – read more in this editorial by Prof. Alois Jungbauer, BTJ co-Editor-in-Chief.
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.
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.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
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.
Numerical Methods for Nonlinear Hillslope Transport Laws
NASA Astrophysics Data System (ADS)
Perron, J. T.
2008-12-01
The numerical methods used to solve nonlinear sediment transport equations often set restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Standard explicit finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. Methods that rely on cell-to-cell sediment routing schemes can introduce significant errors that may not be obvious unless the numerical solution is compared with a known solution. I present a new, implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport but avoids the use of a cell-to-cell sediment routing scheme. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the new method retains the accuracy of the explicit method while allowing timesteps several orders of magnitude longer than the maximum timesteps permitted by the explicit method. The method can be adapted to any transport law in which the expression for sediment flux is differentiable, including coupled systems in which sediment flux is a function of quantities such as soil depth.
Numerical Methods for Initial Value Problems.
1980-07-01
of general multistep methods for ordinary differential equations a4 to implement an efficient algorithm for the solution of stiff equations . Still...integral equations II. Roundoff error for variants of Gaussian elimination III. Multistep methods for ordinary differential equations IV. Multi-grid...62 -! Paige III. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS ....... 63 1. Equivalent Forms of Multistep
Numerical methods for nonlinear hillslope transport laws
NASA Astrophysics Data System (ADS)
Perron, J. Taylor
2011-06-01
The numerical methods used to solve nonlinear sediment transport equations often set very restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Explicit-time finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. I present an implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport and improves stability and accuracy by avoiding the direct calculation of sediment flux. This method can be adapted to any transport law in which the expression for sediment flux is differentiable. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the implicit method retains the accuracy of a standard explicit method while permitting time steps several orders of magnitude longer than the maximum stable time step for the explicit method. The ability to take long time steps affords a substantial savings in overall computation time, despite the implicit method's higher per-iteration computational cost. Implicit models for hillslope evolution also offer a distinct advantage when modeling the response of hillslopes to incising channels.
Numerical comparison between DHF and RHF methods
NASA Astrophysics Data System (ADS)
Kobus, J.; Jaskolski, W.
1987-10-01
A detailed numerical comparison of the Dirac-Hartree-Fock method and the relativistic Hartree-Fock (RHF) method of Cowan and Griffith (1976) is presented, considering the total energy, the orbital energies, and the one-electron and two-electron integrals. The RHF method is found to yield accurate values of the relativistic transition energies. Using accurate values of the correlation corrections for p-electron and d-electron systems, the usefulness of the RHF method in obtaining relativistic corrections to the differential term energies is demonstrated. Advantages of the method for positron scattering on heavy systems are also pointed out.
Recent advances in two-phase flow numerics
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.
Numerical Methods through Open-Ended Projects
ERIC Educational Resources Information Center
Cline, Kelly S.
2005-01-01
We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…
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.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
Numerical Design of Drawbeads for Advanced High Strength Steel Sheets
NASA Astrophysics Data System (ADS)
Keum, Y. T.; Kim, D. J.; Kim, G. S.
2010-06-01
The map for designing the drawbeads used in the stamping dies for advanced high strength steel (AHSS) sheets is numerically investigated and its application is introduced. The bending limit of AHSS sheet is determined from the extreme R/t's obtained simulating numerically the plane-strain process formed by the cylindrical punches and dies with various radii. In addition, the forming allowance defined by the difference between FLC0 and the strain after passing the drawbead, which is observed by the numerical simulation of drawbead pulling test, is computed. Based on the bending limit and forming allowance, the design map for determining the height, width, and shoulder radius of the drawbead which are key parameters in the drawbead design and depend on the restraining force is constructed by aid of the equivalent drawbead model. A drawbead of the stamping die for forming a channel-typed panel is designed by using the design map, and the formability and springback of the panel to be formed are numerically evaluated, from which the availability of the design map is demonstrated.
Recent advances to NEC (Numerical Electromagnetics Code): Applications and validation
Burke, G.J. )
1989-03-03
Capabilities of the antenna modeling code NEC are reviewed and results are presented to illustrate typical applications. Recent developments are discussed that will improve accuracy in modeling electrically small antennas, stepped-radius wires and junctions of tightly coupled wires, and also a new capability for modeling insulated wires in air or earth is described. These advances will be included in a future release of NEC, while for now the results serve to illustrate limitations of the present code. NEC results are compared with independent analytical and numerical solutions and measurements to validate the model for wires near ground and for insulated wires. 41 refs., 26 figs., 1 tab.
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.
A numerical method to model excitable cells.
Joyner, R W; Westerfield, M; Moore, J W; Stockbridge, N
1978-01-01
We have extended a fast, stable, and accurate method for the numerical solution of cable equations to include changes in geometry and membrane properties in order to model a single excitable cell realistically. In addition, by including the provision that the radius may be a function of distance along an axis, we have achieved a general and powerful method for simulating a cell with any number of branched processes, any or all of which may be nonuniform in diameter, and with no restriction on the branching pattern. PMID:656539
Advanced numerical analyses for complex thermal-hydraulics in nuclear engineering
Seiichi Koshizuka; Yoshiaki Oka
2002-07-01
Complex thermal-hydraulic phenomena in the nuclear engineering have been solved by advanced numerical analyses based on fundamental governing equations excluding experimental correlations. A new method, called Moving Particle Semi-implicit (MPS) method, is developed as one of the advanced methods. Governing equations are discretized to particle dynamics using particle interaction models. Grids are not necessary. Therefore, complex motion of interfaces can be calculated without grid tangling or numerical diffusion. This is advantageous to multi-fluid and multi-phase thermal-hydraulic problems which emerge in the nuclear engineering. The analyzed problems are vapor explosions, molten core-concrete interaction, fluid-structure interaction, nucleate boiling, transient boiling at reactivity initiated accidents, and the critical Weber number for droplet breakup. These examples show that the MPS method is being useful for direct simulation of complex thermal-hydraulics, particularly multi-phase flows, in the nuclear engineering. (authors)
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.
Advanced numerics for multi-dimensional fluid flow calculations
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.
Efficient numerical methods for nonlinear Schrodinger equations
NASA Astrophysics Data System (ADS)
Liang, Xiao
The nonlinear Schrodinger equations are widely used to model a number of important physical phenomena, including solitary wave propagations in optical fibers, deep water turbulence, laser beam transmissions, and the Bose-Einstein condensation, just to mention a few. In the field of optics and photonics, the systems of nonlinear Schrodinger equations can be used to model multi-component solitons and the interaction of self-focusing laser beams. In three spatial dimensions, the nonlinear Schrodinger equation is known as the Gross-Pitaevskii equation, which models the soliton in a low-cost graded-index fiber. Recently, research on nonlinear space fractional Schrodinger equations, which capture the self-similarity in the fractional environment, has become prevalent. Our study includes the systems of multi-dimensional nonlinear space fractional Schrodinger equations. To solve the systems of multi-dimensional nonlinear Schrodinger equations efficiently, several novel numerical methods are presented. The central difference and quartic spline approximation based exponential time differencing Crank-Nicolson method is introduced for solving systems of one- and two-dimensional nonlinear Schrodinger equations. A local extrapolation is employed to achieve fourth-order accuracy in time. The numerical examples include the transmission of a self-focusing laser beam. The local discontinuous Galerkin methods combined with the fourth-order exponential time differencing Runge-Kutta time discretization are studied for solving the systems of nonlinear Schrodinger equations with hyperbolic terms, which are critical in modeling optical solitons in the birefringent fibers. The local discontinuous Galerkin method is able to achieve any order of accuracy in space, thanks to the usage of piecewise polynomial spaces. The exponential time differencing methods are employed to deal with the coupled nonlinearities for the reason that there is no need to solve nonlinear systems at every time step
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.
Linearized Implicit Numerical Method for Burgers' Equation
NASA Astrophysics Data System (ADS)
Mukundan, Vijitha; Awasthi, Ashish
2016-12-01
In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers' equation. The Burgers' equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.
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.
Automatic numerical integration methods for Feynman integrals through 3-loop
NASA Astrophysics Data System (ADS)
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.
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.
Mathematica with a Numerical Methods Course
NASA Astrophysics Data System (ADS)
Varley, Rodney
2003-04-01
An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.
Homogenization and Numerical Methods for Hyperbolic Equations
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo
1990-01-01
This dissertation studies three aspects of analysis and numerical methods for partial differential equations with oscillatory solutions. 1. Homogenization theory for certain linear hyperbolic equations is developed. We derive the homogenized convection equations for linear convection problems with rapidly varying velocity in space and time. We find that the oscillatory solutions are very sensitive to the arithmetic properties of certain parameters, such as the corresponding rotation number and the ratio between the components of the mean velocity field in linear convection. We also show that the oscillatory velocity field in two dimensional incompressible flow behaves like shear flows. 2. The homogenization of scalar nonlinear conservation laws in several space variables with oscillatory initial data is also discussed. We prove that the initial oscillations will be eliminated for any positive time when the equations are non-degenerate. This is also true for degenerate equations if there is enough mixing among the initial oscillations in the degenerate direction. Otherwise, the initial oscillation, for which the homogenized equation is obtained, will survive and be propagated. The large-time behavior of conservation laws with several space variables is studied. We show that, under a new nondegenerate condition (the second derivatives of the flux functions are linearly independent in any interval), a piecewise smooth periodic solution with converge strongly to the mean value of initial data. This generalizes Glimm and Lax's result for the one dimensional problem (3). 3. Numerical simulations of the oscillatory solutions are also carried out. We give some error estimate for varepsilon-h resonance ( varepsilon: oscillation wave length, h: numerical step) and prove essential convergence (24) of order alpha < 1 for some numerical schemes. These include upwind schemes and particle methods for linear hyperbolic equations with oscillatory coefficients. A stochastic analysis
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
Advanced three-dimensional dynamic analysis by boundary element methods
NASA Technical Reports Server (NTRS)
Banerjee, P. K.; Ahma, S.
1985-01-01
Advanced formulations of boundary element method for periodic, transient transform domain and transient time domain solution of three-dimensional solids have been implemented using a family of isoparametric boundary elements. The necessary numerical integration techniques as well as the various solution algorithms are described. The developed analysis has been incorporated in a fully general purpose computer program BEST3D which can handle up to 10 subregions. A number of numerical examples are presented to demonstrate the accuracy of the dynamic analyses.
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
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
Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.
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.
Numerical optimization design of advanced transonic wing configurations
NASA Technical Reports Server (NTRS)
Cosentino, G. B.; Holst, T. L.
1985-01-01
A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure disributions and drag-to-lift ratio minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.
Numerical optimization design of advanced transonic wing configurations
NASA Technical Reports Server (NTRS)
Cosentino, G. B.; Holst, T. L.
1984-01-01
A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
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.
Advanced method for oligonucleotide deprotection
Surzhikov, Sergey A.; Timofeev, Edward N.; Chernov, Boris K.; Golova, Julia B.; Mirzabekov, Andrei D.
2000-01-01
A new procedure for rapid deprotection of synthetic oligodeoxynucleotides has been developed. While all known deprotection methods require purification to remove the residual protective groups (e.g. benzamide) and insoluble silicates, the new procedure based on the use of an ammonia-free reagent mixture allows one to avoid the additional purification steps. The method can be applied to deprotect the oligodeoxynucleotides synthesized by using the standard protected nucleoside phosphoramidites dGiBu, dCBz and dABz. PMID:10734206
Advanced Fine Particulate Characterization Methods
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
Recent advances in lattice Boltzmann methods
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.
Advances in the numerical investigation of the immersion quenching process
NASA Astrophysics Data System (ADS)
Zhang, D. S.; Kopun, R.; Kosir, N.; Edelbauer, W.
2017-01-01
A numerical investigation of the immersion quenching process is presented in this paper. Immersion quenching is recognized as one of the common ways to achieve the desirable microstructure, and to improve the mechanical properties after thermal treatment. Furthermore it is important to prevent distortion and cracking of the cast parts. Accurate prediction of all three boiling regimes and the heat transfer inside the structure during quenching are important to finally evaluate the residual stresses and deformations of thermally treated parts. Numerical details focus on the handling of the enthalpy with variable specific heat capacity in the solid. For two application cases, comparison between measured and simulated temperatures at different monitoring positions shows very good agreement. The study demonstrates the capability of the present model to overcome the numerical challenges occurring during immersion quenching and it is capable of predicting the complex physics with good accuracy.
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…
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
uncertainty quantification. In the last decade much progress has been made in the construction of numerical algorithms to efficiently solve SPDES with...applicable SPDES with efficient numerical methods. This project is intended to address the numerical analysis as well as algorithm aspects of SPDES. Three...differential equations. Our work contains algorithm constructions, rigorous error analysis, and extensive numerical experiments to demonstrate our algorithm
A Hybrid Numerical Analysis Method for Structural Health Monitoring
NASA Technical Reports Server (NTRS)
Forth, Scott C.; Staroselsky, Alexander
2001-01-01
A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.
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.
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.
Validation Testing and Numerical Modeling of Advanced Armor Materials
2012-11-01
constitutive material strength response with an appropriate yield surface model. The research is sub-divided into three areas: engineering design...and specimen preparation for Taylor impact testing, analytical solution for the dynamic yield strength of the materials used, and numerical modeling...aluminum alloy only. We perform a detailed analysis of the deformed specimen shapes to determine the dynamic yield strength . Additionally, hydrocode
Numerical analysis of the orthogonal descent method
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.
Numerical methods for reduction of topside ionograms
NASA Technical Reports Server (NTRS)
Mcculley, L.
1972-01-01
Several alternative methods for solving the group height equation are presented. Three of these are now in operation at Ames Research Center and use data contained in a single ionogram trace. From the data an electron density profile N(h) is computed. If the ionogram also exhibits other traces, reverse ionogram traces are computed, using the N(h) profile, for comparison with the redundant data. When agreement is poor, the initial data trace is reinterpreted, another N(h) profile computed, and the reverse traces generated once again. This process is repeated until a desired degree of consistency is achieved. To reduce the necessity for human intervention and eliminate decision making required in conjunction with the preceding methods, a method is proposed that accepts as input, all data from a single ionogram. In general, no electron density function will satisfy these data exactly, but a best N(h) profile can be computed. Finally, a method is described that eliminates the need to assume that the ionosphere is spherically stratified. Horizontal gradients in electron density are detected and accounted for by processing several ionograms from the same satellite pass simultaneously. This idea is derived as an extension of one of the basic methods.
NASA Technical Reports Server (NTRS)
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
Simultaneous source-mask optimization: a numerical combining method
NASA Astrophysics Data System (ADS)
Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.
2010-09-01
A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.
Advances and Challenges in Numerical Weather and Climate Prediction
NASA Astrophysics Data System (ADS)
Yu, Tsann-Wang
2010-10-01
In this review article, the dispersive nature of various waves that exist in the atmosphere is first reviewed. These waves include Rossby waves, Kelvin wave, acoustic wave, internal and external gravity waves and many others, whose intrinsic nature and great relevancy to weather and climate forecasts are described. This paper then describes the latest development in global observations and data analysis and assimilation methodologies. These include three-dimensional and four dimensional variational data assimilation systems that are being used in the world's major operational weather and climate forecasting centers. Some of the recent results in using novel atmospheric satellite and chemical observation data applied to these data assimilation systems and those from the latest development in high resolution modeling and the ensemble forecasting approach in the operational numerical weather forecasting centers are also presented. Finally, problems of inherent errors associated with initial conditions, and those associated with the coupling of dynamics and physics and their related numerical issues in variational data assimilation systems are discussed.
Numerical Methods Using B-Splines
NASA Technical Reports Server (NTRS)
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Modelling asteroid brightness variations. I - Numerical methods
NASA Technical Reports Server (NTRS)
Karttunen, H.
1989-01-01
A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.
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
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
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1988-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.
Efficient Numerical Methods for Stable Distributions
2007-11-02
0 and cutoffs c1 = −128 and c2 = +127 are used, corresponding to the common values used in digital signal processing. Five new functions for discrete...variables using the Chambers- Mallows - Stuck method, rounding them to the nearest integer, and then cutting off if the value is too high or too low...within the common matlab environment they use. We comment briefly on the commercialization of this in the last section. 3 -100 -50 0 50 100 0. 0 0. 01 0
Numerical methods for hypersonic boundary layer stability
NASA Technical Reports Server (NTRS)
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Advanced radioactive waste assay methods: Final report
Cline, J.E.; Robertson, D.E.; DeGroot, S.E.
1987-11-01
This report describes an evaluation of advanced methodologies for the radioassay of low power-plant low-level radioactive waste for compliance with the 10CFR61 classification rules. The project evaluated current assay practices in ten operating plants and identified areas where advanced methods would apply, studied two direct-assay methodologies, demonstrated these two techniques on radwaste in four operating plants and on irradiated components in two plants, and developed techniques for obtaining small representative aliquots from larger samples and for enhancing the /sup 144/Ce activity analysis in samples of waste. The study demonstrated the accuracy, practicality, and ALARA aspects of advanced methods and indicates that cost savings, resulting from the accuracy improvement and reduction in sampling requirements can be significant. 24 refs., 60 figs., 67 tabs.
Advanced analysis methods in particle physics
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.
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.
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.
A Numerical Methods Course Based on B-Learning: Integrated Learning Design and Follow Up
ERIC Educational Resources Information Center
Cepeda, Francisco Javier Delgado
2013-01-01
Information and communication technologies advance continuously, providing a real support for learning processes. Learning technologies address areas which previously have corresponded to face-to-face learning, while mobile resources are having a growing impact on education. Numerical Methods is a discipline and profession based on technology. In…
A numerical method for vortex sheet roll-up
NASA Technical Reports Server (NTRS)
Krasny, R.
1986-01-01
The problem of computing vortex sheet roll-up from periodic analytic initial data is studied. Previous theoretical and numerical work is reviewed. Computational difficulties arising from ill posedness and singularity formation are discussed. A desingularization method is proposed to diminish these difficulties. Computations indicate that this approach converges past the time at which previous numerical investigations have failed to converge.
Numerical Simulation of Turbulent Flames using Vortex Methods.
1987-10-05
layer," Phys. Fluids , 30, pp. 706-721, 1987. (11) Ghoniem, A.F., and Knio, O.M., "Numerical Simulation of Flame Propagation in Constant Volume Chambers...1985. 4. "Numerical solution of a confined shear layer using vortex methods," The International Symposium on Computational Fluid Dynamics, Tokyo...Symposium on Computational Fluid Dynamics, Tokyo, Japan, September 1985. 8. "Application of Computational Methods in Turbulent Reacting Flow
Editorial: Latest methods and advances in biotechnology.
