Foil Bearing Stiffness Estimation with Pseudospectral Scheme
Directory of Open Access Journals (Sweden)
Sankar Balaji
2016-01-01
Full Text Available Compliant foil gas lubricated bearings are used for the support of light loads in the order of few kilograms at high speeds, in the order of 50,000 RPM. The stiffness of the foil bearings depends both on the stiffness of the compliant foil and on the lubricating gas film. The stiffness of the bearings plays a crucial role in the stable operation of the supported rotor over a range of speeds. This paper describes a numerical approach to estimate the stiffness of the bearings using pseudo spectral scheme. Methodology to obtain the stiffness of the foil bearing as a function of weight of the shaft is given and the results are presented.
A Hybrid MPI-OpenMP Scheme for Scalable Parallel Pseudospectral Computations for Fluid Turbulence
Rosenberg, D. L.; Mininni, P. D.; Reddy, R. N.; Pouquet, A.
2010-12-01
A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of fluid turbulence on emerging petascale, high core-count, massively parallel processing systems. The hybrid implementation derives from and augments a well-tested scalable MPI-parallelized pseudospectral code. The hybrid paradigm leads to a new picture for the domain decomposition of the pseudospectral grids, which is helpful in understanding, among other things, the 3D transpose of the global data that is necessary for the parallel fast Fourier transforms that are the central component of the numerical discretizations. Details of the hybrid implementation are provided, and performance tests illustrate the utility of the method. It is shown that the hybrid scheme achieves near ideal scalability up to ~20000 compute cores with a maximum mean efficiency of 83%. Data are presented that demonstrate how to choose the optimal number of MPI processes and OpenMP threads in order to optimize code performance on two different platforms.
An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation
Zhan, Ge
2013-02-19
The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.
Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.
2016-01-01
We apply the pseudospectral discretization approach to nonlinear delay models described by delay differential equations, renewal equations, or systems of coupled renewal equations and delay differential equations. The aim is to derive ordinary differential equations and to investigate the stability
Directory of Open Access Journals (Sweden)
P. Di Maida
2016-01-01
Full Text Available A pseudo-spectral approximation is presented to solve the problem of pull-in instability in a cantilever micro-switch. As well known, pull-in instability arises when the acting force reaches a critical threshold beyond which equilibrium is no longer possible. In particular, Coulomb electrostatic force is considered, although the method can be easily generalized to account for fringe as well as Casimir effects. A numerical comparison is presented between a pseudo-spectral and a Finite Element (FE approximation of the problem, both methods employing the same number of degrees of freedom. It is shown that the pseudo-spectral method appears more effective in accurately approximating the behavior of the cantilever near its tip. This fact is crucial to capturing the threshold voltage on the verge of pull-in. Conversely, the FE approximation presents rapid successions of attracting/repulsing regions along the cantilever, which are not restricted to the near pull-in regime.
A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation
Liu, Yang
2010-03-01
We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.
A numerical scheme for the generalized Burgers–Huxley equation
Directory of Open Access Journals (Sweden)
Brajesh K. Singh
2016-10-01
Full Text Available In this article, a numerical solution of generalized Burgers–Huxley (gBH equation is approximated by using a new scheme: modified cubic B-spline differential quadrature method (MCB-DQM. The scheme is based on differential quadrature method in which the weighting coefficients are obtained by using modified cubic B-splines as a set of basis functions. This scheme reduces the equation into a system of first-order ordinary differential equation (ODE which is solved by adopting SSP-RK43 scheme. Further, it is shown that the proposed scheme is stable. The efficiency of the proposed method is illustrated by four numerical experiments, which confirm that obtained results are in good agreement with earlier studies. This scheme is an easy, economical and efficient technique for finding numerical solutions for various kinds of (nonlinear physical models as compared to the earlier schemes.
A numerical relativity scheme for cosmological simulations
Daverio, David; Dirian, Yves; Mitsou, Ermis
2017-12-01
Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3 + 1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.
Numerical Differentiation and Integration through Aitken-Neville Schemes
Directory of Open Access Journals (Sweden)
Ramesh Kumar Muthumalai
2013-09-01
Full Text Available Some new formulas are given to approximate higher order derivatives and integrals through Aitken-Neville iterative schemes for arbitrary spaced grids. An algorithm is given in MATLAB for numerical differentiation. Also, numerical examples are provided to study error analysis of new formulas for numerical differentiation and integration.
A numerical scheme for solving differential equations with space ...
African Journals Online (AJOL)
fractional coordinate derivatives. Y Khan, S.P.A. Beik, K Sayevand, A Shayganmanesh. Abstract. In this paper, we apply a numerical scheme for solving fractional differential equations. Our approach is based on an operational matrix of fractional ...
Characterization of Numerical Dissipation of PPM and WENO Schemes
Weirs, V. G.; Dursi, L. J.; Calder, A. C.; Fryxell, B.; Rosner, R.; Olson, K.; Ricker, P. M.; Timmes, F. X.; Zingale, M.; MacNeice, P.; Tufo, H.
2000-11-01
For compressible fluid flow simulations, shock-capturing schemes (such as TVD, ENO, PPM, and FCT) selectively add numerical dissipation to prevent or limit oscillations near discontinuities. In general, the numerical dissipation is dependent on the grid resolution and damps smooth high frequency features as well as discontinuities, and because it is highly nonlinear, its effects on the flowfield are difficult to determine. This work seeks to quantify the numerical dissipation of the weighted ENO and PPM schemes using several techniques, ranging from numerical experiments with simple, idealized equations to extracting diagnostic data from full-physics simulations.
Liao, Feng; Zhang, Luming; Wang, Shanshan
2018-02-01
In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.
Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli
2016-10-01
The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.
Energy Technology Data Exchange (ETDEWEB)
Sato, T.; Matsuoka, T. [Japan Petroleum Exploration Corp., Tokyo (Japan); Saeki, T. [Japan National Oil Corp., Tokyo (Japan). Technology Research Center
1997-05-27
Discussed in this report is a wavefield simulation in the 3-dimensional seismic survey. With the level of the object of exploration growing deeper and the object more complicated in structure, the survey method is now turning 3-dimensional. There are several modelling methods for numerical calculation of 3-dimensional wavefields, such as the difference method, pseudospectral method, and the like, all of which demand an exorbitantly large memory and long calculation time, and are costly. Such methods have of late become feasible, however, thanks to the advent of the parallel computer. As compared with the difference method, the pseudospectral method requires a smaller computer memory and shorter computation time, and is more flexible in accepting models. It outputs the result in fullwave just like the difference method, and does not cause wavefield numerical variance. As the computation platform, the parallel computer nCUBE-2S is used. The object domain is divided into the number of the processors, and each of the processors takes care only of its share so that parallel computation as a whole may realize a very high-speed computation. By the use of the pseudospectral method, a 3-dimensional simulation is completed within a tolerable computation time length. 7 refs., 3 figs., 1 tab.
Using SpF to Achieve Petascale for Legacy Pseudospectral Applications
Clune, Thomas L.; Jiang, Weiyuan
2014-01-01
Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community. We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. Highlevel abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely inprocessor. The granularity of domain decomposition provided by SpF is only constrained by the datalocality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures. In this presentation, we will describe our experience in porting legacy pseudospectral models, MoSST and DYNAMO, to use SpF as well as present preliminary
Numerical Comparison of Optimal Charging Schemes for Electric Vehicles
DEFF Research Database (Denmark)
You, Shi; Hu, Junjie; Pedersen, Anders Bro
2012-01-01
The optimal charging schemes for Electric vehicles (EV) generally differ from each other in the choice of charging periods and the possibility of performing vehicle-to-grid (V2G), and have different impacts on EV economics. Regarding these variations, this paper presents a numerical comparison...... of four different charging schemes, namely night charging, night charging with V2G, 24 hour charging and 24 hour charging with V2G, on the basis of real driving data and electricity price of Denmark in 2003. For all schemes, optimal charging plans with 5 minute resolution are derived through the solving...
Numerical solution to nonlinear Tricomi equation using WENO schemes
Directory of Open Access Journals (Sweden)
Adrian Sescu
2010-09-01
Full Text Available Nonlinear Tricomi equation is a hybrid (hyperbolic-elliptic second order partial differential equation, modelling the sonic boom focusing. In this paper, the Tricomi equation is transformed into a hyperbolic system of first order equations, in conservation law form. On the upper boundary, a new mixed boundary condition for the acoustic pressure is used to avoid the inclusion of the Dirac function in the numerical solution. Weighted Essentially Non-Oscillatory (WENO schemes are used for the spatial discretization, and the time marching is carried out using the second order accurate Runge-Kutta total-variation diminishing (TVD scheme.
Symmetry preserving compact schemes for numerical solution of PDEs
Ozbenli, Ersin; Vedula, Prakash
2017-11-01
In this study, a new approach for construction of invariant, high order accurate compact finite difference schemes that preserve Lie symmetry groups of underlying partial differential equations (PDEs) is presented. It is well known that compact numerical schemes based on Pade approximants achieve high order accuracy with a relatively small number of stencil points and are found to have good spectral-like resolution. Considering applicable Lie symmetry groups (such as translation, scaling, rotation, and projection groups) of underlying PDEs, invariant compact schemes are developed based on the use of equivariant moving frames and extended group transformations. This work represents an extension of the authors recent work on construction of invariant, high-order, non-compact, finite difference schemes based on the method of modified equations. Performance of the proposed symmetry preserving compact schemes is evaluated via consideration of some canonical PDEs like linear advection-diffusion equation, inviscid Burgers' equation, and viscous Burgers' equation. Effects on accuracy due to choice of subgroups used in construction of these schemes will be discussed. Generalization of the proposed framework to multidimensional problems and non-orthogonal grids will also be presented.
Development and Validation of A 3d Staggered Fourier Pseudo-spectral Method For Wave Modeling
Seriani, G.; Vuan, A.; Priolo, E.; Carcione, J.
We have developed and implemented an algorithm for the 3D forward modeling of seismic wave-fields in complex geological structures. The algorithm is based on the solution of the elastic full wave equation in heterogeneous media using the Fourier pseudo-spectral method. Numerical accuracy and computational efficiency have been improved using a staggered scheme and parallel implementation, respectively. The parallel code can handle both SHMEM and MPI libraries which allow to perform the computations whether using a single massive parallel computer or distributed PC- clusters. The wave equation is written in a displacement-velocity-stress formulation using the equation of conservation of momentum, and the stress-strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In the time domain, the system of partial differential equations is integrated through a leap-frog finite dif- ference discrete scheme. Spatial derivatives are computed globally by using the FFT. Attenuation is accommodated at each time step by multiplying the stress and velocity field by the attenuation factor. The presence of a free surface is obtained by FFT zero- padding. Wave reflections from the model edges are removed by applying absorbing strips. A generalized moment-tensor source formulation is used to represent source mechanisms. The 3-D staggered Fourier pseudo-spectral method is validated with both analytical and numerical solutions. In particular, we have used as reference solutions the full wave-field in homogeneous and layered media computed by the Cagniard-de Hoop technique and the wave-number integration method, respectively. The compari- son showed that the time histories are in good agreement with the reference solutions. Moreover, because of the staggered approach, the three components of the wave-field are defined on dual meshes displaced by a half grid-step. Therefore three components records are recovered by a fast interpolation.
Directory of Open Access Journals (Sweden)
E. H. Doha
2014-01-01
Full Text Available A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.
A new numerical scheme for the simulation of active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, B.; Engelbrecht, Kurt; Payá, J.
2014-01-01
A 1D model of a parallel-plate active magnetic regenerator (AMR) has been developed based on a new numerical scheme. With respect to the implicit scheme, the new scheme achieves accurate results, minimizes computational time and prevents numerical errors. The model has been used to check the boun......A 1D model of a parallel-plate active magnetic regenerator (AMR) has been developed based on a new numerical scheme. With respect to the implicit scheme, the new scheme achieves accurate results, minimizes computational time and prevents numerical errors. The model has been used to check...... the boundary condition of heat transfer in the regenerator bed....
A New Numerical Scheme for Cosmic-Ray Transport
Jiang, Yan-Fei; Oh, S. Peng
2018-02-01
Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.
Numeric Analysis for Relationship-Aware Scalable Streaming Scheme
Directory of Open Access Journals (Sweden)
Heung Ki Lee
2014-01-01
Full Text Available Frequent packet loss of media data is a critical problem that degrades the quality of streaming services over mobile networks. Packet loss invalidates frames containing lost packets and other related frames at the same time. Indirect loss caused by losing packets decreases the quality of streaming. A scalable streaming service can decrease the amount of dropped multimedia resulting from a single packet loss. Content providers typically divide one large media stream into several layers through a scalable streaming service and then provide each scalable layer to the user depending on the mobile network. Also, a scalable streaming service makes it possible to decode partial multimedia data depending on the relationship between frames and layers. Therefore, a scalable streaming service provides a way to decrease the wasted multimedia data when one packet is lost. However, the hierarchical structure between frames and layers of scalable streams determines the service quality of the scalable streaming service. Even if whole packets of layers are transmitted successfully, they cannot be decoded as a result of the absence of reference frames and layers. Therefore, the complicated relationship between frames and layers in a scalable stream increases the volume of abandoned layers. For providing a high-quality scalable streaming service, we choose a proper relationship between scalable layers as well as the amount of transmitted multimedia data depending on the network situation. We prove that a simple scalable scheme outperforms a complicated scheme in an error-prone network. We suggest an adaptive set-top box (AdaptiveSTB to lower the dependency between scalable layers in a scalable stream. Also, we provide a numerical model to obtain the indirect loss of multimedia data and apply it to various multimedia streams. Our AdaptiveSTB enhances the quality of a scalable streaming service by removing indirect loss.
Energy Technology Data Exchange (ETDEWEB)
Park, Ju Yeop; In, Wang Kee; Chun, Tae Hyun; Oh, Dong Seok [Korea Atomic Energy Research Institute, Taejeon (Korea)
2000-02-01
The development of orthogonal 2-dimensional numerical code is made. The present code contains 9 kinds of turbulence models that are widely used. They include a standard k-{epsilon} model and 8 kinds of low Reynolds number ones. They also include 6 kinds of numerical schemes including 5 kinds of low order schemes and 1 kind of high order scheme such as QUICK. To verify the present numerical code, pipe flow, channel flow and expansion pipe flow are solved by this code with various options of turbulence models and numerical schemes and the calculated outputs are compared to experimental data. Furthermore, the discretization error that originates from the use of standard k-{epsilon} turbulence model with wall function is much more diminished by introducing a new grid system than a conventional one in the present code. 23 refs., 58 figs., 6 tabs. (Author)
Improvements to the RELAP5-3D Nearly-Implicit Numerical Scheme
Energy Technology Data Exchange (ETDEWEB)
Richard A. Riemke; Walter L. Weaver; RIchard R. Schultz
2005-05-01
The RELAP5-3D computer program has been improved with regard to its nearly-implicit numerical scheme for twophase flow and single-phase flow. Changes were made to the nearly-implicit numerical scheme finite difference momentum equations as follows: (1) added the velocity flip-flop mass/energy error mitigation logic, (2) added the modified Henry-Fauske choking model, (3) used the new time void fraction in the horizontal stratification force terms and gravity head, and (4) used an implicit form of the artificial viscosity. The code modifications allow the nearly-implicit numerical scheme to be more implicit and lead to enhanced numerical stability.
On the Radau pseudospectral method: theoretical and implementation advances
Sagliano, Marco; Theil, Stephan; Bergsma, Michiel; D'Onofrio, Vincenzo; Whittle, Lisa; Viavattene, Giulia
2017-09-01
In the last decades the theoretical development of more and more refined direct methods, together with a new generation of CPUs, led to a significant improvement of numerical approaches for solving optimal-control problems. One of the most promising class of methods is based on pseudospectral optimal control. These methods do not only provide an efficient algorithm to solve optimal-control problems, but also define a theoretical framework for linking the discrete numerical solution to the analytical one in virtue of the covector mapping theorem. However, several aspects in their implementation can be refined. In this framework SPARTAN, the first European tool based on flipped-Radau pseudospectral method, has been developed. This paper illustrates the aspects implemented for SPARTAN, which can potentially be valid for any other transcription. The novelties included in this work consist specifically of a new hybridization of the Jacobian matrix computation made of four distinct parts. These contributions include a new analytical formulation for expressing Lagrange cost function for open final-time problems, and the use of dual-number theory for ensuring exact differentiation. Moreover, a self-scaling strategy for primal and dual variables, which combines the projected-Jacobian rows normalization and the covector mapping, is described. Three concrete examples show the validity of the novelties introduced, and the quality of the results obtained with the proposed methods.
Multi-dimensional high-order numerical schemes for Lagrangian hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Dai, William W [Los Alamos National Laboratory; Woodward, Paul R [Los Alamos National Laboratory
2009-01-01
An approximate solver for multi-dimensional Riemann problems at grid points of unstructured meshes, and a numerical scheme for multi-dimensional hydrodynamics have been developed in this paper. The solver is simple, and is developed only for the use in numerical schemes for hydrodynamics. The scheme is truely multi-dimensional, is second order accurate in both space and time, and satisfies conservation laws exactly for mass, momentum, and total energy. The scheme has been tested through numerical examples involving strong shocks. It has been shown that the scheme offers the principle advantages of high-order Codunov schemes; robust operation in the presence of very strong shocks and thin shock fronts.
Hybrid flux splitting schemes for numerical resolution of two-phase flows
Energy Technology Data Exchange (ETDEWEB)
Flaatten, Tore
2003-07-01
This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)
Unconditionally energy stable numerical schemes for phase-field vesicle membrane model
Guillén-González, F.; Tierra, G.
2018-02-01
Numerical schemes to simulate the deformation of vesicles membranes via minimizing the bending energy have been widely studied in recent times due to its connection with many biological motivated problems. In this work we propose a new unconditionally energy stable numerical scheme for a vesicle membrane model that satisfies exactly the conservation of volume constraint and penalizes the surface area constraint. Moreover, we extend these ideas to present an unconditionally energy stable splitting scheme decoupling the interaction of the vesicle with a surrounding fluid. Finally, the well behavior of the proposed schemes are illustrated through several computational experiments.
Benes, Nieck Edwin; Verzijl, Richard; Verweij, H.
1999-01-01
A numerical scheme is presented for computer simulation of multicomponent gas transport possibly accompanied by reversible chemical reactions in a macroporous medium, based on the dusty gas model. Using analytical solutions for simple systems it is shown that the derivation of the scheme is
Time-domain computation of muffler frequency response: Comparison of different numerical schemes
Broatch, A.; Serrano, J. R.; Arnau, F. J.; Moya, D.
2007-08-01
A comparative study of the performance of different schemes used to solve one-dimensional gas flow equations when applied to the computation of the frequency response of exhaust mufflers is presented. Simple but representative systems with well-known acoustic behaviour were considered. Apart from the classical Lax-Wendroff and MacCormack schemes, the total variation diminishing schemes, flux corrected transport techniques or the innovative space-time conservation element and solution element method were considered. The results provide guidelines for a proper choice of the numerical scheme, taking into account the mesh spacing.
Pseudospectral Model for Hybrid PIC Hall-effect Thruster Simulation
2015-07-01
Paper 3. DATES COVERED (From - To) July 2015-July 2015 4. TITLE AND SUBTITLE Pseudospectral model for hybrid PIC Hall-effect thruster simulationect...of a pseudospectral azimuthal-axial hybrid- PIC HET code which is designed to explicitly resolve and filter azimuthal fluctuations in the...661-275-5908 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. 239.18 Pseudospectral model for hybrid PIC Hall-effect thruster simulation IEPC
DEFF Research Database (Denmark)
Hyun, Jaeyub; Kook, Junghwan; Wang, Semyung
2015-01-01
This study proposes an efficient and stable model reduction scheme for the numerical simulation of broadband, inhomogeneous, and anisotropic acoustic systems. Unlike a conventional model reduction scheme, the proposed model reduction scheme uses the adaptive quasi-static Ritz vector (AQSRV...... using the error indicator. "Multiple frequency subintervals" means to divide the frequency band of interest into several frequency bands from the computational time viewpoint. "Adaptive selection of the subinterval information and basis vector" means to select a different number of subintervals...... and basis vectors for use according to the target system. The proposed model reduction scheme is applied to the numerical simulation of the simple mass-damping-spring system and the acoustic metamaterial systems (i.e., acoustic lens and acoustic cloaking device) for the first time. Through these numerical...
Numerical study of read scheme in one-selector one-resistor crossbar array
Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin
2015-12-01
A comprehensive numerical circuit analysis of read schemes of a one selector-one resistance change memory (1S1R) crossbar array is carried out. Three schemes-the ground, V/2, and V/3 schemes-are compared with each other in terms of sensing margin and power consumption. Without the aid of a complex analytical approach or SPICE-based simulation, a simple numerical iteration method is developed to simulate entire current flows and node voltages within a crossbar array. Understanding such phenomena is essential in successfully evaluating the electrical specifications of selectors for suppressing intrinsic drawbacks of crossbar arrays, such as sneaky current paths and series line resistance problems. This method provides a quantitative tool for the accurate analysis of crossbar arrays and provides guidelines for developing an optimal read scheme, array configuration, and selector device specifications.
Evaluation of numerical schemes for the analysis of sound generation by blade-gust interaction
Scott, J. N.; Hariharan, S. I.; Mankbadi, R.
1995-01-01
In this investigation three different numerical algorithms have been utilized to compute the flow about a flat plate in the presence of a transverse gust described by a sinusoidal disturbance. The three schemes include the MacCormack explicit finite difference scheme which is second order accurate in both time and space, the Gottlieb and Turkel modification of MacCormack's scheme which is fourth order accurate in space and second order accurate in time, (referred to as the 2-4 scheme), and a two step scheme developed by Bayliss et al. which has second order temporal accuracy and sixth order spatial accuracy (a 2-6 scheme). The flow field results are obtained with these schemes by using the same code with the only difference being the implementation of the respective solution algorithms. The problem is set up so that the sinusoidal disturbance is imposed at the surface of the flat plate as a surface boundary condition. Thus the problem is treated as scattering problem. The computed results include the time average of the acoustic pressure squared along grid lines five points away from the boundaries; distribution throughout the computational domain is monitored at various times. The numerical results are compared with an exact solution obtained by Atassi, Dusey, and Davis.
Numerical solution of linear Klein-Gordon equation using FDAM scheme
Kasron, Noraini; Suharto, Erni Suryani; Deraman, Ros Fadilah; Othman, Khairil Iskandar; Nasir, Mohd Agos Salim
2017-05-01
Many scientific areas appear in a hyperbolic partial differential equation like the Klien-Gordon equation. The analytical solutions of the Klein-Gordon equation have been approximated by the suggested numerical approaches. However, the arithmetic mean (AM) method has not been studied on the Klein-Gordon equation. In this study, a new proposed scheme has utilized central finite difference formula in time and space (CTCS) incorporated with AM formula averaging of functional values for approximating the solutions of the Klein-Gordon equation. Three-point AM is considered to a linear inhomogeneous Klein-Gordon equation. The theoretical aspects of the numerical scheme for the Klein-Gordon equation are also considered. The stability analysis is analyzed by using von Neumann stability analysis and Miller Norm Lemma. Graphical results verify the necessary conditions of Miller Norm Lemma. Good results obtained relate to the theoretical aspects of the numerical scheme. The numerical experiments are examined to verify the theoretical analysis. Comparative study shows the new CTCS scheme incorporated with three-point AM method produced better accuracy and shown its reliable and efficient over the standard CTCS scheme.
A new numerical scheme for bounding acceleration in the LWR model
LECLERCQ, L; ELSEVIER
2005-01-01
This paper deals with the numerical resolution of bounded acceleration extensions of the LWR model. Two different manners for bounding accelerations in the LWR model will be presented: introducing a moving boundary condition in front of an accelerating flow or defining a field of constraints on the maximum allowed speed in the (x,t) plane. Both extensions lead to the same solutions if the declining branch of the fundamental diagram is linear. The existing numerical scheme for the latter exte...
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge
2015-01-01
A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally...... combines explicit and implicit techniques in order to solve the one-dimensional conjugate heat transfer problem in an accurate and fast manner while ensuring energy conservation. The present model has been thoroughly validated against passive regenerator cases with an analytical solution. Compared...
A New Framework to Compare Mass-Flux Schemes Within the AROME Numerical Weather Prediction Model
Riette, Sébastien; Lac, Christine
2016-08-01
In the Application of Research to Operations at Mesoscale (AROME) numerical weather forecast model used in operations at Météo-France, five mass-flux schemes are available to parametrize shallow convection at kilometre resolution. All but one are based on the eddy-diffusivity-mass-flux approach, and differ in entrainment/detrainment, the updraft vertical velocity equation and the closure assumption. The fifth is based on a more classical mass-flux approach. Screen-level scores obtained with these schemes show few discrepancies and are not sufficient to highlight behaviour differences. Here, we describe and use a new experimental framework, able to compare and discriminate among different schemes. For a year, daily forecast experiments were conducted over small domains centred on the five French metropolitan radio-sounding locations. Cloud base, planetary boundary-layer height and normalized vertical profiles of specific humidity, potential temperature, wind speed and cloud condensate were compared with observations, and with each other. The framework allowed the behaviour of the different schemes in and above the boundary layer to be characterized. In particular, the impact of the entrainment/detrainment formulation, closure assumption and cloud scheme were clearly visible. Differences mainly concerned the transport intensity thus allowing schemes to be separated into two groups, with stronger or weaker updrafts. In the AROME model (with all interactions and the possible existence of compensating errors), evaluation diagnostics gave the advantage to the first group.
Liu, Jianjun; Zhang, Feimin; Pu, Zhaoxia
2017-04-01
Accurate forecasting of the intensity changes of hurricanes is an important yet challenging problem in numerical weather prediction. The rapid intensification of Hurricane Katrina (2005) before its landfall in the southern US is studied with the Advanced Research version of the WRF (Weather Research and Forecasting) model. The sensitivity of numerical simulations to two popular planetary boundary layer (PBL) schemes, the Mellor-Yamada-Janjic (MYJ) and the Yonsei University (YSU) schemes, is investigated. It is found that, compared with the YSU simulation, the simulation with the MYJ scheme produces better track and intensity evolution, better vortex structure, and more accurate landfall time and location. Large discrepancies (e.g., over 10 hPa in simulated minimum sea level pressure) are found between the two simulations during the rapid intensification period. Further diagnosis indicates that stronger surface fluxes and vertical mixing in the PBL from the simulation with the MYJ scheme lead to enhanced air-sea interaction, which helps generate more realistic simulations of the rapid intensification process. Overall, the results from this study suggest that improved representation of surface fluxes and vertical mixing in the PBL is essential for accurate prediction of hurricane intensity changes.
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
Liu, Di
2008-10-01
We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples.
Energy Technology Data Exchange (ETDEWEB)
Baxevanou, Catherine A.; Vlachos, Nicolas S.
2004-07-01
This paper is a comparative study of combining turbulence models and interpolation schemes to calculate turbulent flow around a NACA0012 airfoil before and after separation. The calculations were carried out using the code CAFFA of Peric, which was appropriately modified to include more numerical schemes and turbulence models. This code solves the Navier-Stokes equations for 2D incompressible flow, using finite volumes and structured, collocated, curvilinear, body fitted grids. Seven differencing schemes were investigated: central, upwind, hybrid, QUICK, Harten-Yee upwind TVD with five limiters, Roe-Sweby upwind TVD with three limiters, and Davis-Yee symmetric TVD with three limiters. Turbulence effects were incorporated using four turbulence models: standard {kappa}-{epsilon}, {kappa}-{omega} high Re with wall functions, {kappa}-{omega} high Re with integration up to the wall, and the {kappa}-{omega} low Re model. A parametric study showed that best results are obtained: a) for the {kappa}-{epsilon} model, when using the Harten-Yee upwind TVD scheme for the velocities and the upwind interpolation for the turbulence properties {kappa} and {epsilon}, and b) for the {kappa}-{omega} models, when using the Harten-Yee upwind TVD scheme with different limiters for the velocities and the turbulence quantities {kappa} and {omega}. The turbulence models that integrate up to the wall are more accurate when separation appears, while those using wall functions converge much faster. (Author)
Energy Technology Data Exchange (ETDEWEB)
Baxevanou, C.A.; Vlachos, N.S.
2004-07-01
This paper is a comparative study of combining turbulence models and interpolation schemes to calculate turbulent flow around a NACA0012 airfoil before and after separation. The calculations were carried out using the code CAFFA of Peric, which was appropriately modified to include more numerical schemes and turbulence models. This code solves the Navier-Stokes equations for 2D incompressible flow, using finite volumes and structured, collocated, curvilinear, body fitted grids. Seven differencing schemes were investigated: central, upwind, hybrid, QUICK, Harten-Yee upwind TVD with five limiters, Roe-Sweby upwind TVD with three limiters, and Davis-Yee symmetric TVD with three limiters. Turbulence effects were incorporated using four turbulence models: standard k-{epsilon}, k-{omega} high Re with wall functions, k-{omega} high Re with integration up to the wall, and the k-{omega} low Re model. A parametric study showed that best results are obtained: a) for the k-{epsilon} model, when using the Harten-Yee upwind TVD scheme for the velocities and the upwind interpolation for the turbulence properties k and {epsilon}, and b) for the k-{omega}, models, when using the Harten-Yee upwind TVD scheme with different limiters for the velocities and the turbulence quantities k and {omega}. The turbulence models that integrate up to the wall are more accurate when separation appears, while those using wall functions converge much faster. (author)
Comparison of Accuracy and Efficiency of Time-domain Schemes for Calculating Synthetic Seismograms
Mizutani, Hiromitsu; Geller, Robert J.; Takeuchi, Nozomu
2000-04-01
We conduct numerical experiments for several simple models to illustrate the advantages and disadvantages of various schemes for computing synthetic seismograms in the time domain. We consider both schemes that use the pseudo-spectral method (PSM) to compute spatial derivatives and schemes that use the finite difference method (FDM) to compute spatial derivatives. We show that schemes satisfying the criterion for optimal accuracy of Geller and Takeuchi (1995) are significantly more cost-effective than non-optimally accurate schemes of the same type. We then compare optimally accurate PSM schemes to optimally accurate FDM schemes. For homogeneous or smoothly varying heterogeneous media, PSM schemes require significantly fewer grid points per wavelength than FDM schemes, and are thus more cost-effective. In contrast, we show that FDM schemes are more cost-effective for media with sharp boundaries or steep velocity gradients. Thus FDM schemes appear preferable to PSM schemes for practical seismological applications. We analyze the solution error of various schemes and show that widely cited Lax-Wendroff PSM or FDM schemes that are frequently referred to as higher order schemes are in fact equivalent to second-order optimally accurate PSM or FDM schemes implemented as two-step (predictor-corrector) schemes. The error of solutions obtained using such schemes is thus second-order, rather than fourth-order.
Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods
Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard
2013-04-01
Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme
An Approximate Optimal Maximum Range Guidance Scheme for Subsonic Unpowered Gliding Vehicles
Directory of Open Access Journals (Sweden)
Dao-Chi Zhang
2015-01-01
Full Text Available This study investigates the maximum gliding range problems of subsonic unpowered gliding vehicles and proposes an approximate optimal maximum range guidance scheme. First, the gliding flight path angle corresponding to constant dynamic pressure is derived. A lift-to-drag ratio (L/D inversely proportional to the dynamic pressure is then proven. On this basis, the calculation method of an optimal dynamic pressure (ODP profile with a maximum L/D throughout the flight is presented. A guidance scheme for tracking the ODP profile, which uses the flight path angle as control variable, is then designed. The maximum ranges of the unpowered gliding vehicle obtained by the proposed guidance scheme and pseudospectral method are compared. Results show that the guidance scheme provides an accurate approximation of the optimal results, and the errors are less than 2%. The proposed guidance scheme is easy to implement and is not influenced by wind compared with numerical schemes.
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Energy Technology Data Exchange (ETDEWEB)
Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
A chaos detectable and time step-size adaptive numerical scheme for nonlinear dynamical systems
Chen, Yung-Wei; Liu, Chein-Shan; Chang, Jiang-Ren
2007-02-01
The first step in investigation the dynamics of a continuous time system described by ordinary differential equations is to integrate them to obtain trajectories. In this paper, we convert the group-preserving scheme (GPS) developed by Liu [International Journal of Non-Linear Mechanics 36 (2001) 1047-1068] to a time step-size adaptive scheme, x=x+hf(x,t), where x∈R is the system variables we are concerned with, and f(x,t)∈R is a time-varying vector field. The scheme has the form similar to the Euler scheme, x=x+Δtf(x,t), but our step-size h is adaptive automatically. Very interestingly, the ratio h/Δt, which we call the adaptive factor, can forecast the appearance of chaos if the considered dynamical system becomes chaotical. The numerical examples of the Duffing equation, the Lorenz equation and the Rossler equation, which may exhibit chaotic behaviors under certain parameters values, are used to demonstrate these phenomena. Two other non-chaotic examples are included to compare the performance of the GPS and the adaptive one.
Chen, Huangxin
2017-09-01
In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.
Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case
Fernández-Nieto, Enrique D.; Gallardo, José M.; Vigneaux, Paul
2018-01-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such schemes in 2D as the follow up of the companion paper treating the 1D case. Numerical tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham-Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix-Mont-Blanc to show the usability of these schemes on real topographies from digital elevation models (DEM).
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
Directory of Open Access Journals (Sweden)
Hakon A. Hoel
2007-07-01
Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
On numerical instabilities of Godunov-type schemes for strong shocks
Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha
2017-12-01
It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. Numerical results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed scheme.
Numerical Optimization of an Organic Rankine Cycle Scheme for Co-generation
Potenza, Marco; Naccarato, Fabrizio; Stigliano, Gianbattista; Risi, Arturo de
2016-01-01
The aim of the present work was the optimization of a small size Organic Rankine Cycle (ORC) system powered by a linear Parabolic Trough Collector (PTC) solar field by means of numerical model code developed on purpose. In the proposed scheme the solar energy is collected by a newly designed low cost PTC of 20m2 with a single tracking axis and it is concentrated on an opaque pipe collector in which flows as thermal fluid the Therminol® 66 oil. An oil-free scroll expander coupled with a 2 kW e...
Analysis of Linear Piecewise Constant Delay Systems Using a Hybrid Numerical Scheme
Directory of Open Access Journals (Sweden)
H. R. Marzban
2016-01-01
Full Text Available An efficient computational technique for solving linear delay differential equations with a piecewise constant delay function is presented. The new approach is based on a hybrid of block-pulse functions and Legendre polynomials. A key feature of the proposed framework is the excellent representation of smooth and especially piecewise smooth functions. The operational matrices of delay, derivative, and product corresponding to the mentioned hybrid functions are implemented to transform the original problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the proposed numerical scheme.
Rostamy, D.; Emamjome, M.; Abbasbandy, S.
2017-06-01
In this paper, the pseudospectral radial basis functions method is proposed for solving the second-order two-space-dimensional telegraph equation in regular and irregular domain. The proposed numerical method, which is truly meshless, is based on a time stepping procedure to deal with the temporal part of the solution combined with radial basis function differentiation matrices for discretizing the spatial derivatives. Here, we extended the pseudospectral radial basis functions method for two-dimensional hyperbolic telegraph equations in irregular domain. A cross-validation technique is used to optimize the shape parameter for the basis functions. Numerical results and comparisons are given to validate the presented method for solving the two-dimensional telegraph equation on both regular and irregular domains which show that the approximate solutions are in good agreement with the exact solution. The obtained results showed that the proposed method is easy to apply for multidimensional problems and equally applicable to both the regular and irregular domains.
Directory of Open Access Journals (Sweden)
B. C. Backeberg
2009-06-01
Full Text Available A 4th order advection scheme is applied in a nested eddy-resolving Hybrid Coordinate Ocean Model (HYCOM of the greater Agulhas Current system for the purpose of testing advanced numerics as a means for improving the model simulation for eventual operational implementation. Model validation techniques comparing sea surface height variations, sea level skewness and variogram analyses to satellite altimetry measurements quantify that generally the 4th order advection scheme improves the realism of the model simulation. The most striking improvement over the standard 2nd order momentum advection scheme, is that the southern Agulhas Current is simulated as a well-defined meandering current, rather than a train of successive eddies. A better vertical structure and stronger poleward transports in the Agulhas Current core contribute toward a better southwestward penetration of the current, and its temperature field, implying a stronger Indo-Atlantic inter-ocean exchange. It is found that the transport, and hence this exchange, is sensitive to the occurrences of mesoscale features originating upstream in the Mozambique Channel and southern East Madagascar Current, and that the improved HYCOM simulation is well suited for further studies of these inter-actions.
Numerical Investigation of the Influence of Injection Scheme on the Ethylene Supersonic Combustion
Directory of Open Access Journals (Sweden)
Hao Ouyang
2014-02-01
Full Text Available Ethylene supersonic combustion flow field in different injection schemes was studied numerically in the flight Mach 4. The results show that injection pressure has significant influence on the location of the separation zone and the heat release region, but the starting point of the separation region was mostly influenced by the heat release rather than by the injection pressure; the combustion efficiency of the injection schemes including two injection points is higher than that of three injection points, while the total pressure recovery coefficient of the former injection schemes is lower than the latter; excessive ethylene injected in upstream will lead to the change of free-stream flow conditions, which behaves as the inlet unstart in practical application; more ethylene could be injected in downstream to avoid the problem; on the condition of avoiding thermal choke in isolator, it is more advantageous that injection points were arranged more closely to the starting point of separation zone in upside and to the front of the cavity in downside.
Qiu, Zhongfeng; Doglioli, Andrea M.; He, Yijun; Carlotti, Francois
2011-03-01
This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion: numerical schemes and time steps. Firstly, we compared three numerical schemes using idealized circulations. Results show that the precisions of the advanced Adams-Bashfold-Moulton (ABM) method and the Runge-Kutta (RK) method were in the same order and both were much higher than that of the Euler method. Furthermore, the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption. We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm. Secondly, we performed a sensitivity test for time steps, using outputs of the hydrodynamic model, Symphonie. Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields. The method introduced by Oliveira et al. in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models, at least when only considering advection.
Navas-Montilla, A.; Murillo, J.
2017-07-01
When designing a numerical scheme for the resolution of conservation laws, the selection of a particular source term discretization (STD) may seem irrelevant whenever it ensures convergence with mesh refinement, but it has a decisive impact on the solution. In the framework of the Shallow Water Equations (SWE), well-balanced STD based on quiescent equilibrium are unable to converge to physically based solutions, which can be constructed considering energy arguments. Energy based discretizations can be designed assuming dissipation or conservation, but in any case, the STD procedure required should not be merely based on ad hoc approximations. The STD proposed in this work is derived from the Generalized Hugoniot Locus obtained from the Generalized Rankine Hugoniot conditions and the Integral Curve across the contact wave associated to the bed step. In any case, the STD must allow energy-dissipative solutions: steady and unsteady hydraulic jumps, for which some numerical anomalies have been documented in the literature. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump. The former issue can be addressed by proposing a modification of the energy-conservative STD that ensures a correct dissipation rate across the hydraulic jump, whereas the latter is of greater complexity and cannot be fixed by simply choosing a suitable STD, as there are more variables involved. The problem concerning the spike of discharge is a well-known problem in the scientific community, also known as slowly-moving shock anomaly, it is produced by a nonlinearity of the Hugoniot locus connecting the states at both sides of the jump. However, it seems that this issue is more a feature than a problem when considering steady solutions of the SWE containing hydraulic jumps. The presence of the spurious spike in the discharge has been taken for granted and has become a feature of the solution. Even though
The generalized pseudospectral approach to the bound states of the ...
Indian Academy of Sciences (India)
Abstract. The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are ...
Benchmarking and scaling studies of pseudospectral code Tarang ...
Indian Academy of Sciences (India)
Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 10243, 20483, and ...
Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.
Heaps, Charles W; Mazziotti, David A
2016-04-28
Trajectory-based Gaussian basis sets have been tremendously successful in describing high-dimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussian-based method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O(N) potential energy calculations, in contrast to O(N(2)) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O(N) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant.
Goloviznin, V. M.; Karabasov, S. A.; Kozubskaya, T. K.; Maksimov, N. V.
2009-12-01
A generalization of the CABARET finite difference scheme is proposed for linearized one-dimensional Euler equations based on the characteristic decomposition into local Riemann invariants. The new method is compared with several central finite difference schemes that are widely used in computational aeroacoustics. Numerical results for the propagation of an acoustic wave in a homogeneous field and the refraction of this wave through a contact discontinuity obtained on a strongly nonuniform grid are presented.
Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad
2017-07-01
This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.
Mukkavilli, S. K.; Kay, M. J.; Taylor, R.; Prasad, A. A.; Troccoli, A.
2014-12-01
The Australian Solar Energy Forecasting System (ASEFS) project requires forecasting timeframes which range from nowcasting to long-term forecasts (minutes to two years). As concentrating solar power (CSP) plant operators are one of the key stakeholders in the national energy market, research and development enhancements for direct normal irradiance (DNI) forecasts is a major subtask. This project involves comparing different radiative scheme codes to improve day ahead DNI forecasts on the national supercomputing infrastructure running mesoscale simulations on NOAA's Weather Research & Forecast (WRF) model. ASEFS also requires aerosol data fusion for improving accurate representation of spatio-temporally variable atmospheric aerosols to reduce DNI bias error in clear sky conditions over southern Queensland & New South Wales where solar power is vulnerable to uncertainities from frequent aerosol radiative events such as bush fires and desert dust. Initial results from thirteen years of Bureau of Meteorology's (BOM) deseasonalised DNI and MODIS NASA-Terra aerosol optical depth (AOD) anomalies demonstrated strong negative correlations in north and southeast Australia along with strong variability in AOD (~0.03-0.05). Radiative transfer schemes, DNI and AOD anomaly correlations will be discussed for the population and transmission grid centric regions where current and planned CSP plants dispatch electricity to capture peak prices in the market. Aerosol and solar irradiance datasets include satellite and ground based assimilations from the national BOM, regional aerosol researchers and agencies. The presentation will provide an overview of this ASEFS project task on WRF and results to date. The overall goal of this ASEFS subtask is to develop a hybrid numerical weather prediction (NWP) and statistical/machine learning multi-model ensemble strategy that meets future operational requirements of CSP plant operators.
Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
2017-05-01
A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
The HIRLAM fast radiation scheme for mesoscale numerical weather prediction models
Rontu, Laura; Gleeson, Emily; Räisänen, Petri; Pagh Nielsen, Kristian; Savijärvi, Hannu; Hansen Sass, Bent
2017-07-01
This paper provides an overview of the HLRADIA shortwave (SW) and longwave (LW) broadband radiation schemes used in the HIRLAM numerical weather prediction (NWP) model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, schemes is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE-AROME NWP system
The HIRLAM fast radiation scheme for mesoscale numerical weather prediction models
Directory of Open Access Journals (Sweden)
L. Rontu
2017-07-01
Full Text Available This paper provides an overview of the HLRADIA shortwave (SW and longwave (LW broadband radiation schemes used in the HIRLAM numerical weather prediction (NWP model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, schemes is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE
Direct numerical simulation of dynamo transition for nonhelical MHD
Energy Technology Data Exchange (ETDEWEB)
Nath, Dinesh; Verma, Mahendra K [Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016 (India); Lessinnes, Thomas; Carati, Daniele [Physique Statistique et Plasmas, Universite Libre de Bruxellers, B-1050 Bruxelles (Belgium); Sarris, Ioannis [Department of Mechanical and Industrial Engineering, University of Thessaly, Volos (Greece)
2010-02-01
Pseudospectral Direct Numerical Simulation (DNS) has been performed to simulate dynamo transition for nonhelical magnetohydrodynamics turbulence. The numerical results are compared with a recent low-dimensional model [Verma et al. [13
Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier
2014-05-01
Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the numerical solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit scheme, and the friction contribution to the dynamics is treated with a suited numerical scheme [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by
Han, Lanshan; Camlibel, M. Kanat; Pang, Jong-Shi; Heemels, W. P. Maurice H.
2012-01-01
This paper presents a numerical scheme for solving the continuous-time convex linear-quadratic (LQ) optimal control problem with mixed polyhedral state and control constraints. Unifying a discretization of this optimal control problem as often employed in model predictive control and that obtained
A numerical scheme for modelling reacting flow with detailed chemistry and transport.
Energy Technology Data Exchange (ETDEWEB)
Knio, Omar M. (The Johns Hopkins University, Baltimore, MD); Najm, Habib N.; Paul, Phillip H. (Eksigent Technologies LLC, Livermore, CA)
2003-09-01
An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C{sub 1}C{sub 2} methane-air mechanism and a detailed mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.
Wang, Zhiheng
2015-01-01
A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results. © Taylor & Francis Group, LLC.
Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media
Zhang, K.; Luo, Y.; Xia, J.; Chen, C.
2011-01-01
Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P
Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models
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Leo G. Rebholz
2009-01-01
Full Text Available We present enhanced physics-based finite element schemes for two families of turbulence models, the NS- models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007, that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.
Directory of Open Access Journals (Sweden)
Parovik Roman I.
2016-09-01
Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.
Directory of Open Access Journals (Sweden)
Andranik Tsakanian
2012-05-01
Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.
Boukandou-Mombo, Charlotte; Bakrim, Hassan; Claustre, Jonathan; Margot, Joëlle; Matte, Jean-Pierre; Vidal, François
2017-11-01
We present a new numerical method for solving the time-dependent isotropic Fokker-Planck equation. We show analytically and numerically that the numerical scheme provides accurate particle and energy density conservation in practical conditions, an equilibrium solution close to the Maxwellian distribution, and the decrease of entropy with time. The slight nonconservation of particle and energy density is only due to the finite value of the upper bound of the energy grid. Additionally, the totally implicit scheme proves to provide positive solutions and to be unconditionally stable. The implicit forms of the scheme can be set as a nonlinear tridiagonal system of equations and solved iteratively. For a uniform grid in energy with N points, the number of operations required to compute the solution at a given time is only O(N) , in contrast to the totally explicit variant, which requires O(N3) operations due to the restriction on the time step. The time-centered variant is more accurate than the totally implicit one, and uses an equivalent CPU time, but does not provide positive solutions for very large timesteps. The results of the method are analyzed for the classical problem of an initially Gaussian distribution as well as for an initially quasi-truncated Maxwellian distribution.
Development of Non-staggered, semi-implicit ICE numerical scheme for a two-fluid, three-field model
Energy Technology Data Exchange (ETDEWEB)
Jeong, Jae Jun; Yoon, H. Y.; Bae, S. W
2007-11-15
A pilot code for one-dimensional, transient, two-fluid, three-field model has been developed. In this code, the semi-implicit ICE numerical scheme has been adapted to a 'non-staggered' grid. Using several conceptual problems, the numerical scheme has been verified. The results of the verifications are summarized below: - It was confirmed that the basic pilot code can simulate various flow conditions (such as single-phase liquid flow, two-phase mixture flow, and single-phase vapor flow) and transitions of the flow conditions. A mist flow was not simulated, but it seems that the basic pilot code can simulate mist flow conditions. - The mass and energy conservation was confirmed for single-phase liquid and single-phase vapor flows. - It was confirmed that the inlet pressure and velocity boundary conditions work properly. - It was confirmed that, for single- and two-phase flows, the velocity and temperature of non-existing phase are calculated as intended. The non-staggered, semi-implicit ICE numerical scheme, which has been developed in this study, will be a starting point of a new code development that adopts an unstructured finite volume method.
Numerical Simulations of Reacting Flows Using Asynchrony-Tolerant Schemes for Exascale Computing
Cleary, Emmet; Konduri, Aditya; Chen, Jacqueline
2017-11-01
Communication and data synchronization between processing elements (PEs) are likely to pose a major challenge in scalability of solvers at the exascale. Recently developed asynchrony-tolerant (AT) finite difference schemes address this issue by relaxing communication and synchronization between PEs at a mathematical level while preserving accuracy, resulting in improved scalability. The performance of these schemes has been validated for simple linear and nonlinear homogeneous PDEs. However, many problems of practical interest are governed by highly nonlinear PDEs with source terms, whose solution may be sensitive to perturbations caused by communication asynchrony. The current work applies the AT schemes to combustion problems with chemical source terms, yielding a stiff system of PDEs with nonlinear source terms highly sensitive to temperature. Examples shown will use single-step and multi-step CH4 mechanisms for 1D premixed and nonpremixed flames. Error analysis will be discussed both in physical and spectral space. Results show that additional errors introduced by the AT schemes are negligible and the schemes preserve their accuracy. We acknowledge funding from the DOE Computational Science Graduate Fellowship administered by the Krell Institute.
A numerical scheme for the two phase Mullins-Sekerka problem
Directory of Open Access Journals (Sweden)
Peter W. Bates
1995-08-01
Full Text Available problem arising in the theory of phase transition. The problem is one in which a collection of simple closed curves (particles evolves in such a way that the enclosed area remains constant while the total arclength decreases. Material is transported between particles and within particles by diffusion, driven by curvature which expresses the effect of surface tension. The algorithm is based on a reformulation of the problem, using boundary integrals, which is then discretized and cast as a semi-implicit scheme. This scheme is implemented with a variety of configurations of initial curves showing that convexity or even topological type may not be preserved.
Symbolic-numeric stability investigations of Jameson's scheme for this-layer Navier-Stokes equations
Ganzha, V.G.; Vorozhtsov, E.V.; Boers, J.; van Hulzen, J.A.; van Hulzen, J.A.
1994-01-01
The Navier-Stokes equations governing the three-dimensional flows of viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes
Hajarolasvadi, Setare; Elbanna, Ahmed E.
2017-11-01
The finite difference (FD) and the spectral boundary integral (SBI) methods have been used extensively to model spontaneously-propagating shear cracks in a variety of engineering and geophysical applications. In this paper, we propose a new modelling approach in which these two methods are combined through consistent exchange of boundary tractions and displacements. Benefiting from the flexibility of FD and the efficiency of SBI methods, the proposed hybrid scheme will solve a wide range of problems in a computationally efficient way. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low-velocity layer and the other in which off-fault plasticity is permitted. We discuss possible potential uses of the hybrid scheme in earthquake cycle simulations as well as an exact absorbing boundary condition.
Hall, Eric Joseph
2013-01-01
First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where...
Role of numerical scheme choice on the results of mathematical modeling of combustion and detonation
Yakovenko, I. S.; Kiverin, A. D.; Pinevich, S. G.; Ivanov, M. F.