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.
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.
Numerical design of advanced multi-element airfoils
NASA Technical Reports Server (NTRS)
Mathias, Donovan L.; Cummings, Russell M.
1994-01-01
The current study extends the application of computational fluid dynamics to three-dimensional high-lift systems. Structured, overset grids are used in conjunction with an incompressible Navier-Stokes flow solver to investigate flow over a two-element high-lift configuration. The computations were run in a fully turbulent mode using the one-equation Baldwin-Barth turbulence model. The geometry consisted of an unswept wing which spanned a wind tunnel test section. Flows over full and half-span Fowler flap configurations were computed. Grid resolution issues were investigated in two dimensional studies of the flapped airfoil. Results of the full-span flap wing agreed well with experimental data and verified the method. Flow over the wing with the half-span was computed to investigate the details of the flow at the free edge of the flap. The results illustrated changes in flow streamlines, separation locations, and surface pressures due to the vortex shed from the flap edge.
A numerical method for phase-change problems
NASA Technical Reports Server (NTRS)
Kim, Charn-Jung; Kaviany, Massoud
1990-01-01
A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.
Simulation methods for advanced scientific computing
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.
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.
Advances in Geometric Acoustic Propagation Modeling Methods
NASA Astrophysics Data System (ADS)
Blom, P. S.; Arrowsmith, S.
2013-12-01
Geometric acoustics provides an efficient numerical method to model propagation effects. At leading order, one can identify ensonified regions and calculate celerities of the predicted arrivals. Beyond leading order, the solution of the transport equation provides a means to estimate the amplitude of individual acoustic phases. The auxiliary parameters introduced in solving the transport equation have been found to provide a means of identifying ray paths connecting source and receiver, or eigenrays, for non-planar propagation. A detailed explanation of the eigenray method will be presented as well as an application to predicting azimuth deviations for infrasonic data recorded during the Humming Roadrunner experiment of 2012.
Numerical methods for solving ODEs on the infinity computer
NASA Astrophysics Data System (ADS)
Mazzia, F.; Sergeyev, Ya. D.; Iavernaro, F.; Amodio, P.; Mukhametzhanov, M. S.
2016-10-01
New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial conditions are proposed. They are designed for working on a new kind of a supercomputer - the Infinity Computer - that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods are able to work with the exact values of the derivatives, instead of their approximations. Within this context, variants of one-step multi-point methods closely related to the classical Taylor formulae and to the Obrechkoff methods are considered. To get numerical evidence of the theoretical results, test problems are solved by means of the new methods and the results compared with the performance of classical methods.
Advanced Methods in Black-Hole Perturbation Theory
NASA Astrophysics Data System (ADS)
Pani, Paolo
2013-09-01
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved space-time. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.
An advanced Gibbs-Duhem integration method: theory and applications.
van 't Hof, A; Peters, C J; de Leeuw, S W
2006-02-07
The conventional Gibbs-Duhem integration method is very convenient for the prediction of phase equilibria of both pure components and mixtures. However, it turns out to be inefficient. The method requires a number of lengthy simulations to predict the state conditions at which phase coexistence occurs. This number is not known from the outset of the numerical integration process. Furthermore, the molecular configurations generated during the simulations are merely used to predict the coexistence condition and not the liquid- and vapor-phase densities and mole fractions at coexistence. In this publication, an advanced Gibbs-Duhem integration method is presented that overcomes above-mentioned disadvantage and inefficiency. The advanced method is a combination of Gibbs-Duhem integration and multiple-histogram reweighting. Application of multiple-histogram reweighting enables the substitution of the unknown number of simulations by a fixed and predetermined number. The advanced method has a retroactive nature; a current simulation improves the predictions of previously computed coexistence points as well. The advanced Gibbs-Duhem integration method has been applied for the prediction of vapor-liquid equilibria of a number of binary mixtures. The method turned out to be very convenient, much faster than the conventional method, and provided smooth simulation results. As the employed force fields perfectly predict pure-component vapor-liquid equilibria, the binary simulations were very well suitable for testing the performance of different sets of combining rules. Employing Lorentz-Hudson-McCoubrey combining rules for interactions between unlike molecules, as opposed to Lorentz-Berthelot combining rules for all interactions, considerably improved the agreement between experimental and simulated data.
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
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.
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.
Advances in numerical solutions to integral equations in liquid state theory
NASA Astrophysics Data System (ADS)
Howard, Jesse J.
Solvent effects play a vital role in the accurate description of the free energy profile for solution phase chemical and structural processes. The inclusion of solvent effects in any meaningful theoretical model however, has proven to be a formidable task. Generally, methods involving Poisson-Boltzmann (PB) theory and molecular dynamic (MD) simulations are used, but they either fail to accurately describe the solvent effects or require an exhaustive computation effort to overcome sampling problems. An alternative to these methods are the integral equations (IEs) of liquid state theory which have become more widely applicable due to recent advancements in the theory of interaction site fluids and the numerical methods to solve the equations. In this work a new numerical method is developed based on a Newton-type scheme coupled with Picard/MDIIS routines. To extend the range of these numerical methods to large-scale data systems, the size of the Jacobian is reduced using basis functions, and the Newton steps are calculated using a GMRes solver. The method is then applied to calculate solutions to the 3D reference interaction site model (RISM) IEs of statistical mechanics, which are derived from first principles, for a solute model of a pair of parallel graphene plates at various separations in pure water. The 3D IEs are then extended to electrostatic models using an exact treatment of the long-range Coulomb interactions for negatively charged walls and DNA duplexes in aqueous electrolyte solutions to calculate the density profiles and solution thermodynamics. It is found that the 3D-IEs provide a qualitative description of the density distributions of the solvent species when compared to MD results, but at a much reduced computational effort in comparison to MD simulations. The thermodynamics of the solvated systems are also qualitatively reproduced by the IE results. The findings of this work show the IEs to be a valuable tool for the study and prediction of
Numeric Modified Adomian Decomposition Method for Power System Simulations
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.
A numerical method for solving singular De`s
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.
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…
Advanced boundary element methods in aeroacoustics and elastodynamics
NASA Astrophysics Data System (ADS)
Lee, Li
In the first part of this dissertation, advanced boundary element methods (BEM) are developed for acoustic radiation in the presence of subsonic flows. A direct boundary integral formulation is first introduced for acoustic radiation in a uniform flow. This new formulation uses the Green's function derived from the adjoint operator of the governing differential equation. Therefore, it requires no coordinate transformation. This direct BEM formulation is then extended to acoustic radiation in a nonuniform-flow field. All the terms due to the nonuniform-flow effect are taken to the right-hand side and treated as source terms. The source terms result in a domain integral in the standard boundary integral formulation. The dual reciprocity method is then used to convert the domain integral into a number of boundary integrals. The second part of this dissertation is devoted to the development of advanced BEM algorithms to overcome the multi-frequency and nonuniqueness difficulties in steady-state elastodynamics. For the multi-frequency difficulty, two different interpolation schemes, borrowed from recent developments in acoustics, are first extended to elastodynamics to accelerate the process of matrix re-formation. Then, a hybrid scheme that retains only the merits of the two different interpolation schemes is suggested. To overcome the nonuniqueness difficulty, an enhanced CHIEF (Combined Helmholtz Integral Equation Formulation) method using a linear combination of the displacement and the traction boundary integral equations on the surface of a small interior volume is proposed. Numerical examples are given to demonstrate all the advanced BEM formulations.
The numerical mirage method for photothermal characterization of materials.
Demko, Michael T; Hostler, Stephen R; Abramson, Alexis R
2008-04-01
Noncontact thermal measurement techniques offer rapid thermal characterization without modification or destruction of the sample being studied. A simple and versatile method has been developed, termed the "numerical mirage method," that utilizes the transient photothermal deflection of a laser beam traversing a modulated temperature gradient. This method expands the range and simplifies the experimental procedure of traditional mirage methods. A numerical solver is used to create accurate deflection profile models and a linear curve fitting routine is developed, from which the thermal diffusivity of a material may be determined. This method allows for rapid modification of sample and heating configurations. Verification of the method is performed on bismuth and fused quartz reference samples, and good agreement with literature is obtained.
A numerical method for acoustic oscillations in tubes
NASA Technical Reports Server (NTRS)
Gary, John M.
1988-01-01
A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium-filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second-order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.
Numerical results for extended field method applications. [thin plates
NASA Technical Reports Server (NTRS)
Donaldson, B. K.; Chander, S.
1973-01-01
This paper presents the numerical results obtained when a new method of analysis, called the extended field method, was applied to several thin plate problems including one with non-rectangular geometry, and one problem involving both beams and a plate. The numerical results show that the quality of the single plate solutions was satisfactory for all cases except those involving a freely deflecting plate corner. The results for the beam and plate structure were satisfactory even though the structure had a freely deflecting corner.
Use advanced methods to treat wastewater
Davis, M. )
1994-08-01
Common sense guidelines offer plausible, progressive techniques to treat wastewater. Because current and pending local, state and federal regulations are ratcheting lower effluent discharge limits, familiar treatment methods, such as biological, don't meet new restrictions. Now operating facilities must combine traditional methods with advanced remedial options such as thermal, physical, electro and chemical treatments. these new techniques remove organics, metals, nonhazardous dissolved salts, etc., but carry higher operating and installation costs. Due to tighter effluent restrictions and pending zero-discharge initiatives, managers of operating facilities must know and understand the complexity, composition and contaminant concentration of their wastewaters. No one-size-fits-all solution exists. However, guidelines can simplify decision making and help operators nominate the most effective and economical strategy to handle their waste situation. The paper describes the common treatment and the importance of alternatives, then describes biological, electro, physical, thermal, and chemical treatments.
NASA Technical Reports Server (NTRS)
Homicz, G. F.; Moselle, J. R.
1985-01-01
A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.
Numerical methods for solving terminal optimal control problems
NASA Astrophysics Data System (ADS)
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Numerical methods and calculations for droplet flow, heating and ignition
NASA Technical Reports Server (NTRS)
Dwyer, H. A.; Sanders, B. R.; Dandy, D.
1982-01-01
A numerical method was devised and employed to solve a variety of problems related to liquid droplet combustion. The basic transport equations of mass, momentum and energy were formulated in terms of generalized nonorthogonal coordinates, which allows for adaptive griding and arbitrary particle shape. Example problems are solved for internal droplet heating, droplet ignition and high Reynolds number flow over a droplet.
A numerical method for unsteady aerodynamics via acoustics
NASA Technical Reports Server (NTRS)
Hodge, Steve
1991-01-01
Formal solutions to the wave equation may be conveniently described within the framework of generalized function theory. A generalized function theory is used to yield a formulation and formal solution of a wave equation describing oscillation of a flat plate from which a numerical method may be derived.
COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE
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
Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems
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.
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.
Efficient numerical methods for entropy-linear programming problems
NASA Astrophysics Data System (ADS)
Gasnikov, A. V.; Gasnikova, E. B.; Nesterov, Yu. E.; Chernov, A. V.
2016-04-01
Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.
A novel gas-droplet numerical method for spray combustion
NASA Technical Reports Server (NTRS)
Chen, C. P.; Shang, H. M.; Jiang, Y.
1991-01-01
This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.
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)
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.
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.
A numerical method for interface problems in elastodynamics
NASA Technical Reports Server (NTRS)
Mcghee, D. S.
1984-01-01
The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.
Advanced Numerical Methods for Simulating Nonlinear Multirate Lumped Parameter Models
1991-05-01
power from one frequency to another. Even the ship service system onboard mechanical drive ships can experience frequency fluctuations lasting up to 2...none can be found and the circuitgroup_singular flag is zero Warn user that a singular system may exist with the group nodes. If none can be found then...In fact, the flow variable should normally equal zero if the rest of the circuit is indeed linearly dependent. As a convenience to the user , WAVESIM
Application of advanced Monte Carlo Methods in numerical dosimetry.
Reichelt, U; Henniger, J; Lange, C
2006-01-01
Many tasks in different sectors of dosimetry are very complex and highly sensitive to changes in the radiation field. Often, only the simulation of radiation transport is capable of describing the radiation field completely. Down to sub-cellular dimensions the energy deposition by cascades of secondary electrons is the main pathway for damage induction in matter. A large number of interactions take place until such electrons are slowed down to thermal energies. Also for some problems of photon transport a large number of photon histories need to be processed. Thus the efficient non-analogue Monte Carlo program, AMOS, has been developed for photon and electron transport. Various applications and benchmarks are presented showing its ability. For radiotherapy purposes the radiation field of a brachytherapy source is calculated according to the American Association of Physicists in Medicine Task Group Report 43 (AAPM/TG43). As additional examples, results for the detector efficiency of a high-purity germanium (HPGe) detector and a dose estimation for an X-ray shielding for radiation protection are shown.
NASA Astrophysics Data System (ADS)
Ivanov, D. S.; Ovchinnikov, M. Yu.; Penkov, V. I.; Roldugin, D. S.; Doronin, D. M.; Ovchinnikov, A. V.
2017-03-01
Attitude motion of a satellite equipped with magnetic control system is considered. System comprises of three magnetorquers and one three-axis magnetometer. Satellite is stabilized in orbital reference frame using PD controller and extended Kalman filter. Three-axis attitude is analyzed numerically with advanced assumptions: inertia tensor uncertainty, disturbances of unknown nature, magnetometer errors are taken into account. Stabilization and determination accuracy dependence on orbit inclination is studied.
Numerical Polynomial Homotopy Continuation Method and String Vacua
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
Projected discrete ordinates methods for numerical transport problems
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.
Simple numerical method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible inviscid flows is developed. The method is based on the concept of flux vector splitting in its implicit form and is tested on several demanding configurations. Time marching to steady state is accelerated by the implementation of the multigrid procedure which very effectively increases the rate of convergence. Steady-state results are obtained for various test cases. Only short computational times are required due to the relative efficiency of the basic method.
A Numerical Method for Incompressible Flow with Heat Transfer
NASA Technical Reports Server (NTRS)
Sa, Jong-Youb; Kwak, Dochan
1997-01-01
A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.
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.
Numerical Method and Analysis of Consistency for Electrodiffusion Problem
NASA Astrophysics Data System (ADS)
Filipek, R.; Szyszkiewicz, K.; Danielewski, M.; Lewenstam, A.
2007-12-01
Numerical procedure based on method of lines for time-dependent electrodiffusion transport is developed. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analyzed and compared. The resulting stiff system of ODEs is effectively solved using the Radau IIa integrator. The applications to selected electrochemical systems: liquid junction, bi-ionic case and fused salts have been tested. Results for ion-selective electrodes are demonstrated.
Advanced fault diagnosis methods in molecular networks.
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.
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.
Numerical methods for control optimization in linear systems
NASA Astrophysics Data System (ADS)
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
Modeling collisional processes in plasmas using discontinuous numerical methods
NASA Astrophysics Data System (ADS)
Miller, Sean
Fluid-based plasma models are typically applied to parameter regimes where a local thermal equilibrium is assumed. The applicability of this regime is valid for many plasmas, however, it is limited to plasma dynamics dominated by collisional effects. This study attempts to extend the validity of the collisional fluid regime using an anisotropic 13-moment fluid model derived from the Pearson type-IV probability distribution. The model explicitly evolves the heat flux hyperbolically alongside the density, momentum, and energy in order to capture dynamics usually restricted to costly kinetic models. Each particle species is modeled individually and collectively coupled through electromagnetic and collision operators. To remove electromagnetic divergence errors inherent to numerical representations of Maxwell's equations, both hyperbolic and parabolic cleaning methods are presented. The plasma models are implemented using high-order finite volume and discontinuous Galerkin numerical methods designed for unstructured meshes. The unstructured code framework, numerical methods, and plasma models were developed in the University of Washington's WARPXM code for use on heterogeneous accelerated clusters.
The instanton method and its numerical implementation in fluid mechanics
NASA Astrophysics Data System (ADS)
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
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.
Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies
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.
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.
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
Computational methods of the Advanced Fluid Dynamics Model
Bohl, W.R.; Wilhelm, D.; Parker, F.R.; Berthier, J.; Maudlin, P.J.; Schmuck, P.; Goutagny, L.; Ichikawa, S.; Ninokata, H.; Luck, L.B.
1987-01-01
To more accurately treat severe accidents in fast reactors, a program has been set up to investigate new computational models and approaches. The product of this effort is a computer code, the Advanced Fluid Dynamics Model (AFDM). This paper describes some of the basic features of the numerical algorithm used in AFDM. Aspects receiving particular emphasis are the fractional-step method of time integration, the semi-implicit pressure iteration, the virtual mass inertial terms, the use of three velocity fields, higher order differencing, convection of interfacial area with source and sink terms, multicomponent diffusion processes in heat and mass transfer, the SESAME equation of state, and vectorized programming. A calculated comparison with an isothermal tetralin/ammonia experiment is performed. We conclude that significant improvements are possible in reliably calculating the progression of severe accidents with further development.
Advanced continuous cultivation methods for systems microbiology.
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.
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.
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.
Computational and design methods for advanced imaging
NASA Astrophysics Data System (ADS)
Birch, Gabriel C.
This dissertation merges the optical design and computational aspects of imaging systems to create novel devices that solve engineering problems in optical science and attempts to expand the solution space available to the optical designer. This dissertation is divided into two parts: the first discusses a new active illumination depth sensing modality, while the second part discusses a passive illumination system called plenoptic, or lightfield, imaging. The new depth sensing modality introduced in part one is called depth through controlled aberration. This technique illuminates a target with a known, aberrated projected pattern and takes an image using a traditional, unmodified imaging system. Knowing how the added aberration in the projected pattern changes as a function of depth, we are able to quantitatively determine depth of a series of points from the camera. A major advantage this method permits is the ability for illumination and imaging axes to be coincident. Plenoptic cameras capture both spatial and angular data simultaneously. This dissertation present a new set of parameters that permit the design and comparison of plenoptic devices outside the traditionally published plenoptic 1.0 and plenoptic 2.0 configurations. Additionally, a series of engineering advancements are presented, including full system raytraces of raw plenoptic images, Zernike compression techniques of raw image files, and non-uniform lenslet arrays to compensate for plenoptic system aberrations. Finally, a new snapshot imaging spectrometer is proposed based off the plenoptic configuration.
New numerical method to study phase transitions and its applications
Lee, Jooyoung; Kosterlitz, J.M.
1991-11-01
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/{xi} < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.
An explicit mixed numerical method for mesoscale model
NASA Technical Reports Server (NTRS)
Hsu, H.-M.
1981-01-01
A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
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.
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.
Applying multi-resolution numerical methods to geodynamics
NASA Astrophysics Data System (ADS)
Davies, David Rhodri
Computational models yield inaccurate results if the underlying numerical grid fails to provide the necessary resolution to capture a simulation's important features. For the large-scale problems regularly encountered in geodynamics, inadequate grid resolution is a major concern. The majority of models involve multi-scale dynamics, being characterized by fine-scale upwelling and downwelling activity in a more passive, large-scale background flow. Such configurations, when coupled to the complex geometries involved, present a serious challenge for computational methods. Current techniques are unable to resolve localized features and, hence, such models cannot be solved efficiently. This thesis demonstrates, through a series of papers and closely-coupled appendices, how multi-resolution finite-element methods from the forefront of computational engineering can provide a means to address these issues. The problems examined achieve multi-resolution through one of two methods. In two-dimensions (2-D), automatic, unstructured mesh refinement procedures are utilized. Such methods improve the solution quality of convection dominated problems by adapting the grid automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. Thermal and thermo-chemical validation tests illustrate that the technique is robust and highly successful, improving solution accuracy whilst increasing computational efficiency. These points are reinforced when the technique is applied to geophysical simulations of mid-ocean ridge and subduction zone magmatism. To date, successful goal-orientated/error-guided grid adaptation techniques have not been utilized within the field of geodynamics. The work included herein is therefore the first geodynamical application of such methods. In view of the existing three-dimensional (3-D) spherical mantle dynamics codes, which are built upon a quasi-uniform discretization of the sphere and closely coupled
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.
Numerical integration of population models satisfying conservation laws: NSFD methods.
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.
Performance analysis of a mirror by numerical iterative method.
Park, Kwijong; Cho, Myung; Lee, Dae-Hee; Moon, Bongkon
2014-12-29
Zernike polynomials are generally used to predict the optical performance of a mirror. However, it can also be done by a numerical iterative method. As piston, tip, tilt, and defocus (P.T.T.F) aberrations can be easily removed by optical alignment, we iteratively used a rotation transformation and a paraboloid graph subtraction for removal of the aberrations from a raw deformation of the optical surface through a Finite Element Method (FEM). The results of a 30 cm concave circular mirror corrected by the iterative method were almost the same as those yielded by Zernike polynomial fitting, and the computational time was fast. In addition, a concave square mirror whose surface area is π was analyzed in order to visualize the deformation maps of a general mirror aperture shape. The iterative method can be applicable efficiently because it does not depend on the mirror aperture shape.
Numerical method for gas dynamics combining characteristic and conservation concepts
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1981-01-01
An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.
Advanced Numerical Prediction and Modeling of Tropical Cyclones Using WRF-NMM modeling system
NASA Astrophysics Data System (ADS)
Gopalakrishnan, S. G.; Rogers, R. F.; Marks, F. D.; Atlas, R.
2007-12-01
Dramatic improvement in tropical cyclone track forecasts have occurred through advancements in high quality observations, high speed computers and improvements in dynamical models. Similar advancements now need to be made for tropical cyclone intensity, structure and rainfall prediction. The Weather Research Forecasting Model (WRF) is a general purpose, multi-institutional mesoscale modeling system. A version of the WRF model called the HWRF/WRF-NMM modeling system, developed at the National Center for Environmental Protection (NCEP) was recently adopted for hurricane forecasting (Gopalakrishnan et al, 2006) by the National Hurricane Center (NHC). At the Hurricane Research Division (HRD/AOML/OAR) we are developing and further advancing a research version of this modeling system. This work is done in collaboration with the Developmental Test bed Center (DTC), Boulder, CO, Global Systems division (GSD/ESRL/OAR), Boulder, CO, The Air Resources Laboratory (ARL/OAR), Washington, D.C., the U.S. university community, the Indian Institute of Technology, IIT.Delhi, India, and the India Meteorological Department, New Delhi, India Our modeling effort includes advancing the WRF system for Ensemble Hurricane Forecasting, advancing our understanding of Ensemble-vs- High Resolution Forecasting of Hurricanes, advancing WRF/WRF-NMM with better analysis techniques (e.g. Four Dimensional Data Assimilation) for improving forecasts and above all, advancing our understanding of hurricane processes using a high resolution numerical modeling approach. Examples of some of these applications will be shown here. Reference: NCEP's Two-way-Interactive-Moving-Nest NMM-WRF modeling system for Hurricane Forecasting, S.G. Gopalakrishnan, N. Surgi, R. Tuleya, and Z. Janjic 27th Conference on Hurricanes and Tropical Meteorology, 24- 28 April 2006, Monterey, California.
The numerical methods for the fluid flow of UCMCWS
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.
Advances in direct and diffraction methods for surface structural determination
NASA Astrophysics Data System (ADS)
Tong, S. Y.
1999-08-01
I describe recent advances in low-energy electron diffraction holography and photoelectron diffraction holography. These are direct methods for determining the surface structure. I show that for LEED and PD spectra taken in an energy and angular mesh, the relative phase between the reference wave and the scattered wave has a known geometric form if the spectra are always taken from within a small angular cone in the near backscattering direction. By using data in the backscattering small cone at each direction of interest, a simple algorithm is developed to invert the spectra and extract object atomic positions with no input of calculated dynamic factors. I also describe the use of a convergent iterative method of PD and LEED. The computation time of this method scales as N2, where N is the dimension of the propagator matrix, rather than N3 as in conventional Gaussian substitutional methods. Both the Rehr-Albers separable-propagator cluster approach and the slab-type non-separable approach can be cast in the new iterative form. With substantial savings in computational time and no loss in numerical accuracy, this method is very useful in applications of multiple scattering theory, particularly for systems involving either very large unit cells (>300 atoms) or where no long-range order is present.
Numerical methods and measurement systems for nonlinear magnetic circuits (abstract)
NASA Astrophysics Data System (ADS)
Heitbrink, Axel; Dieter Storzer, Hans; Beyer, Adalbert
1994-05-01
In the past years an increasing interest in calculation methods of circuits containing magnetic nonlinearities could be observed. For this reason a new method was developed which makes it possible to calculate the steady state solution of such circuits by the help of an interactive cad program. The modular concept of the software allows to separate the circuit into nonlinear and linear subnetworks. When regarding nonlinear magnetic elements one can choose between several numerical models for the description of the hysteresis loops or an inbuilt realtime measurement system can be activated to get the dynamic hysteresis loops. The measurement system is also helpful for the parameter extraction for the numerical hysteresis models. A modified harmonic-balance algorithm and a set of iteration schemes is used for solving the network function. The combination of the realtime measurement system and modern numerical methods brings up a productive total concept for the exact calculation of nonlinear magnetic circuits. A special application class will be discussed which is given by earth-leakage circuit breakers. These networks contain a toroidal high permeable NiFe alloy and a relay as nonlinear elements (cells) and some resistors, inductors, and capacitors as linear elements. As input dc signals at the primary winding of the core any curveform must be regarded, especially 135° phasecutted pulses. These signals with extreme higher frequency components make it impossible to use numerical models for the description of the nonlinear behavior of the core and the relays. So for both elements the realtime measurement system must be used during the iteration process. During each iteration step the actual magnetization current is sent to the measurement system, which measures the dynamic hysteresis loop at the probe. These values flow back into the iteration process. A graphic subsystem allows a look at the waveforms of all voltages and current when the iterations take place. One
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.
Comparison of four stable numerical methods for Abel's integral equation
NASA Technical Reports Server (NTRS)
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
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.
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
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.
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
The present numerical method for the solution of the isenthalpic form of the governing equations for compressible viscous and inviscid flows has its basis in the concept of flux vector splitting in its implicit form, and has been tested in the cases of several difficult viscous and inviscid configurations. An acceleration of time-marching to steady state is accomplished by implementing a multigrid procedure which effectively increases the convergence rate. The steady state results obtained are largely of good quality, and required only short computational times.
Numerical Methods for Computing Turbulence-Induced Noise
2005-12-16
consider the finite dimensional subspace Vhl C Vh . Let vhi -= phlu be the optimal representation of u in Vhl and phi : V+_+ Vhl be the appropriate...mapping. We consider the following numerical method which is obtained by replacing h with hi in (2.4). Find uhl E Vhi , such that B(whi, uhl) + M(whUhl, f...the same functional form of the model that leads to the optimal solution on Vh, also leads to the optimal solution on Vhi . Thus, requiring uhl = vh
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.
NASA Astrophysics Data System (ADS)
Scovazzi, Guglielmo; Wheeler, Mary F.; Mikelić, Andro; Lee, Sanghyun
2017-04-01
The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns - referred to as viscous fingering - may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods.
NASA Astrophysics Data System (ADS)
Saanouni, Kkemais; Labergère, Carl; Issa, Mazen; Rassineux, Alain
2010-06-01
This work proposes a complete adaptive numerical methodology which uses `advanced' elastoplastic constitutive equations coupling: thermal effects, large elasto-viscoplasticity with mixed non linear hardening, ductile damage and contact with friction, for 2D machining simulation. Fully coupled (strong coupling) thermo-elasto-visco-plastic-damage constitutive equations based on the state variables under large plastic deformation developed for metal forming simulation are presented. The relevant numerical aspects concerning the local integration scheme as well as the global resolution strategy and the adaptive remeshing facility are briefly discussed. Applications are made to the orthogonal metal cutting by chip formation and segmentation under high velocity. The interactions between hardening, plasticity, ductile damage and thermal effects and their effects on the adiabatic shear band formation including the formation of cracks are investigated.
Application of numerical optimization to the design of advanced supercritical airfoils
NASA Technical Reports Server (NTRS)
Johnson, R. R.; Hicks, R. M.
1979-01-01
An application of numerical optimization to the design of advanced airfoils for transonic aircraft showed that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while minimizing the drag coefficient at the design Mach number. This multiple design-point numerical optimization has been implemented with the use of airfoil shape functions which permit a wide range of attainable profiles during the optimization process. Analytical data for the starting airfoil shape, a single design-point optimized shape, and a double design-point optimized shape are presented. Experimental data obtained in the NASA Ames two-by two-foot wind tunnel are also presented and discussed.
Numerical study of Alfvén eigenmodes in the Experimental Advanced Superconducting Tokamak
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.
Numerical methods for large eddy simulation of acoustic combustion instabilities
NASA Astrophysics Data System (ADS)
Wall, Clifton T.
Acoustic combustion instabilities occur when interaction between the combustion process and acoustic modes in a combustor results in periodic oscillations in pressure, velocity, and heat release. If sufficiently large in amplitude, these instabilities can cause operational difficulties or the failure of combustor hardware. In many situations, the dominant instability is the result of the interaction between a low frequency acoustic mode of the combustor and the large scale hydrodynamics. Large eddy simulation (LES), therefore, is a promising tool for the prediction of these instabilities, since both the low frequency acoustic modes and the large scale hydrodynamics are well resolved in LES. Problems with the tractability of such simulations arise, however, due to the difficulty of solving the compressible Navier-Stokes equations efficiently at low Mach number and due to the large number of acoustic periods that are often required for such instabilities to reach limit cycles. An implicit numerical method for the solution of the compressible Navier-Stokes equations has been developed which avoids the acoustic CFL restriction, allowing for significant efficiency gains at low Mach number, while still resolving the low frequency acoustic modes of interest. In the limit of a uniform grid the numerical method causes no artificial damping of acoustic waves. New, non-reflecting boundary conditions have also been developed for use with the characteristic-based approach of Poinsot and Lele (1992). The new boundary conditions are implemented in a manner which allows for significant reduction of the computational domain of an LES by eliminating the need to perform LES in regions where one-dimensional acoustics significantly affect the instability but details of the hydrodynamics do not. These new numerical techniques have been demonstrated in an LES of an experimental combustor. The new techniques are shown to be an efficient means of performing LES of acoustic combustion
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.
1986-01-01
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been 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. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
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.
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.
Advanced Source Deconvolution Methods for Compton Telescopes
NASA Astrophysics Data System (ADS)
Zoglauer, Andreas
The next generation of space telescopes utilizing Compton scattering for astrophysical observations is destined to one day unravel the mysteries behind Galactic nucleosynthesis, to determine the origin of the positron annihilation excess near the Galactic center, and to uncover the hidden emission mechanisms behind gamma-ray bursts. Besides astrophysics, Compton telescopes are establishing themselves in heliophysics, planetary sciences, medical imaging, accelerator physics, and environmental monitoring. Since the COMPTEL days, great advances in the achievable energy and position resolution were possible, creating an extremely vast, but also extremely sparsely sampled data space. Unfortunately, the optimum way to analyze the data from the next generation of Compton telescopes has not yet been found, which can retrieve all source parameters (location, spectrum, polarization, flux) and achieves the best possible resolution and sensitivity at the same time. This is especially important for all sciences objectives looking at the inner Galaxy: the large amount of expected sources, the high background (internal and Galactic diffuse emission), and the limited angular resolution, make it the most taxing case for data analysis. In general, two key challenges exist: First, what are the best data space representations to answer the specific science questions? Second, what is the best way to deconvolve the data to fully retrieve the source parameters? For modern Compton telescopes, the existing data space representations can either correctly reconstruct the absolute flux (binned mode) or achieve the best possible resolution (list-mode), both together were not possible up to now. Here we propose to develop a two-stage hybrid reconstruction method which combines the best aspects of both. Using a proof-of-concept implementation we can for the first time show that it is possible to alternate during each deconvolution step between a binned-mode approach to get the flux right and a
[The Study of Advanced Fundamental Parameter Method in EDXRFA].
Cheng, Feng; Zhang, Qing-xian; Ge, Liang-quan; Gu, Yi; Zeng, Guo-qiang; Luo, Yao-yao; Chen, Shuang; Wang, Lei; Zhao, Jian-kun
2015-07-01
The X-ray Fluorescence Analysis(XRFA) is an important and efficient method on the element anylsis and is used in geology, industry and environment protection. But XRFA has a backdraw that the determination limit and accuracy are effected by the matrix of the sample. Now the fundamental parameter is usually used to calculate the content of elements in XRFA, and it is an efficient method if the matrix and net area of characteristic X-ray peak are obtained. But this is invalide in in-stu XRFA. Also the method of net area and the "black material" of sample are the key point of the fundamental parameter method when the Energy Dispersive X-ray Fluorescence Analysis(EDXRFA) method is used in the low content sample. In this paper a advanced fundamental parameter method is discussed. The advanced fundamental parameter method includes the spectra analysis and the fundamental parameter method, which inserts the overlapping peaks separation method into the iteration process of the fundamental parameter method. The advanced method can resolve the net area and the quantitative analysis. The advanced method is used to analyse the standard sample. Compare to the content obtained from the coefficient method, the precision of Cu, Ni and Zn is better than coeffieciency method. The result shows that the advanced method could improve the precision of the EDXRFA, so the advanced method is better than the coefficient method.
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
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.
Arkundato, Artoto; Su'ud, Zaki; Abdullah, Mikrajuddin; Widayani,; Celino, Massimo
2012-06-06
In this present work, we report numerical results of iron (cladding) corrosion study in interaction with lead-bismuth eutectic coolant of advanced nuclear reactors. The goal of this work is to study how the oxygen can be used to reduce the corrosion rate of cladding. The molecular dynamics method was applied to simulate corrosion process. By evaluating the diffusion coefficients, RDF functions, MSD curves of the iron and also observed the crystal structure of iron before and after oxygen injection to the coolant then we concluded that a significant and effective reduction can be achieved by issuing about 2% number of oxygen atoms to lead-bismuth eutectic coolant.
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.
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.
Controlling template erosion with advanced cleaning methods
NASA Astrophysics Data System (ADS)
Singh, SherJang; Yu, Zhaoning; Wähler, Tobias; Kurataka, Nobuo; Gauzner, Gene; Wang, Hongying; Yang, Henry; Hsu, Yautzong; Lee, Kim; Kuo, David; Dress, Peter
2012-03-01
We studied the erosion and feature stability of fused silica patterns under different template cleaning conditions. The conventional SPM cleaning is compared with an advanced non-acid process. Spectroscopic ellipsometry optical critical dimension (SE-OCD) measurements were used to characterize the changes in pattern profile with good sensitivity. This study confirmed the erosion of the silica patterns in the traditional acid-based SPM cleaning mixture (H2SO4+H2O2) at a rate of ~0.1nm per cleaning cycle. The advanced non-acid clean process however only showed CD shift of ~0.01nm per clean. Contamination removal & pattern integrity of sensitive 20nm features under MegaSonic assisted cleaning is also demonstrated.
Advanced Waveform Research Methods for Geress Recordings
1993-04-15
interested institutions via e-mail (e~g. Bundesaustalt fu-r Geowissenschaften und Rohstoffe (BGR), Frankfurt University, Grfenberg Array, ORFEUS , seismo...numerous broad band seismological stations and several broad band networks and arrays worldwide. The ORFEUS data center was founded in 1987 and dedicates...damped harmonic oscillation in the s-domain with free circu- lar frequency we and damping constant h < 1. Their solutions are 51/2 = h ± 1- h2)1/2 (6
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.
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
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.
Numerical Method of Characteristics for One-Dimensional Blood Flow.
Acosta, Sebastian; Puelz, Charles; Riviére, 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.
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.
Space-time adaptive numerical methods for geophysical applications.
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.
Numerical Method of Characteristics for One–Dimensional Blood Flow
Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-01-01
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. PMID:25931614
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…
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.
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.
Numerical simulation on snow melting phenomena by CIP method
NASA Astrophysics Data System (ADS)
Mizoe, H.; Yoon, Seong Y.; Josho, M.; Yabe, T.
2001-04-01
A numerical scheme based on the C-CUP method to simulate melting phenomena in snow is proposed. To calculate these complex phenomena we introduce the phase change, elastic-plastic model, porous model, and verify each model by using some simple examples. This scheme is applied to a practical model, such as the snow piled on the insulator of electrical transmission line, in which snow is modeled as a compound material composed of air, water, and ice, and is calculated by elastic-plastic model. The electric field between two electrodes is solved by the Poisson equation giving the Joule heating in the energy conservation that eventually leads to snow melting. Comparison is made by changing the fraction of water in the snow to see its effect on melting process for the cases of applied voltage of 50 and 500 kV on the two electrodes.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
[Contemporary methods of treatment in local advanced prostate cancer].