2016-11-01
The present study discusses capabilities of dissipation-free CABARET numerical method application to unsteady reactive gasdynamic flows modeling. In framework of present research the method was adopted for reactive flows governed by real gas equation of state and applied for several typical problems of unsteady gas dynamics and combustion modeling such as ignition and detonation initiation by localized energy sources. Solutions were thoroughly analyzed and compared with that derived by using of the modified Euler-Lagrange method of “coarse” particles. Obtained results allowed us to distinguish range of phenomena where artificial effects of numerical approach may counterfeit their physical nature and to develop guidelines for numerical approach selection appropriate for unsteady reactive gasdynamic flows numerical modeling.
Numerical Investigation of a Novel Wiring Scheme Enabling Simple and Accurate Impedance Cytometry
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Federica Caselli
2017-09-01
Full Text Available Microfluidic impedance cytometry is a label-free approach for high-throughput analysis of particles and cells. It is based on the characterization of the dielectric properties of single particles as they flow through a microchannel with integrated electrodes. However, the measured signal depends not only on the intrinsic particle properties, but also on the particle trajectory through the measuring region, thus challenging the resolution and accuracy of the technique. In this work we show via simulation that this issue can be overcome without resorting to particle focusing, by means of a straightforward modification of the wiring scheme for the most typical and widely used microfluidic impedance chip.
Dzhumagulova, K. N.; Ramazanov, T. S.
2017-10-01
The method, which allows one to carry out computer simulation of a system of charged particles in a strong external homogeneous magnetic field with a time step that is independent on the Larmor oscillation time, was generalized for the case of the presence of the surrounding background for the moving particles. Correctly taking into account a strong magnetic field and friction force, which both depend on the particles velocities, we obtained solution resistant to a change in the time step within the second-order Velocity Verlet propagation scheme.
Efficient scheme for numerical simulations of the spin-bath decoherence
Dobrovitski, VV; De Raedt, HA
We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of a few coupled spins: (i) determining the pointer states of
Global communication schemes for the numerical solution of high-dimensional PDEs
DEFF Research Database (Denmark)
Hupp, Philipp; Heene, Mario; Jacob, Riko
2016-01-01
The numerical treatment of high-dimensional partial differential equations is among the most compute-hungry problems and in urgent need for current and future high-performance computing (HPC) systems. It is thus also facing the grand challenges of exascale computing such as the requirement to red...
A three–step discretization scheme for direct numerical solution of ...
African Journals Online (AJOL)
In this paper, a three-step discretization (numerical) formula is developed for direct integration of second-order initial value problems in ordinary differential equations. The development of the method and analysis of its basic properties adopt Taylor series expansion and Dahlquist stability test methods. The results show that ...
Tin melting: Effect of grid size and scheme on the numerical solution
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Vasilios Alexiades
2003-02-01
Full Text Available Benchmark solutions in Computational Fluid Dynamics are necessary for testing and for the verification of newly developed algorithms and codes. For flows involving heat transfer coupled to solid-liquid phase change and convection in the melt, such benchmark solutions do not exist. A set of benchmark problems has recently been proposed for melting of metals and waxes and several researchers responded by providing solutions for the given problems. It was shown in two recent publications that there were large discrepancies in the results obtained by those contributors. In the present, work we focus on one of the four test problems, tin melting at Rayleigh number $Ra=2.5imes 10^{5}$. Solutions obtained for several grids and two discretization schemes are presented and compared. Our results are used to explain the origin of the discrepancies in earlier results. Suggestions for future work are also provided.
European Workshop on High Order Nonlinear Numerical Schemes for Evolutionary PDEs
Beaugendre, Héloïse; Congedo, Pietro; Dobrzynski, Cécile; Perrier, Vincent; Ricchiuto, Mario
2014-01-01
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Improved computational schemes for the numerical modeling of hydrothermal resources in Wyoming
Energy Technology Data Exchange (ETDEWEB)
Heasler, H.P.; George, J.H.; Allen, M.B.
1990-05-01
A new method, the Conjugate Gradient Squared (CGS) solution technique, is shown to be extremely effective when applied to the finite-difference solution of conductive and convective heat transfer in geologic systems. The CGS method is compared to the Successive Over/Under Relaxation schemes, a version of the Gaussian elimination method, and the Generalized Minimum Residual (GMRES) approach. The CGS procedure converges at least ten times faster than the nearest competitor. The model is applied to the Thermopolis hydrothermal system, located in northwestern Wyoming. Modeled results are compared with measured temperature-depth profiles and results from other studies. The temperature decrease from 72{degree}C to 54{degrees}C along the crest of the Thermopolis anticline is shown to result from cooling of the geothermal fluid as it moves to the southeast. Modeled results show correct general trends, however, a time-varying three-dimensional model will be needed to fully explain the effects of mixing within the aquifers along the crest of the anticline and thermal affects of surface surface topography. 29 refs., 18 figs., 2 tabs.
Energy Technology Data Exchange (ETDEWEB)
Lode, Axel U.J.
2013-06-03
This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one- and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.
Toivanen, Elias A; Losilla, Sergio A; Sundholm, Dage
2015-12-21
Algorithms and working expressions for a grid-based fast multipole method (GB-FMM) have been developed and implemented. The computational domain is divided into cubic subdomains, organized in a hierarchical tree. The contribution to the electrostatic interaction energies from pairs of neighboring subdomains is computed using numerical integration, whereas the contributions from further apart subdomains are obtained using multipole expansions. The multipole moments of the subdomains are obtained by numerical integration. Linear scaling is achieved by translating and summing the multipoles according to the tree structure, such that each subdomain interacts with a number of subdomains that are almost independent of the size of the system. To compute electrostatic interaction energies of neighboring subdomains, we employ an algorithm which performs efficiently on general purpose graphics processing units (GPGPU). Calculations using one CPU for the FMM part and 20 GPGPUs consisting of tens of thousands of execution threads for the numerical integration algorithm show the scalability and parallel performance of the scheme. For calculations on systems consisting of Gaussian functions (α = 1) distributed as fullerenes from C20 to C720, the total computation time and relative accuracy (ppb) are independent of the system size.
Numerical study of silica-water based nanofluid nucleate pool boiling by two-phase Eulerian scheme
Salehi, H.; Hormozi, F.
2017-10-01
In this research, numerical simulation of nucleate pool boiling of water and water-silica nanofluid was investigated using Eulerian multiphase approach. At first, nucleate pool boiling of pure water was simulated. Classic heat flux partitioning (HFP) model was used for the prediction of bubble parameters. To validate proposed approach, numerical results were compared with experimental data. In the next step, this scheme has been used for water-silica nanofluid. Due to dilute nanofluid (0.1% volume) concentration, it was assumed as a homogenous liquid and therefore, a two-phase approach was applied to simulate its boiling. Meanwhile, various correlations were compared to determine nucleation site density and bubble departure frequency and the best equation was found. Results demonstrated nanoparticle deposition on the heater surface was a key factor that could change the heat transfer performance in boiling nanofluid. Therefore, accurate investigation of bubble behavior in nucleate boiling of nanofluids is a necessary concern to be focused in future modeling studies.
Evolutions of centered Brill waves with a pseudospectral method
Hilditch, David; Weyhausen, Andreas; Brügmann, Bernd
2017-11-01
The pseudospectral code bamps is used to evolve axisymmetric gravitational waves. We consider a one-parameter family of Brill wave initial data, taking the seed function and strength parameter of Holz et al. A careful comparison is made to earlier work. Our results are mostly in agreement with the literature, but we do find that some amplitudes reported elsewhere as subcritical evolve to form apparent horizons. Related to this point we find that by altering the slicing condition, the position of the peak of the Kretschmann scalar in these supercritical data can be controlled so that it appears away from the symmetry axis before the method fails, demonstrating that such behavior is at least partially a coordinate effect. We are able to tune the strength parameter to an interval of range 1 -A⋆/A ≃10-6 around the onset of apparent horizon formation. In this regime we find that large spikes appear in the Kretschmann scalar on the symmetry axis but away from the origin. From the supercritical side disjoint apparent horizons form around these spikes. On the subcritical side, down to this range, evidence of power-law scaling of the Kretschmann scalar is not conclusive, but the data can be fitted as a power-law with periodic wiggle.
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
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Mohammad Maleki
2012-01-01
Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.
Seismic waves modeling with the Fourier pseudo-spectral method on massively parallel machines.
Klin, Peter
2015-04-01
The Fourier pseudo-spectral method (FPSM) is an approach for the 3D numerical modeling of the wave propagation, which is based on the discretization of the spatial domain in a structured grid and relies on global spatial differential operators for the solution of the wave equation. This last peculiarity is advantageous from the accuracy point of view but poses difficulties for an efficient implementation of the method to be run on parallel computers with distributed memory architecture. The 1D spatial domain decomposition approach has been so far commonly adopted in the parallel implementations of the FPSM, but it implies an intensive data exchange among all the processors involved in the computation, which can degrade the performance because of communication latencies. Moreover, the scalability of the 1D domain decomposition is limited, since the number of processors can not exceed the number of grid points along the directions in which the domain is partitioned. This limitation inhibits an efficient exploitation of the computational environments with a very large number of processors. In order to overcome the limitations of the 1D domain decomposition we implemented a parallel version of the FPSM based on a 2D domain decomposition, which allows to achieve a higher degree of parallelism and scalability on massively parallel machines with several thousands of processing elements. The parallel programming is essentially achieved using the MPI protocol but OpenMP parts are also included in order to exploit the single processor multi - threading capabilities, when available. The developed tool is aimed at the numerical simulation of the seismic waves propagation and in particular is intended for earthquake ground motion research. We show the scalability tests performed up to 16k processing elements on the IBM Blue Gene/Q computer at CINECA (Italy), as well as the application to the simulation of the earthquake ground motion in the alluvial plain of the Po river (Italy).
Parand, K.; Rad, J. A.; Ahmadi, M.
2016-09-01
Natural convective heat transfer in porous media which is of importance in the design of canisters for nuclear waste disposal has received considerable attention during the past few decades. This paper presents a comparison between two different analytical and numerical methods, i.e. pseudospectral and Adomian decomposition methods. The pseudospectral approach makes use of the orthogonal rational Jacobi functions; this method reduces the solution of the problem to a solution of a system of algebraic equations. Numerical results are compared with each other, showing that the pseudospectral method leads to more accurate results and is applicable on similar problems.
Kotov, D. V.; Yee, H. C.; Wray, A. A.; Sjögreen, Björn; Kritsuk, A. G.
2018-01-01
The authors regret for the typographic errors that were made in equation (4) and missing phrase after equation (4) in the article ;Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows; [J. Comput. Phys. 307 (2016) 189-202].
Weisman, Andrew L.
Electronic structure calculation is an essential approach for determining the structure and function of molecules and is therefore of critical interest to physics, chemistry, and materials science. Of the various algorithms for calculating electronic structure, the pseudospectral method is among the fastest. However, the trade-off for its speed is more up-front programming and testing, and as a result, applications using the pseudospectral method currently lag behind those using other methods. In Part I of this dissertation, we first advance the pseudospectral method by optimizing it for an important application, polarized Raman spectroscopy, which is a well-established tool used to characterize molecular properties. This is an application of particular importance because often the easiest and most economical way to obtain the polarized Raman spectrum of a material is to simulate it; thus, utilization of the pseudospectral method for this purpose will accelerate progress in the determination of molecular properties. We demonstrate that our implementation of Raman spectroscopy using the pseudospectral method results in spectra that are just as accurate as those calculated using the traditional analytic method, and in the process, we derive the most comprehensive formulation to date of polarized Raman intensity formulas, applicable to both crystalline and isotropic systems. Next, we apply our implementation to determine the orientations of crystalline oligothiophenes -- a class of materials important in the field of organic electronics -- achieving excellent agreement with experiment and demonstrating the general utility of polarized Raman spectroscopy for the determination of crystal orientation. In addition, we derive from first-principles a method for using polarized Raman spectra to establish unambiguously whether a uniform region of a material is crystalline or isotropic. Finally, we introduce free, open-source software that allows a user to determine any of a
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T. Chourushi
2017-01-01
Full Text Available Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme (UDS is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes (HRS were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all HRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number E≈5. Furthermore, by E, a clear relationship between numerical stability of HRS and E was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to E.
Energy Technology Data Exchange (ETDEWEB)
López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es
2017-03-15
Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.
DEFF Research Database (Denmark)
Tong, M.S.; Lu, Y.; Chen, Y.
2005-01-01
A planar stratified dielectric slab medium, which is an interesting problem in optics and geophysics, is studied using a pseudo-spectral time-domain (PSTD) algorithm. Time domain electric fields and frequency domain propagation characteristics of both single and periodic dielectric slab...
Blaclard, G.; Vincenti, H.; Lehe, R.; Vay, J. L.
2017-09-01
With the advent of petawatt class lasers, the very large laser intensities attainable on target should enable the production of intense high-order Doppler harmonics from relativistic laser-plasma mirror interactions. At present, the modeling of these harmonics with particle-in-cell (PIC) codes is extremely challenging as it implies an accurate description of tens to hundreds of harmonic orders on a broad range of angles. In particular, we show here that due to the numerical dispersion of waves they induce in vacuum, standard finite difference time domain (FDTD) Maxwell solvers employed in most PIC codes can induce a spurious angular deviation of harmonic beams potentially degrading simulation results. This effect was extensively studied and a simple toy model based on the Snell-Descartes law was developed that allows us to finely predict the angular deviation of harmonics depending on the spatiotemporal resolution and the Maxwell solver used in the simulations. Our model demonstrates that the mitigation of this numerical artifact with FDTD solvers mandates very high spatiotemporal resolution preventing realistic three-dimensional (3D) simulations even on the largest computers available at the time of writing. We finally show that nondispersive pseudospectral analytical time domain solvers can considerably reduce the spatiotemporal resolution required to mitigate this spurious deviation and should enable in the near future 3D accurate modeling on supercomputers in a realistic time to solution.
Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip
2016-04-01
The flow of water in rivers and oceans can, under general assumptions, be efficiently modelled using Saint-Venant's shallow water system of equations (SWE). SWE is a hyperbolic system of conservation laws (HSCL) which can be derived from a starting point of incompressible Navier-Stokes. A common difficulty in the numerical simulation of HSCLs is the conservation of physical entropy. Work by Audusse, Bristeau, Perthame (2000) and Perthame, Simeoni (2001), proposed numerical SWE solvers known as kinetic schemes (KSs), which can be shown to have desirable entropy-consistent properties, and are thus called well-balanced schemes. A KS is derived from kinetic equations that can be integrated into the SWE. In flood risk assessment models the SWE must be coupled with other equations describing interacting meteorological and hydrogeological phenomena such as rain and groundwater flows. The SWE must therefore be appropriately modified to accommodate source and sink terms, so kinetic schemes are no longer valid. While modifications of SWE in this direction have been recently proposed, e.g., Delestre (2010), we depart from the extant literature by proposing a novel model that is "entropy-consistent" and naturally extends the SWE by respecting its kinetic formulation connections. This allows us to derive a system of partial differential equations modelling flow of a one-dimensional river with both a precipitation term and a groundwater flow model to account for potential infiltration and recharge. We exhibit numerical simulations of the corresponding kinetic schemes. These simulations can be applied to both real world flood prediction and the tackling of wider issues on how climate and societal change are affecting flood risk.
Zou, Peng
2017-05-10
Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.
Qu, Mengmeng; Jiang, Dazhi; Lu, Lucy X.
2016-11-01
To address the multiscale deformation and fabric development in Earth's ductile lithosphere, micromechanics-based self-consistent homogenization is commonly used to obtain macroscale rheological properties from properties of constituent elements. The homogenization is heavily based on the solution of an Eshelby viscous inclusion in a linear viscous medium and the extension of the solution to nonlinear viscous materials. The homogenization requires repeated numerical evaluation of Eshelby tensors for constituent elements and becomes ever more computationally challenging as the elements are deformed to more elongate or flattened shapes. In this paper, we develop an optimal scheme for evaluating Eshelby tensors, using a combination of a product Gaussian quadrature and the Lebedev quadrature. We first establish, through numerical experiments, an empirical relationship between the inclusion shape and the computational time it takes to evaluate its Eshelby tensors. We then use the relationship to develop an optimal scheme for selecting the most efficient quadrature to obtain the Eshelby tensors. The optimal scheme is applicable to general homogenizations. In this paper, it is implemented in a MATLAB package for investigating the evolution of solitary rigid or deformable inclusions and the development of shape preferred orientations in multi-inclusion systems during deformation. The MATLAB package, upgrading an earlier effort written in MathCad, can be downloaded online.
Heaps, Charles W
2016-01-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schr\\"{o}dinger equation with $N$ Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from $\\mathcal{O}(N^2)$ to $\\mathcal{O}(N)$. By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems; the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-d...
Chai, Runqi; Savvaris, Al; Tsourdos, Antonios
2016-06-01
In this paper, a fuzzy physical programming (FPP) method has been introduced for solving multi-objective Space Manoeuvre Vehicles (SMV) skip trajectory optimization problem based on hp-adaptive pseudospectral methods. The dynamic model of SMV is elaborated and then, by employing hp-adaptive pseudospectral methods, the problem has been transformed to nonlinear programming (NLP) problem. According to the mission requirements, the solutions were calculated for each single-objective scenario. To get a compromised solution for each target, the fuzzy physical programming (FPP) model is proposed. The preference function is established with considering the fuzzy factor of the system such that a proper compromised trajectory can be acquired. In addition, the NSGA-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the FPP solution. Simulation results indicate that the proposed method is effective and feasible in terms of dealing with the multi-objective skip trajectory optimization for the SMV.
Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations
VERMA, MAHENDRA K
2013-09-21
Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 10243, 20483, and 40963 grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.
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M. Boumaza
2015-07-01
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.
A high-order CESE scheme with a new divergence-free method for MHD numerical simulation
Yang, Yun; Feng, Xue-Shang; Jiang, Chao-Wei
2017-11-01
In this paper, we give a high-order space-time conservation element and solution element (CESE) method with a most compact stencil for magneto-hydrodynamics (MHD) equations. This is the first study to extend the second-order CESE scheme to a high order for MHD equations. In the CESE method, the conservative variables and their spatial derivatives are regarded as the independent marching quantities, making the CESE method significantly different from the finite difference method (FDM) and finite volume method (FVM). To utilize the characteristics of the CESE method to the maximum extent possible, our proposed method based on the least-squares method fundamentally keeps the magnetic field divergence-free. The results of some test examples indicate that this new method is very efficient.
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Buscaglia Gustavo C.
2001-01-01
Full Text Available A new numerical approach is proposed to alleviate the computational cost of solving non-linear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost. The overall efficiency of the numerical methodology makes it feasible to apply rigorous homogenization techniques in the analysis of compressible fluid contact considering roughness effects. Previous work makes use of an heuristic averaging technique. Numerical comparison proves that homogenization-based methods are superior when the roughness is strongly anisotropic and not aligned with the flow direction.
Mihailovic, Dragutin T.; Lazic, Jelena; Leśny, Jacek; Olejnik, Janusz; Lalic, Branislava; Kapor, Darko; Cirisan, Ana
2010-05-01
Numerical simulations and tests with the recently redesigned land-air parameterization scheme (LAPS) are presented. In all experiments, supported either by one-point micrometeorological, 1D or 3D simulations, the attention has been directed to: (1) comparison of simulation outputs, expressing the energy transfer over and through heterogeneous and non-heterogeneous surfaces, versus observations and (2) analysis of uncertainties occurring in the solution of the energy balance equation at the land-air interface. To check the proposed method for aggregation of albedo, "propagating hole" sensitivity tests with LAPS over a sandstone rock grid cell have been performed with the forcing meteorological data for July 17, 1999 in Baxter site, Philadelphia (USA). Micrometeorological and biophysical measurements from the surface experiments conducted over crops and apple orchard in Serbia, Poland, Austria and France were used to test the operation of LAPS in calculating surface fluxes and canopy environment temperatures within and above plant covers of different densities. In addition, sensitivity tests with single canopy covers over the Central Europe region and comparison against the observations taken from SYNOP data using 3D simulations were made. Validation of LAPS performances over a solid surface has been done by comparison of 2 m air temperature observations against 5-day simulations over the Sahara Desert rocky ground using 3D model. To examine how realistically the LAPS simulates surface processes over a heterogeneous surface, we compared the air temperature measured at 2 m and that predicted by the 1D model with the LAPS as the surface scheme. Finally, the scheme behaviour over urban surface was tested by runs over different parts of a hypothetical urban area. The corresponding 1D simulations were carried out with an imposed meteorological dataset collected during HAPEX-MOBILHY experiment at Caumont (France). The quantities predicted by the LAPS compare well with the
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H. Khalil
2015-06-01
Full Text Available We study shifted Legendre polynomials and develop some operational matrices of integrations. We use these operational matrices and develop new sophisticated technique for numerical solutions to the following coupled system of fredholm integro differential equations DU(x = f(x + 11 Z 1 0 K11(x, tU(tdt + 12 Z 1 0 K12(x, tV (tdt, DV (x = g(x + 21 Z 1 0 K21(x, tU(tdt + 22 Z 1 0 K22(x, tV (tdt, U(0 = C1, V (0 = C2, where D is fractional derivative of order with respect to x, 0 < 6 1, 11, 12, 21, 22 are real constants, f, g 2 C([0, 1] and K11, K12, K21, K22 2 C([0, 1]×[0, 1]. We develop simple procedure to reduce the coupled system of equations to a system of algebraic equations without discretizing the system. We provide examples and numerical simulations to show the applicability and simplicity of our results and to demonstrate that the results obtained using the new technique matches well with the exact solutions of the problem. We also provide error analysis.
A hybrid radial basis function-pseudospectral method for thermal convection in a 3-D spherical shell
Wright, G. B.
2010-07-01
A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a "2 + 1" approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3-D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface-based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be "scattered" over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth\\'s mantle, which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle. Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number (Ra) 7 × 10^{3} and 10^{5}. Results from a Ra = 10^{6} simulation are also given. The algorithmic simplicity of the code (mostly due to RBFs) allows it to be written in less than 400 lines of MATLAB and run on a single workstation. We find that our method is very competitive with those currently used in the literature. Copyright 2010 by the American Geophysical Union.
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Gustavo C. Buscaglia
2001-01-01
Full Text Available A new numerical approach is proposed to alleviate the computational cost of solving non-linear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost.
Directory of Open Access Journals (Sweden)
V. N. Romaniuk
2016-01-01
Full Text Available Further improvement of natural gas usage in power industry is associated with transition to the combined-cycle gas technology, primarily at combined heat and power plants (CHP. Renovation of technology of conversion of fuel energy into heat and electricity flows is effective while it is performed simultaneously with the elaboration of thermal circuits of CHP by insertion heat accumulators and absorption lithium bromide heat pumps (ALBHP in the structure of CHP; the mentioned insertion amends thermodynamic as well as economic and environmental indicators of CHP renovation and also develops CHP maneuverability. The ability of CHP to provide heat in required quantity, their capacity to change electricity generation output without excessive fuel consumption is extremely relevant for the energy system that incorporates thermal power plants as dominating component. At the same time the displacement of traditional electrical power regulators take place. Implementation of projects of this kind requires the elaboration of CHP flow diagram calculation methods and determining relevant indicators. The results of the numerical study of the energy characteristics of CHP with the aid of the topological models of the existing heat flow diagrams of CHP that incorporate ALBHP for recovery of low-temperature waste of heat flows of systems of cooling water circulating are presented in the article. An example of calculation, the results of the CHP thermodynamic efficiency evaluation, the change of the energy characteristics for different modes of operation of CHP caused by implementation of ALBHP are shown. The conditions for the effective application of lithium bromide absorption heat pumps are specified, as well as the rate of increase of thermodynamic efficiency; the changes of maneuverability of CHP with high initial parameters are identified, the natural gas savings in The Republic of Belarus are determined.
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Farsi Mohammad
2014-09-01
Full Text Available Main aim of this paper is to find the best combination of numerical schemes for 2-D SPH simulation of wedge water entry. Diffusion term is considered as laminar, turbulent, and artificial viscosity. Density filter that seriously affects the pressure distribution is investigated by adopting no filter, first order filter, and second order filter. Validation of the results indicates that turbulent model and first order density filter can lead to more reasonable solutions. This simulation was then conducted for wedge water entry with wide range of deadrise angles including 10 degrees, 20 degrees, 30 degrees, 45 degrees, 60 degrees and 81 degrees, with extreme deadrise angles of 10 degrees, 60 degrees and 81 degrees being considered. Comparison of SPH results with BEM solutions has displayed favorable agreement. In two particular cases where experimental data are available, the SPH results are shown to be closer to the experiments than BEM solution. While, accuracy of the obtained results for moderate deadrise angles is desirable, numerical findings for very small or very large deadrise angles are also very reasonable
On the formulation and numerical simulation of distributed-order fractional optimal control problems
Zaky, M. A.; Machado, J. A. Tenreiro
2017-11-01
In a fractional optimal control problem, the integer order derivative is replaced by a fractional order derivative. The fractional derivative embeds implicitly the time delays in an optimal control process. The order of the fractional derivative can be distributed over the unit interval, to capture delays of distinct sources. The purpose of this paper is twofold. Firstly, we derive the generalized necessary conditions for optimal control problems with dynamics described by ordinary distributed-order fractional differential equations (DFDEs). Secondly, we propose an efficient numerical scheme for solving an unconstrained convex distributed optimal control problem governed by the DFDE. We convert the problem under consideration into an optimal control problem governed by a system of DFDEs, using the pseudo-spectral method and the Jacobi-Gauss-Lobatto (J-G-L) integration formula. Next, we present the numerical solutions for a class of optimal control problems of systems governed by DFDEs. The convergence of the proposed method is graphically analyzed showing that the proposed scheme is a good tool for the simulation of distributed control problems governed by DFDEs.