Brzozowska, Anna; Mazurkiewicz, Maria; Starosławska, Elzbieta; Stasiewicz, Dominika; Mocarska, Agnieszka; Burdan, Franciszek
2012-10-01
The prostate cancer is one of the most often cancers amongst males. Its frequency is increasing with age. Thanks to widespread of screening denomination of specific prostate specific antigen (PSA), ultrasonography including the one in transrectal (TRUS), computed tomography, magnetic resonance and especially the awareness of society, the number of patients with low local advance of illness is increasing. The basic method of treatment in such cases is still the surgical removal of prostate with seminal bladder or radiotherapy. To this purpose tele-(IMRT, VMAT) or brachytherapy (J125, Ir192, Pa103) is used. In patients with higher risk of progression the radiotherapy may be associated with hormonotherapy (total androgen blockage-LH-RH analog and androgen). Despite numerous clinical researches conducted there is still no selection of optimal sequence of particular methods. Moreover, no explicit effectiveness was determined. The general rule of treatment in patients suffering from prostate cancer still remains individual selection of therapeutic treatment depending on the age of a patient, general condition and especially patient's general preferences. In case of elderly patients and patients with low risk of progression, recommendation of direct observation including systematical PSA denomination, clinical transrectal examination, TRUS, MR of smaller pelvis or scintigraphy of the whole skeleton may be considered.
Introduction to finite-difference methods for numerical fluid dynamics
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.
A survey of numerical methods for shock physics applications
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.
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
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.
Numerical methods for determining interstitial oxygen in silicon
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.
A numerical solution method for acoustic radiation from axisymmetric bodies
NASA Technical Reports Server (NTRS)
Caruthers, John E.; Raviprakash, G. K.
1995-01-01
A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.
Numerical modelling methods for predicting antenna performance on aircraft
NASA Astrophysics Data System (ADS)
Kubina, S. J.
1983-09-01
Typical case studies that involve the application of Moment Methods to the prediction of the radiation characteristics of antennas in the HF frequency band are examined. The examples consist of the analysis of a shorted transmission line HF antenna on a CHSS-2/Sea King helicopter, wire antennas on the CP-140/Aurora patrol aircraft and a long dipole antenna on the Space Shuttle Orbiter spacecraft. In each of these cases the guidelines for antenna modeling by the use of the program called the Numerical Electromagnetic Code are progressively applied and results are compared to measurements made by the use of scale-model techniques. In complex examples of this type comparisons based on individual radiation patterns are insufficient for the validation of computer models. A volumetric method of radiation pattern comparison is used based on criteria that result from pattern integration and that are related to communication system performance. This is supplemented by hidden-surface displays of an entire set of conical radiation patterns resulting from measurements and computations. Antenna coupling considerations are discussed for the case of the dual HF installation on the CP-140/Aurora aircraft.
Simplified method for numerical modeling of fiber lasers.
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.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Vandoormaal, J. P.; Turan, A.; Raithby, G. D.
1986-01-01
The objective of the present study is to improve both the accuracy and computational efficiency of existing numerical techniques used to predict viscous recirculating flows in combustors. A review of the status of the study is presented along with some illustrative results. The effort to improve the numerical techniques consists of the following technical tasks: (1) selection of numerical techniques to be evaluated; (2) two dimensional evaluation of selected techniques; and (3) three dimensional evaluation of technique(s) recommended in Task 2.
Numerical approach for the voloxidation process of an advanced spent fuel conditioning process (ACP)
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)
Advanced particulate matter control apparatus and methods
Miller, Stanley J [Grand Forks, ND; Zhuang, Ye [Grand Forks, ND; Almlie, Jay C [East Grand Forks, MN
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.
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).
Advanced reliability methods for structural evaluation
NASA Technical Reports Server (NTRS)
Wirsching, P. H.; Wu, Y.-T.
1985-01-01
Fast probability integration (FPI) methods, which can yield approximate solutions to such general structural reliability problems as the computation of the probabilities of complicated functions of random variables, are known to require one-tenth the computer time of Monte Carlo methods for a probability level of 0.001; lower probabilities yield even more dramatic differences. A strategy is presented in which a computer routine is run k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k 'data' sets, and FPI methods are employed for this explicit form.
Indentation Methods in Advanced Materials Research Introduction
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.
Striking against bioterrorism with advanced proteomics and reference methods.
Armengaud, Jean
2017-01-01
The intentional use by terrorists of biological toxins as weapons has been of great concern for many years. Among the numerous toxins produced by plants, animals, algae, fungi, and bacteria, ricin is one of the most scrutinized by the media because it has already been used in biocrimes and acts of bioterrorism. Improving the analytical toolbox of national authorities to monitor these potential bioweapons all at once is of the utmost interest. MS/MS allows their absolute quantitation and exhibits advantageous sensitivity, discriminative power, multiplexing possibilities, and speed. In this issue of Proteomics, Gilquin et al. (Proteomics 2017, 17, 1600357) present a robust multiplex assay to quantify a set of eight toxins in the presence of a complex food matrix. This MS/MS reference method is based on scheduled SRM and high-quality standards consisting of isotopically labeled versions of these toxins. Their results demonstrate robust reliability based on rather loose scheduling of SRM transitions and good sensitivity for the eight toxins, lower than their oral median lethal doses. In the face of an increased threat from terrorism, relevant reference assays based on advanced proteomics and high-quality companion toxin standards are reliable and firm answers.
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.
Methods of Numerical Analysis of One-Dimensional Two-Body Problem in Wheeler-Feynman Electrodynamics
NASA Astrophysics Data System (ADS)
Klimenko, S. V.; Nikitin, I. N.; Urazmetov, W. F.
Numerical methods for solutions of differential equations with deviating arguments describing one-dimensional ultra-relativistic scattering of two identical charged particles in Wheeler-Feynman electrodynamics with half-retarded/half-advanced interaction are developed. Utilization of the methods for the physical problem analysis leads to the discovery of a bifurcation of solutions and breaking of their reflectional symmetry for particles asymptotic velocity v>0.937c in their center-of-mass frame.
Advanced spectral methods for climatic time series
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.
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Numerical methods for incompressible viscous flows with engineering applications
NASA Technical Reports Server (NTRS)
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
On the potential of computational methods and numerical simulation in ice mechanics
NASA Astrophysics Data System (ADS)
Bergan, Pål G.; Cammaert, Gus; Skeie, Geir; Tharigopula, Venkatapathi
2010-06-01
This paper deals with the challenge of developing better methods and tools for analysing interaction between sea ice and structures and, in particular, to be able to calculate ice loads on these structures. Ice loads have traditionally been estimated using empirical data and "engineering judgment". However, it is believed that computational mechanics and advanced computer simulations of ice-structure interaction can play an important role in developing safer and more efficient structures, especially for irregular structural configurations. The paper explains the complexity of ice as a material in computational mechanics terms. Some key words here are large displacements and deformations, multi-body contact mechanics, instabilities, multi-phase materials, inelasticity, time dependency and creep, thermal effects, fracture and crushing, and multi-scale effects. The paper points towards the use of advanced methods like ALE formulations, mesh-less methods, particle methods, XFEM, and multi-domain formulations in order to deal with these challenges. Some examples involving numerical simulation of interaction and loads between level sea ice and offshore structures are presented. It is concluded that computational mechanics may prove to become a very useful tool for analysing structures in ice; however, much research is still needed to achieve satisfactory reliability and versatility of these methods.
Numerical Analysis of Maneuvering Rotorcraft Using Moving Overlapped Grid Method
NASA Astrophysics Data System (ADS)
Yang, Choongmo; Aoyama, Takashi
In transient flight, rotor wakes and tip vortex generated by unsteady blade air-loads and blade motions are fully unsteady and 3-dimensionally-aperiodic, giving rise to significant complicity in accurate analysis compared to steady flight. We propose a hybrid approach by splitting the motions of a maneuvering helicopter into translation and rotation. Translation is simulated using a non-inertial moving (translating) coordinate for which new governing equations are derived, and rotations are simulated by moving each grid in the frame. A flow simulation (CFD) code is constructed by using the hybrid approach, then two simple cases (accelerating/decelerating flight and right-turn flight) for maneuvering helicopter are calculated using the moving overlapped grid method, which is now one of the most advanced techniques for tip-vortex capture. The vortex bundling phenomena, which is a main characteristic of right-turn flight, is well captured by the simulation code. The results of the present study provide better understanding of the characteristics for maneuvering rotorcraft, which can be valuable in full helicopter design.
Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods
NASA Astrophysics Data System (ADS)
Zhu, Honggeng; Zhang, Rentian; Deng, Dongsheng; Feng, Xusong; Yao, Linbi
2010-06-01
Since the flow in tubular pumping systems is basically along axial direction and passes symmetrically through the impeller, most satisfying the basic hypotheses in the design of impeller and having higher pumping system efficiency in comparison with vertical pumping system, they are being widely applied to low-head pumping engineering. In a pumping station, the fluctuation of water levels in the sump and discharge pool is most common and at most time the pumping system runs under off-design conditions. Hence, the operation of pump has to be flexibly regulated to meet the needs of flow rates, and the selection of regulation method is as important as that of pump to reduce operation cost and achieve economic operation. In this paper, the three dimensional time-averaged Navier-Stokes equations are closed by RNG κ-ɛ turbulent model, and two tubular pumping systems with different regulation methods, equipped with the same pump model but with different designed system structures, are numerically simulated respectively to predict the pumping system performances and analyze the influence of regulation device and help designers make final decision in the selection of design schemes. The computed results indicate that the pumping system with blade-adjusting device needs longer suction box, and the increased hydraulic loss will lower the pumping system efficiency in the order of 1.5%. The pumping system with permanent magnet motor, by means of variable speed regulation, obtains higher system efficiency partly for shorter suction box and partly for different structure design. Nowadays, the varied speed regulation is realized by varied frequency device, the energy consumption of which is about 3˜4% of output power of the motor. Hence, when the efficiency of variable frequency device is considered, the total pumping system efficiency will probably be lower.
Advanced method for making vitreous waste forms
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.
Advanced methods in synthetic aperture radar imaging
NASA Astrophysics Data System (ADS)
Kragh, Thomas
2012-02-01
For over 50 years our world has been mapped and measured with synthetic aperture radar (SAR). A SAR system operates by transmitting a series of wideband radio-frequency pulses towards the ground and recording the resulting backscattered electromagnetic waves as the system travels along some one-dimensional trajectory. By coherently processing the recorded backscatter over this extended aperture, one can form a high-resolution 2D intensity map of the ground reflectivity, which we call a SAR image. The trajectory, or synthetic aperture, is achieved by mounting the radar on an aircraft, spacecraft, or even on the roof of a car traveling down the road, and allows for a diverse set of applications and measurement techniques for remote sensing applications. It is quite remarkable that the sub-centimeter positioning precision and sub-nanosecond timing precision required to make this work properly can in fact be achieved under such real-world, often turbulent, vibrationally intensive conditions. Although the basic principles behind SAR imaging and interferometry have been known for decades, in recent years an explosion of data exploitation techniques enabled by ever-faster computational horsepower have enabled some remarkable advances. Although SAR images are often viewed as simple intensity maps of ground reflectivity, SAR is also an exquisitely sensitive coherent imaging modality with a wealth of information buried within the phase information in the image. Some of the examples featured in this presentation will include: (1) Interferometric SAR, where by comparing the difference in phase between two SAR images one can measure subtle changes in ground topography at the wavelength scale. (2) Change detection, in which carefully geolocated images formed from two different passes are compared. (3) Multi-pass 3D SAR tomography, where multiple trajectories can be used to form 3D images. (4) Moving Target Indication (MTI), in which Doppler effects allow one to detect and
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…
Advancing-layers method for generation of unstructured viscous grids
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A novel approach for generating highly stretched grids which is based on a modified advancing-front technique and benefits from the generality, flexibility, and grid quality of the conventional advancing-front-based Euler grid generators is presented. The method is self-sufficient for the insertion of grid points in the boundary layer and beyond. Since it is based on a totally unstructured grid strategy, the method alleviates the difficulties stemming from the structural limitations of the prismatic techniques.
A method of numerically controlled machine part programming
NASA Technical Reports Server (NTRS)
1970-01-01
Computer program is designed for automatically programmed tools. Preprocessor computes desired tool path and postprocessor computes actual commands causing machine tool to follow specific path. It is used on a Cincinnati ATC-430 numerically controlled machine tool.
Basic numerical methods. [of unsteady and transonic flow
NASA Technical Reports Server (NTRS)
Steger, Joseph L.; Van Dalsem, William R.
1989-01-01
Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.
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.
Numerical divergence effects of equivalence theory in the nodal expansion method
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.
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,…
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.
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Yang, H. Q.
1989-01-01
The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.
A Fast Numerical Method for a Nonlinear Black-Scholes Equation
NASA Astrophysics Data System (ADS)
Koleva, Miglena N.; Vulkov, Lubin G.
2009-11-01
In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.
A numerical analysis method for evaluating rod lenses using the Monte Carlo method.
Yoshida, Shuhei; Horiuchi, Shuma; Ushiyama, Zenta; Yamamoto, Manabu
2010-12-20
We propose a numerical analysis method for evaluating GRIN lenses using the Monte Carlo method. Actual measurements of the modulation transfer function (MTF) of a GRIN lens using this method closely match those made by conventional methods. Experimentally, the MTF is measured using a square wave chart, and is then calculated based on the distribution of output strength on the chart. In contrast, the general method using computers evaluates the MTF based on a spot diagram made by an incident point light source. However the results differ greatly from those from experiments. We therefore developed an evaluation method similar to the experimental system based on the Monte Carlo method and verified that it more closely matches the experimental results than the conventional method.
Advanced Fuzzy Potential Field Method for Mobile Robot Obstacle Avoidance
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
Advanced Fuzzy Potential Field Method for Mobile Robot Obstacle Avoidance.
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.
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.
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
Modeling supersonic combustion using a fully-implicit numerical method
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Wilson, Gregory J.
1990-01-01
A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.
Moreira, S F; Belinha, J; Dinis, L M J S; Jorge, R M Natal
2014-09-01
In this work the maxillary central incisor is numerically analysed with an advance discretization technique--Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM permits to organically determine the nodal connectivity, which is essential to construct the interpolation functions. The NNRPIM procedure, based uniquely in the computational nodal mesh discretizing the problem domain, allows to obtain autonomously the required integration mesh, permitting to numerically integrate the differential equations ruling the studied physical phenomenon. A numerical analysis of a tooth structure using a meshless method is presented for the first time. A two-dimensional model of the maxillary central incisor, based on the clinical literature, is established and two distinct analyses are performed. First, a complete elasto-static analysis of the incisor/maxillary structure using the NNRPIM is evaluated and then a non-linear iterative bone tissue remodelling analysis of the maxillary bone, surrounding the central incisive, is performed. The obtained NNRPIM solutions are compared with other numerical methods solutions available in the literature and with clinical cases. The results show that the NNRPIM is a suitable numerical method to analyse numerically dental biomechanics problems.
Application of numerical methods to planetary radiowave scattering
NASA Technical Reports Server (NTRS)
Simpson, Richard A.; Tyler, G. Leonard
1987-01-01
Existing numerical techniques for the solution of scattering problems were investigated to determine those which might be applicable to planetary surface studies, with the goal of improving the interpretation of radar data from Venus, Mars, the Moon, and icy satellites. The general characteristics of the models are described along with computational concerns. In particular, the Numerical Electrogmatics Code (NEC) developed at the Lawrence Livermore Laboratory is discussed. Though not developed for random rough surfaces, the NEC contains elements which may be generalized and which could be valuable in the study of scattering by planetary surfaces.
The Design of CAL Packages for Teaching Numerical Methods to Chemistry Students.
ERIC Educational Resources Information Center
Norris, A. C.
1979-01-01
Discusses the design of computational exercises useful for a course in numerical methods for chemists. Some of the exercises make use of available programs while others require the student to write programs incorporating numerical routines. The emphasis throughout is on the use of numerical methods to solve chemical problems. (Author)
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…
Numerical modeling of shallow magma intrusions with finite element method
NASA Astrophysics Data System (ADS)
Chen, Tielin; Cheng, Shaozhen; Fang, Qian; Zhou, Cheng
2017-03-01
A numerical approach for simulation of magma intrusion process, considering the couplings of the stress distribution, the viscous fluid flow of magma, and the fracturing of host rock, has been developed to investigate the mechanisms of fracture initiation and propagation in host rock during magma intrusion without pre-placing a set of fractures. The study focused on the dike intrusions filled with injected viscous magma in shallow sediments. A series of numerical modellings were carried out to simulate the process of magma intrusion in host rocks, with particular attention on the magma propagation processes and the formation of intrusion shapes. The model materials were Mohr-Coulomb materials with tension failure and shear failure. The scenarios of both stochastically heterogeneous host rocks and layered host rocks were analyzed. The injected magma formed intrusions shapes of (a) dyke, (b) sill, (c) cup-shaped intrusion, (d) saucer-shaped intrusion. The numerical results were in agreement with the experimental and field observed results, which confirmed the adequacy and the power of the numerical approach.
Numerical Simulation of Turbulent Combustion Using Vortex Methods
1990-01-08
Electric Co., Schenectady, October 1988. 2. DOD and EPA Tyndall Conference on Halon, the Ozone Layer and Research on Alternative Chemicals, Tyndall...26th Aerospace Sciences Meetin , January 11-14, Reno, Nevada, AIAA-88-0729. 13. Ghoniem A.F., and Ng K.K., Numerical study of a forced shear layet
Unstructured viscous grid generation by advancing-front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.
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.
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…
Numerical modeling of fiber specklegram sensors by using finite element method (FEM).