Henle, James M.
This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…
Hornikx, Maarten; Dragna, Didier
2015-07-01
The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.
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N. V. Kantartzis
2012-10-01
Full Text Available A generalized conformal time-domain method with adjustable spectral accuracy is introduced in this paper for the consistent analysis of large-scale electromagnetic compatibility problems. The novel 3-D hybrid schemes blend a stencil-optimized finite-volume time-domain and a multimodal Fourier-Chebyshev pseudo-spectral time-domain algorithm that split the overall space into smaller and flexible areas. A key asset is that both techniques are updated independently and interconnected by robust boundary conditions. Also, combining a family of spatial derivative approximators with controllable precision in general curvilinear coordinates, the proposed method launches a conformal field flux formulation to derive electromagnetic quantities in regions with fine details. For advanced grid reliability at dissimilar media interfaces, dispersion-reduced adaptive operators, which assign the proper weights to each spatial increment, are developed. So, the resulting discretization yields highly rigorous and computationally affordable simulations, devoid of lattice errors. Numerical results, addressing detailed comparisons of various realistic applications with reference or measurement data verify our methodology and reveal its significant applicability.
Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation
Pagán Muñoz, Raúl; Hornikx, Maarten
2017-11-01
The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.
Energy Technology Data Exchange (ETDEWEB)
Morinishi, K.; Satofuka, N. (Kyoto Inst. of Technology., Kyoto (Japan))
1990-07-25
Numerical analysis of the compressible equations for the flow field with low-mach-number is performed. The method using the finite difference method and the rational Runge-Kutta scheme is applied to the compressible Navier-Stokes equations. Numerical computation for the fundamental flow field is carried out in the range of 0.4-0.01 of basic mach-number, and following conclusion is obtained. The results obtained for driven cavity flows and flows past a circular cylinder with Reynolds number of 40 are represented well the numerical solution which is obtained from before through the incompressible Navier-Stokes equations, and are entirely reliable. Though the convergence rate to a steady-state solution becomes slower proportionally as the Mach number is reduced, vibration of the pressure distribution which diverges the numerical computation is not found even at Mach number 0.01. Stable computation can be done. The result of numerical computation of the flow field obtained around the NACA0012 airfoil at Reynolds number 3.0 {times} 10 {sup 6}, is in agreement well with Harris {prime} s experimental data. 14 refs., 11 figs., 2 tabs.
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L. Wang
2015-01-01
Full Text Available Economical space transportation systems to launch small satellites into Earth’s orbits are researched in many countries. Using aerospace systems, included aircraft and air-launched launch vehicle, is one of the low cost technical solutions. The airborne launch vehicle application to launch a small satellite with the purpose of remote sensing requires high precision exit on specified sun-synchronous orbit. So a problem is stated to construct an optimal ascent trajectory and optimal control.In this paper, the mathematical motion model of the air-launched launch vehicle with the external disturbances caused by the Earth’s non-sphericity, drag and wind is put forward based on the three-stage flight program with passive intermediate section. A discrete process based on pseudo-spectral method is used to solve the problem, which allows converting the initial problem into a nonlinear programming problem with dynamic constraints and aims for the criteria of maximization of the final mass released onto the target orbit.Application of the proposed solution procedure is illustrated by calculating the optimal control and the corresponding trajectory for two-stage liquid launch vehicle, which places the small spacecraft on the orbit of sun-synchronous at the height of 512 km. The numerical simulation results have demonstrated the effectiveness of the proposed algorithm and allow us to analyze three-stage trajectory parameters with intermediate passive flight phase. It can be noted that in the resulting ascent trajectory, the intermediate passive flight part is a suborbital trajectory with low energy integral, perigee of which is under the surface of the Earth.
Simulation of seismograms in a 2-D viscoelastic Earth by pseudospectral methods
Energy Technology Data Exchange (ETDEWEB)
Carcione, Jose M [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Trieste (Italy); Helle, Hans B [Norsk Hydro a.s., 0 and E Research Centre, Bergen (Norway); Seriani, Geza [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Trieste (Italy); Plasencia Linares, Milton P [Facultad de Ciencias Astronomicas y Geofisicas, Universidad Nacional de La Plata, La Plata (Argentina)
2005-04-15
Using an improved global pseudospectral modeling algorithm we synthesize seismograms generated by oceanic and continental earthquakes. Attention is given to attenuation, to explicit modeling of boundary conditions at the ocean-bottom interface, simulation of the Rayleigh window and interface-wave propagation. The algorithm is based on Fourier and Chebyshev differential operators and a domain-decomposition technique - one grid for the fluid and another grid for the solid. Wave propagation in the oceanic and continent crusts and mantle is modeled by using a viscoelastic stress-strain relation based on memory variables. The main physical phenomena associated with an ocean-crust system are modeled, including Scholte waves, leaking Rayleigh waves, dispersive modes, and the Rayleigh-window phenomenon due to a minimum in the reflection coefficient of the ocean bottom, which has not been simulated with direct methods. In particular, we model Rayleigh modes (mainly the M11 mode), and coupled Rayleigh-Scholte waves, for which the dispersion relation is solved in simple cases. Also, we model the effects of random. [Spanish] El algoritmo de modulacion seudoespectral es mejorado y aplicado a la simulacion de sismogramas generados por sismos oceanicos y continentales, como atencion a la atenuacion y a la modelacion explicita de condiciones a la frontera en el fondo oceanico y a la simulacion de la ventana de Rayleigh y la propagacion en interfases. El algoritmo se basa en los operadores diferenciales de Fourier y de Chebyshev con una tecnica de decomposicion de dominios, una malla para el fluido y otra para el solido. Para la propagacion se usa una relacion de esfuerzo-deformacion basada en variables de memoria. Entre los fenomenos modelados se incluyen las ondas de Scholte, las ondas evanescentes de Rayleigh y los modos dispersivos, asi como la ventana de Rayleigh, un minimo del coeficiente de reflexion en el fondo oceanico que nunca ha sido simulado con metodos directos. Hemos
Hershkovitz, Yaron; Anker, Yaakov; Ben-Dor, Eyal; Schwartz, Guy; Gasith, Avital
2010-05-01
In-stream vegetation is a key ecosystem component in many fluvial ecosystems, having cascading effects on stream conditions and biotic structure. Traditionally, ground-level surveys (e.g. grid and transect analyses) are commonly used for estimating cover of aquatic macrophytes. Nonetheless, this methodological approach is highly time consuming and usually yields information which is practically limited to habitat and sub-reach scales. In contrast, remote-sensing techniques (e.g. satellite imagery and airborne photography), enable collection of large datasets over section, stream and basin scales, in relatively short time and reasonable cost. However, the commonly used spatial high resolution (1m) is often inadequate for examining aquatic vegetation on habitat or sub-reach scales. We examined the utility of a pseudo-spectral methodology, using RGB digital photography for estimating the cover of in-stream vegetation in a small Mediterranean-climate stream. We compared this methodology with that obtained by traditional ground-level grid methodology and with an airborne hyper-spectral remote sensing survey (AISA-ES). The study was conducted along a 2 km section of an intermittent stream (Taninim stream, Israel). When studied, the stream was dominated by patches of watercress (Nasturtium officinale) and mats of filamentous algae (Cladophora glomerata). The extent of vegetation cover at the habitat and section scales (100 and 104 m, respectively) were estimated by the pseudo-spectral methodology, using an airborne Roli camera with a Phase-One P 45 (39 MP) CCD image acquisition unit. The swaths were taken in elevation of about 460 m having a spatial resolution of about 4 cm (NADIR). For measuring vegetation cover at the section scale (104 m) we also used a 'push-broom' AISA-ES hyper-spectral swath having a sensor configuration of 182 bands (350-2500 nm) at elevation of ca. 1,200 m (i.e. spatial resolution of ca. 1 m). Simultaneously, with every swath we used an Analytical
Energy Technology Data Exchange (ETDEWEB)
Gomez T, A.M.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico); Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)] e-mail: armagotorres@aol.com
2003-07-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as {theta} scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
Dijkstra, D.
2002-01-01
In the conventional pseudo-spectral collocation method to solve an ordinary first order differential equation, the derivative is obtained from Lagrange interpolation and has degree of precision N for a grid of (N+1) points. In the present, novel method Hermite interpolation is used as point of
Mittal, H. V. R.; Ray, Rajendra K.; Al-Mdallal, Qasem M.
2017-09-01
The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate αm on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points, and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and vorticity profiles at the surface of the cylinder are also shown. The effect of increase in αm on the timing of the formation of the vortices, the closed wake length, and the thickness of the boundary layer is investigated.
Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores
Chatterjee, Anando G.
2017-11-04
In this paper we present scaling results of a FFT library, FFTK, and a pseudospectral code, Tarang, on grid resolutions up to 81923 grid using 65536 cores of Blue Gene/P and 196608 cores of Cray XC40 supercomputers. We observe that communication dominates computation, more so on the Cray XC40. The computation time scales as Tcomp∼p−1, and the communication time as Tcomm∼n−γ2 with γ2 ranging from 0.7 to 0.9 for Blue Gene/P, and from 0.43 to 0.73 for Cray XC40. FFTK, and the fluid and convection solvers of Tarang exhibit weak as well as strong scaling nearly up to 196608 cores of Cray XC40. We perform a comparative study of the performance on the Blue Gene/P and Cray XC40 clusters.
Directory of Open Access Journals (Sweden)
Kong Minxiu
2016-01-01
Full Text Available Optimal point-to-point motion planning of flexible parallel manipulator was investigated in this paper and the 3RRR parallel manipulator is taken as the object. First, an optimal point-to-point motion planning problem was constructed with the consideration of the rigid-flexible coupling dynamic model and actuator dynamics. Then, the multi-interval Legendre–Gauss–Radau (LGR pseudospectral method was introduced to transform the optimal control problem into Nonlinear Programming (NLP problem. At last, the simulation and experiment were carried out on the flexible parallel manipulator. Compared with the line motion of quantic polynomial planning, the proposed method could constrain the flexible displacement amplitude and suppress the residue vibration.
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR ...
African Journals Online (AJOL)
This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give ...
DEFF Research Database (Denmark)
van Leeuwen, Theo
2013-01-01
This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation.......This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation....
Frontiers in Numerical Relativity
Evans, Charles R.; Finn, Lee S.; Hobill, David W.
2011-06-01
Preface; Participants; Introduction; 1. Supercomputing and numerical relativity: a look at the past, present and future David W. Hobill and Larry L. Smarr; 2. Computational relativity in two and three dimensions Stuart L. Shapiro and Saul A. Teukolsky; 3. Slowly moving maximally charged black holes Robert C. Ferrell and Douglas M. Eardley; 4. Kepler's third law in general relativity Steven Detweiler; 5. Black hole spacetimes: testing numerical relativity David H. Bernstein, David W. Hobill and Larry L. Smarr; 6. Three dimensional initial data of numerical relativity Ken-ichi Oohara and Takashi Nakamura; 7. Initial data for collisions of black holes and other gravitational miscellany James W. York, Jr.; 8. Analytic-numerical matching for gravitational waveform extraction Andrew M. Abrahams; 9. Supernovae, gravitational radiation and the quadrupole formula L. S. Finn; 10. Gravitational radiation from perturbations of stellar core collapse models Edward Seidel and Thomas Moore; 11. General relativistic implicit radiation hydrodynamics in polar sliced space-time Paul J. Schinder; 12. General relativistic radiation hydrodynamics in spherically symmetric spacetimes A. Mezzacappa and R. A. Matzner; 13. Constraint preserving transport for magnetohydrodynamics John F. Hawley and Charles R. Evans; 14. Enforcing the momentum constraints during axisymmetric spacelike simulations Charles R. Evans; 15. Experiences with an adaptive mesh refinement algorithm in numerical relativity Matthew W. Choptuik; 16. The multigrid technique Gregory B. Cook; 17. Finite element methods in numerical relativity P. J. Mann; 18. Pseudo-spectral methods applied to gravitational collapse Silvano Bonazzola and Jean-Alain Marck; 19. Methods in 3D numerical relativity Takashi Nakamura and Ken-ichi Oohara; 20. Nonaxisymmetric rotating gravitational collapse and gravitational radiation Richard F. Stark; 21. Nonaxisymmetric neutron star collisions: initial results using smooth particle hydrodynamics
Directory of Open Access Journals (Sweden)
M.M. Khader
2014-10-01
Full Text Available In this article, we present a new numerical method to solve the integro-differential equations (IDEs. The proposed method uses the Legendre cardinal functions to express the approximate solution as a finite series. In our method the operational matrix of derivatives is used to reduce IDEs to a system of algebraic equations. To demonstrate the validity and applicability of the proposed method, we present some numerical examples. We compare the obtained numerical results from the proposed method with some other methods. The results show that the proposed algorithm is of high accuracy, more simple and effective.
Dehghan, Mehdi; Mohammadi, Vahid
2017-08-01
In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.
Nonstandard finite difference schemes for differential equations
Directory of Open Access Journals (Sweden)
Mohammad Mehdizadeh Khalsaraei
2014-12-01
Full Text Available In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs. Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with standard methods.
Directory of Open Access Journals (Sweden)
Yu-Ju Wang
2016-02-01
Full Text Available Ground motions from normal-faulting earthquakes are generally considered to be smaller than those of strike-slip and thrust events. On 11 April 2011 a crustal normal-faulting earthquake [the Fukushima earthquake (Mw 6.6] occurred in Eastern Japan. The peak ground acceleration (PGA observed was considerably higher than the predictions of several ground-motion prediction equations (GMPEs, which were derived mainly from thrust or strike-slip earthquakes. In northeast Taiwan, the tectonic structure of the Ryukyu Arc and the Okinawa Trough typically entail normal-faulting earthquakes. Because of the normal-faulting earthquakes relevance to ground motions and nuclear power plant sites in northeast Taiwan, we evaluated the impact of the ground motion of normal-faulting earthquakes in offshore northeast Taiwan using a newly constructed attenuation relationship for PGA and pseudo-spectral acceleration (Sa. We collected 832 records from 13 normal-faulting earthquakes with focal depths of less than 50 km. The moment magnitude (Mw of the 13 events was between 4 - 6. The Sa and PGA of normal-faulting earthquakes offshore northeast Taiwan determined with the newly constructed attenuation relationship were higher and lower, respectively, than those obtained using attenuation equations commonly used in the Taiwan subduction zone.
Multiuser Switched Diversity Scheduling Schemes
Shaqfeh, Mohammad; Alouini, Mohamed-Slim
2012-01-01
Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback sys...
Additive operator-difference schemes splitting schemes
Vabishchevich, Petr N
2013-01-01
Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy
Sidler, Rolf; Carcione, José M.; Holliger, Klaus
2014-02-01
We present a novel approach for the comprehensive, flexible and accurate simulation of poroelastic wave propagation in 3-D cylindrical coordinates. An important application of this method is the realistic modelling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, as of yet largely unresolved, problem in exploration geophysics. To this end, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the centre followed by the mudcake and/or casing, and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction and Fourier expansions in the vertical and azimuthal directions as well as a Runge-Kutta integration scheme for the time evolution. Trigonometric interpolation and a domain decomposition method based on the method of characteristics are used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces as well as to reduce the number of gridpoints in the innermost domain for computational efficiency. We apply this novel modelling approach to the particularly challenging scenario of near-surface borehole environments. To this end, we compare 3-D heterogeneous and corresponding rotationally invariant simulations, assess the sensitivity of Stoneley waves to formation permeability in the presence of a casing and evaluate the effects of an excavation damage zone behind a casing on sonic log recordings. Our results indicate that only first arrival times of fast modes are reasonably well described by rotationally invariant approximations of 3-D heterogenous media. We also find that Stoneley waves are indeed remarkably sensitive to the average permeability behind a perforated PVC casing, and that the presence of an excavation damage zone behind a casing tends to dominate the overall signature of recorded seismograms.
Scheme Program Documentation Tools
DEFF Research Database (Denmark)
Nørmark, Kurt
2004-01-01
This paper describes and discusses two different Scheme documentation tools. The first is SchemeDoc, which is intended for documentation of the interfaces of Scheme libraries (APIs). The second is the Scheme Elucidator, which is for internal documentation of Scheme programs. Although the tools...
Hybrid scheme for Brownian semistationary processes
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.
is to approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes...... the asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments......We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme...
A rational function based scheme for solving advection equation
Energy Technology Data Exchange (ETDEWEB)
Xiao, Feng [Gunma Univ., Kiryu (Japan). Faculty of Engineering; Yabe, Takashi
1995-07-01
A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author).
Electrical Injection Schemes for Nanolasers
DEFF Research Database (Denmark)
Lupi, Alexandra; Chung, Il-Sug; Yvind, Kresten
2014-01-01
Three electrical injection schemes based on recently demonstrated electrically pumped photonic crystal nanolasers have been numerically investigated: 1) a vertical p-i-n junction through a post structure; 2) a lateral p-i-n junction with a homostructure; and 3) a lateral p-i-n junction....... For this analysis, the properties of different schemes, i.e., electrical resistance, threshold voltage, threshold current, and internal efficiency as energy requirements for optical interconnects are compared and the physics behind the differences is discussed....
Central schemes for open-channel flow
Gottardi, Guido; Venutelli, Maurizio
2003-03-01
The resolution of the Saint-Venant equations for modelling shock phenomena in open-channel flow by using the second-order central schemes of Nessyahu and Tadmor (NT) and Kurganov and Tadmor (KT) is presented. The performances of the two schemes that we have extended to the non-homogeneous case and that of the classical first-order Lax-Friedrichs (LF) scheme in predicting dam-break and hydraulic jumps in rectangular open channels are investigated on the basis of different numerical and physical conditions. The efficiency and robustness of the schemes are tested by comparing model results with analytical or experimental solutions.
Simple and High-Accurate Schemes for Hyperbolic Conservation Laws
Directory of Open Access Journals (Sweden)
Renzhong Feng
2014-01-01
Full Text Available The paper constructs a class of simple high-accurate schemes (SHA schemes with third order approximation accuracy in both space and time to solve linear hyperbolic equations, using linear data reconstruction and Lax-Wendroff scheme. The schemes can be made even fourth order accurate with special choice of parameter. In order to avoid spurious oscillations in the vicinity of strong gradients, we make the SHA schemes total variation diminishing ones (TVD schemes for short by setting flux limiter in their numerical fluxes and then extend these schemes to solve nonlinear Burgers’ equation and Euler equations. The numerical examples show that these schemes give high order of accuracy and high resolution results. The advantages of these schemes are their simplicity and high order of accuracy.
On Optimal Designs of Some Censoring Schemes
Directory of Open Access Journals (Sweden)
Dr. Adnan Mohammad Awad
2016-03-01
Full Text Available The main objective of this paper is to explore suitability of some entropy-information measures for introducing a new optimality censoring criterion and to apply it to some censoring schemes from some underlying life-time models. In addition, the paper investigates four related issues namely; the effect of the parameter of parent distribution on optimal scheme, equivalence of schemes based on Shannon and Awad sup-entropy measures, the conjecture that the optimal scheme is one stage scheme, and a conjecture by Cramer and Bagh (2011 about Shannon minimum and maximum schemes when parent distribution is reflected power. Guidelines for designing an optimal censoring plane are reported together with theoretical and numerical results and illustrations.
Status of numerical relativity
Indian Academy of Sciences (India)
schemes are described in [48]. 2.5 Black hole finder. In many simulations of numerical relativity, black holes are formed or exist from the beginning of simulation (e.g., in merger of binary black holes). To confirm the existence of black holes and to find their location, apparent horizon finder and/or event horizon finder have to ...
Multiuser switched diversity scheduling schemes
Shaqfeh, Mohammad
2012-09-01
Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback systems in Rayleigh fading conditions. © 2012 IEEE.
Computational evaluation of convection schemes in fluid dynamics problems
Directory of Open Access Journals (Sweden)
Paulo Laerte Natti
2012-11-01
Full Text Available This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are analyzed and implemented in the context of normalized variables of Leonard. In order to access the performance of the schemes, Riemann problems for 1D Burgers, Euler and shallow water equations are considered. From the numerical results, the schemes are ranked according to their performance in solving these non-linear equations. The best scheme is then applied in the numerical simulation of tridimensional incompressible moving free surface flows.
Towards an "All Speed" Unstructured Upwind Scheme
Loh, Ching Y.; Jorgenson, Philip C.E.
2009-01-01
In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).
Energy Technology Data Exchange (ETDEWEB)
Sidler, Rolf, E-mail: rsidler@gmail.com [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland); Carcione, José M. [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy); Holliger, Klaus [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)
2013-02-15
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.
Two Conservative Difference Schemes for Rosenau-Kawahara Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2014-01-01
Full Text Available Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.
A simplification of the unified gas kinetic scheme
Chen, Songze; Xu, Kun
2016-01-01
Unified gas kinetic scheme (UGKS) is an asymptotic preserving scheme for the kinetic equations. It is superior for transition flow simulations, and has been validated in the past years. However, compared to the well known discrete ordinate method (DOM) which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. Based on the observation that the equilibrium part of the UGKS fluxes can be evaluated analytically, the equilibrium part in the UGKS flux is not necessary to be discretized in velocity space. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-S...
Numerical bifurcation analysis of a class of nonlinear renewal equations
Directory of Open Access Journals (Sweden)
Dimitri Breda
2016-09-01
Full Text Available We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic- and Ricker-type population equations and exhibits transcritical, Hopf and period doubling bifurcations. The reliability is demonstrated by comparing the results to those obtained by a reduction to a Hamiltonian Kaplan-Yorke system and to those obtained by direct application of collocation methods (the latter also yield estimates for positive Lyapunov exponents in the chaotic regime. We conclude that the methodology described here works well for a class of delay equations for which currently no tailor-made tools exist (and for which it is doubtful that these will ever be constructed.
Parallelization of a numerical simulation code for isotropic turbulence
Energy Technology Data Exchange (ETDEWEB)
Sato, Shigeru; Yokokawa, Mitsuo; Watanabe, Tadashi; Kaburaki, Hideo
1996-03-01
A parallel pseudospectral code which solves the three-dimensional Navier-Stokes equation by direct numerical simulation is developed and execution time, parallelization efficiency, load balance and scalability are evaluated. A vector parallel supercomputer, Fujitsu VPP500 with up to 16 processors is used for this calculation for Fourier modes up to 256x256x256 using 16 processors. Good scalability for number of processors is achieved when number of Fourier mode is fixed. For small Fourier modes, calculation time of the program is proportional to NlogN which is ideal complexity of calculation for 3D-FFT on vector parallel processors. It is found that the calculation performance decreases as the increase of the Fourier modes. (author).
Numerical Analysis of Constrained, Time-Optimal Satellite Reorientation
Directory of Open Access Journals (Sweden)
Robert G. Melton
2012-01-01
Full Text Available Previous work on time-optimal satellite slewing maneuvers, with one satellite axis (sensor axis required to obey multiple path constraints (exclusion from keep-out cones centered on high-intensity astronomical sources reveals complex motions with no part of the trajectory touching the constraint boundaries (boundary points or lying along a finite arc of the constraint boundary (boundary arcs. This paper examines four cases in which the sensor axis is either forced to follow a boundary arc, or has initial and final directions that lie on the constraint boundary. Numerical solutions, generated via a Legendre pseudospectral method, show that the forced boundary arcs are suboptimal. Precession created by the control torques, moving the sensor axis away from the constraint boundary, results in faster slewing maneuvers. A two-stage process is proposed for generating optimal solutions in less time, an important consideration for eventual onboard implementation.
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
2017-01-01
Although Arabic numerals (like ‘2016’ and ‘3.14’) are ubiquitous, we show that in interactive computer applications they are often misleading and surprisingly unreliable. We introduce interactive numerals as a new concept and show, like Roman numerals and Arabic numerals, interactive numerals introduce another way of using and thinking about numbers. Properly understanding interactive numerals is essential for all computer applications that involve numerical data entered by users, including finance, medicine, aviation and science. PMID:28484609
Staggered Schemes for Fluctuating Hydrodynamics
Balboa, F; Delgado-Buscalioni, R; Donev, A; Fai, T; Griffith, B; Peskin, C S
2011-01-01
We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive, advective and stochastic fluxes that satisfies a discrete fluctuation-dissipation balance, and construct temporal discretizations that are at least second-order accurate in time deterministically and in a weak sense. Specifically, the methods reproduce the correct equilibrium covariances of the fluctuating fields to third (compressible) and second (incompressible) order in the time step, as we verify numerically. We apply our techniques to model recent experimental measurements of giant fluctuations in diffusively mixing fluids in a micro-gravity environment [A. Vailati et. al., Nature Communications 2:290, 2011]. Numerical results for the static spectrum of non-equilibrium concentration fluctuations are in excellent agreement between the compressible and incompressible simula...
Love, Patrick G.; Guthrie, Victoria L.
1999-01-01
Summarizes William Perry's intellectual scheme and places it in the context of the 1990's. Perry's scheme of cognitive development, though more than thirty years old, is still being used by practitioners today to enhance practice in and out of the classroom. It laid a foundation for new research to extend, challenge, and build onto the scheme.…
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
Dynamic Restarting Schemes for Eigenvalue Problems
Energy Technology Data Exchange (ETDEWEB)
Wu, Kesheng; Simon, Horst D.
1999-03-10
In studies of restarted Davidson method, a dynamic thick-restart scheme was found to be excellent in improving the overall effectiveness of the eigen value method. This paper extends the study of the dynamic thick-restart scheme to the Lanczos method for symmetric eigen value problems and systematically explore a range of heuristics and strategies. We conduct a series of numerical tests to determine their relative strength and weakness on a class of electronic structure calculation problems.