Arístizabal, V H; Vélez, F J; Rueda, E; Gómez, N D; Gómez, J A
2016-11-28
Although experimental advances in the implementation and characterization of fiber speckle sensor have been reported, a suitable model to interpret the speckle-pattern variation under perturbation is desirable but very challenging to be developed due to the various factors influencing the speckle pattern. In this work, a new methodology based on the finite element method (FEM) for modeling and optimizing fiber specklegram sensors (FSSs) is proposed. The numerical method allows computational visualization and quantification, in near field, of changes of a step multi-mode fiber (SMMF) specklegram, due to the application of a uniformly distributed force line (UDFL). In turn, the local modifications of the fiber speckle produce changes in the optical power captured by a step single-mode fiber (SSMF) located just at the output end of the SMMF, causing a filtering effect that explains the operation of the FSSs. For each external force, the stress distribution and the propagations modes supported by the SMMF are calculated numerically by means of FEM. Then, those modes are vectorially superposed to reconstruct each perturbed fiber specklegram. Finally, the performance of the sensing mechanism is evaluated for different radius of the filtering SSMF and force-gauges, what evidences design criteria for these kinds of measuring systems. Results are in agreement with those theoretical and experimental ones previously reported.
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.
Some variance reduction methods for numerical stochastic homogenization.
Blanc, X; Le Bris, C; Legoll, F
2016-04-28
We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.
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.
Variable inertia method: A novel numerical method for mantle convection simulation
NASA Astrophysics Data System (ADS)
Takeyama, Kosuke; Saitoh, Takayuki R.; Makino, Junichiro
2017-01-01
3D numerical simulations have been very useful for the understanding of mantle convection of the earth. In almost all previous simulations of mantle convection, the (extended) Boussinesq approximation has been used. This method is implicit in the sense that buoyancy force and viscosity are balanced, and allows the use of long timesteps that are not limited by the CFL condition. However, the resulting matrix is ill-conditioned, in particular since the viscosity strongly depends on the temperature. It is not well-suited to modern large-scale parallel machines. In this paper, we propose an explicit method which can be used to solve the mantle convection problem. If we can reduce the sound speed without changing the characteristics of the flow, we can increase the timestep and thus can use the explicit method. In order to reduce the sound speed, we multiplied the inertia term of the equation of motion by a large and viscosity-dependent coefficient. Theoretically, we can expect that this modification would not change the flow as long as the Reynolds number and the Mach number are sufficiently smaller than unity. We call this method the variable inertia method (VIM). We have performed an extensive set of numerical tests of the proposed method for thermal convection, and concluded that it works well. In particular, it can handle differences in viscosity of more than five orders of magnitude.
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.
Methods, Software and Tools for Three Numerical Applications. Final report
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).
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Turan, A.
1985-01-01
The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.
Overview: Applications of numerical optimization methods to helicopter design problems
NASA Technical Reports Server (NTRS)
Miura, H.
1984-01-01
There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.
Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM
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
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
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.
Sources of Chaos in Planetary Systems Formed Through Numerical Methods
NASA Astrophysics Data System (ADS)
Clement, Matthew S.
2017-01-01
The formation of the solar system’s terrestrial planets has been numerically modeled in countless works, and many other studies have been devoted to char- acterizing our modern planets’ chaotic dynamical state. However, it is still not known whether our planets fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a large suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib & Cowan (2015). These systems were created in the presence of a fully formed Jupiter and Saturn, using a variety of different initial conditions. We provide the first analysis of the dynamical states of fully evolved (4.5 Gyr) planetary systems formed using numerical simulations. We find that dynamical chaos is preva- lent in roughly half of the systems, with the largest source of the chaos being perturbations from Jupiter. Chaos is most prevalent in systems that form 4 or 5 terrestrial planets. Additionally, an eccentric Jupiter and Saturn is shown to enhance the prevalence of chaos in systems. Furthermore, systems with a center of mass highly concentrated between 0.8-1.2 AU generally prove to be less chaotic than systems with more exotic mass distributions. Through the process of evolving systems to the current epoch, we show that late instabilities are quite common in our systems. Of greatest interest, many of the sources of chaos observed in our own solar system (such as the secularly driven chaos between Mercury and Jupiter) are shown to be common outcomes of terrestrial planetary formation. Thus, the solar system’s marginally stable, chaotic state may naturally arise from the process of terrestrial planet formation.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
Numerical methods for a general class of porous medium equations
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.
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.
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.
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.
Method for numerical simulation of two-term exponentially correlated colored noise
Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.
2006-04-15
A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.
Numerical conformal mapping methods for exterior and doubly connected regions
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.
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,…
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.
Modeling Collisional Cascades in Debris Disks: The Numerical Method
NASA Astrophysics Data System (ADS)
Gáspár, András; Psaltis, Dimitrios; Özel, Feryal; Rieke, George H.; Cooney, Alan
2012-04-01
We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.
[Numerical flow simulation : A new method for assessing nasal breathing].
Hildebrandt, T; Osman, J; Goubergrits, L
2016-08-01
The current options for objective assessment of nasal breathing are limited. The maximum they can determine is the total nasal resistance. Possibilities to analyze the endonasal airstream are lacking. In contrast, numerical flow simulation is able to provide detailed information of the flow field within the nasal cavity. Thus, it has the potential to analyze the nasal airstream of an individual patient in a comprehensive manner and only a computed tomography (CT) scan of the paranasal sinuses is required. The clinical application is still limited due to the necessary technical and personnel resources. In particular, a statistically based referential characterization of normal nasal breathing does not yet exist in order to be able to compare and classify the simulation results.
MODELING COLLISIONAL CASCADES IN DEBRIS DISKS: THE NUMERICAL METHOD
Gaspar, Andras; Psaltis, Dimitrios; Oezel, Feryal; Rieke, George H.; Cooney, Alan E-mail: dpsaltis@as.arizona.edu E-mail: grieke@as.arizona.edu
2012-04-10
We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.
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.
METHODS ADVANCEMENT FOR MILK ANALYSIS: THE MAMA STUDY
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...
Advanced boundary layer transition measurement methods for flight applications
NASA Technical Reports Server (NTRS)
Holmes, B. J.; Croom, C. C.; Gail, P. D.; Manuel, G. S.; Carraway, D. L.
1986-01-01
In modern laminar flow flight research, it is important to understand the specific cause(s) of laminar to turbulent boundary-layer transition. Such information is crucial to the exploration of the limits of practical application of laminar flow for drag reduction on aircraft. The transition modes of interest in current flight investigations include the viscous Tollmien-Schlichting instability, the inflectional instability at laminar separation, and the crossflow inflectional instability, as well as others. This paper presents the results to date of research on advanced devices and methods used for the study of laminar boundary-layer transition phenomena in the flight environment. Recent advancements in the development of arrayed hot-film devices and of a new flow visualization method are discussed. Arrayed hot-film devices have been designed to detect the presence of laminar separation, and of crossflow vorticity. The advanced flow visualization method utilizes color changes in liquid-crystal coatings to detect boundary-layer transition at high altitude flight conditions. Flight and wind tunnel data are presented to illustrate the design and operation of these advanced methods. These new research tools provide information on disturbance growth and transition mode which is essential to furthering our understanding of practical design limits for applications of laminar flow technology.
Numerical methods for simulating blood flow at macro, micro, and multi scales.
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.
Domain Decomposition By the Advancing-Partition Method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2008-01-01
A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.
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.
NASA Astrophysics Data System (ADS)
Brunet, V.; Molton, P.; Bézard, H.; Deck, S.; Jacquin, L.
2012-01-01
This paper describes the results obtained during the European Union JEDI (JEt Development Investigations) project carried out in cooperation between ONERA and Airbus. The aim of these studies was first to acquire a complete database of a modern-type engine jet installation set under a wall-to-wall swept wing in various transonic flow conditions. Interactions between the engine jet, the pylon, and the wing were studied thanks to ¤advanced¥ measurement techniques. In parallel, accurate Reynolds-averaged Navier Stokes (RANS) simulations were carried out from simple ones with the Spalart Allmaras model to more complex ones like the DRSM-SSG (Differential Reynolds Stress Modef of Speziale Sarkar Gatski) turbulence model. In the end, Zonal-Detached Eddy Simulations (Z-DES) were also performed to compare different simulation techniques. All numerical results are accurately validated thanks to the experimental database acquired in parallel. This complete and complex study of modern civil aircraft engine installation allowed many upgrades in understanding and simulation methods to be obtained. Furthermore, a setup for engine jet installation studies has been validated for possible future works in the S3Ch transonic research wind-tunnel. The main conclusions are summed up in this paper.
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.
A numerical oil spill model based on a hybrid method.
Guo, W J; Wang, Y X
2009-05-01
The purpose of this paper is the development of a hybrid particle tracking/Eulerian-Lagrangian approach for the simulation of spilled oil in coastal areas. Oil discharge from the source is modeled by the release of particles. When the oil slick thickness or the oil concentration reaches a critical value, particles are mapped on slick thickness or node concentrations, and the calculations proceed in the Eulerian-Lagrangian mode. To acquire accurate environment information, the model is coupled with the 3-D free-surface hydrodynamics model (POM) and the third-generation wave model (SWAN). By simulating the oil processes of spreading, advection, turbulent diffusion, evaporation, emulsification, dissolution and shoreline deposition, it has the ability to predict the horizontal movement of surface oil slick, the vertical distribution of oil particles, the concentration in the water column and the mass balance of spilled oil. An accidental oil release near Dalian coastal waters is simulated to validate the developed model. Compared with the satellite images of oil slicks on the surface, the numerical results indicate that the model has a reasonable accuracy.
A numerical method for eigenvalue problems in modeling liquid crystals
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.
Advances in nucleic acid-based detection methods.
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
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.
Validation of a Numerical Method for Determining Liner Impedance
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.
1996-01-01
This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, non-progressive acoustic wave environment without flow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies.
Numerical method for the stochastic projected Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Rooney, S. J.; Blakie, P. B.; Bradley, A. S.
2014-01-01
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
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.
2007-12-06
problems studied in this project involve numerically solving partial differential equations with either discontinuous or rapidly changing solutions ...REPORT Algorithm Development and Application of High Order Numerical Methods for Shocked and Rapid Changing Solutions 14. ABSTRACT 16. SECURITY...discontinuous Galerkin finite element methods, for solving partial differential equations with discontinuous or rapidly changing solutions . Algorithm
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.
Numerical continuation methods for large-scale dissipative dynamical systems
NASA Astrophysics Data System (ADS)
Umbría, Juan Sánchez; Net, Marta
2016-11-01
A tutorial on continuation and bifurcation methods for the analysis of truncated dissipative partial differential equations is presented. It focuses on the computation of equilibria, periodic orbits, their loci of codimension-one bifurcations, and invariant tori. To make it more self-contained, it includes some definitions of basic concepts of dynamical systems, and some preliminaries on the general underlying techniques used to solve non-linear systems of equations by inexact Newton methods, and eigenvalue problems by means of subspace or Arnoldi iterations.
On numerical methods for Hamiltonian PDEs and a collocation method for the Vlasov-Maxwell equations
Holloway, J.P.
1996-11-01
Hamiltonian partial differential equations often have implicit conservation laws-constants of the motion-embedded within them. It is not, in general, possible to preserve these conservation laws simply by discretization in conservative form because there is frequently only one explicit conservation law. However, by using weighted residual methods and exploiting the Hamiltonian structure of the equations it is shown that at least some of the conservation laws are preserved in a method of lines (continuous in time). In particular, the Hamiltonian can always be exactly preserved as a constant of the motion. Other conservation laws, in particular linear and quadratic Casimirs and momenta, can sometimes be conserved too, depending on the details of the equations under consideration and the form of discretization employed. Collocation methods also offer automatic conservation of linear and quadratic Casimirs. Some standard discretization methods, when applied to Hamiltonian problems are shown to be derived from a numerical approximation to the exact Poisson bracket of the system. A method for the Vlasov-Maxwell equations based on Legendre-Gauss-Lobatto collocation is presented as an example of these ideas. 22 refs.
Ye, Jingfei; Wang, Wei; Gao, Zhishan; Liu, Zhiying; Wang, Shuai; Benítez, Pablo; Miñano, Juan C; Yuan, Qun
2015-10-05
Wavefront estimation from the slope-based sensing metrologies zis important in modern optical testing. A numerical orthogonal transformation method is proposed for deriving the numerical orthogonal gradient polynomials as numerical orthogonal basis functions for directly fitting the measured slope data and then converting to the wavefront in a straightforward way in the modal approach. The presented method can be employed in the wavefront estimation from its slopes over the general shaped aperture. Moreover, the numerical orthogonal transformation method could be applied to the wavefront estimation from its slope measurements over the dynamic varying aperture. The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified by the examples. They indicate that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.
Advanced Doubling Adding Method for Radiative Transfer in Planetary Atmospheres
NASA Astrophysics Data System (ADS)
Liu, Quanhua; Weng, Fuzhong
2006-12-01
The doubling adding method (DA) is one of the most accurate tools for detailed multiple-scattering calculations. The principle of the method goes back to the nineteenth century in a problem dealing with reflection and transmission by glass plates. Since then the doubling adding method has been widely used as a reference tool for other radiative transfer models. The method has never been used in operational applications owing to tremendous demand on computational resources from the model. This study derives an analytical expression replacing the most complicated thermal source terms in the doubling adding method. The new development is called the advanced doubling adding (ADA) method. Thanks also to the efficiency of matrix and vector manipulations in FORTRAN 90/95, the advanced doubling adding method is about 60 times faster than the doubling adding method. The radiance (i.e., forward) computation code of ADA is easily translated into tangent linear and adjoint codes for radiance gradient calculations. The simplicity in forward and Jacobian computation codes is very useful for operational applications and for the consistency between the forward and adjoint calculations in satellite data assimilation.
Applications of numerical methods to simulate the movement of contaminants in groundwater.
Sun, N Z
1989-01-01
This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327
General advancing front packing algorithm for the discrete element method
NASA Astrophysics Data System (ADS)
Morfa, Carlos A. Recarey; Pérez Morales, Irvin Pablo; de Farias, Márcio Muniz; de Navarra, Eugenio Oñate Ibañez; Valera, Roberto Roselló; Casañas, Harold Díaz-Guzmán
2016-11-01
A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.
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.
FULLY COUPLED SIMULATION OF COSMIC REIONIZATION. I. NUMERICAL METHODS AND TESTS
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.
Fully coupled simulation of cosmic reionization. I. numerical methods and tests
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.
Fully coupled simulation of cosmic reionization. I. numerical methods and tests
Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; ...
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
Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.
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
Hybrid Particle-Continuum Numerical Methods for Aerospace Applications
2011-01-01
public release, distribution unlimited 13. SUPPLEMENTARY NOTES See also ADA579248. Models and Computational Methods for Rarefied Flows (Modeles et...References [1] Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows , Clarendon Press, 1994. [2] Wilmoth, R. G., Mitcheltree...Mechanics, ASME Winter Annual Meeting , Chicago, 1994, pp. 5156. [11] Arkilic, E. B., Measurement of the Mass Flow and Tangential Momentum
Extremal polynomials and methods of optimization of numerical algorithms
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.
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.
Application of Methods of Numerical Analysis to Physical and Engineering Data.
1980-10-15
for tbe estimated fo. Part E extends the method to include an arbitrary signal noise power function. Part F discusses a method for obtaining initial...7 AD-AI02 685 BEDFORD RESEARCH ASSOCIATES MA F/6 4/1APPLICATION OF METHODS OF NUMERICAL ANALYSIS TO PHYSICAL AND EN--ETC(U) OCT 80 R BOUCHER, T...APPLICATION OF METHODS OF NUMERICAL .) ANALYSIS TO PHYSICAL AND! ENGINEERING DATA R. Boucher T. Costello ~ P. Meehan J. Noonan Bedford Research Associates 2
Design of braided composite tubes by numerical analysis method
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.
Riser Feeding Evaluation Method for Metal Castings Using Numerical Analysis
NASA Astrophysics Data System (ADS)
Ahmad, Nadiah
One of the design aspects that continues to create a challenge for casting designers is the optimum design of casting feeders (risers). As liquid metal solidifies, the metal shrinks and forms cavities inside the casting. In order to avoid shrinkage cavities, risers are added to the casting shape to supply additional molten metal when shrinkage occurs during solidification. The shrinkage cavities in the casting are compensated by controlling the cooling rate to promote directional solidification. This control can be achieved by designing the casting such that the cooling begins at the sections that are farthest away from the risers and ends at the risers. Therefore, the risers will solidify last and feed the casting with the molten metal. As a result, the shrinkage cavities formed during solidification are in the risers which are later removed from the casting. Since casting designers have to usually go through iterative processes of validating the casting designs which are very costly due to expensive simulation processes or manual trials and errors on actual casting processes, this study investigates more efficient methods that will help casting designers utilize their casting experiences systematically to develop good initial casting designs. The objective is to reduce the casting design method iterations; therefore, reducing the cost involved in that design processes. The aim of this research aims at finding a method that can help casting designers design effective risers used in sand casting process of aluminum-silicon alloys by utilizing the analysis of solidification simulation. The analysis focuses on studying the significance of pressure distribution of the liquid metal at the early stage of casting solidification, when heat transfer and convective fluid flow are taken into account in the solidification simulation. The mathematical model of casting solidification was solved using the finite volume method (FVM). This study focuses to improve our
Numerical method for evolving the projected Gross-Pitaevskii equation.
Blakie, P Blair
2008-08-01
In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and nonequilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.
Nuclear methods of analysis in the advanced neutron source
Robinson, L.; Dyer, F.F.
1994-12-31
The Advanced Neutron Source (ANS) research reactor is presently in the conceptual design phase. The thermal power of this heavy water cooled and moderated reactor will be about 350 megawatts. The core volume of 27 liter is designed to provide the optimum neutron fluence rate for the numerous experimental facilities. The peak thermal neutron fluence rate is expected to be slightly less than 10{sup 20} neutrons/m{sup 2}s. In addition to the more than 40 neutron scattering stations, there will be extensive facilities for isotope production, material irradiation and analytical chemistry including neutron activation analysis (NAA) and a slow positron source. The highlight of this reactor will be the capability that it will provide for conducting research using cold neutrons. Two cryostats containing helium-cooled liquid deuterium will be located in the heavy water reflector tank. Each cryostat will provide low-temperature neutrons to researchers via numerous guides. A hot source with two beam tubes and several thermal beam tubes will also be available. The NAA facilities in the ANS will consist of seven pneumatic tubes, one cold neutron guide for prompt gamma-ray neutron activation analysis (PGNAA), and one cold neutron slanted guide for neutron depth profiling (NDP). In addition to these neutron interrogation systems, a gamma-ray irradiation facility for materials testing will be housed in a spent fuel storage pool. This paper will provide detailed information regarding the design and use of these various experimental systems.
A model and numerical method for compressible flows with capillary effects
NASA Astrophysics Data System (ADS)
Schmidmayer, Kevin; Petitpas, Fabien; Daniel, Eric; Favrie, Nicolas; Gavrilyuk, Sergey
2017-04-01
A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.
NASA Astrophysics Data System (ADS)
Shen, Fabin; Wang, Anbo
2006-02-01
The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.
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.
Two Different Methods for Numerical Solution of the Modified Burgers' Equation
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
Two different methods for numerical solution of the modified Burgers' equation.
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.
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
IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.
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
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
A numerical method for solving optimal control problems using state parametrization
NASA Astrophysics Data System (ADS)
Mehne, H.; Borzabadi, A.
2006-06-01
A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
Advances in Statistical Methods for Substance Abuse Prevention Research
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
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1989-01-01
Recent advances in computational fluid dynamics (CFD) are discussed in reviews and reports. Topics addressed include CFD models in plasma dynamics, parallel computation for simulation studies, CFD for hypersonic airbreathing aircraft, multigrid methods for the steady incompressible Navier-Stokes equations, upwind differencing techniques, TV stable schemes for shock-interacting flows, Euler models of hypersonic vortex flows, parallel multilevel adaptive methods, and vortex methods for slightly viscous three-dimensional flows. Consideration is given to the accuracy of node-based solutions on irregular meshes, multigrid calculations for cascades, a finite-volume-element method for planar cavity flow, parallel heterogeneous mesh refinement for advection-diffusion equations, the convergence of the spectral-viscosity method for nonlinear conservation laws, and numerical simulations of Taylor vortices in a spherical gap.
NASA Astrophysics Data System (ADS)
Dwoyer, D. L.; Hussaini, M. Y.; Voigt, R. G.
Recent advances in computational fluid dynamics (CFD) are discussed in reviews and reports. Topics addressed include CFD models in plasma dynamics, parallel computation for simulation studies, CFD for hypersonic airbreathing aircraft, multigrid methods for the steady incompressible Navier-Stokes equations, upwind differencing techniques, TV stable schemes for shock-interacting flows, Euler models of hypersonic vortex flows, parallel multilevel adaptive methods, and vortex methods for slightly viscous three-dimensional flows. Consideration is given to the accuracy of node-based solutions on irregular meshes, multigrid calculations for cascades, a finite-volume-element method for planar cavity flow, parallel heterogeneous mesh refinement for advection-diffusion equations, the convergence of the spectral-viscosity method for nonlinear conservation laws, and numerical simulations of Taylor vortices in a spherical gap.
NASA Astrophysics Data System (ADS)
Karafyllis, Iasson; Grüne, Lars
2009-09-01
In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based stabilization methods are exploited.
Methods of numerical analysis of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics
NASA Astrophysics Data System (ADS)
Klimenko, S. V.; Nikitin, I. N.; Urazmetov, W. F.
2000-04-01
Numerical methods for solution of differential equations with deviating arguments describing 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with half-retarded/halfadvanced interaction (Wheeler and Feynman, 1949) are developed. A bifurcation of solutions and violation of their reflectional symmetries in the region of velocities v>0.937c are found in numerical analysis.
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.
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.
NASA Astrophysics Data System (ADS)
Xie, Shuisheng; Huang, Guojie; Zhang, Xiaoli; Yang, Haoqiang
2007-05-01
Damper Cooling Tube (DCT) Method to fabricate the semi-solid metal slurry has been studied in this paper. Firstly, numerical simulation is adopted to investigate the flow process in order to optimize the technical parameters. The temperature effects on the rheological properties of the slurries are also considered. The effects of technical parameters on the slurry properties are studied in detail. Then the experiment was carried out with AZ91 magnesium alloy in order to examine the numerical simulation results. The results of numerical simulation are consistent with the experimental results. According to the numerical and experiment results, the DCT device can fabricate fine semisolid slurry with primary globular phase.
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.
Some numerical methods for integrating systems of first-order ordinary differential equations
NASA Technical Reports Server (NTRS)
Clark, N. W.
1969-01-01
Report on numerical methods of integration includes the extrapolation methods of Bulirsch-Stoer and Neville. A comparison is made nith the Runge-Kutta and Adams-Moulton methods, and circumstances are discussed under which the extrapolation method may be preferred.
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.
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.
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…
Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J
2017-01-01
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.
NASA Astrophysics Data System (ADS)
Zamolo, R.; Nobile, E.
2017-01-01
A Least Squares Collocation Meshless Method based on Radial Basis Function (RBF) interpolation is used to solve steady state heat conduction problems on 2D polygonal domains using MATLAB® environment. The point distribution process required by the numerical method can be fully automated, taking account of boundary conditions and geometry of the problem to get higher point distribution density where needed. Several convergence tests have been carried out comparing the numerical results to the corresponding analytical solutions to outline the properties of this numerical approach, considering various combinations of parameters. These tests showed favorable convergence properties in the simple cases considered: along with the geometry flexibility, these features confirm that this peculiar numerical approach can be an effective tool in the numerical simulation of heat conduction problems.
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.
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.
A Review of Element-Based Galerkin Methods for Numerical Weather Prediction
2015-04-01
Weather Prediction 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK...Numerical Weather Prediction (NWP) is in a period of transition. As resolutions increase global models are moving towards fully nonhydrostatic dynamical...Review of numerical methods for nonhydrostatic weather prediction models Meteorol. Atmos. Phys. 82, 2003], this review discusses EBG methods as a viable
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.
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2016-12-01
In this work we consider trigonometrically fitted two step hybrid methods for the numerical solution of second-order initial value problems. We follow the approach of Simos and derive trigonometrically fitting conditions for methods with five stages. As an example we modify a seventh order method and apply to three well known oscillatory problems.
Numerical method for estimating the size of chaotic regions of phase space
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)
On Numerical Methods of Solving Some Optimal Path Problems on the Plane
NASA Astrophysics Data System (ADS)
Ushakov, V. N.; Matviychuk, A. R.; Malev, A. G.
Three numerical methods of solution of some time optimal control problems for a system under phase constraints are described in the paper. Two suggested methods are based on transition to the discrete time model, constructing attainability sets and application of the guide construction. The third method is based on the Deikstra algorithm.
Advanced Computational Aeroacoustics Methods for Fan Noise Prediction
NASA Technical Reports Server (NTRS)
Envia, Edmane (Technical Monitor); Tam, Christopher
2003-01-01
Direct computation of fan noise is presently not possible. One of the major difficulties is the geometrical complexity of the problem. In the case of fan noise, the blade geometry is critical to the loading on the blade and hence the intensity of the radiated noise. The precise geometry must be incorporated into the computation. In computational fluid dynamics (CFD), there are two general ways to handle problems with complex geometry. One way is to use unstructured grids. The other is to use body fitted overset grids. In the overset grid method, accurate data transfer is of utmost importance. For acoustic computation, it is not clear that the currently used data transfer methods are sufficiently accurate as not to contaminate the very small amplitude acoustic disturbances. In CFD, low order schemes are, invariably, used in conjunction with unstructured grids. However, low order schemes are known to be numerically dispersive and dissipative. dissipative errors are extremely undesirable for acoustic wave problems. The objective of this project is to develop a high order unstructured grid Dispersion-Relation-Preserving (DRP) scheme. would minimize numerical dispersion and dissipation errors. contains the results of the funded portion of the project. scheme on an unstructured grid has been developed. constructed in the wave number space. The characteristics of the scheme can be improved by the inclusion of additional constraints. Stability of the scheme has been investigated. Stability can be improved by adopting the upwinding strategy.
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.).
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.).
Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method.
Ghasempour Nesheli, A; Mirjalili, A; Yazdanpanah, M M
2016-01-01
We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.'s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.
Application of numerical methods for diffusion-based modeling of skin permeation.
Frasch, H Frederick; Barbero, Ana M
2013-02-01
The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions.
Method for Numerical Solution of the Stationary Schrödinger Equation
NASA Astrophysics Data System (ADS)
Knyazev, S. Yu.; Shcherbakova, E. E.
2017-02-01
The aim of this work is to describe a method of numerical solution of the stationary Schrödinger equation based on the integral equation that is identical to the Schrödinger equation. The method considered here allows one to find the eigenvalues and eigensolutions for quantum-mechanical problems of different dimensionality. The method is tested by solving problems for one-dimensional and two-dimensional quantum oscillators, and results of these tests are presented. Satisfactory agreement of the results obtained using this numerical method with well-known analytical solutions is demonstrated.
Numerical methods for estimating J integral in models with regular rectangular meshes
NASA Astrophysics Data System (ADS)
Kozłowiec, B.
2017-02-01
Cracks and delaminations are the common structural degradation mechanisms studied recently using numerous methods and techniques. Among them, numerical methods based on FEM analyses are in widespread commercial use. The scope of these methods has focused i.e. on energetic approach to linear elastic fracture mechanics (LEFM) theory, encompassing such quantities as the J-integral and the energy release rate G. This approach enables to introduce damage criteria of analyzed structures without dealing with the details of the physical singularities occurring at the crack tip. In this paper, two numerical methods based on LEFM are used to analyze both isotropic and orthotropic specimens and the results are compared with well-known analytical solutions as well as (in some cases) VCCT results. These methods are optimized for industrial use with simple, rectangular meshes. The verification is made based on two dimensional mode partitioning.
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.
NASA Astrophysics Data System (ADS)
Katsuro-Hopkins, Oksana; Sabbagh, S. A.; Bialek, J. M.; Park, H. K.; Kim, J. Y.; You, K.-I.; Glasser, A. H.; Lao, L. L.
2007-11-01
Stability to ideal MHD kink/ballooning modes and the resistive wall mode (RWM) is investigated for the KSTAR tokamak. Free-boundary equilibria that comply with magnetic field coil current constraints are computed for monotonic and reversed shear safety factor profiles and H-mode tokamak pressure profiles. Advanced tokamak operation at moderate to low plasma internal inductance shows that a factor of two improvement in the plasma beta limit over the no-wall beta limit is possible for toroidal mode number of unity. The KSTAR conducting structure, passive stabilizers, and in-vessel control coils are modeled by the VALEN-3D code and the active RWM stabilization performance of the device is evaluated using both standard and advanced feedback algorithms. Steady-state power and voltage requirements for the system are estimated based on the expected noise on the RWM sensor signals. Using NSTX experimental RWM sensors noise data as input, a reduced VALEN state-space LQG controller is designed to realistically assess KSTAR stabilization system performance.
Critical study of higher order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.
Application of higher-order numerical methods to the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Kamiya, Tetsu; Toyama, Yoshio; Michiwaki, Yukihiro; Kikuchi, Takahiro
2013-01-01
The aim of the present study was to evaluate the possibility of numerical simulation of the swallowing process using a moving particle simulation (MPS) method, which defined the food bolus as a number of particles in a fluid, a solid, and an elastic body. In order to verify the accuracy of the simulation results, a simple water bolus falling model was solved using the three-dimensional (3D) MPS method. We also examined the simplified swallowing simulation using a two-dimensional (2D) MPS method to confirm the interactions between the liquid, solid, elastic bolus, and organ structure. In a comparison of the 3D MPS simulation and experiments, the falling time of the water bolus and the configuration of the interface between the liquid and air corresponded exactly to the experimental measurements and the visualization images. The results showed that the accuracy of the 3D MPS simulation was qualitatively high for the simple falling model. Based on the results of the simplified swallowing simulation using the 2D MPS method, each bolus, defined as a liquid, solid, and elastic body, exhibited different behavior when the organs were transformed forcedly. This confirmed that the MPS method could be used for coupled simulations of the fluid, the solid, the elastic body, and the organ structures. The results suggested that the MPS method could be used to develop a numerical simulator of the swallowing process.
Mathematical model and its fast numerical method for the tumor growth.
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.
NASA Technical Reports Server (NTRS)
Chen, Y. S.
1986-01-01
In the present paper, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BEC) systems has been developed and evaluated. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme and a central differencing plus artificial dissipation scheme are used to approximate the convection terms in the governing equations. Effects of these two schemes on the accuracy of numerical predictions are studied. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm, SIMPLE-C. Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present numerical method.
NASA Technical Reports Server (NTRS)
Thomas, P. D.
1980-01-01
A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.
An improved mixed numerical-experimental method for stress field calculation
NASA Astrophysics Data System (ADS)
Lopes, H. M. R.; Guedes, R. M.; Vaz, M. A.
2007-07-01
In this work a numerical-experimental method is used to study the dynamic behavior of an aluminum plate subjected to a small mass impact. The out-of-plane displacements, due to transient bending wave propagation, were assessed for successive time instants, using double pulse TV-holography, also known as pulsed ESPI. The experimental setup and the image processing methods were improved to allow the calculation of the plate transient stress field. Integral transforms are used to obtain the strain fields from spatial derivatives of displacements noisy data. A numerical simulation of the plate transient response was carried out with FEM Ansys ®. For this purpose a PZT transducer was used to record the impact force history, which was inputted in the numerical model. Finally, the comparisons between numerical and experimental results are presented in order to validate the present methodology.
NASA Astrophysics Data System (ADS)
Liu, H. S.; Xing, Z. W.; Bao, J.; Song, B. Y.
2010-04-01
Hot forming is a new way to manufacture complex-shaped components of advanced high-strength steel (AHSS) sheet with a minimum of spring-back. Numerical simulation is an effective way to examine the hot-forming process, particularly to determine thermal and thermo-mechanical characteristics and their dependencies on temperature, strain and strain rate. The flow behavior of the 22MnB5 AHSS is investigated through hot tensile tests. A 3D finite element (FE) model of hot-stamping process for the [InlineMediaObject not available: see fulltext.] shaped part is built under the ABAQUS/Explicit environment based on the solutions of several key problems, such as treatment of contact between blank and tools, determination of material characteristics and meshing, etc. Numerical simulation is carried out to investigate the influence of blank holder force (BHF) and die gap on the hot-forming process for the [InlineMediaObject not available: see fulltext.] shaped part. Numerical results show the FE model is effective in simulation of hot-forming process. Large BHF reduces the amount of spring-back and improves the contact of flange with tools while avoiding cracking of stamped part. Die gap has a considerable influence on the distribution of temperature on side walls; the larger the die gap, higher is the temperature on the sidewall of [InlineMediaObject not available: see fulltext.] shaped part.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
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.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
Advances in the Surface Renewal Flux Measurement Method
NASA Astrophysics Data System (ADS)
Shapland, T. M.; McElrone, A.; Paw U, K. T.; Snyder, R. L.
2011-12-01
The measurement of ecosystem-scale energy and mass fluxes between the planetary surface and the atmosphere is crucial for understanding geophysical processes. Surface renewal is a flux measurement technique based on analyzing the turbulent coherent structures that interact with the surface. It is a less expensive technique because it does not require fast-response velocity measurements, but only a fast-response scalar measurement. It is therefore also a useful tool for the study of the global cycling of trace gases. Currently, surface renewal requires calibration against another flux measurement technique, such as eddy covariance, to account for the linear bias of its measurements. We present two advances in the surface renewal theory and methodology that bring the technique closer to becoming a fully independent flux measurement method. The first advance develops the theory of turbulent coherent structure transport associated with the different scales of coherent structures. A novel method was developed for identifying the scalar change rate within structures at different scales. Our results suggest that for canopies less than one meter in height, the second smallest coherent structure scale dominates the energy and mass flux process. Using the method for resolving the scalar exchange rate of the second smallest coherent structure scale, calibration is unnecessary for surface renewal measurements over short canopies. This study forms the foundation for analysis over more complex surfaces. The second advance is a sensor frequency response correction for measuring the sensible heat flux via surface renewal. Inexpensive fine-wire thermocouples are frequently used to record high frequency temperature data in the surface renewal technique. The sensible heat flux is used in conjunction with net radiation and ground heat flux measurements to determine the latent heat flux as the energy balance residual. The robust thermocouples commonly used in field experiments
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.
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.
Impact of numerical method on a side jets formation in a round jet
NASA Astrophysics Data System (ADS)
Wawrzak, K.; Boguslawski, A.
2016-10-01
Numerical analysis of a formation of side jets in an externally modulated round jet is presented. The research is performed applying Large Eddy Simulation method and high-order codes based on Cartesian and cylindrical coordinates. The main attention is paid to an impact of numerical approach on the formation of the side jets, their number and localisation. The results obtained suggest that on Cartesian meshes the number and directions of the side jets are dependent on the distribution of the mesh nodes.
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.
Numerical study of the inverse problem for the diffusion-reaction equation using optimization method
NASA Astrophysics Data System (ADS)
Soboleva, O. V.; Brizitskii, R. V.
2016-04-01
The model of transfer of substance with mixed boundary condition is considered. The inverse extremum problem of identification of the main coefficient in a nonstationary diffusion-reaction equation is formulated. The numerical algorithm based on the Newton-method of nonlinear optimization and finite difference discretization for solving this extremum problem is developed and realized on computer. The results of numerical experiments are discussed.
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.
NASA Astrophysics Data System (ADS)
Labergere, C.; Saanouni, K.; Benafia, S.; Galmiche, J.; Sulaiman, H.
2013-05-01
This paper presents the modelling and adaptive numerical simulation of the fine blanking process. Thermodynamically-consistent constitutive equations, strongly coupled with ductile damage, together with specific boundary conditions (particular command of forces on blank holder and counterpunch) are presented. This model is implemented into ABAQUS/EXPLICIT using the Vumat user subroutine and connected with an adaptive 2D remeshing procedure. The different material parameters are identified for the steel S600MC using experimental tensile tests conducted until the final fracture. A parametric study aiming to examine the sensitivity of the process parameters (die radius, clearance die/punch) to the punch force and fracture surfaces topology (convex zone, sheared zone, fracture zone and the burr).
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).
Integration of isothermal amplification methods in microfluidic devices: Recent advances.
Giuffrida, Maria Chiara; Spoto, Giuseppe
2017-04-15
The integration of nucleic acids detection assays in microfluidic devices represents a highly promising approach for the development of convenient, cheap and efficient diagnostic tools for clinical, food safety and environmental monitoring applications. Such tools are expected to operate at the point-of-care and in resource-limited settings. The amplification of the target nucleic acid sequence represents a key step for the development of sensitive detection protocols. The integration in microfluidic devices of the most popular technology for nucleic acids amplifications, polymerase chain reaction (PCR), is significantly limited by the thermal cycling needed to obtain the target sequence amplification. This review provides an overview of recent advances in integration of isothermal amplification methods in microfluidic devices. Isothermal methods, that operate at constant temperature, have emerged as promising alternative to PCR and greatly simplify the implementation of amplification methods in point-of-care diagnostic devices and devices to be used in resource-limited settings. Possibilities offered by isothermal methods for digital droplet amplification are discussed.