Parallel Pseudo Arc-Length Moving Mesh Schemes for Multidimensional Detonation
Jianguo Ning; Xinpeng Yuan; Tianbao Ma; Jian Li
2017-01-01
We have discussed the multidimensional parallel computation for pseudo arc-length moving mesh schemes, and the schemes can be used to capture the strong discontinuity for multidimensional detonations. Different from the traditional Euler numerical schemes, the problems of parallel schemes for pseudo arc-length moving mesh schemes include diagonal processor communications and mesh point communications, which are illustrated by the schematic diagram and key pseudocodes. Finally, the numerical e...
Homogenization scheme for acoustic metamaterials
Yang, Min
2014-02-26
We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial\\'s structural unit cell with a piece of homogenized material. From the Green\\'s theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme\\'s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2000-05-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented.
Hybrid undulator numerical optimization
Energy Technology Data Exchange (ETDEWEB)
Hairetdinov, A.H. [Kurchatov Institute, Moscow (Russian Federation); Zukov, A.A. [Solid State Physics Institute, Chernogolovka (Russian Federation)
1995-12-31
3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.
de Bont, Chris
2018-01-01
This booklet was written to share research results with farmers and practitioners in Tanzania. It gives a summary of the empirical material collected during three months of field work in the Mawala irrigation scheme (Kilimanjaro Region), and includes maps, tables and photos. It describes the history of the irrigation scheme, as well current irrigation and farming practices. It especially focuses on the different kinds of infrastructural improvement in the scheme (by farmers and the government...
Directory of Open Access Journals (Sweden)
D. S. Moreira
2013-08-01
Full Text Available This article presents the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. This new numerical system is denominated JULES-CCATT-BRAMS. We demonstrate the performance of this new model system in relation to several meteorological variables and the CO2 mixing ratio over a large part of South America, focusing on the Amazon basin. The evaluation was conducted for two time periods, the wet (March and dry (September seasons of 2010. The model errors were calculated in relation to meteorological observations at conventional stations in airports and automatic stations. In addition, CO2 mixing ratios in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with observations obtained with airborne instruments. The results of this study show that the JULES-CCATT-BRAMS modeling system provided a significant gain in performance for the considered atmospheric fields relative to those simulated by the LEAF (version 3 surface model originally employed by CCATT-BRAMS. In addition, the new system significantly increases the ability to simulate processes involving air–surface interactions, due to the ability of JULES to simulate photosynthesis, respiration and dynamic vegetation, among other processes. We also discuss a wide range of numerical studies involving coupled atmospheric, land surface and chemistry processes that could be done with the system introduced here. Thus, this work presents to the scientific community a free modeling tool, with good performance in comparison with observational data and reanalysis model data, at least for the region and time period discussed here. Therefore, in principle, this model is able to produce atmospheric hindcast/forecast simulations at different spatial resolutions for any time period and any region of the globe.
On the monotonicity of multidimensional finite difference schemes
Kovyrkina, O.; Ostapenko, V.
2016-10-01
The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.
High order accurate finite difference schemes based on symmetry preservation
Ozbenli, Ersin; Vedula, Prakash
2017-11-01
In this paper, we present a mathematical approach that is based on modified equations and the method of equivariant moving frames for construction of high order accurate invariant finite difference schemes that preserve Lie symmetry groups of underlying partial differential equations (PDEs). In the proposed approach, invariant (or symmetry preserving) numerical schemes with a desired (or fixed) order of accuracy are constructed from some non-invariant (base) numerical schemes. Modified forms of PDEs are used to improve the order of accuracy of existing schemes and these modified forms are obtained through addition of defect correction terms to the original forms of PDEs. These defect correction terms of modified PDEs that are noted from truncation error analysis are either completely removed from schemes or their representation is significantly simplified by considering convenient moving frames. This feature of the proposed method can especially be useful to avoid cumbersome numerical representations when high order schemes are developed from low order ones via the method of modified equations. The proposed method is demonstrated via construction of invariant numerical schemes with fixed (and higher) order of accuracy for some common linear and nonlinear problems (including the linear advection-diffusion equation in 1D and 2D, inviscid Burgers' equation, and viscous Burgers' equation) and the performance of these invariant numerical schemes is further evaluated. Our results indicate that such invariant numerical schemes obtained from existing base numerical schemes have the potential to significantly improve the quality of results not only in terms of desired higher order accuracy but also in the context of preservation of appropriate symmetry properties of underlying PDEs.
Towards Symbolic Encryption Schemes
DEFF Research Database (Denmark)
Ahmed, Naveed; Jensen, Christian D.; Zenner, Erik
2012-01-01
, namely an authenticated encryption scheme that is secure under chosen ciphertext attack. Therefore, many reasonable encryption schemes, such as AES in the CBC or CFB mode, are not among the implementation options. In this paper, we report new attacks on CBC and CFB based implementations of the well...
Multiresolution signal decomposition schemes
J. Goutsias (John); H.J.A.M. Heijmans (Henk)
1998-01-01
textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis
Energy Technology Data Exchange (ETDEWEB)
D' Ambros, Alder C.; Vitorassi, Pedro H.; Franco, Admilson T.; Morales, Rigoberto E.M. [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Matins, Andre Leibsohn [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES). Tecnologia de Engenharia de Perfuracao
2008-07-01
The success of oil well drilling process depends on the correct prediction of the velocities and stresses fields inside the gap between the drill string and the rock formation. Using CFD is possible to predict the behavior of the drilling fluid flow along the annular space, from the bottom to the top of the well. Commonly the drilling fluid is modeled as a Herschel-Bulkley fluid. An alternative is to employ a non-linear viscoelastic model, like the one developed by Phan-Thien-Tanner (PTT). In the present work the PTT constitutive equation is used to model the drilling fluid flow along the annular space. Thus, this work investigates the influence of the Deborah number on the laminar flow pattern through the numerical solution of the equations formed by the coupled velocity-pressure-stress fields. The results are analyzed and validated against the analytical solution for the fully developed annular pipe flow. The relation between the Deborah number (De) and the entry length is investigated, along with the influence of high values of Deborah number on the friction factor, stress and velocity fields. (author)
Directory of Open Access Journals (Sweden)
R. Sitharthan
2016-09-01
Full Text Available This paper aims at modelling an electronically coupled distributed energy resource with an adaptive protection scheme. The electronically coupled distributed energy resource is a microgrid framework formed by coupling the renewable energy source electronically. Further, the proposed adaptive protection scheme provides a suitable protection to the microgrid for various fault conditions irrespective of the operating mode of the microgrid: namely, grid connected mode and islanded mode. The outstanding aspect of the developed adaptive protection scheme is that it monitors the microgrid and instantly updates relay fault current according to the variations that occur in the system. The proposed adaptive protection scheme also employs auto reclosures, through which the proposed adaptive protection scheme recovers faster from the fault and thereby increases the consistency of the microgrid. The effectiveness of the proposed adaptive protection is studied through the time domain simulations carried out in the PSCAD⧹EMTDC software environment.
Shibata, Masaru
2016-01-01
This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.
Khabaza, I M
1960-01-01
Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in comput
An ASI Suppression Scheme Based on Array Synthesis
Zhu, Jinhua; Liu, Peixi; Luo, Wu
2017-10-01
An adjacent satellite interference (ASI) suppression scheme based on transmitting antennas array synthesis is proposed in this paper. The scheme ensures the ASI under the upper bound specified by international regulations, and simultaneously maximize the main-axis radiated power. Specifically, the interference suppression problem is converted into a uniform linear array (ULA) synthesis problem, and then solved by two algorithms. Numerical results are presented to illustrate the performance of the scheme.
Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives
Directory of Open Access Journals (Sweden)
Yuxin Zhang
2014-01-01
Full Text Available We propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively. It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method. Finally, some numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence orders.
DEFF Research Database (Denmark)
Juhl, Hans Jørn; Stacey, Julia
2001-01-01
It is usual practice to evaluate the success of a labelling scheme by looking at the awareness percentage, but in many cases this is not sufficient. The awareness percentage gives no indication of which of the consumer segments that are aware of and use labelling schemes and which do not....... In the spring of 2001 MAPP carried out an extensive consumer study with special emphasis on the Nordic environmentally friendly label 'the swan'. The purpose was to find out how much consumers actually know and use various labelling schemes. 869 households were contacted and asked to fill in a questionnaire....... 664 households returned a completed questionnaire. There were five answering categories for each label in the questionnaire: * have not seen the label before. * I have seen the label before but I do not know the precise contents of the labelling scheme. * I have seen the label before, I do not know...
Energy Technology Data Exchange (ETDEWEB)
Willcock, J J; Lumsdaine, A; Quinlan, D J
2008-08-19
Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.
A numerical solution for a telegraph equation
Ashyralyev, Allaberen; Modanli, Mahmut
2014-08-01
In this study, the initial value problem for a telegraph equation in a Hilbert space is considered. The stability estimate for the solution of this problem is given. A first and a second order of approximation difference schemes approximately solving the initial value problem are presented. The stability estimates for the solution of these difference schemes are given. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2003-01-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.
Numerical investigation of sixth order Boussinesq equation
Kolkovska, N.; Vucheva, V.
2017-10-01
We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.
Operator theory and numerical methods
Fujita, H; Suzuki, T
2001-01-01
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.
Bright, William
In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…
Electrical injection schemes for nanolasers
DEFF Research Database (Denmark)
Lupi, Alexandra; Chung, Il-Sug; Yvind, Kresten
2013-01-01
threshold current has been achieved with the lateral electrical injection through the BH; while the lowest resistance has been obtained from the current post structure even though this model shows a higher current threshold because of the lack of carrier confinement. Final scope of the simulations......The performance of injection schemes among recently demonstrated electrically pumped photonic crystal nanolasers has been investigated numerically. The computation has been carried out at room temperature using a commercial semiconductor simulation software. For the simulations two electrical...... of 3 InGaAsP QWs on an InP substrate has been chosen for the modeling. In the simulations the main focus is on the electrical and optical properties of the nanolasers i.e. electrical resistance, threshold voltage, threshold current and wallplug efficiency. In the current flow evaluation the lowest...
Rao, G Shanker
2006-01-01
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...
Scheme for achieving coherent perfect absorption by anisotropic metamaterials
Zhang, Xiujuan
2017-02-22
We propose a unified scheme to achieve coherent perfect absorption of electromagnetic waves by anisotropic metamaterials. The scheme describes the condition on perfect absorption and offers an inverse design route based on effective medium theory in conjunction with retrieval method to determine practical metamaterial absorbers. The scheme is scalable to frequencies and applicable to various incident angles. Numerical simulations show that perfect absorption is achieved in the designed absorbers over a wide range of incident angles, verifying the scheme. By integrating these absorbers, we further propose an absorber to absorb energy from two coherent point sources.
A chaos secure communication scheme based on multiplication modulation
Fallahi, Kia; Leung, Henry
2010-02-01
A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
An Energy Preserving Monolithic Eulerian Fluid-Structure Numerical Scheme *
Pironneau, Olivier
2016-01-01
The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown , monolithic methods for fluid structure interactions (FSI) are built. In this article such a formulation is analyzed when the fluid is compressible and the fluid is incompressible. The i...
An Energy stable Monolithic Eulerian Fluid-Structure Numerical Scheme *
Pironneau, Olivier
2017-01-01
The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown , monolithic methods for fluid structure interactions (FSI) are built. In this article such a formulation is analyzed when the fluid is compressible and the fluid is incompressible. The i...
Digital Repository Service at National Institute of Oceanography (India)
Unnikrishnan, A.S.; Manoj, N.T.
Various numerical models used to study the dynamics and horizontal distribution of salinity in Mandovi-Zuari estuaries, Goa, India is discussed in this chapter. Earlier, a one-dimensional network model was developed for representing the complex...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Electronic Commerce - Payment Schemes. V Rajaraman. Series Article Volume 6 Issue 2 February 2001 pp 6-13. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/02/0006-0013 ...
Alternative health insurance schemes
DEFF Research Database (Denmark)
Keiding, Hans; Hansen, Bodil O.
2002-01-01
In this paper, we present a simple model of health insurance with asymmetric information, where we compare two alternative ways of organizing the insurance market. Either as a competitive insurance market, where some risks remain uninsured, or as a compulsory scheme, where however, the level...... competitive insurance; this situation turns out to be at least as good as either of the alternatives...
1991-01-01
their Butterfly Scheme Reference, and to Margaret O’Connell for translating it from BBN’s text-formatting language to ours. Special thanks to Richard ... Stallman , Bob Chassell, and Brian Fox, all of the Free Software Foundation, for creating and maintaining the Texinfo formatting language in which this
Chu, Chunlei
2009-01-01
We present two Lax‐Wendroff type high‐order time stepping schemes and apply them to solving the 3D elastic wave equation. The proposed schemes have the same format as the Taylor series expansion based schemes, only with modified temporal extrapolation coefficients. We demonstrate by both theoretical analysis and numerical examples that the modified schemes significantly improve the stability conditions.
System for Oriya handwritten numeral recognition
Tripathy, N.; Panda, M.; Pal, U.
2003-12-01
To take care of variability involved in the writing style of different individuals, a scheme for off-line Oriya isolated handwritten numeral recognition is presented here. Oriya is a popular script in India. The scheme is mainly based on features obtained from water reservoir concept as well as topological and structural features of the numerals. Reservoir based features like number of reservoirs, their size, heights and positions, water flow direction, topological feature like number of loops, centre of gravity positions of loops, the ratio of reservoir/loop height to the numeral height, profile based features, features based on jump discontinuity etc. are some of the features used in the recognition scheme. The proposed scheme is tested on 3550 data collected from different individuals of various background and we obtained an overall recognition accuracy of about 97.74%.
Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
Goloviznin, V. M.; Isakov, V. A.
2017-07-01
The CABARET scheme is used for the numerical solution of the one-dimensional shallow water equations over a rough bottom. The scheme involves conservative and flux variables, whose values at a new time level are calculated by applying the characteristic properties of the shallow water equations. The scheme is verified using a series of test and model problems.
A Class of Convergent Rational Runge-Kutta Schemes for solution ...
African Journals Online (AJOL)
A Class of Convergent Rational Runge-Kutta Schemes for solution Of Ordinary Differential Equations (ODEs) ... computerized to solve ODEs. Numerical results arising from the new schemes compare favourably with the existing Euler's method. Furthermore, the results show that the schemes are effective and efficient.
MIMO transmit scheme based on morphological perceptron with competitive learning.
Valente, Raul Ambrozio; Abrão, Taufik
2016-08-01
This paper proposes a new multi-input multi-output (MIMO) transmit scheme aided by artificial neural network (ANN). The morphological perceptron with competitive learning (MP/CL) concept is deployed as a decision rule in the MIMO detection stage. The proposed MIMO transmission scheme is able to achieve double spectral efficiency; hence, in each time-slot the receiver decodes two symbols at a time instead one as Alamouti scheme. Other advantage of the proposed transmit scheme with MP/CL-aided detector is its polynomial complexity according to modulation order, while it becomes linear when the data stream length is greater than modulation order. The performance of the proposed scheme is compared to the traditional MIMO schemes, namely Alamouti scheme and maximum-likelihood MIMO (ML-MIMO) detector. Also, the proposed scheme is evaluated in a scenario with variable channel information along the frame. Numerical results have shown that the diversity gain under space-time coding Alamouti scheme is partially lost, which slightly reduces the bit-error rate (BER) performance of the proposed MP/CL-NN MIMO scheme. Copyright © 2016 Elsevier Ltd. All rights reserved.
Brezinski, C
2012-01-01
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<
On usage of CABARET scheme for tracer transport in INM ocean model
Diansky, Nikolay; Kostrykin, Sergey; Gusev, Anatoly; Salnikov, Nikolay
2010-06-01
The contemporary state of ocean numerical modelling sets some requirements for the numerical advection schemes used in ocean general circulation models (OGCMs). The most important requirements are conservation, monotonicity and numerical efficiency including good parallelization properties. Investigation of some advection schemes shows that one of the best schemes satisfying the criteria is CABARET scheme. 3D-modification of the CABARET scheme was used to develop a new transport module (for temperature and salinity) for the Institute of Numerical Mathematics ocean model (INMOM). Testing of this module on some common benchmarks shows a high accuracy in comparison with the second-order advection scheme used in the INMOM. This new module was incorporated in the INMOM and experiments with the modified model showed a better simulation of oceanic circulation than its previous version.
Selectively strippable paint schemes
Stein, R.; Thumm, D.; Blackford, Roger W.
1993-03-01
In order to meet the requirements of more environmentally acceptable paint stripping processes many different removal methods are under evaluation. These new processes can be divided into mechanical and chemical methods. ICI has developed a paint scheme with intermediate coat and fluid resistant polyurethane topcoat which can be stripped chemically in a short period of time with methylene chloride free and phenol free paint strippers.
Directory of Open Access Journals (Sweden)
Hai Bi
2012-01-01
Full Text Available This paper discusses efficient numerical methods for the Steklov eigenvalue problem and establishes a new multiscale discretization scheme and an adaptive algorithm based on the Rayleigh quotient iterative method. The efficiency of these schemes is analyzed theoretically, and the constants appeared in the error estimates are also analyzed elaborately. Finally, numerical experiments are provided to support the theory.
Baker, John G.
2009-01-01
Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.
Efficient Scheme for Chemical Flooding Simulation
Directory of Open Access Journals (Sweden)
Braconnier Benjamin
2014-07-01
Full Text Available In this paper, we investigate an efficient implicit scheme for the numerical simulation of chemical enhanced oil recovery technique for oil fields. For the sake of brevity, we only focus on flows with polymer to describe the physical and numerical models. In this framework, we consider a black oil model upgraded with the polymer modeling. We assume the polymer only transported in the water phase or adsorbed on the rock following a Langmuir isotherm. The polymer reduces the water phase mobility which can change drastically the behavior of water oil interfaces. Then, we propose a fractional step technique to resolve implicitly the system. The first step is devoted to the resolution of the black oil subsystem and the second to the polymer mass conservation. In such a way, jacobian matrices coming from the implicit formulation have a moderate size and preserve solvers efficiency. Nevertheless, the coupling between the black-oil subsystem and the polymer is not fully resolved. For efficiency and accuracy comparison, we propose an explicit scheme for the polymer for which large time step is prohibited due to its CFL (Courant-Friedrichs-Levy criterion and consequently approximates accurately the coupling. Numerical experiments with polymer are simulated : a core flood, a 5-spot reservoir with surfactant and ions and a 3D real case. Comparisons are performed between the polymer explicit and implicit scheme. They prove that our polymer implicit scheme is efficient, robust and resolves accurately the coupling physics. The development and the simulations have been performed with the software PumaFlow [PumaFlow (2013 Reference manual, release V600, Beicip Franlab].
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR ...
African Journals Online (AJOL)
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR SOLUTION OF NONLINEAR INITIAL VALUE PROBLEMS OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. ... Global Journal of Mathematical Sciences ... KEY WORDS: backward differentiation scheme, collocation, initial value problems. Global Jnl ...
Nakamura, T
1993-01-01
In GR13 we heard many reports on recent. progress as well as future plans of detection of gravitational waves. According to these reports (see the report of the workshop on the detection of gravitational waves by Paik in this volume), it is highly probable that the sensitivity of detectors such as laser interferometers and ultra low temperature resonant bars will reach the level of h ~ 10—21 by 1998. in this level we may expect the detection of the gravitational waves from astrophysical sources such as coalescing binary neutron stars once a year or so. Therefore the progress in numerical relativity is urgently required to predict the wave pattern and amplitude of the gravitational waves from realistic astrophysical sources. The time left for numerical relativists is only six years or so although there are so many difﬁculties in principle as well as in practice.
Two-step rational cononical function in the numerical integration of ...
African Journals Online (AJOL)
By collocation, an explicit nonlinerar two-step scheme is obtained. Numerical examples are provided to demonstrate the performance of the scheme. The results obtained were found to be quite comparable with those by existing schemes. Key Words: Collocation two-step scheme. [Global Jnl Mathematical Sci Vol.2(1) 2003: ...
Agelet de Saracibar Bosch, Carlos; Boman, Romain; Bussetta, Philippe; Cajas García, Juan Carlos; Cervera Ruiz, Miguel; Chiumenti, Michèle; Coll Sans, Abel; Dadvand, Pooyan; Hernández Ortega, Joaquín Alberto; Houzeaux, Guillaume; Pasenau de Riera, Miguel; Ponthot, Jean Philippe
2016-01-01
As one of the results of an ambitious project, this handbook provides a well-structured directory of globally available software tools in the area of Integrated Computational Materials Engineering (ICME). The compilation covers models, software tools, and numerical methods allowing describing electronic, atomistic, and mesoscopic phenomena, which in their combination determine the microstructure and the properties of materials. It reaches out to simulations of component manufacture compris...
Adaptive transmission schemes for MISO spectrum sharing systems
Bouida, Zied
2013-06-01
We propose three adaptive transmission techniques aiming to maximize the capacity of a multiple-input-single-output (MISO) secondary system under the scenario of an underlay cognitive radio network. In the first scheme, namely the best antenna selection (BAS) scheme, the antenna maximizing the capacity of the secondary link is used for transmission. We then propose an orthogonal space time bloc code (OSTBC) transmission scheme using the Alamouti scheme with transmit antenna selection (TAS), namely the TAS/STBC scheme. The performance improvement offered by this scheme comes at the expense of an increased complexity and delay when compared to the BAS scheme. As a compromise between these schemes, we propose a hybrid scheme using BAS when only one antenna verifies the interference condition and TAS/STBC when two or more antennas are illegible for communication. We first derive closed-form expressions of the statistics of the received signal-to-interference-and-noise ratio (SINR) at the secondary receiver (SR). These results are then used to analyze the performance of the proposed techniques in terms of the average spectral efficiency, the average number of transmit antennas, and the average bit error rate (BER). This performance is then illustrated via selected numerical examples. © 2013 IEEE.
Bonus Schemes and Trading Activity
Pikulina, E.S.; Renneboog, L.D.R.; Ter Horst, J.R.; Tobler, P.N.
2013-01-01
Abstract: Little is known about how different bonus schemes affect traders’ propensity to trade and which bonus schemes improve traders’ performance. We study the effects of linear versus threshold (convex) bonus schemes on traders’ behavior. Traders purchase and sell shares in an experimental stock
Bonus schemes and trading activity
Pikulina, E.S.; Renneboog, L.D.R.; ter Horst, J.R.; Tobler, P.N.
2014-01-01
Little is known about how different bonus schemes affect traders' propensity to trade and which bonus schemes improve traders' performance. We study the effects of linear versus threshold bonus schemes on traders' behavior. Traders buy and sell shares in an experimental stock market on the basis of
Calatroni, Luca
2013-08-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Metaprogramming Applied to Numerical Problems
Mulansky, Mario; Ahnert, Karsten
2011-09-01
From the discovery that the template system of C++ forms a Turing complete language in 1994, a programming technique called Template Metaprogramming has emerged that allows for the creation of faster, more generic and better code. Here, we apply Template Metaprogramming to implement a generic Runge-Kutta scheme that can be used to numerically solve ordinary differential equations. We show that using Template Metaprogramming results in a significantly improved performance compared to a classical implementation.
Numerical and symbolic scientific computing
Langer, Ulrich
2011-01-01
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from
Hybrid update / invalidate schemes for cache coherence protocols
Directory of Open Access Journals (Sweden)
R. V. Dovgopol
2015-01-01
Full Text Available In general when considering cache coherence, write back schemes are the default. These schemes invalidate all other copies of a data block during a write. In this paper we propose several hybrid schemes that will switch between updating and invalidating on processor writes at runtime, depending on program conditions. This kind of approaches tend to improve the overall performance of systems in numerous fields ranging from the Information Security to the Civil Aviation. We created our own cache simulator on which we could implement our schemes, and generated data sets from both commercial benchmarks and through artificial methods to run on the simulator. We analyze the results of running the benchmarks with various schemes, and suggest further research that can be done in this area.
A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model
Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model
Energy Technology Data Exchange (ETDEWEB)
Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr [CMAP, École Polytechnique CNRS, UMR 7641, Route de Saclay, F-91128 Palaiseau cedex (France); Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr [EDF-R& D, Département MFEE, 6 Quai Watier, F-78401 Chatou Cedex (France); Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr [Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 bd 11 novembre 1918, F-69622 Villeurbanne cedex (France)
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
Three-level schemes of the alternating triangular method
Vabishchevich, P. N.
2014-06-01
In this paper, the schemes of the alternating triangular method are set out in the class of splitting methods used for the approximate solution of Cauchy problems for evolutionary problems. These schemes are based on splitting the problem operator into two operators that are conjugate transposes of each other. Economical schemes for the numerical solution of boundary value problems for parabolic equations are designed on the basis of an explicit-implicit splitting of the problem operator. The alternating triangular method is also of interest for the construction of numerical algorithms that solve boundary value problems for systems of partial differential equations and vector systems. The conventional schemes of the alternating triangular method used for first-order evolutionary equations are two-level ones. The approximation properties of such splitting methods can be improved by transiting to three-level schemes. Their construction is based on a general principle for improving the properties of difference schemes, namely, on the regularization principle of A.A. Samarskii. The analysis conducted in this paper is based on the general stability (or correctness) theory of operator-difference schemes.