Advances in nondestructive evaluation methods for inspection of refractory concretes
Ellingson, W. A.
1980-01-01
Refractory concrete linings are essential to protect steel pressure boundaries from high-temperature agressive erosive/corrosive environments. Castable refractory concretes have been gaining more acceptance as information about their performance increases. Economic factors, however, have begun to impose high demands on the reliability of refractory materials. Advanced nondestructive evaluation methods are being developed to assist the refractory user. Radiographic techniques, thermography, acoustic-emission detection, and interferometry have been shown to yield information on the structural status of refractory concrete. Methods using /sup 60/Co radiation sources are capable of yielding measurements of refractory wear rate as well as images of cracks and/or voids in pre- and post-fired refractory linings up to 60 cm thick. Thermographic (infrared) images serve as a qualitative indicator of refractory spalling, but quantitative measurements are difficult to obtain from surface-temperature mapping. Acoustic emission has been shown to be a qualitative indicator of thermomechanical degradation of thick panels of 50 and 95% Al/sub 2/O/sub 3/ during initial heating and cooling at rates of 100 to 220/sup 0/C/h. Laser interferometry methods have been shown to be capable of complete mappings of refractory lining thicknesses. This paper will present results obtained from laboratory and field applications of these methods in petrochemical, steel, and coal-conversion plants.
A critical study of higher-order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
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
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Technical Reports Server (NTRS)
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Astrophysics Data System (ADS)
Cerro, J. A.; Scotti, S. J.
1991-07-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
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.
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.
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.
NASA Astrophysics Data System (ADS)
Simmel, Martin; Trautmann, Thomas; Tetzlaff, Gerd
The Linear Discrete Method is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made with the Method of Moments, the Berry-Reinhardt model and the Linear Flux Method. Simulations for all numerical methods are shown for the kernel after Golovin [Bull. Acad. Sci. USSR, Geophys. Ser. 5 (1963) 783] and are compared with the analytical solution for two different initial distributions. BRM seems to give the best results and LDM gives good results, too. LFM overestimates the drop growth for the right tail of the distribution and MOM does the same but over the entire drop spectrum. For the hydrodynamic kernel after Long [J. Atmos. Sci. 31 (1974) 1040], simulations are presented using the four numerical methods (LDM, MOM, BRM, LFM). Especially for high resolutions, the solutions of LDM and LFM approach each other very closely. In addition, LDM simulations using the hydrodynamic kernel after Böhm [Atmos. Res. 52 (1999) 167] are presented, which show good correspondence between low- and high-resolution results. Computation efficiency is especially important when numerical schemes are to be included in larger models. Therefore, the computation times of the four methods were compared for the cases with the Golovin kernel. The result is that LDM is the fastest method by far, needing less time than other methods by a factor of 2-7, depending on the case and the bin resolution. For high resolutions, MOM is the slowest. For the lowest resolution, this holds for LFM.
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®.
Comparative Assessment of Advanced Gay Hydrate Production Methods
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.
Advanced Motion Compensation Methods for Intravital Optical Microscopy
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
Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.
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.
[Advances in development of gene-gene interaction analysis methods based on SNP data: a review].
Luan, Yi-Zhao; Zuo, Xiao-Yu; Liu, Ke; Li, Gu; Rao, Shao-Qi
2013-12-01
The SNP-based association analysis has become one of the most important approaches to interpret the underlying molecular mechanisms for human complex diseases. Nevertheless, the widely-used singe-locus analysis is only capable of capturing a small portion of susceptible SNPs with prominent marginal effects, leaving the important genetic component, epistasis or joint effects, to be undetectable. Identifying the complex interplays among multiple genes in the genome-wide context is an essential task for systematically unraveling the molecular mechanisms for complex diseases. Many approaches have been used to detect genome-wide gene-gene interactions and provided new insights into the genetic basis of complex diseases. This paper reviewed recent advances of the methods for detecting gene-gene interaction, categorized into three types, model-based and model-free statistical methods, and data mining methods, based on their characteristics in theory and numerical algorithm. In particular, the basic principle, numerical implementation and cautions for application for each method were elucidated. In addition, this paper briefly discussed the limitations and challenges associated with detecting genome-wide epistasis, in order to provide some methodological consultancies for scientists in the related fields.
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
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.
Advanced physical models and monitoring methods for in situ bioremediation
Simon, K.; Chalmer, P.
1996-05-30
Numerous reports have indicated that contamination at DOE facilities is widespread and pervasive. Existing technology is often too costly or ineffective in remediating these contamination problems. An effective method to address one class of contamination, petroleum hydrocarbons, is in situ bioremediation. This project was designed to provide tools and approaches for increasing the reliability of in situ bioremediation. An example of the recognition within DOE for developing these tools is in the FY-1995 Technology Development Needs Summary of the Office of Technology Development of the US DOE. This document identifies specific needs addressed by this research. For example, Section 3.3 Need Statement IS-3 identifies the need for a {open_quotes}Rapid method to detect in situ biodegradation products.{close_quotes} Also, BW-I identifies the need to recognize boundaries between clean and contaminated materials and soils. Metabolic activity could identify these boundaries. Measuring rates of in situ microbial activity is critical to the fundamental understanding of subsurface microbiology and in selecting natural attenuation as a remediation option. Given the complexity and heterogeneity of subsurface environments, a significant cost incurred during bioremediation is the characterization of microbial activity, in part because so many intermediate end points (biomass, gene frequency, laboratory measurements of activity, etc.) must be used to infer in situ activity. A fast, accurate, real-time, and cost-effective method is needed to determine success of bioremediation at DOE sites.
Johnsen, Eric Larsson, Johan Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.
2010-02-20
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
NASA Astrophysics Data System (ADS)
Rockway, J. W.; Logan, J. C.; Deneris, C. A.
1991-10-01
The principal goal of the Electromagnetic Compatibility (EMC) Project is to minimize exterior electromagnetic interference (EMI) problems during the life-cycle of Navy surface ships. An important aspect of mitigating exterior EMI problems is the characterization of antenna performance. At the present time, for shipboard MF and HF (2 to 30 MHz) antennas, there exists two techniques for performing a topside antenna study: brass scale modeling and numerical modeling. Brass scale models have a few drawbacks: they are time-consuming to build, difficult to rapidly modify, troublesome to accurately measure near fields on scale models, and they are somewhat limited in their application. This report is an evaluation of the progress in development of two advanced computer programs for antenna modeling. One is the performance of the JUNCTION Code, under development at the University of Houston, and the other is the performance of the Numerical Electromagnetic Code - Version 4 (NEC4) being developed at the Lawrence Livermore National Laboratory.
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
A review on recent advances in numerical modelling of bone cutting.
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.
Advanced numerical techniques for accurate unsteady simulations of a wingtip vortex
NASA Astrophysics Data System (ADS)
Ahmad, Shakeel
A numerical technique is developed to simulate the vortices associated with stationary and flapping wings. The Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations are used over an unstructured grid. The present work assesses the locations of the origins of vortex generation, models those locations and develops a systematic mesh refinement strategy to simulate vortices more accurately using the URANS model. The vortex center plays a key role in the analysis of the simulation data. A novel approach to locating a vortex center is also developed referred to as the Max-Max criterion. Experimental validation of the simulated vortex from a stationary NACA0012 wing is achieved. The tangential velocity along the core of the vortex falls within five percent of the experimental data in the case of the stationary NACA0012 simulation. The wing surface pressure coefficient also matches with the experimental data. The refinement techniques are then focused on unsteady simulations of pitching and dual-mode wing flapping. Tip vortex strength, location, and wing surface pressure are analyzed. Links to vortex behavior and wing motion are inferred. Key words: vortex, tangential velocity, Cp, vortical flow, unsteady vortices, URANS, Max-Max, Vortex center
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.
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
A numerical study of the European option by the MLPG method with moving kriging interpolation.
Phaochoo, P; Luadsong, A; Aschariyaphotha, N
2016-01-01
In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively. We show that the spectral radius of amplification matrix with the discrete operator is less than 1. This ensures that this numerical scheme is stable. Numerical experiments are performed with time varying volatility and the results are compared with the analytical and the numerical results of other methods.
Advances in Time Estimation Methods for Molecular Data.
Kumar, Sudhir; Hedges, S Blair
2016-04-01
Molecular dating has become central to placing a temporal dimension on the tree of life. Methods for estimating divergence times have been developed for over 50 years, beginning with the proposal of molecular clock in 1962. We categorize the chronological development of these methods into four generations based on the timing of their origin. In the first generation approaches (1960s-1980s), a strict molecular clock was assumed to date divergences. In the second generation approaches (1990s), the equality of evolutionary rates between species was first tested and then a strict molecular clock applied to estimate divergence times. The third generation approaches (since ∼2000) account for differences in evolutionary rates across the tree by using a statistical model, obviating the need to assume a clock or to test the equality of evolutionary rates among species. Bayesian methods in the third generation require a specific or uniform prior on the speciation-process and enable the inclusion of uncertainty in clock calibrations. The fourth generation approaches (since 2012) allow rates to vary from branch to branch, but do not need prior selection of a statistical model to describe the rate variation or the specification of speciation model. With high accuracy, comparable to Bayesian approaches, and speeds that are orders of magnitude faster, fourth generation methods are able to produce reliable timetrees of thousands of species using genome scale data. We found that early time estimates from second generation studies are similar to those of third and fourth generation studies, indicating that methodological advances have not fundamentally altered the timetree of life, but rather have facilitated time estimation by enabling the inclusion of more species. Nonetheless, we feel an urgent need for testing the accuracy and precision of third and fourth generation methods, including their robustness to misspecification of priors in the analysis of large phylogenies and data
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
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.
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
NASA Astrophysics Data System (ADS)
Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao
2013-10-01
The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases
An analytically based numerical method for computing view factors in real urban environments
NASA Astrophysics Data System (ADS)
Lee, Doo-Il; Woo, Ju-Wan; Lee, Sang-Hyun
2016-11-01
A view factor is an important morphological parameter used in parameterizing in-canyon radiative energy exchange process as well as in characterizing local climate over urban environments. For realistic representation of the in-canyon radiative processes, a complete set of view factors at the horizontal and vertical surfaces of urban facets is required. Various analytical and numerical methods have been suggested to determine the view factors for urban environments, but most of the methods provide only sky-view factor at the ground level of a specific location or assume simplified morphology of complex urban environments. In this study, a numerical method that can determine the sky-view factors (ψ ga and ψ wa ) and wall-view factors (ψ gw and ψ ww ) at the horizontal and vertical surfaces is presented for application to real urban morphology, which are derived from an analytical formulation of the view factor between two blackbody surfaces of arbitrary geometry. The established numerical method is validated against the analytical sky-view factor estimation for ideal street canyon geometries, showing a consolidate confidence in accuracy with errors of less than 0.2 %. Using a three-dimensional building database, the numerical method is also demonstrated to be applicable in determining the sky-view factors at the horizontal (roofs and roads) and vertical (walls) surfaces in real urban environments. The results suggest that the analytically based numerical method can be used for the radiative process parameterization of urban numerical models as well as for the characterization of local urban climate.
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
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.
Numerical wave tank based on a conserved wave-absorbing method
NASA Astrophysics Data System (ADS)
Hu, Zhe; Tang, Wen-yong; Xue, Hong-xiang; Zhang, Xiao-ying
2016-03-01
Recently the numerical wave tank has become a widely-used tool to study waves as well as wave-structure interactions, and the wave-absorbing method is very important as its effect on the quality of waves generated. The relaxation method and the derived momentum source method are often utilized, however, the damping weight is constant during calculation and repeated trials are required to obtain an acceptable wave-absorbing effect. To address the abovementioned issues, a conserved wave-absorbing method is developed. The damping weight is determined by solving the mass conservation equation of the absorbing region at every time step. Based on this method, a two-dimensional numerical wave tank is established by using the VB language to simulate various waves by which the validation of this method is evaluated.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179
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.
A numerical method to solve the Stokes problem with a punctual force in source term
NASA Astrophysics Data System (ADS)
Lacouture, Loïc
2015-03-01
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the knowledge of a fundamental solution to the associated operator over the whole space. This method is motivated by the modeling of the movement of active thin structures in a viscous fluid.
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.
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.
NASA Astrophysics Data System (ADS)
Ma, Ning; Park, Taejoon; Kim, Dongun; Kim, Chongmin; Chung, Kwansoo
2010-06-01
The impact performance in a Charpy impact test was experimentally and numerically studied for the advanced high-strength steel sheets (AHSS) TWIP940 and TRIP590 as well as the high-strength grade known as 340R. To characterize the mechanical properties, uni-axial simple tension tests were conducted to determine the anisotropic properties and strain rate sensitivities of these materials. In particular, the high-speed strain-rate sensitivity of TRIP590 and 340R (rate sensitive) was also characterized to account for the high strain rates involved in the Charpy impact test. To evaluate fracture behavior in the Charpy impact test, a new damage model including a triaxiality-dependent fracture criterion and hardening behavior with stiffness deterioration was introduced. The model was calibrated via numerical simulations and experiments involving simple tension and V-notch tests. The new damage model along with the anisotropic yield function Hill 1948 was incorporated into the ABAQUS/Explicit FEM code, which performed reasonably well to predict the impact energy absorbed during the Charpy impact test.
Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations
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.
VERSE-Guided Numerical RF Pulse Design: A Fast Method for Peak RF Power Control
Lee, Daeho; Grissom, William A.; Lustig, Michael; Kerr, Adam B.; Stang, Pascal P.; Pauly, John M.
2013-01-01
In parallel excitation, the computational speed of numerical radiofrequency (RF) pulse design methods is critical when subject dependencies and system nonidealities need to be incorporated on-the-fly. One important concern with optimization-based methods is high peak RF power exceeding hardware or safety limits. Hence, online controllability of the peak RF power is essential. Variable-rate selective excitation pulse reshaping is ideally suited to this problem due to its simplicity and low computational cost. In this work, we first improve the fidelity of variable-rate selective excitation implementation for discrete-time waveforms through waveform oversampling such that variable-rate selective excitation can be robustly applied to numerically designed RF pulses. Then, a variable-rate selective excitation-guided numerical RF pulse design is suggested as an online RF pulse design framework, aiming to simultaneously control peak RF power and compensate for off-resonance. PMID:22135085
Numerical built-in method for the nonlinear JRC/JCS model in rock joint.
Liu, Qunyi; Xing, Wanli; Li, Ying
2014-01-01
The joint surface is widely distributed in the rock, thus leading to the nonlinear characteristics of rock mass strength and limiting the effectiveness of the linear model in reflecting characteristics. The JRC/JCS model is the nonlinear failure criterion and generally believed to describe the characteristics of joints better than other models. In order to develop the numerical program for JRC/JCS model, this paper established the relationship between the parameters of the JRC/JCS and Mohr-Coulomb models. Thereafter, the numerical implement method and implementation process of the JRC/JCS model were discussed and the reliability of the numerical method was verified by the shear tests of jointed rock mass. Finally, the effect of the JRC/JCS model parameters on the shear strength of the joint was analyzed.
The stability of numerical methods for second order ordinary differential equations
NASA Technical Reports Server (NTRS)
Gear, C. W.
1978-01-01
An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem dy/dt = Ay are inside this region, the numerical method is stable. If the second order system d/dt(dy/dt) = 2Ady/dt - By is solved as a first order system, the same result applies to the eigenvalues of the generalized eigenvalue problem (lambda-squared)I 2(lambda)A + B. No such region exists for general methods for second order equations, but in some cases a region of absolute stability can be defined for methods for the single second order equation d/dt(dy/dt) = 2ady/dt - by. The absence of a region of absolute stability can occur when different members of a system of first order equations are solved by different methods.
A Numerical Method for Simulation of Three Dimensional Ice Accretion on Aircrafts
NASA Astrophysics Data System (ADS)
Yi, X.; Wang, K. C.; Zhu, G. L.; Gui, Y. W.
2011-09-01
A numerical method for simulation of three dimensional ice accretion on aircraft is proposed in this paper. An Eulerian method for computation of collection efficiency on icing surface is presented at first. The external flow field of gas phase is calculated with computational fluid dynamics (CFD) method, based on which the governing equations of water phase are solved, and the corresponding collection efficiency is obtained. A three-dimensional model, considering effects of runback water, is then presented, and an iterative arithmetic for solving the model is developed. The impingement characteristics of a three elements wing are computed to evaluate the numerical method for collection efficiency calculation. Ice accretion on a MS-317 swept wing is calculated, and the consequent ice shape is compared with that of an experiment and Lewice3D. All the computational results are in good agreement with data of the experiment and reference, which indicates that the proposed method is feasible.
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.
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.
A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids
NASA Astrophysics Data System (ADS)
Hu, Guanghui
2017-02-01
In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.
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.
Advanced discretizations and multigrid methods for liquid crystal configurations
NASA Astrophysics Data System (ADS)
Emerson, David B.
Liquid crystals are substances that possess mesophases with properties intermediate between liquids and crystals. Here, we consider nematic liquid crystals, which consist of rod-like molecules whose average pointwise orientation is represented by a unit-length vector, n( x, y, z) = (n1, n 2, n3)T. In addition to their self-structuring properties, nematics are dielectrically active and birefringent. These traits continue to lead to many important applications and discoveries. Numerical simulations of liquid crystal configurations are used to suggest the presence of new physical phenomena, analyze experiments, and optimize devices. This thesis develops a constrained energy-minimization finite-element method for the efficient computation of nematic liquid crystal equilibrium configurations based on a Lagrange multiplier formulation and the Frank-Oseen free-elastic energy model. First-order optimality conditions are derived and linearized via a Newton approach, yielding a linear system of equations. Due to the nonlinear unit-length constraint, novel well-posedness theory for the variational systems, as well as error analysis, is conducted. The approach is shown to constitute a convergent and well-posed approach, absent typical simplifying assumptions. Moreover, the energy-minimization method and well-posedness theory developed for the free-elastic case are extended to include the effects of applied electric fields and flexoelectricity. In the computational algorithm, nested iteration is applied and proves highly effective at reducing computational costs. Additionally, an alternative technique is studied, where the unit-length constraint is imposed by a penalty method. The performance of the penalty and Lagrange multiplier methods is compared. Furthermore, tailored trust-region strategies are introduced to improve robustness and efficiency. While both approaches yield effective algorithms, the Lagrange multiplier method demonstrates superior accuracy per unit cost. In
Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method
NASA Astrophysics Data System (ADS)
Bekhoucha, F.; Rechak, S.; Cadou, J. M.