Optimizing multiplexing scheme in interferometric microscopy
Tayebi, Behnam; Jaferzadeh, Keyvan; Sharif, Farnaz; Han, Jae-Ho
2016-08-01
In single exposure off-axis interferometry, multiple information can be recorded by spatial frequency multiplexing. We investigate optimum conditions for designing 2D sampling schemes to record larger field of view in off-axis interferometry multiplexing. The spatial resolution of the recorded image is related to the numerical aperture of the system and sensor pixel size. The spatial resolution should preserve by avoiding crosstalk in the frequency domain. Furthermore, the field of view depends on the sensor size and magnification of the imaging system. In order to preserve resolution and have a larger field of view, the frequency domain should be designed correctly. The experimental results demonstrate that selecting the wrong geometrical scheme in frequency domain decrease the recorded image area.
Energy Technology Data Exchange (ETDEWEB)
Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)
2016-06-08
In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.
Mukhadiyev, Nurzhan
2017-05-01
velocity drift. Also, dynamic inlet control was implemented which retained flame inside of a domain even at very high fuel consumption fluctuations. Last part of this work was to implement pseudospectral method into KARFS. Direct numerical simulations performed previously are targeting real engines and turbines conditions as an ultimate goal. These targeted simulations are prohibitively computationally expensive. This work suggested and implemented into KARFS a pseudospectral method for reacting turbulent flows, as an attempt to decrease computational cost. Approximately four times computational CPU hours savings were achieved.
Numerical Simulations of X-Ray Free Electron Lasers (XFEL)
Antonelli, Paolo
2014-11-04
We study a nonlinear Schrödinger equation which arises as an effective single particle model in X-ray free electron lasers (XFEL). This equation appears as a first principles model for the beam-matter interactions that would take place in an XFEL molecular imaging experiment in [A. Fratalocchi and G. Ruocco, Phys. Rev. Lett., 106 (2011), 105504]. Since XFEL are more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective time-averaged one is examined. We use an operator splitting pseudospectral method to investigate numerically the behavior of the model versus that of its time-averaged version in complex situations, namely the energy subcritical/mass supercritical case and in the presence of a periodic lattice. We find the time-averaged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases [P. Antonelli, A. Athanassoulis, H. Hajaiej, and P. Markowich, Arch. Ration. Mech. Anal., 211 (2014), pp. 711--732].
Parallel Pseudo Arc-Length Moving Mesh Schemes for Multidimensional Detonation
Directory of Open Access Journals (Sweden)
Jianguo Ning
2017-01-01
Full Text Available We have discussed the multidimensional parallel computation for pseudo arc-length moving mesh schemes, and the schemes can be used to capture the strong discontinuity for multidimensional detonations. Different from the traditional Euler numerical schemes, the problems of parallel schemes for pseudo arc-length moving mesh schemes include diagonal processor communications and mesh point communications, which are illustrated by the schematic diagram and key pseudocodes. Finally, the numerical examples are given to show that the pseudo arc-length moving mesh schemes are second-order convergent and can successfully capture the strong numerical strong discontinuity of the detonation wave. In addition, our parallel methods are proved effectively and the computational time is obviously decreased.
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method
Directory of Open Access Journals (Sweden)
Feng Wu
Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
Schmitz, R; Dünweg, B
2012-11-21
A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearize the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialized numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening versus counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i.e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.
Jacques, Ian
1987-01-01
This book is primarily intended for undergraduates in mathematics, the physical sciences and engineering. It introduces students to most of the techniques forming the core component of courses in numerical analysis. The text is divided into eight chapters which are largely self-contained. However, with a subject as intricately woven as mathematics, there is inevitably some interdependence between them. The level of difficulty varies and, although emphasis is firmly placed on the methods themselves rather than their analysis, we have not hesitated to include theoretical material when we consider it to be sufficiently interesting. However, it should be possible to omit those parts that do seem daunting while still being able to follow the worked examples and to tackle the exercises accompanying each section. Familiarity with the basic results of analysis and linear algebra is assumed since these are normally taught in first courses on mathematical methods. For reference purposes a list of theorems used in the t...
Small-scale classification schemes
DEFF Research Database (Denmark)
Hertzum, Morten
2004-01-01
Small-scale classification schemes are used extensively in the coordination of cooperative work. This study investigates the creation and use of a classification scheme for handling the system requirements during the redevelopment of a nation-wide information system. This requirements classificat....... This difference between the written requirements specification and the oral discussions at the meetings may help explain software engineers general preference for people, rather than documents, as their information sources.......Small-scale classification schemes are used extensively in the coordination of cooperative work. This study investigates the creation and use of a classification scheme for handling the system requirements during the redevelopment of a nation-wide information system. This requirements....... While coordination mechanisms focus on how classification schemes enable cooperation among people pursuing a common goal, boundary objects embrace the implicit consequences of classification schemes in situations involving conflicting goals. Moreover, the requirements specification focused on functional...
Honohan, Patrick
1987-01-01
A Ponzi scheme is an arrangement whereby a promoter offers an investment opportunity with attractive dividends, but where the only basis for the dividends is the future receipts from new investors. The first of these two notes explores some of the analytical properties of a Ponzi scheme, addressing in particular the question whether it is possible for a Ponzi scheme to exist if all the participants are rational. The second note briefly examines the collapse of the PMPA insurance company whos...
Madhulatha, A.; Rajeevan, M.
2018-02-01
Main objective of the present paper is to examine the role of various parameterization schemes in simulating the evolution of mesoscale convective system (MCS) occurred over south-east India. Using the Weather Research and Forecasting (WRF) model, numerical experiments are conducted by considering various planetary boundary layer, microphysics, and cumulus parameterization schemes. Performances of different schemes are evaluated by examining boundary layer, reflectivity, and precipitation features of MCS using ground-based and satellite observations. Among various physical parameterization schemes, Mellor-Yamada-Janjic (MYJ) boundary layer scheme is able to produce deep boundary layer height by simulating warm temperatures necessary for storm initiation; Thompson (THM) microphysics scheme is capable to simulate the reflectivity by reasonable distribution of different hydrometeors during various stages of system; Betts-Miller-Janjic (BMJ) cumulus scheme is able to capture the precipitation by proper representation of convective instability associated with MCS. Present analysis suggests that MYJ, a local turbulent kinetic energy boundary layer scheme, which accounts strong vertical mixing; THM, a six-class hybrid moment microphysics scheme, which considers number concentration along with mixing ratio of rain hydrometeors; and BMJ, a closure cumulus scheme, which adjusts thermodynamic profiles based on climatological profiles might have contributed for better performance of respective model simulations. Numerical simulation carried out using the above combination of schemes is able to capture storm initiation, propagation, surface variations, thermodynamic structure, and precipitation features reasonably well. This study clearly demonstrates that the simulation of MCS characteristics is highly sensitive to the choice of parameterization schemes.
Remarks on quantum duopoly schemes
Fraçkiewicz, Piotr
2016-01-01
The aim of this paper is to discuss in some detail the two different quantum schemes for duopoly problems. We investigate under what conditions one of the schemes is more reasonable than the other one. Using the Cournot's duopoly example, we show that the current quantum schemes require a slight refinement so that they output the classical game in a particular case. Then, we show how the amendment changes the way of studying the quantum games with respect to Nash equilibria. Finally, we define another scheme for the Cournot's duopoly in terms of quantum computation.
DEFF Research Database (Denmark)
Rotbart, Noy Galil
times, effectively eliminating the second penalty mentioned. We continue this theoretical study in several ways. First, we dedicate a large part of the thesis to the graph family of trees, for which we provide an overview of labeling schemes supporting several important functions such as ancestry......, routing and especially adjacency. The survey is complemented by novel contributions to this study, among which are the first asymptotically optimal adjacency labeling scheme for bounded degree trees, improved bounds on ancestry labeling schemes, dynamic multifunctional labeling schemes and an experimental...
A robust anonymous biometric-based authenticated key agreement scheme for multi-server environments.
Guo, Hua; Wang, Pei; Zhang, Xiyong; Huang, Yuanfei; Ma, Fangchao
2017-01-01
In order to improve the security in remote authentication systems, numerous biometric-based authentication schemes using smart cards have been proposed. Recently, Moon et al. presented an authentication scheme to remedy the flaws of Lu et al.'s scheme, and claimed that their improved protocol supports the required security properties. Unfortunately, we found that Moon et al.'s scheme still has weaknesses. In this paper, we show that Moon et al.'s scheme is vulnerable to insider attack, server spoofing attack, user impersonation attack and guessing attack. Furthermore, we propose a robust anonymous multi-server authentication scheme using public key encryption to remove the aforementioned problems. From the subsequent formal and informal security analysis, we demonstrate that our proposed scheme provides strong mutual authentication and satisfies the desirable security requirements. The functional and performance analysis shows that the improved scheme has the best secure functionality and is computational efficient.
A robust anonymous biometric-based authenticated key agreement scheme for multi-server environments
Huang, Yuanfei; Ma, Fangchao
2017-01-01
In order to improve the security in remote authentication systems, numerous biometric-based authentication schemes using smart cards have been proposed. Recently, Moon et al. presented an authentication scheme to remedy the flaws of Lu et al.’s scheme, and claimed that their improved protocol supports the required security properties. Unfortunately, we found that Moon et al.’s scheme still has weaknesses. In this paper, we show that Moon et al.’s scheme is vulnerable to insider attack, server spoofing attack, user impersonation attack and guessing attack. Furthermore, we propose a robust anonymous multi-server authentication scheme using public key encryption to remove the aforementioned problems. From the subsequent formal and informal security analysis, we demonstrate that our proposed scheme provides strong mutual authentication and satisfies the desirable security requirements. The functional and performance analysis shows that the improved scheme has the best secure functionality and is computational efficient. PMID:29121050
Wu, Jilian; Shen, Jie; Feng, Xinlong
2017-11-01
We construct in this paper two Gauge-Uzawa schemes, one in conserved form and the other in convective form, for solving natural convection problems with variable density, and prove that the first-order versions of both schemes are unconditionally stable. We also show that a full discretized version of the conserved scheme with finite elements is also unconditionally stable. These schemes lead to a sequence of decoupled elliptic equations to solve at each step, hence, they are very efficient and easy to implement. We present several numerical tests to validate the analysis and demonstrate the effectiveness of these schemes for simulating natural convection problems with large density differences.
Accuracy of spectral and finite difference schemes in 2D advection problems
DEFF Research Database (Denmark)
Naulin, V.; Nielsen, A.H.
2003-01-01
In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....
The sensitivity to the microphysical schemes on the skill of ...
Indian Academy of Sciences (India)
Devanil Choudhury
2017-06-15
Jun 15, 2017 ... WRF (Weather Research and Forecasting) model have started using more complex microphysical schemes. The ARW (Advanced Research WRF) is a next generation mesoscale forecast model and assimilation system that has incorporated a modern software framework, advanced dynamics, numeric and ...
A hybrid iterative scheme for optimal control problems governed by ...
African Journals Online (AJOL)
This paper presents an iterative approach based on hybrid of perturbation and parametrization methods for obtaining approximate solutions of optimal control problems governed by some Fredholm integral equations. By some numerical examples, it is emphasized that this scheme is very effective and it produces ...
A new iterative scheme for solving the discrete Smoluchowski equation
Smith, Alastair J.; Wells, Clive G.; Kraft, Markus
2018-01-01
This paper introduces a new iterative scheme for solving the discrete Smoluchowski equation and explores the numerical convergence properties of the method for a range of kernels admitting analytical solutions, in addition to some more physically realistic kernels typically used in kinetics applications. The solver is extended to spatially dependent problems with non-uniform velocities and its performance investigated in detail.
Shao, X.; Veldhuis, Raymond N.J.
2013-01-01
The helper data scheme utilizes a secret key to protect biometric templates. The current helper data scheme requires binary feature representations that introduce quantization error and thus reduce the capacity of biometric channels. For spectral-minutiae based fingerprint recognition systems,
Efficient scheme for parametric fitting of data in arbitrary dimensions.
Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching
2008-07-01
We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.
Numerical methods in astrophysics an introduction
Bodenheimer, Peter; Rozyczka, Michal; Plewa, Tomasz; Yorke, Harold W; Yorke, Harold W
2006-01-01
Basic Equations The Boltzmann Equation Conservation Laws of Hydrodynamics The Validity of the Continuous Medium Approximation Eulerian and Lagrangian Formulation of Hydrodynamics Viscosity and Navier-Stokes Equations Radiation Transfer Conducting and Magnetized Media Numerical Approximations to Partial Differential Equations Numerical Modeling with Finite-Difference Equations Difference Quotient Discrete Representation of Variables, Functions, and Derivatives Stability of Finite-Difference Methods Physical Meaning of Stability Criterion A Useful Implicit Scheme Diffusion
Advanced in numerical modelling of two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Paillere, H.; Kumbaro, A.; Toumi, I. [CEA Saclay, Dept. de Mecanique et de Technologie, 91 - Gif-sur-Yvette (France)
2001-07-01
Numerical modelling of two-phase flow using Godunov-type solvers is making progress. Schemes such as the Roe scheme, or the less sophisticated AUSM+scheme, have the ability to resolve propagating waves such as void or shock waves with no oscillations. Transition from two-phase to single phase flow can also be modelled, and interfaces captured in a satisfactory way. Extension to 3D and validation on more complex flow fields are also presently being performed. (authors)
Chen, Rangfu
A computational methodology has been developed in the first part of the thesis for the simulations of acoustic radiation, propagation and reflection. The developed methodology is high order accurate, uses less grid points per wave length comparing to standard high order accurate numerical methods, and automatically damps out spurious short waves. Furthermore, the methodology can be applied to acoustic problems in the presence of objects with curved geometries. To achieve these results, high order accurate optimized upwind schemes, which are applied to discretize spatial derivatives on interior grid points, have been developed. High order accurate optimized one- side biased schemes, which are only applied to discretize the spatial derivatives on grid points near computational boundaries, have also been constructed. The developed schemes are combined with a time difference scheme to fully discretize acoustic field equations in multi- dimension in arbitrary curvilinear coordinates. Numerical boundary conditions are investigated and intuitively illustrated. Applications of the developed methodology to a sequence of one-dimensional and multi-dimensional acoustic problems are performed. The numerical results have validated the developed methodology and demonstrated advantages of the methodology over central-difference Dispersion-Relation-Preserving method. Numerical results have also shown that the optimized upwind schemes minimize not only the dissipation error but also the dissipation error, while retaining the numerical stability. The second part of the thesis deals with a fully conservative Chimera methodology. The fully conservative Chimera was originally developed based on a finite volume approach. A finite difference scheme is shown to be identical to a finite volume scheme with proper definition of control volumes and metrics. The fully conservative Chimera has been successfully extended to finite difference schemes for viscous flows including turbulence models
An Energy-Work Relationship Integration Scheme for Nonconservative Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Fu Jingli
2008-01-01
Full Text Available This letter focuses on studying a new energy-work relationship numerical integration scheme of nonconservative Hamiltonian systems. The signal-stage, multistage, and parallel composition numerical integration schemes are presented for this system. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multistage scheme of order 2 which its order of accuracy is 2n. The connection, which is discrete analog of usual case, between the change of energy and work of nonconservative force is obtained for nonconservative Hamiltonian systems.This letter also shows that the more the stages of the schemes are, the less the error rate of the scheme is for nonconservative Hamiltonian systems. Finally, an applied example is discussed to illustrate these results.
Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows
Herbin, Raphaele; Latché, J.-C; Saleh, K
2017-01-01
International audience; We study the incompressible limit of a pressure correction MAC scheme [3] for the unstationary compressible barotropic Navier-Stokes equations. Provided the initial data are well-prepared, the solution of the numerical scheme converges, as the Mach number tends to zero, towards the solution of the classical pressure correction inf-sup stable MAC scheme for the incompressible Navier-Stokes equations.
Coordinated renewable energy support schemes
DEFF Research Database (Denmark)
Morthorst, P.E.; Jensen, S.G.
2006-01-01
This paper illustrates the effect that can be observed when support schemes for renewable energy are regionalised. Two theoretical examples are used to explain interactive effects on, e.g., the price of power, conditions for conventional power producers, and changes in import and export of power...... RES-E support schemes already has a common liberalised power market. In this case the introduction of a common support scheme for renewable technologies will lead to more efficient sitings of renewable plants, improving economic and environmental performance of the total power system...
Sman, van der R.G.M.
2014-01-01
In this paper we present a novel numerical scheme for simulating the one-dimensional deformation of hydrogel material due to drying or rehydration. The scheme is based on the versatile Lattice Boltzmann method, which has been extended such that the computational grid (lattice) deforms due to
On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem
Directory of Open Access Journals (Sweden)
Ozgur Yildirim
2015-01-01
Full Text Available This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.
High order boron transport scheme in TRAC-BF1
Energy Technology Data Exchange (ETDEWEB)
Barrachina, Teresa; Jambrina, Ana; Miro, Rafael; Verdu, Gumersindo, E-mail: tbarrachina@iqn.upv.es, E-mail: rmiro@iqn.upv.es, E-mail: gverdu@iqn.upv.es [Universidade Politecnica de Valencia (UPV), Valencia, (Spain). Institute for the Industrial, Radiophysical and Environmental Safety; Soler, Amparo, E-mail: asoler@iberdrola.es [SEA Propulsion S.L., Madrid (Spain); Concejal, Alberto, E-mail: acbe@iberdrola.es [Iberdrola Ingenieria y Construcion S.A.U, Madrid (Spain)
2013-07-01
In boiling water reactors (BWR), unlike pressurized water reactors (PWR) in which the reactivity control is accomplished through movement of the control rods and boron dilution, the importance of boron transport lies in maintaining the core integrity during ATWS-kind severe accidents in which under certain circumstances a boron injection is required. This is the reason for implementing boron transport models thermal-hydraulic codes as TRAC-BF1, RELAP5 and TRACE, bringing an improvement in the accuracy of the simulations. TRAC-BF1 code provides a best estimate analysis capability for the analysis of the full range of postulated accidents in boiling water reactors systems and related facilities. The boron transport model implemented in TRAC-BF1 code is based on a calculation according to a first order accurate upwind difference scheme. There is a need in reviewing and improving this model. Four numerical schemes that solve the boron transport model have been analyzed and compared with the analytical solution that provides the Burgers equation. The studied numerical schemes are: first order Upwind, second order Godunov, second-order modified Godunov adding physical diffusion term and a third-order QUICKEST using the ULTIMATE universal limiter (UL). The modified Godunov scheme has been implemented in TRAC-BF1 source code. The results using these new schemes are presented in this paper. (author)
A Novel Iris Segmentation Scheme
Directory of Open Access Journals (Sweden)
Chen-Chung Liu
2014-01-01
Full Text Available One of the key steps in the iris recognition system is the accurate iris segmentation from its surrounding noises including pupil, sclera, eyelashes, and eyebrows of a captured eye-image. This paper presents a novel iris segmentation scheme which utilizes the orientation matching transform to outline the outer and inner iris boundaries initially. It then employs Delogne-Kåsa circle fitting (instead of the traditional Hough transform to further eliminate the outlier points to extract a more precise iris area from an eye-image. In the extracted iris region, the proposed scheme further utilizes the differences in the intensity and positional characteristics of the iris, eyelid, and eyelashes to detect and delete these noises. The scheme is then applied on iris image database, UBIRIS.v1. The experimental results show that the presented scheme provides a more effective and efficient iris segmentation than other conventional methods.
Good governance for pension schemes
Thornton, Paul
2011-01-01
Regulatory and market developments have transformed the way in which UK private sector pension schemes operate. This has increased demands on trustees and advisors and the trusteeship governance model must evolve in order to remain fit for purpose. This volume brings together leading practitioners to provide an overview of what today constitutes good governance for pension schemes, from both a legal and a practical perspective. It provides the reader with an appreciation of the distinctive characteristics of UK occupational pension schemes, how they sit within the capital markets and their social and fiduciary responsibilities. Providing a holistic analysis of pension risk, both from the trustee and the corporate perspective, the essays cover the crucial role of the employer covenant, financing and investment risk, developments in longevity risk hedging and insurance de-risking, and best practice scheme administration.
Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness
Directory of Open Access Journals (Sweden)
Tong Zhang
2014-01-01
stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.
Convergence rates for dispersive approximation schemes to nonlinear Schr\\"odinger equations
Ignat, Liviu; Zuazua, Enrique
2011-01-01
This article is devoted to the analysis of the convergence rates of several nu- merical approximation schemes for linear and nonlinear Schr\\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schr\\"odinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L2(R), a fact that ...
Breeding schemes in reindeer husbandry
Directory of Open Access Journals (Sweden)
Lars Rönnegård
2003-04-01
Full Text Available The objective of the paper was to investigate annual genetic gain from selection (G, and the influence of selection on the inbreeding effective population size (Ne, for different possible breeding schemes within a reindeer herding district. The breeding schemes were analysed for different proportions of the population within a herding district included in the selection programme. Two different breeding schemes were analysed: an open nucleus scheme where males mix and mate between owner flocks, and a closed nucleus scheme where the males in non-selected owner flocks are culled to maximise G in the whole population. The theory of expected long-term genetic contributions was used and maternal effects were included in the analyses. Realistic parameter values were used for the population, modelled with 5000 reindeer in the population and a sex ratio of 14 adult females per male. The standard deviation of calf weights was 4.1 kg. Four different situations were explored and the results showed: 1. When the population was randomly culled, Ne equalled 2400. 2. When the whole population was selected on calf weights, Ne equalled 1700 and the total annual genetic gain (direct + maternal in calf weight was 0.42 kg. 3. For the open nucleus scheme, G increased monotonically from 0 to 0.42 kg as the proportion of the population included in the selection programme increased from 0 to 1.0, and Ne decreased correspondingly from 2400 to 1700. 4. In the closed nucleus scheme the lowest value of Ne was 1300. For a given proportion of the population included in the selection programme, the difference in G between a closed nucleus scheme and an open one was up to 0.13 kg. We conclude that for mass selection based on calf weights in herding districts with 2000 animals or more, there are no risks of inbreeding effects caused by selection.
Constrained H1-regularization schemes for diffeomorphic image registration
Mang, Andreas; Biros, George
2017-01-01
We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss–)Newton–Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient. PMID:29075361
A Multiserver Biometric Authentication Scheme for TMIS using Elliptic Curve Cryptography.
Chaudhry, Shehzad Ashraf; Khan, Muhammad Tawab; Khan, Muhammad Khurram; Shon, Taeshik
2016-11-01
Recently several authentication schemes are proposed for telecare medicine information system (TMIS). Many of such schemes are proved to have weaknesses against known attacks. Furthermore, numerous such schemes cannot be used in real time scenarios. Because they assume a single server for authentication across the globe. Very recently, Amin et al. (J. Med. Syst. 39(11):180, 2015) designed an authentication scheme for secure communication between a patient and a medical practitioner using a trusted central medical server. They claimed their scheme to extend all security requirements and emphasized the efficiency of their scheme. However, the analysis in this article proves that the scheme designed by Amin et al. is vulnerable to stolen smart card and stolen verifier attacks. Furthermore, their scheme is having scalability issues along with inefficient password change and password recovery phases. Then we propose an improved scheme. The proposed scheme is more practical, secure and lightweight than Amin et al.'s scheme. The security of proposed scheme is proved using the popular automated tool ProVerif.
Uncertainty of Microphysics Schemes in CRMs
Tao, W. K.; van den Heever, S. C.; Wu, D.; Saleeby, S. M.; Lang, S. E.
2015-12-01
Microphysics is the framework through which to understand the links between interactive aerosol, cloud and precipitation processes. These processes play a critical role in the water and energy cycle. CRMs with advanced microphysics schemes have been used to study the interaction between aerosol, cloud and precipitation processes at high resolution. But, there are still many uncertainties associated with these microphysics schemes. This has arisen, in part, from the fact microphysical processes cannot be measured directly; instead, cloud properties, which can be measured, are and have been used to validate model results. The utilization of current and future global high-resolution models is rapidly increasing and are at what has been traditional CRM resolutions and are using microphysics schemes that were developed in traditional CRMs. A potential NASA satellite mission called the Cloud and Precipitation Processes Mission (CaPPM) is currently being planned for submission to the NASA Earth Science Decadal Survey. This mission could provide the necessary global estimates of cloud and precipitation properties with which to evaluate and improve dynamical and microphysical parameterizations and the feedbacks. In order to facilitate the development of this mission, CRM simulations have been conducted to identify microphysical processes responsible for the greatest uncertainties in CRMs. In this talk, we will present results from numerical simulations conducted using two CRMs (NU-WRF and RAMS) with different dynamics, radiation, land surface and microphysics schemes. Specifically, we will conduct sensitivity tests to examine the uncertainty of the some of the key ice processes (i.e. riming, melting, freezing and shedding) in these two-microphysics schemes. The idea is to quantify how these two different models' respond (surface rainfall and its intensity, strength of cloud drafts, LWP/IWP, convective-stratiform-anvil area distribution) to changes of these key ice
A second order derivative scheme based on Bregman algorithm class
Campagna, Rosanna; Crisci, Serena; Cuomo, Salvatore; Galletti, Ardelio; Marcellino, Livia
2016-10-01
The algorithms based on the Bregman iterative regularization are known for efficiently solving convex constraint optimization problems. In this paper, we introduce a second order derivative scheme for the class of Bregman algorithms. Its properties of convergence and stability are investigated by means of numerical evidences. Moreover, we apply the proposed scheme to an isotropic Total Variation (TV) problem arising out of the Magnetic Resonance Image (MRI) denoising. Experimental results confirm that our algorithm has good performance in terms of denoising quality, effectiveness and robustness.