2016-12-01
In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.
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.
A novel method of including Landau level mixing in numerical studies of the quantum Hall effect
Wooten, Rachel; Quinn, John; Macek, Joseph
2013-12-04
Landau level mixing should influence the quantum Hall effect for all except the strongest applied magnetic fields. We propose a simple method for examining the effects of Landau level mixing by incorporating multiple Landau levels into the Haldane pseudopotentials through exact numerical diagonalization. Some of the resulting pseudopotentials for the lowest and first excited Landau levels will be presented.
A novel method of including Landau level mixing in numerical studies of the quantum Hall effect
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Quinn, John; Macek, Joseph
2013-12-01
Landau level mixing should influence the quantum Hall effect for all except the strongest applied magnetic fields. We propose a simple method for examining the effects of Landau level mixing by incorporating multiple Landau levels into the Haldane pseudopotentials through exact numerical diagonalization. Some of the resulting pseudopotentials for the lowest and first excited Landau levels will be presented.
A semi-analytical method for simulating matrix diffusion in numerical transport models
NASA Astrophysics Data System (ADS)
Falta, Ronald W.; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.
A semi-analytical method for simulating matrix diffusion in numerical transport models.
Falta, Ronald W; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.
Numerical simulation of pseudoelastic shape memory alloys using the large time increment method
NASA Astrophysics Data System (ADS)
Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad
2017-04-01
The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki–Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1978-01-01
The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.
Numerical Simulation of Drophila Flight Based on Arbitrary Langrangian-Eulerian Method
NASA Astrophysics Data System (ADS)
Erzincanli, Belkis; Sahin, Mehmet
2012-11-01
A parallel unstructured finite volume algorithm based on Arbitrary Lagrangian Eulerian (ALE) method has been developed in order to investigate the wake structure around a pair of flapping Drosophila wings. The numerical method uses a side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. A radial basis function (RBF) interpolation method is also implemented in order to achieve large mesh deformations. For the parallel solution of resulting large-scale algebraic equations, a matrix factorization is introduced similar to that of the projection method for the whole coupled system and two-cycle of BoomerAMG solver is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wing in hover flight. The time variation of the near wake structure is shown along with the aerodynamic loads and particle traces. The authors acknowledge financial support from Turkish National Scientific and Technical Research Council (TUBITAK) through project number 111M332. The authors would like to thank Michael Dickinson and Michael Elzinga for providing the experimental data.
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…
Numerical simulation of the process of production of single crystals by the Verneuil method
NASA Astrophysics Data System (ADS)
Grzymkowski, Radoslaw; Mochnacki, Bohdan; Suchy, Josef
1985-12-01
The paper presents the mathematical model of non-stationary crystallization of Al 2O 3 by Verneuil method, while taking into account the bilateral conjugation of this process with the admixture segregation phenomenon (Cr + for example). The numerical results are also shown.
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.
Underwater Photosynthesis of Submerged Plants – Recent Advances and Methods
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
Advances in the analysis of iminocyclitols: Methods, sources and bioavailability.
Amézqueta, Susana; Torres, Josep Lluís
2016-05-01
Iminocyclitols are chemically and metabolically stable, naturally occurring sugar mimetics. Their biological activities make them interesting and extremely promising as both drug leads and functional food ingredients. The first iminocyclitols were discovered using preparative isolation and purification methods followed by chemical characterization using nuclear magnetic resonance spectroscopy. In addition to this classical approach, gas and liquid chromatography coupled to mass spectrometry are increasingly used; they are highly sensitive techniques capable of detecting minute amounts of analytes in a broad spectrum of sources after only minimal sample preparation. These techniques have been applied to identify new iminocyclitols in plants, microorganisms and synthetic mixtures. The separation of iminocyclitol mixtures by chromatography is particularly difficult however, as the most commonly used matrices have very low selectivity for these highly hydrophilic structurally similar molecules. This review critically summarizes recent advances in the analysis of iminocyclitols from plant sources and findings regarding their quantification in dietary supplements and foodstuffs, as well as in biological fluids and organs, from bioavailability studies.
Regenerative medicine: advances in new methods and technologies.
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.
Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending
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
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.
Numerical manifold method for the forced vibration of thin plates during bending.
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.
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.
A short introduction to numerical methods used in cosmological N-body simulations
NASA Astrophysics Data System (ADS)
Hellwing, Wojciech
2015-12-01
We give a short introduction to modern numerical methods commonly used in cosmological N-body simulations. First, we present some simple considerations based on linear perturbation theory which indicate the necessity for N-body simulations. Then, based on a working example of the publicly available gadget-2 code, we describe particle mesh and Barnes-Hut oct-tree methods used in numerical gravity N-body solvers. We also briefly discuss methods used in an elementary hydrodynamic implementation used for baryonic gas. Next, we give a very basic description of time integration of equations of motion commonly used in N-body codes. Finally we describe the Zeldovitch approximation as an example method for generating initial conditions for computer simulations.
NASA Astrophysics Data System (ADS)
Pedram, Masoud; Esfandiari, Akbar; Khedmati, Mohammad Reza
2017-06-01
This paper investigates the viability of damage detection using power spectral density (PSD) of structural response both numerically and experimentally. The paper establishes a sensitivity based damage detection method to use PSD. The advantages of PSD as a model updating metric are explained and its challenges are addressed. An approximate frequency response function of damaged model is used to redeem the method for the effect of incomplete measurement. The robust solution of the developed sensitivity equation is achieved through a least-squares error minimization scheme, and the challenging issues are discussed. The ability of the method in localizing and quantifying the damage and its robustness against measurement and modeling errors is investigated by a numerical example. Experimental vibration test data of a laboratory concrete beam with various level of distributed damage is used to probe the method in practical conditions. The results show that PSD of response can be used to detect damages in lower frequency ranges with acceptable accuracy.
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
NASA Astrophysics Data System (ADS)
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.
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.
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 thermodynamic 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.
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.
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.
Applications of numerical optimization methods to helicopter design problems - A survey
NASA Technical Reports Server (NTRS)
Miura, H.
1985-01-01
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.
Assessment of modern methods in numerical simulations of high speed flows
NASA Technical Reports Server (NTRS)
Pindera, M. Z.; Yang, H. Q.; Przekwas, A. J.; Tucker, K.
1992-01-01
Results of extensive studies on CFD algorithms for 2D inviscid flows in Cartesian and body fitted coordinates geometries are reviewed. These studies represent part of an ongoing investigation of combustion instabilities involving the interactions of high-speed nonlinear acoustic waves. Four numerical methods for the treatment of high speed flows are compared, namely, Roe-Sweby TVD, Yee symmetric TVD; Osher-Chakravarthy TVD; and the Colella's multi-dimensional Godunov method.
Lin, W.L.; Carlson, K.D.; Chen, C.J. |
1999-05-01
In this study, a diagonal Cartesian method for thermal analysis is developed for simulation of conjugate heat transfer over complex boundaries. This method uses diagonal line segments in addition to Cartesian coordinates. The velocity fields are also modeled using the diagonal Cartesian method. The transport equations are discretized with the finite analytic (FA) method. The current work is validated by simulating a rotated lid-driven cavity flow with conjugate heat transfer, and accurate results are obtained.
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.
Numerical study of boundary layer interaction with shocks: Method and code validation
NASA Technical Reports Server (NTRS)
Adams, Nikolaus A.
1994-01-01
A major problem in modeling of turbulent supersonic flows is the correct assessment of viscous-inviscid interaction problems. Of particular interest is the interaction of boundary layers with shocks. Present turbulence models give in most cases unsatisfactory results in the region of rapid distortion and in the separation region (if one is present) in particular with regard to mean flow profiles and turbulence quantities. The objective of the present work is the direct numerical simulation of shock boundary layer interaction. This report summarizes the first phase during which a numerical method suitable for this problem has been developed and a computer code has been written and tested.
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.
A numerical study of rays in random media. [Monte Carlo method simulation
NASA Technical Reports Server (NTRS)
Youakim, M. Y.; Liu, C. H.; Yeh, K. C.
1973-01-01
Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.
NASA Astrophysics Data System (ADS)
Penenko, Alexey; Antokhin, Pavel
2016-11-01
The performance of a variational data assimilation algorithm for a transport and transformation model of atmospheric chemical composition is studied numerically in the case where the emission inventories are missing while there are additional in situ indirect concentration measurements. The algorithm is based on decomposition and splitting methods with a direct solution of the data assimilation problems at the splitting stages. This design allows avoiding iterative processes and working in real-time. In numerical experiments we study the sensitivity of data assimilation to measurement data quantity and quality.
Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F
2015-11-05
We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.
Recent advances in nanoparticle preparation by spray and micro-emulsion methods.
Eslamian, Morteza; Shekarriz, Marzieh
2009-01-01
Micro- and nano-sized metal, semiconductor, pharmaceutical, and simple or complex ceramic particles have numerous applications in the development of sensors, thermal barrier coatings, catalysts, pigments, drugs, etc. The challenges include controlling the particle size, size distribution, particle crystallinity, morphology and shape, being able to use the nanoparticles for a given purpose, and to produce them from a variety of precursors. There are several methods to produce nanoparticles, each suitable for a range of applications. In this article, two methods that are receiving increasing attention are considered: spray and microemulsion methods. Spray techniques are single-step methods of producing a broad spectrum of simple to multicomponent functional micro and nanoparticles and quantum dots. Microemulsion is a wet chemistry method. A micro-emulsion system consists of aqueous domains, called reverse micelles, dispersed in a continuous oil phase. In this article, the above mentioned methods of nanoparticle production are introduced and recent advances, research directions and challenges, and the pertinent patents are reviewed and discussed.
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.
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.
Roy, R; Sevick-Muraca, E
2001-07-02
Numerical performance of two gradient-based methods, a truncated-Newton method with trust region (TN) and a nonlinear conjugate gradient (NCG), is studied and compared for a given data set and conditions specific for the contrast enhanced optical tomography problem. Our results suggest that the relative performance of the two methods depends upon the error functions, specific to the problem to be solved. The TN outperforms the NCG when maps of fluorescence lifetime are reconstructed while both methods performed well when the absorption coefficient constitutes the parameter set that is to be recovered.
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.
NASA Astrophysics Data System (ADS)
Wu, Zhijun; Wong, Louis Ngai Yuen; Fan, Lifeng
2013-11-01
The viscoelastic deformation behavior of a sedimentary rock under different loading rates is numerically modeled and investigated by the numerical manifold method (NMM). By incorporating a modified 3-element viscoelastic constitutive mode in the NMM, crack initiation and propagation criteria, and crack identification and evolution techniques, the effects of the loading rates on the cracking behavior of a sedimentary rock, such as crack open displacement, crack sliding displacement, crack initiation, crack propagation and final failure mode, are successfully modeled. The numerical results reveal that under a high loading rate (>1,000 MPa/s), due to the viscoelastic property of the sedimentary rock, not only the structural behavior deviates from that of elastic model, but also different cracking processes and final failure modes are obtained.
NASA Astrophysics Data System (ADS)
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.
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.
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.
Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; ...
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
Bioinformatics Methods and Tools to Advance Clinical Care
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
Advances in Experimental Neuropathology: New Methods and Insights.
Roth, Kevin A
2016-03-01
This Editorial introduces this month's special Neuropathology Theme Issue, a series of Reviews on advances in our understanding of rare human hereditary neuropathies, peripheral nervous system tumors, and common degenerative diseases.
A comparative study of time-marching and space-marching numerical methods. [for flowfield codes
NASA Technical Reports Server (NTRS)
Gupta, R. N.; Moss, J. N.; Simmonds, A. L.
1983-01-01
Menees (1981) has conducted an evaluation of three different flowfield codes for the Jupiter entry conditions. However, a comparison of the codes has been made difficult by the fact that the three codes use different solution procedures, different computational mesh sizes, and a different convergence criterion. There are also other differences. For an objective evaluation of the different numerical solution methods employed by the codes, it would be desirable to select a simple no-blowing perfect-gas flowfield case for which the turbulent models are well established. The present investigation is concerned with the results of such a study. It is found that the choice of the numerical method is rather problem dependent. The time-marching and the space-marching method provide both comparable results if care is taken in selecting the appropriate mesh size near the body surface.
Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method
NASA Astrophysics Data System (ADS)
Korkmaz, Bahar; Dereli, Yilmaz
2016-04-01
In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.
An efficient numerical scheme for spreading resistance calculations based on the variational method
NASA Astrophysics Data System (ADS)
Choo, S. C.; Leong, M. S.; Sim, J. H.
1983-08-01
This paper presents a simple and efficient numerical scheme for evaluating the correction factor integrals that arise in the variational method. The scheme is a modification of one recently proposed by Berkowitz and Lux for the uniform flux method. The abscissae and the weights required for the integration are given in a form which allows the numerical scheme to be readily implemented. Using this scheme, it takes, on an average, 0.8 sec to compute one value of correction factor on an Apple II Microcomputer. For a slab of varying thickness, backed by either a perfectly conducting or a high resistivity substrate, the correction factors obtained agree with those derived from the exact constant-potential method to within 1%.
NASA Astrophysics Data System (ADS)
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
ADVANCED SEISMIC BASE ISOLATION METHODS FOR MODULAR REACTORS
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
a Numerical Method for Scattering from Acoustically Soft and Hard Thin Bodies in Two Dimensions
NASA Astrophysics Data System (ADS)
YANG, S. A.
2002-03-01
This paper presents a numerical method for predicting the acoustic scattering from two-dimensional (2-D) thin bodies. Both the Dirichlet and Neumann problems are considered. Applying the thin-body formulation leads to the boundary integral equations involving weakly singular and hypersingular kernels. Completely regularizing these kinds of singular kernels is thus the main concern of this paper. The basic subtraction-addition technique is adopted. The purpose of incorporating a parametric representation of the boundary surface with the integral equations is two-fold. The first is to facilitate the numerical implementation for arbitrarily shaped bodies. The second one is to facilitate the expansion of the unknown function into a series of Chebyshev polynomials. Some of the resultant integrals are evaluated by using the Gauss-Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral. The numerical implementation basically includes only two parts, one for evaluating the ordinary integrals and the other for solving a system of algebraic equations. Thus, the current method is highly efficient and accurate because these two solution procedures are easy and straightforward. Numerical calculations consist of the acoustic scattering by flat and curved plates. Comparisons with analytical solutions for flat plates are made.
Liu, Li; Lai, Choi-Hong; Zhou, Shao-Dan; Xie, Fen; Rui, Lu
2011-04-01
In order to predict variations of drug concentration during a given period of time, numerical solutions of pharmacokinetic models need to be obtained efficiently. Analytical solutions of linear pharmacokinetic models are usually obtained using the Laplace transform and inverse Laplace tables. The derivations of solutions to complex nonlinear models are tedious, and such solution process may be difficult to implement as a robust software code. For nonlinear models, the fourth-order Runge-Kutta (RK4) is the most classical numerical method in obtaining approximate numerical solutions, which is impossible to be implemented in distributed computing environments without much modification. The reason is that numerical solutions obtained by using RK4 can only be computed in sequential time steps. In this paper, time-domain decomposition methods are adapted for nonlinear pharmacokinetic models. The numerical Inverse Laplace method for PharmacoKinetic models (ILPK) is implemented to solve pharmacokinetic models with iterative inverse Laplace transform in each time interval. The distributed ILPK algorithm, which is based on a two-level time-domain decomposition concept, is proposed to improve its efficiency. Solutions on the coarser temporal mesh at the top level are obtained one by one, and then those on the finer temporal mesh at the bottom level are calculated concurrently by using those initial solutions that have been obtained at the top level decomposition. Accuracy and efficiency of the proposed algorithm and its distributed equivalent are investigated by using several test models. Results indicate that the ILPK algorithm and its distributed equivalent are good candidates for both linear and nonlinear pharmacokinetic models.
Numerical methods for time-domain and frequency-domain analysis: applications in engineering
NASA Astrophysics Data System (ADS)
Tamas, R. D.
2015-11-01
Numerical methods are widely used for modeling different physical phenomena in engineering, especially when an analytic approach is not possible. Time-domain or frequency- domain type variations are generally investigated, depending on the nature of the process under consideration. Some methods originate from mechanics, although most of their applications belong to other fields, such as electromagnetism. Conversely, other methods were firstly developed for electromagnetism, but their field of application was extended to other fields. This paper presents some results that we have obtained by using a general purpose method for solving linear equations, i.e., the method of moments (MoM), and a time-domain method derived for electromagnetism, i.e., the Transmission Line Matrix method (TLM).
Processing of alnico permanent magnets by advanced directional solidification methods
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 (H_{ci}) of 2.0 kOe, a remanence (B_{r}) 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/m^{2} 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
Processing of alnico permanent magnets by advanced directional solidification methods
Zou, Min; Johnson, Francis; Zhang, Wanming; ...
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
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
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.
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.
Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...
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
A unified convergence theory of a numerical method, and applications to the replenishment policies.
Mi, Xiang-jiang; Wang, Xing-hua
2004-01-01
In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.
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.
A numerical method for the design and analysis of counter-rotating propellers
NASA Technical Reports Server (NTRS)
Playle, S. C.; Korkan, K. D.; Von Lavante, E.
1986-01-01
A numerical method has been developed using the techniques of Lock and Theodorsen as described by Davidson to design and analyze counter-rotating propellers. The design method develops the optimum propeller geometry by calculating the planform and twist distribution for each propeller disk through the use of specific inputs of engine shaft horsepower, diameter, and disk spacing. The analysis method calculates the performance of a given counter-rotating propeller system at any flight condition. Using the NACA four-digit airfoil family, the performance of a counter-rotating propeller design for a given flight condition was investigated in the design and analysis mode.
A numerical method for the solution of the bidomain equations in cardiac tissue.
Keener, J. P.; Bogar, K.
1998-03-01
A numerical scheme for efficient integration of the bidomain model of action potential propagation in cardiac tissue is presented. The scheme is a mixed implicit-explicit scheme with no stability time step restrictions and requires that only linear systems of equations be solved at each time step. The method is faster than a fully explicit scheme and there is no increase in algorithmic complexity to use this method instead of a fully explicit method. The speedup factor depends on the timestep size, which can be set solely on the basis of the demands for accuracy. (c) 1998 American Institute of Physics.