Computing homogeneous models with finite volume upwind schemes
Energy Technology Data Exchange (ETDEWEB)
Herard, J.M. [Electricite de France (EDF/DRD/DMFTT), 78 - Chatou (France); Universite de Provence, Centre de Mathematiques et d' Informatique, L.A.T.P. - UMR CNRS 6632, 13 - Marseille (France); Kokh, S. [CEA Saclay, Dir. de l' Energie Nucleaire (DEN/SFME), 91 - Gif sur Yvette (France)
2003-07-01
We provide in this paper some algorithms to deal with homogeneous equilibrium models on any type of mesh. These schemes rely on the exact Godunov scheme or on some rough Godunov schemes. We first recall some basic ideas which were recently introduced in the 1D framework. We then turn to the 2D framework, and define a class of first order schemes which enable to improve the accuracy on coarse unstructured 2D meshes. We have also tried to underline that current computing power does not enable to perform accurate enough computations for reasonable CPU time, in a few situations including sharp contact discontinuities; this is due in some sense to some kind of loss of pressure consistency between PDE and numerical schemes in conservative form. We have also indicated that some specific remedies available in the literature are not adequate for nuclear safety problems, both in a one dimensional framework (owing to EOS), and in the two dimensional framework (due to differences between mesh interfaces and waves fronts). Comments pertaining to other hybrid schemes are then made. The last part of the paper will focus on computations of three dimensional gas-liquid flows including sharp interfaces. (authors)
A literature survey on numerical heat transfer
Shih, T. M.
1982-12-01
Technical papers in the area of numerical heat transfer published from 1977 through 1981 are reviewed. The journals surveyed include: (1) ASME Journal of Heat Transfer, (2) International Journal of Heat and Mass Transfer, (3) AIAA Journal, (4) Numerical Heat Transfer, (5) Computers and Fluids, (6) International Journal for Numerical Methods in Engineering, (7) SIAM Journal of Numerical Analysis, and (8) Journal of Computational Physics. This survey excludes experimental work in heat transfer and numerical schemes that are not applied to equations governing heat transfer phenomena. The research work is categorized into the following areas: (A) conduction, (B) boundary-layer flows, (C) momentum and heat transfer in cavities, (D) turbulent flows, (E) convection around cylinders and spheres or within annuli, (F) numerical convective instability, (G) radiation, (H) combustion, (I) plumes, jets, and wakes, (J) heat transfer in porous media, (K) boiling, condensation, and two-phase flows, (L) developing and fully developed channel flows, (M) combined heat and mass transfer, (N) applications, (O) comparison and properties of numerical schemes, and (P) body-fitted coordinates and nonuniform grids.
On the Numerical Stability of Some Symplectic Integrators
Liu, Fu-yao; Wu, Xin; Lu, Ben-kui
2007-04-01
In this paper, we analyze the linear stabilities of several symplectic integrators, such as the first-order implicit Euler scheme, the second-order implicit mid-point Euler difference scheme, the first-order explicit Euler scheme, the second-order explicit leapfrog scheme and some of their combinations. For a linear Hamiltonian system, we find the stable regions of each scheme by theoretical analysis and check them by numerical tests. When the Hamiltonian is real symmetric quadratic, a diagonalizing by a similar transformation is suggested so that the theoretical analysis of the linear stability of the numerical method would be simplified. A Hamiltonian may be separated into a main part and a perturbation, or it may be spontaneously separated into kinetic and potential energy parts, but the former separation generally is much more charming because it has a much larger maximum step size for the symplectic being stable, no matter this Hamiltonian is linear or nonlinear.
Numerical solution of the stochastic parabolic equation with the dependent operator coefficient
Energy Technology Data Exchange (ETDEWEB)
Ashyralyev, Allaberen [Department of Elementary Mathematics Education, Fatih University, 34500, Istanbul (Turkey); Department of Mathematics, ITTU, Ashgabat (Turkmenistan); Okur, Ulker [Institute for Stochastics and Applications, Department of Mathematics, University of Stuttgart, 70569, Stuttgart (Germany)
2015-09-18
In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.
Numerical Methods for the Design and Analysis of Photonic Crystal Fibres
DEFF Research Database (Denmark)
Roberts, John
2008-01-01
The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted.......The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted....
A nonstandard numerical method for the modified KdV equation
Aydin, Ayhan; Koroglu, Canan
2017-11-01
A linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg-de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.
Auction dynamics: A volume constrained MBO scheme
Jacobs, Matt; Merkurjev, Ekaterina; Esedoǧlu, Selim
2018-02-01
We show how auction algorithms, originally developed for the assignment problem, can be utilized in Merriman, Bence, and Osher's threshold dynamics scheme to simulate multi-phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases. The resulting algorithms are highly efficient and robust, and can be used in simulations ranging from minimal partition problems in Euclidean space to semi-supervised machine learning via clustering on graphs. In the case of the latter application, numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state-of-the-art methods, while requiring a fraction of the computation time.
New scheme for braiding Majorana fermions
Wu, Long-Hua; Liang, Qi-Feng; Hu, Xiao
2014-01-01
Non-Abelian statistics can be achieved by exchanging two vortices in topological superconductors with each grabbing a Majorana fermion (MF) as zero-energy quasi-particle at the cores. However, in experiments it is difficult to manipulate vortices. In the present work, we propose a way to braid MFs without moving vortices. The only operation required in the present scheme is to turn on and off local gate voltages, which liberates a MF from its original host vortex and transports it along the prepared track. We solve the time-dependent Bogoliubov–de Gennes equation numerically, and confirm that the MFs are protected provided the switching of gate voltages for exchanging MFs are adiabatic, which takes only several nano seconds given reasonable material parameters. By monitoring the time evolution of MF wave-functions, we show that non-Abelian statistics is achieved. PMID:27877725
A well-balanced scheme for Ten-Moment Gaussian closure equations with source term
Meena, Asha Kumari; Kumar, Harish
2018-02-01
In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.
Homman, Ahmed-Amine; Maillet, Jean-Bernard; Roussel, Julien; Stoltz, Gabriel
2016-01-14
This work presents new parallelizable numerical schemes for the integration of dissipative particle dynamics with energy conservation. So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small time steps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations.
The same number of optimized parameters scheme for determining intermolecular interaction energies
DEFF Research Database (Denmark)
Kristensen, Kasper; Ettenhuber, Patrick; Eriksen, Janus Juul
2015-01-01
We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave...... as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP...
A subgrid parameterization scheme for precipitation
Directory of Open Access Journals (Sweden)
S. Turner
2012-04-01
Full Text Available With increasing computing power, the horizontal resolution of numerical weather prediction (NWP models is improving and today reaches 1 to 5 km. Nevertheless, clouds and precipitation formation are still subgrid scale processes for most cloud types, such as cumulus and stratocumulus. Subgrid scale parameterizations for water vapor condensation have been in use for many years and are based on a prescribed probability density function (PDF of relative humidity spatial variability within the model grid box, thus providing a diagnosis of the cloud fraction. A similar scheme is developed and tested here. It is based on a prescribed PDF of cloud water variability and a threshold value of liquid water content for droplet collection to derive a rain fraction within the model grid. Precipitation of rainwater raises additional concerns relative to the overlap of cloud and rain fractions, however. The scheme is developed following an analysis of data collected during field campaigns in stratocumulus (DYCOMS-II and fair weather cumulus (RICO and tested in a 1-D framework against large eddy simulations of these observed cases. The new parameterization is then implemented in a 3-D NWP model with a horizontal resolution of 2.5 km to simulate real cases of precipitating cloud systems over France.
Extended lattice Boltzmann scheme for droplet combustion.
Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas
2017-05-01
The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.
Numerical aspects of compressible turbulence simulations
Honein, Albert Edward
Nonlinear instabilities present a long standing hurdle for compact, high order, non dissipative, finite difference computation of compressible turbulence. The spectral-like accuracy of these schemes, while attractive, results in significant aliasing errors that corrupt the solution. As a result, successful simulations have been limited to moderate Reynolds numbers ( Re) and low-order or upwind schemes with inherent numerical dissipation. However, resorting to dissipative schemes in discretizing the nonlinear terms was shown to have a detrimental effect on turbulence. A recent LES approach is to abandon the subgrid model altogether and rely on the scheme dissipation to mimic the effect of small scales. A dissipative monotone integrated LES (MILES) algorithm based on a multidimensional flux-corrected transport (FCT) algorithm has been developed and tested for decaying compressible isotropic turbulence. Agreement with the benchmark experiments of Comte-Bellot and Corrsin is very sensitive to the parameters involved in the FCT algorithm, while the evolution of thermodynamic fluctuations do not compare well with direct numerical simulations. An under-resolved simulation of inviscid, compressible, isotropic turbulence at low Mach number is chosen as a severe benchmark to investigate the nonlinear stability properties of nondissipative schemes. The behavior of this benchmark is predicted by performing a fully de-aliased spectral simulation on a 32 3 grid with turbulent Mach number of Mto = 0.07. The kinetic energy and thermodynamic fluctuations are found to decay for finite Re, and remain constant at infinite Re for a long time before the occurrence of numerical shocks. Extending the proof of Kraichnan (Journal of the Acoustical Society of America, 27(3), 1955), this inviscid statistical equilibrium is demonstrated to be a consequence of the discrete equivalent of the Liouville theorem of classical statistical mechanics. Several existing non-dissipative methods are
An assessment of the differential quadrature time integration scheme for nonlinear dynamic equations
Liu, Jian; Wang, Xinwei
2008-07-01
In 1996, Xie [An assessment of time integration schemes for non-linear dynamic equations, Journal of Sound and Vibration 192(1) (1996) 321-331] presented an assessment on seven existing and commonly used time integration schemes for nonlinear dynamic equations. In this work, the differential quadrature (DQ) time integration scheme proposed by Fung in 2001 is assessed following the same procedures as Xie's. It is shown that accurate numerical results can be obtained by the DQ method when using much larger time step over the commonly used time integration schemes. Based on the results reported herein, some conclusions are drawn.
Al Jarro, Ahmed
2012-11-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
A Hybrid Combination Scheme for Cooperative Spectrum Sensing in Cognitive Radio Networks
Directory of Open Access Journals (Sweden)
Changhua Yao
2014-01-01
Full Text Available We propose a novel hybrid combination scheme in cooperative spectrum sensing (CSS, which utilizes the diversity of reporting channels to achieve better throughput performance. Secondary users (SUs with good reporting channel quality transmit quantized local observation statistics to fusion center (FC, while others report their local decisions. FC makes the final decision by carrying out hybrid combination. We derive the closed-form expressions of throughput and detection performance as a function of the number of SUs which report local observation statistics. The simulation and numerical results show that the hybrid combination scheme can achieve better throughput performance than hard combination scheme and soft combination scheme.
Devnagari numeral recognition by combining decision of multiple ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
written Devnagari numerals. Many schemes for digit classification have been reported in literature. .... indicate the degree to which the sample is similar to the particular character represented by this classifier. Provision for ... This representation is referred to as the normalised character image. These numeral images are ...
An all-speed relaxation scheme for gases and compressible materials
Abbate, Emanuela; Iollo, Angelo; Puppo, Gabriella
2017-12-01
We present a novel relaxation scheme for the simulation of compressible material flows at all speeds. An Eulerian model describing gases, fluids and elastic solids with the same system of conservation laws is adopted. The proposed numerical scheme is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in all different Mach regimes. The scheme is validated by simulating gas and liquid flows with different Mach numbers. The simulation of the deformation of compressible solids is also approached, assessing the ability of the scheme in approximating material waves in hyperelastic media.
Versypt, Ashlee N Ford; Braatz, Richard D
2014-12-04
Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivity, (III) spatially-dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly-defined, temporally- and spatially-dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position.
Modulation Schemes for Wireless Access
Directory of Open Access Journals (Sweden)
F. Vejrazka
2000-12-01
Full Text Available Four modulation schemes, namely minimum shift keying (MSK, Gaussianminimum shift keying (GMSK, multiamplitude minimum shift keying(MAMSK and ÃÂ€/4 differential quadrature phase shift keying (ÃÂ€/4-QPSKare described and their applicability to wireless access is discussedin the paper. Low complexity receiver structures based on differentialdetection are analysed to estimate the performance of the modulationschemes in the additive Gaussian noise and the Rayleigh and Riceenvelope fast fading channel. The bandwidth efficiency is calculated toevaluate the modulation schemes. The results show that the MAMSK schemegives the greatest bandwidth efficiency, but its performance in theRayleigh channel is rather poor. In contrast, the MSK scheme is lessbandwidth efficient, but it is more resistant to Rayleigh fading. Theperformance of ÃÂ€/4-QPSK signal is considerably improved by appropriateprefiltering.
High performance Python for direct numerical simulations of turbulent flows
Mortensen, Mikael; Langtangen, Hans Petter
2016-06-01
Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS code that nearly matches the performance of C++ for thousands of processors and billions of unknowns. We also describe a version optimized through Cython, that is found to match the speed of C++. The solvers are written from scratch in Python, both the mesh, the MPI domain decomposition, and the temporal integrators. The solvers have been verified and benchmarked on the Shaheen supercomputer at the KAUST supercomputing laboratory, and we are able to show very good scaling up to several thousand cores. A very important part of the implementation is the mesh decomposition (we implement both slab and pencil decompositions) and 3D parallel Fast Fourier Transforms (FFT). The mesh decomposition and FFT routines have been implemented in Python using serial FFT routines (either NumPy, pyFFTW or any other serial FFT module), NumPy array manipulations and with MPI communications handled by MPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFT in Python for a slab mesh decomposition using 4 lines of compact Python code, for which the parallel performance on Shaheen is found to be slightly better than similar routines provided through the FFTW library. For a pencil mesh decomposition 7 lines of code is required to execute a transform.
A reduced feedback proportional fair multiuser scheduling scheme
Shaqfeh, Mohammad
2011-12-01
Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed and ordered scheduling mechanism. A slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we propose a novel proportional fair multiuser switched-diversity scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the per-user feedback thresholds. We demonstrate by numerical examples that our reduced feedback proportional fair scheduler operates within 0.3 bits/sec/Hz from the achievable rates by the conventional full feedback proportional fair scheduler in Rayleigh fading conditions. © 2011 IEEE.
A General Symbolic PDE Solver Generator: Beyond Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
Consistent forcing scheme in the cascaded lattice Boltzmann method
Fei, Linlin; Luo, Kai Hong
2017-11-01
In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.
Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme
Energy Technology Data Exchange (ETDEWEB)
Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)
A Comparison of three high-precision quadrature schemes
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Li, Xiaoye S.
2003-07-01
The authors have implemented three numerical quadrature schemes, using the new Arbitrary Precision (ARPREC) software package, with the objective of seeking a completely ''automatic'' arbitrary precision quadrature facility, namely one that does not rely on a priori information of the function to be integrated. Such a facility is required, for example, to permit the experimental identification of definite integrals based on their numerical values. The performance and accuracy of these three quadrature schemes are compared using a suite of 15 integrals, ranging from continuous, well-behaved functions on finite intervals to functions with vertical derivatives and integrable singularities at endpoints, as well as several integrals on an infinite interval.
Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics
Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter
2018-01-01
This paper presents a high order hybrid discontinuous Galerkin/finite volume scheme for solving the equations of the magnetohydrodynamics (MHD) and of the relativistic hydrodynamics (SRHD) on quadrilateral meshes. In this approach, for the spatial discretization, an arbitrary high order discontinuous Galerkin spectral element (DG) method is combined with a finite volume (FV) scheme in order to simulate complex flow problems involving strong shocks. Regarding the time discretization, a fourth order strong stability preserving Runge-Kutta method is used. In the proposed hybrid scheme, a shock indicator is computed at the beginning of each Runge-Kutta stage in order to flag those elements containing shock waves or discontinuities. Subsequently, the DG solution in these troubled elements and in the current time step is projected onto a subdomain composed of finite volume subcells. Right after, the DG operator is applied to those unflagged elements, which, in principle, are oscillation-free, meanwhile the troubled elements are evolved with a robust second/third order FV operator. With this approach we are able to numerically simulate very challenging problems in the context of MHD and SRHD in one, and two space dimensions and with very high order polynomials. We make convergence tests and show a comprehensive one- and two dimensional testbench for both equation systems, focusing in problems with strong shocks. The presented hybrid approach shows that numerical schemes of very high order of accuracy are able to simulate these complex flow problems in an efficient and robust manner.
A potential enstrophy and energy conserving scheme for the shallow water equations
Arakawa, A.; Lamb, V. R.
1981-01-01
To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.
Multiple-image encryption scheme based on cascaded fractional Fourier transform.
Kong, Dezhao; Shen, Xueju; Xu, Qinzu; Xin, Wang; Guo, Haiqiong
2013-04-20
A multiple-image encryption scheme based on cascaded fractional Fourier transform is proposed. In the scheme, images are successively coded into the amplitude and phase of the input by cascading stages, which ends up with an encrypted image and a series of keys. The scheme takes full advantage of multikeys and the cascaded relationships of all stages, and it not only realizes image encryption but also achieves higher safety and more diverse applications. So multiuser authentication and hierarchical encryption are achieved. Numerical simulation verifies the feasibility of the method and demonstrates the security of the scheme and decryption characteristics. Finally, flexibility and variability of the scheme in application are discussed, and the simple photoelectric mixed devices to realize the scheme are proposed.
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Directory of Open Access Journals (Sweden)
Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
Distance labeling schemes for trees
DEFF Research Database (Denmark)
Alstrup, Stephen; Gørtz, Inge Li; Bistrup Halvorsen, Esben
2016-01-01
We consider distance labeling schemes for trees: given a tree with n nodes, label the nodes with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the distance in the tree between the two nodes. A lower bound by Gavoille et al. [Gavoill...
Distance labeling schemes for trees
DEFF Research Database (Denmark)
Alstrup, Stephen; Gørtz, Inge Li; Bistrup Halvorsen, Esben
2016-01-01
(log(n)) bits for constant ε> 0. (1 + ε)-stretch labeling schemes with polylogarithmic label size have previously been established for doubling dimension graphs by Talwar [Talwar, STOC, 2004]. In addition, we present matching upper and lower bounds for distance labeling for caterpillars, showing that labels...
An integration scheme for stiff solid-gas reactor models
Directory of Open Access Journals (Sweden)
Bjarne A. Foss
2001-04-01
Full Text Available Many dynamic models encounter numerical integration problems because of a large span in the dynamic modes. In this paper we develop a numerical integration scheme for systems that include a gas phase, and solid and liquid phases, such as a gas-solid reactor. The method is based on neglecting fast dynamic modes and exploiting the structure of the algebraic equations. The integration method is suitable for a large class of industrially relevant systems. The methodology has proven remarkably efficient. It has in practice performed excellent and been a key factor for the success of the industrial simulator for electrochemical furnaces for ferro-alloy production.
A convergent finite difference scheme for the variational heat equation
Coclite, Giuseppe Maria; Ridder, Johanna; Risebro, Nils Henrik
2017-12-01
The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed, possibly degenerate version of this equation and prove that a subsequence of the numerical solutions converges to a weak solution. This result is supplemented by numerical examples that show that weak solutions are not unique and give some intuition about how to obtain a viscosity type solution.
Constructing space difference schemes which satisfy a cell entropy inequality
Merriam, Marshal L.
1989-01-01
A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.
Nonlinear inversion schemes for fluorescence optical tomography.
Freiberger, Manuel; Egger, Herbert; Scharfetter, Hermann
2010-11-01
Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.
Auzinger, Winfried
2016-07-28
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
Energy Technology Data Exchange (ETDEWEB)
Zou, Ling [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhao, Haihua [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Hongbin [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists.
Blaclard, G; Lehe, R; Vay, J L
2016-01-01
With the advent of PW class lasers, the very large laser intensities attainable on-target should enable the production of intense high order Doppler harmonics from relativistic laser-plasma mirrors interactions. At present, the modeling of these harmonics with Particle-In-Cell (PIC) codes is extremely challenging as it implies an accurate description of tens of harmonic orders on a a broad range of angles. In particular, we show here that standard Finite Difference Time Domain (FDTD) Maxwell solvers used in most PIC codes partly fail to model Doppler harmonic generation because they induce numerical dispersion of electromagnetic waves in vacuum which is responsible for a spurious angular deviation of harmonic beams. This effect was extensively studied and a simple toy-model based on Snell-Descartes law was developed that allows us to finely predict the angular deviation of harmonics depending on the spatio-temporal resolution and the Maxwell solver used in the simulations. Our model demonstrates that the miti...
Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows
Wang, Wei; Yee, H. C.; Sjogreen, Bjorn; Magin, Thierry; Shu, Chi-Wang
2009-01-01
The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.
High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids
Mazaheri, Alireza; Nishikawa, Hiroaki
2015-01-01
In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.
Numerical Optimization in Microfluidics
DEFF Research Database (Denmark)
Jensen, Kristian Ejlebjærg
2017-01-01
Numerical modelling can illuminate the working mechanism and limitations of microfluidic devices. Such insights are useful in their own right, but one can take advantage of numerical modelling in a systematic way using numerical optimization. In this chapter we will discuss when and how numerical...
Numerical simulation of second-order hyperbolic telegraph type equations with variable coefficients
Pandit, Sapna; Kumar, Manoj; Tiwari, Surabhi
2015-02-01
In this article, the authors proposed a numerical scheme based on Crank-Nicolson finite difference scheme and Haar wavelets to find numerical solutions of different types of second order hyperbolic telegraph equations (i.e. telegraph equation with constant coefficients, with variable coefficients, and singular telegraph equation). This work is an extension of the scheme by Jiwari (2012) for hyperbolic equations. The use of Haar basis function is made with multiresolution analysis to get the fast and accurate results on collocation points. The convergence of the proposed scheme is proved by doing its error analysis. Four test examples are considered to demonstrate the accuracy and efficiency of the scheme. The scheme is easy and very suitable for computer implementation and provides numerical solutions close to the exact solutions and available in the literature.
A numerical solution for a class of time fractional diffusion equations with delay
Directory of Open Access Journals (Sweden)
Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
High-order asynchrony-tolerant finite difference schemes for partial differential equations
Aditya, Konduri; Donzis, Diego A.
2017-12-01
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.
Universal Numeric Segmented Display
Azad, Md. Abul Kalam; Sharmeen, Rezwana; S. M. Kamruzzaman
2010-01-01
Segmentation display plays a vital role to display numerals. But in today's world matrix display is also used in displaying numerals. Because numerals has lots of curve edges which is better supported by matrix display. But as matrix display is costly and complex to implement and also needs more memory, segment display is generally used to display numerals. But as there is yet no proposed compact display architecture to display multiple language numerals at a time, this paper proposes uniform...
Support Schemes and Ownership Structures
DEFF Research Database (Denmark)
Ropenus, Stephanie; Schröder, Sascha Thorsten; Costa, Ana
for promoting combined heat and power and energy from renewable sources. These Directives are to be implemented at the national level by the Member States. Section 3 conceptually presents the spectrum of national support schemes, ranging from investment support to market‐based operational support. The choice...... an introduction to the policy context for mCHP. Section 1 describes the rationale for the promotion of mCHP by explaining its potential contribution to European energy policy goals. Section 2 addresses the policy context at the supranational European level by outlining relevant EU Directives on support schemes......In recent years, fuel cell based micro‐combined heat and power has received increasing attention due to its potential contribution to energy savings, efficiency gains, customer proximity and flexibility in operation and capacity size. The FC4Home project assesses technical and economic aspects...
Network Regulation and Support Schemes
DEFF Research Database (Denmark)
Ropenus, Stephanie; Schröder, Sascha Thorsten; Jacobsen, Henrik
2009-01-01
-in tariffs to market-based quota systems, and network regulation approaches, comprising rate-of-return and incentive regulation. National regulation and the vertical structure of the electricity sector shape the incentives of market agents, notably of distributed generators and network operators....... This article seeks to investigate the interactions between the policy dimensions of support schemes and network regulation and how they affect the deployment of distributed generation. Firstly, a conceptual analysis examines how the incentives of the different market agents are affected. In particular......At present, there exists no explicit European policy framework on distributed generation. Various Directives encompass distributed generation; inherently, their implementation is to the discretion of the Member States. The latter have adopted different kinds of support schemes, ranging from feed...
Subranging scheme for SQUID sensors
Penanen, Konstantin I. (Inventor)
2008-01-01
A readout scheme for measuring the output from a SQUID-based sensor-array using an improved subranging architecture that includes multiple resolution channels (such as a coarse resolution channel and a fine resolution channel). The scheme employs a flux sensing circuit with a sensing coil connected in series to multiple input coils, each input coil being coupled to a corresponding SQUID detection circuit having a high-resolution SQUID device with independent linearizing feedback. A two-resolution configuration (course and fine) is illustrated with a primary SQUID detection circuit for generating a fine readout, and a secondary SQUID detection circuit for generating a course readout, both having feedback current coupled to the respective SQUID devices via feedback/modulation coils. The primary and secondary SQUID detection circuits function and derive independent feedback. Thus, the SQUID devices may be monitored independently of each other (and read simultaneously) to dramatically increase slew rates and dynamic range.
Liu, Xin; Zhang, Ruisheng; Liu, Qidong
2017-01-01
Wireless sensor networks (WSNs), which consist of a large number of sensor nodes, have become among the most important technologies in numerous fields, such as environmental monitoring, military surveillance, control systems in nuclear reactors, vehicle safety systems, and medical monitoring. The most serious drawback for the widespread application of WSNs is the lack of security. Given the resource limitation of WSNs, traditional security schemes are unsuitable. Approaches toward withstanding related attacks with small overhead have thus recently been studied by many researchers. Numerous studies have focused on the authentication scheme for WSNs, but most of these works cannot achieve the security performance and overhead perfectly. Nam et al. proposed a two-factor authentication scheme with lightweight sensor computation for WSNs. In this paper, we review this scheme, emphasize its drawbacks, and propose a temporal credential-based mutual authentication with a multiple-password scheme for WSNs. Our scheme uses multiple passwords to achieve three-factor security performance and generate a session key between user and sensor nodes. The security analysis phase shows that our scheme can withstand related attacks, including a lost password threat, and the comparison phase shows that our scheme involves a relatively small overhead. In the comparison of the overhead phase, the result indicates that more than 95% of the overhead is composed of communication and not computation overhead. Therefore, the result motivates us to pay further attention to communication overhead than computation overhead in future research.
Supporting Argumentation Schemes in Argumentative Dialogue Games
Directory of Open Access Journals (Sweden)
Wells Simon
2014-03-01
Full Text Available This paper reports preliminary work into the exploitation of argumentation schemes within dialogue games. We identify a property of dialogue games that we call “scheme awareness” that captures the relationship between dialogue game systems and argumentation schemes. Scheme awareness is used to examine the ways in which existing dialogue games utilise argumentation schemes and consequently the degree with which a dialogue game can be used to construct argument structures. The aim is to develop a set of guidelines for dialogue game design, which feed into a set of Dialogue Game Description Language (DGDL extensions in turn enabling dialogue games to better exploit argumentation schemes.
An Arbitrated Quantum Signature Scheme without Entanglement*
Li, Hui-Ran; Luo, Ming-Xing; Peng, Dai-Yuan; Wang, Xiao-Jun
2017-09-01
Several quantum signature schemes are recently proposed to realize secure signatures of quantum or classical messages. Arbitrated quantum signature as one nontrivial scheme has attracted great interests because of its usefulness and efficiency. Unfortunately, previous schemes cannot against Trojan horse attack and DoS attack and lack of the unforgeability and the non-repudiation. In this paper, we propose an improved arbitrated quantum signature to address these secure issues with the honesty arbitrator. Our scheme takes use of qubit states not entanglements. More importantly, the qubit scheme can achieve the unforgeability and the non-repudiation. Our scheme is also secure for other known quantum attacks.
A biometric signcryption scheme without bilinear pairing
Wang, Mingwen; Ren, Zhiyuan; Cai, Jun; Zheng, Wentao
2013-03-01
How to apply the entropy in biometrics into the encryption and remote authentication schemes to simplify the management of keys is a hot research area. Utilizing Dodis's fuzzy extractor method and Liu's original signcryption scheme, a biometric identity based signcryption scheme is proposed in this paper. The proposed scheme is more efficient than most of the previous proposed biometric signcryption schemes for that it does not need bilinear pairing computation and modular exponentiation computation which is time consuming largely. The analysis results show that under the CDH and DL hard problem assumption, the proposed scheme has the features of confidentiality and unforgeability simultaneously.
Cambridge community Optometry Glaucoma Scheme.
Keenan, Jonathan; Shahid, Humma; Bourne, Rupert R; White, Andrew J; Martin, Keith R
2015-04-01
With a higher life expectancy, there is an increased demand for hospital glaucoma services in the United Kingdom. The Cambridge community Optometry Glaucoma Scheme (COGS) was initiated in 2010, where new referrals for suspected glaucoma are evaluated by community optometrists with a special interest in glaucoma, with virtual electronic review and validation by a consultant ophthalmologist with special interest in glaucoma. 1733 patients were evaluated by this scheme between 2010 and 2013. Clinical assessment is performed by the optometrist at a remote site. Goldmann applanation tonometry, pachymetry, monoscopic colour optic disc photographs and automated Humphrey visual field testing are performed. A clinical decision is made as to whether a patient has glaucoma or is a suspect, and referred on or discharged as a false positive referral. The clinical findings, optic disc photographs and visual field test results are transmitted electronically for virtual review by a consultant ophthalmologist. The number of false positive referrals from initial referral into the scheme. Of the patients, 46.6% were discharged at assessment and a further 5.7% were discharged following virtual review. Of the patients initially discharged, 2.8% were recalled following virtual review. Following assessment at the hospital, a further 10.5% were discharged after a single visit. The COGS community-based glaucoma screening programme is a safe and effective way of evaluating glaucoma referrals in the community and reducing false-positive referrals for glaucoma into the hospital system. © 2014 Royal Australian and New Zealand College of Ophthalmologists.
Waveform inversion schemes for 3D density structure
Blom, N.; Fichtner, A.
2014-12-01
We develop waveform inversion schemes for density, based on numerical wave propagation, adjoint techniques and various non-seismological constraints to enhance resolution. Density variations drive convection in the Earth and serve as a discriminator between thermal and compositional heterogeneities. However, classical seismological observables and gravity provide only weak constraints, with strong trade-offs. To put additional constraints on density structure, we develop waveform inversion schemes that exploit the seismic waveform itself for the benefit of improved density resolution. Our inversion scheme is intended to incorporate any information that can help to constrain 3D density structure. This includes non-seismological information, such as gravity and the geoid, the mass and moment of inertia of the Earth, and mineral physical constraints on maximum density heterogeneities (assuming reasonable variations in temperature and composition). In a series of initial synthetic experiments, we aim to construct efficient optimisation schemes that allow us to assimilate all the available types of information. For this, we use 2D numerical wave propagation combined with adjoint techniques for the computation of sensitivity kernels. With these kernels, we drive gradient-based optimisation schemes that incorporate our non-seismological constraints. Specifically, we assess the usefulness of an inversion strategy where additional information is used as hard constraints, as opposed to the optimisation of a single objective functional that incorporates all the information. Hard constraints may consist of the Earth's mass or moment of inertia, and are applied by solving a separate optimisation problem to project the initial (unconstrained) solution onto an allowed range. These synthetic experiments will allow us to assess to what extent velocity and density structure need to be coupled in order to obtain useful and meaningful results to a density inversion.
Asymptotic-induced numerical methods for conservation laws
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.
Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei
2017-04-01
Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.
Peng, Qiujin
2017-09-18
In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L-infinity convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.
METAPHORIC MECHANISMS IN IMAGE SCHEME DEVELOPMENT
National Research Council Canada - National Science Library
Pankratova, S.A
2017-01-01
.... In the summary the author underscores that both ways of image scheme development are of importance to cognitive science, both heuristic epiphora and image-based diaphora play a significant role in the explication of image scheme development.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
DEFF Research Database (Denmark)
Fasano, Andrea; Rasmussen, Henrik K.
2017-01-01
A third order accurate, in time and space, finite element scheme for the numerical simulation of three- dimensional time-dependent flow of the molecular stress function type of fluids in a generalized formu- lation is presented. The scheme is an extension of the K-BKZ Lagrangian finite element...
A Split-Step Scheme for the Incompressible Navier-Stokes
Energy Technology Data Exchange (ETDEWEB)
Henshaw, W; Petersson, N A
2001-06-12
We describe a split-step finite-difference scheme for solving the incompressible Navier-Stokes equations on composite overlapping grids. The split-step approach decouples the solution of the velocity variables from the solution of the pressure. The scheme is based on the velocity-pressure formulation and uses a method of lines approach so that a variety of implicit or explicit time stepping schemes can be used once the equations have been discretized in space. We have implemented both second-order and fourth-order accurate spatial approximations that can be used with implicit or explicit time stepping methods. We describe how to choose appropriate boundary conditions to make the scheme accurate and stable. A divergence damping term is added to the pressure equation to keep the numerical dilatation small. Several numerical examples are presented.
A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation
Directory of Open Access Journals (Sweden)
S. Battal Gazi Karakoç
2016-02-01
Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.
Xing, Yanyuan; Yan, Yubin
2018-03-01
Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
The Ubiquity of Smooth Hilbert Schemes
Staal, Andrew P.
2017-01-01
We investigate the geography of Hilbert schemes that parametrize closed subschemes of projective space with a specified Hilbert polynomial. We classify Hilbert schemes with unique Borel-fixed points via combinatorial expressions for their Hilbert polynomials. We realize the set of all nonempty Hilbert schemes as a probability space and prove that Hilbert schemes are irreducible and nonsingular with probability greater than $0.5$.
MIRD radionuclide data and decay schemes
Eckerman, Keith F
2007-01-01
For all physicians, scientists, and physicists working in the nuclear medicine field, the MIRD: Radionuclide Data and Decay Schemes updated edition is an essential sourcebook for radiation dosimetry and understanding the properties of radionuclides. Includes CD Table of Contents Decay schemes listed by atomic number Radioactive decay processes Serial decay schemes Decay schemes and decay tables This essential reference for nuclear medicine physicians, scientists and physicists also includes a CD with tabulations of the radionuclide data necessary for dosimetry calculations.
Accelerating convergence for backward Euler and trapezoid time discretization schemes
Directory of Open Access Journals (Sweden)
Osman Raşit Işık
2014-12-01
Full Text Available In this study, we introduce two algorithms to numerically solve any initial value problem (IVP. These algorithms depend on time relaxation model (TRM which is obtained adding a time relaxation term into IVP. Discretizing TRM by using backward Euler (BE method gives the first algorithm. Similarly, the second algorithm is followed by using trapezoid (TR time stepping scheme . Under some conditions, the first algorithm increases the order of convergence from one to two and the second one increases the order from two to three. Thus, more accurate results can be obtained. To verify the accuracy of the methods, they are applied to some numerical examples. Numerical results overlap with the theoretical results.
THROUGHPUT ANALYSIS OF EXTENDED ARQ SCHEMES
African Journals Online (AJOL)
PUBLICATIONS1
and Wait (SW), Selective Repeat (SR), Stutter. (ST) and Go-Back-N (GBN) (Lin and Costello,. 2003). Combinations of these schemes lead to mixed mode schemes which include the SR-. GBN, SR-ST1 and SR-ST2. In the mixed mode schemes, when a prescribed number of failures occur in the SR mode, the GBN or ST ...
Energy Technology Data Exchange (ETDEWEB)
Bonaventura, L. [GKSS-Forschungszentrum Geesthacht GmbH (Germany). Inst. fuer Hydrophysik
1998-12-31
A semiimplicit, semiLagrangian scheme for the fully compressible Euler equations of the atmosphere has been developed using a Cartesian coordinate system with height as the vertical coordinate. As a result, an efficient algorithm is obtained, which only requires the solution of a symmetric and well conditioned system at each timestep. Furthermore, no spurious flows are generated around steep orography. Numerical simulations of well known lee wave test cases demonstrate the soundness and feasibility of the proposed scheme. (orig.) 34 refs.
Emission trading beyond Europe: linking schemes in a post-Kyoto world
Anger, Niels
2006-01-01
This paper assesses the economic impacts of linking the EU Emission Trading Scheme (ETS) to emerging schemes beyond Europe, in the presence of a post-Kyoto agreement in 2020. Simulations with a numerical multi-country model of the world carbon market show that linking the European ETS induces only marginal economic benefits: As trading is restricted to energy-intensive industries that are assigned generous initial emissions, the major compliance burden is carried by non-trading industries exc...
Ulku, Huseyin Arda
2012-09-01
An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.
Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations
Energy Technology Data Exchange (ETDEWEB)
Bank, Randolph E. [Univ. of California, San Diego, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Bulgarian Academy of Sciences, Sofia (Bulgaria)
2016-01-20
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space-time domain demonstrate the feasibility of the proposed approach.
Reverse flood routing with the inverted Muskingum storage routing scheme
Directory of Open Access Journals (Sweden)
A. D. Koussis
2012-01-01
Full Text Available This work treats reverse flood routing aiming at signal identification: inflows are inferred from observed outflows by orienting the Muskingum scheme against the wave propagation direction. Routing against the wave propagation is an ill-posed, inverse problem (small errors amplify, leading to large spurious responses; therefore, the reverse solution must be smoothness-constrained towards stability and uniqueness (regularised. Theoretical constrains on the coefficients of the reverse routing scheme assist in error control, but optimal grids are derived by numerical experimentation. Exact solutions of the convection-diffusion equation, for a single and a composite wave, are reverse-routed and in both instances the wave is backtracked well for a range of grid parameters. In the arduous test of a square pulse, the result is comparable to those of more complex methods. Seeding outflow data with random errors enhances instability; to cope with the spurious oscillations, the reversed solution is conditioned by smoothing via low-pass filtering or optimisation. Good-quality inflow hydrographs are recovered with either smoothing treatment, yet the computationally demanding optimisation is superior. Finally, the reverse Muskingum routing method is compared to a reverse-solution method of the St. Venant equations of flood wave motion and is found to perform equally well, at a fraction of the computing effort. This study leads us to conclude that the efficiently attained good inflow identification rests on the simplicity of the Muskingum reverse routing scheme that endows it with numerical robustness.
Application of the GRP scheme to open channel flow equations
Birman, A.; Falcovitz, J.
2007-03-01
The GRP (generalized Riemann problem) scheme, originally conceived for gasdynamics, is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross-section, variable width and bed profile, including a friction model for the fluid-channel shear stress. This scheme is a second-order analytic extension of the first-order Godunov-scheme, based on time-derivatives of flow variables at cell-interfaces resulting from piecewise-linear data reconstruction in cells. The second-order time-integration is based on solutions to generalized Riemann problems at cell-interfaces, thus accounting for the full governing equations, including source terms. The source term due to variable bed elevation is treated in a well-balanced way so that quiescent flow is exactly replicated; this is done by adopting the Surface Gradient Method (SGM). Several problems of steady or unsteady open channel flow are considered, including the terms corresponding to variable channel width and bed elevation, as well as to shear stress at the fluid-channel interface (using the Manning friction model). In all these examples remarkable agreement is obtained between the numerical integration and the exact or accurate solutions.
The Original Management Incentive Schemes
Richard T. Holden
2005-01-01
During the 1990s, the structure of pay for top corporate executives shifted markedly as the use of stock options greatly expanded. By the early 2000s, as the dot-com boom ended and the Nasdaq stock index melted down, these modern executive incentive schemes were being sharply questioned on many grounds—for encouraging excessive risk-taking and a short-run orientation, for being an overly costly and inefficient method of providing incentives, and even for tempting managers of firms like Enron,...
Adaptive Optics Metrics & QC Scheme
Girard, Julien H.
2017-09-01
"There are many Adaptive Optics (AO) fed instruments on Paranal and more to come. To monitor their performances and assess the quality of the scientific data, we have developed a scheme and a set of tools and metrics adapted to each flavour of AO and each data product. Our decisions to repeat observations or not depends heavily on this immediate quality control "zero" (QC0). Atmospheric parameters monitoring can also help predict performances . At the end of the chain, the user must be able to find the data that correspond to his/her needs. In Particular, we address the special case of SPHERE."
The mathematics of Ponzi schemes
Artzrouni, Marc
2009-01-01
A first order linear differential equation is used to describe the dynamics of an investment fund that promises more than it can deliver, also known as a Ponzi scheme. The model is based on a promised, unrealistic interest rate; on the actual, realized nominal interest rate; on the rate at which new deposits are accumulated and on the withdrawal rate. Conditions on these parameters are given for the fund to be solvent or to collapse. The model is fitted to data available on Charles...
Amin, Ruhul; Islam, S K Hafizul; Biswas, G P; Khan, Muhammad Khurram; Kumar, Neeraj
2015-11-01
In the last few years, numerous remote user authentication and session key agreement schemes have been put forwarded for Telecare Medical Information System, where the patient and medical server exchange medical information using Internet. We have found that most of the schemes are not usable for practical applications due to known security weaknesses. It is also worth to note that unrestricted number of patients login to the single medical server across the globe. Therefore, the computation and maintenance overhead would be high and the server may fail to provide services. In this article, we have designed a medical system architecture and a standard mutual authentication scheme for single medical server, where the patient can securely exchange medical data with the doctor(s) via trusted central medical server over any insecure network. We then explored the security of the scheme with its resilience to attacks. Moreover, we formally validated the proposed scheme through the simulation using Automated Validation of Internet Security Schemes and Applications software whose outcomes confirm that the scheme is protected against active and passive attacks. The performance comparison demonstrated that the proposed scheme has lower communication cost than the existing schemes in literature. In addition, the computation cost of the proposed scheme is nearly equal to the exiting schemes. The proposed scheme not only efficient in terms of different security attacks, but it also provides an efficient login, mutual authentication, session key agreement and verification and password update phases along with password recovery.
Distributed Group-Based Mobility Management Scheme in Wireless Body Area Networks
Directory of Open Access Journals (Sweden)
Moneeb Gohar
2017-01-01
Full Text Available For group-based mobility management in 6LoWPAN-based wireless body area networks (WBAN, some schemes using the Proxy Mobile IPv6 (PMIP have been proposed. However, the existing PMIP-based mobility schemes tend to induce large registration delay and handover delay. To overcome such limitations, we propose a new distributed group-based mobility management scheme, in which the Local Mobility Anchor (LMA function is implemented by each Mobile Access Gateway (MAG and the handover operation is performed between two neighboring MAGs without the help of LMA. Besides, each MAG maintains the information of the group of mobile sensors and aggregates the Authentication-Authorization-Accounting (AAA query messages for a group of mobile sensors as a “single” message to decrease the control overhead. By numerical analysis, it is shown that the proposed scheme can reduce the registration and handover delays, compared to the existing PMIP-based mobility schemes.
Directory of Open Access Journals (Sweden)
Y. Lee
2014-12-01
Full Text Available In orthogonal frequency division multiplexing (OFDM systems, an integer part of a frequency offset (IFO that causes ambiguity in data demodulation is estimated generally by comparing correlations between the received and local signals for IFO candidates. In this paper, we propose an IFO estimation scheme that provides a tradeoff between the estimation performance and the computational complexity including a conventional scheme as a special case. In the proposed scheme, template signals are formed by combining frequency-shifted training symbols, allowing the receiver to reduce the number of IFO candidates in the estimation process. Numerical results illustrate the tradeoff of the proposed scheme: The proposed scheme exhibits a tradeoff between the correct estimation probability and the computational complexity taking the number of the training symbols used to construct the template signal as a parameter.
Conservative arbitrary order finite difference schemes for shallow-water flows
Skiba, Yuri N.; Filatov, Denis M.
2008-09-01
The classical nonlinear shallow-water model (SWM) of an ideal fluid is considered. For the model, a new method for the construction of mass and total energy conserving finite difference schemes is suggested. In fact, it produces an infinite family of finite difference schemes, which are either linear or nonlinear depending on the choice of certain parameters. The developed schemes can be applied in a variety of domains on the plane and on the sphere. The method essentially involves splitting of the model operator by geometric coordinates and by physical processes, which provides substantial benefits in the computational cost of solution. Besides, in case of the whole sphere it allows applying the same algorithms as in a doubly periodic domain on the plane and constructing finite difference schemes of arbitrary approximation order in space. Results of numerical experiments illustrate the skillfulness of the schemes in describing the shallow-water dynamics.
El-Amin, Mohamed
2012-01-01
The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.
An OFDM Carrier Frequency Offset Estimation Scheme with Wide Fractional Offset Estimation Range
Directory of Open Access Journals (Sweden)
C. Yu
2013-04-01
Full Text Available In this paper, we propose a carrier frequency offset (CFO estimation scheme which is robust to the fractional CFO variation for orthogonal frequency division multiplexing (OFDM systems. The proposed scheme first performs the envelope equalization process to convert the offset estimation problem to a carrier estimation problem, and then, estimates the integer and fractional parts of CFO by using periodogram of the received signal. Especially, in the estimation stage for fraction CFO, the ratio of the square-roots of periodograms is employed enlarging the estimation range of the stage than that of the conventional scheme. Numerical results demonstrate that the proposed scheme has better estimation performance than the conventional scheme for wider fractional CFO range in various channel conditions.
Study of stability of the difference scheme for the model problem of the gaslift process
Temirbekov, Nurlan; Turarov, Amankeldy
2017-09-01
The paper studies a model of the gaslift process where the motion in a gas-lift well is described by partial differential equations. The system describing the studied process consists of equations of motion, continuity, equations of thermodynamic state, and hydraulic resistance. A two-layer finite-difference Lax-Vendroff scheme is constructed for the numerical solution of the problem. The stability of the difference scheme for the model problem is investigated using the method of a priori estimates, the order of approximation is investigated, the algorithm for numerical implementation of the gaslift process model is given, and the graphs are presented. The development and investigation of difference schemes for the numerical solution of systems of equations of gas dynamics makes it possible to obtain simultaneously exact and monotonic solutions.
Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation
Pötz, Walter; Schreilechner, Magdalena
2017-11-01
An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space-time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space-time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac-Lindblad equation, real-space-time Green's function formulations, and higher-order finite-difference schemes are discussed.
REMINDER: Saved Leave Scheme (SLS)
2003-01-01
Transfer of leave to saved leave accounts Under the provisions of the voluntary saved leave scheme (SLS), a maximum total of 10 days'* annual and compensatory leave (excluding saved leave accumulated in accordance with the provisions of Administrative Circular No 22B) can be transferred to the saved leave account at the end of the leave year (30 September). We remind you that unused leave of all those taking part in the saved leave scheme at the closure of the leave year accounts is transferred automatically to the saved leave account on that date. Therefore, staff members have no administrative steps to take. In addition, the transfer, which eliminates the risk of omitting to request leave transfers and rules out calculation errors in transfer requests, will be clearly shown in the list of leave transactions that can be consulted in EDH from October 2003 onwards. Furthermore, this automatic leave transfer optimizes staff members' chances of benefiting from a saved leave bonus provided that they ar...
Directory of Open Access Journals (Sweden)
G. Akinci
2014-12-01
Full Text Available Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method. ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage scheme becomes negligible for large scale problems. On the other hand, our analyses show that the redundancy is still considerable for the occasions where facet or edge elements have to be used.
A Suboptimal Scheme for Multi-User Scheduling in Gaussian Broadcast Channels
Zafar, Ammar
2014-05-28
This work proposes a suboptimal multi-user scheduling scheme for Gaussian broadcast channels which improves upon the classical single user selection, while considerably reducing complexity as compared to the optimal superposition coding with successful interference cancellation. The proposed scheme combines the two users with the maximum weighted instantaneous rate using superposition coding. The instantaneous rate and power allocation are derived in closed-form, while the long term rate of each user is derived in integral form for all channel distributions. Numerical results are then provided to characterize the prospected gains of the proposed scheme.
Directory of Open Access Journals (Sweden)
Yanli Zhou
2013-01-01
Full Text Available Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient for Monte Carlo simulations for jump-diffusion stochastic delay differential equations.
A Temporal Domain Decomposition Algorithmic Scheme for Large-Scale Dynamic Traffic Assignment
Directory of Open Access Journals (Sweden)
Eric J. Nava
2012-03-01
This paper presents a temporal decomposition scheme for large spatial- and temporal-scale dynamic traffic assignment, in which the entire analysis period is divided into Epochs. Vehicle assignment is performed sequentially in each Epoch, thus improving the model scalability and confining the peak run-time memory requirement regardless of the total analysis period. A proposed self-turning scheme adaptively searches for the run-time-optimal Epoch setting during iterations regardless of the characteristics of the modeled network. Extensive numerical experiments confirm the promising performance of the proposed algorithmic schemes.
ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS
B. Hamilton; S. Bilbao
2013-01-01
In this paper, we investigate ﬁnite difference schemes forthe 3-D wave equation using 27-point stencils on the cubiclattice, a 13-point stencil on the face-centered cubic (FCC)lattice, and a 9-point stencil on the body-centered cubic(BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numericaldispersion. Schemes are compared for computational efﬁ-ciency in terms of minimising numerical wave speed error.It is shown that the 13-point scheme...
Positivity-preserving space-time CE/SE scheme for high speed flows
Shen, Hua
2017-03-02
We develop a space-time conservation element and solution element (CE/SE) scheme using a simple slope limiter to preserve the positivity of the density and pressure in computations of inviscid and viscous high-speed flows. In general, the limiter works with all existing CE/SE schemes. Here, we test the limiter on a central Courant number insensitive (CNI) CE/SE scheme implemented on hybrid unstructured meshes. Numerical examples show that the proposed limiter preserves the positivity of the density and pressure without disrupting the conservation law; it also improves robustness without losing accuracy in solving high-speed flows.
Directory of Open Access Journals (Sweden)
C. Bommaraju
2005-01-01
Full Text Available Numerical methods are extremely useful in solving real-life problems with complex materials and geometries. However, numerical methods in the time domain suffer from artificial numerical dispersion. Standard numerical techniques which are second-order in space and time, like the conventional Finite Difference 3-point (FD3 method, Finite-Difference Time-Domain (FDTD method, and Finite Integration Technique (FIT provide estimates of the error of discretized numerical operators rather than the error of the numerical solutions computed using these operators. Here optimally accurate time-domain FD operators which are second-order in time as well as in space are derived. Optimal accuracy means the greatest attainable accuracy for a particular type of scheme, e.g., second-order FD, for some particular grid spacing. The modified operators lead to an implicit scheme. Using the first order Born approximation, this implicit scheme is transformed into a two step explicit scheme, namely predictor-corrector scheme. The stability condition (maximum time step for a given spatial grid interval for the various modified schemes is roughly equal to that for the corresponding conventional scheme. The modified FD scheme (FDM attains reduction of numerical dispersion almost by a factor of 40 in 1-D case, compared to the FD3, FDTD, and FIT. The CPU time for the FDM scheme is twice of that required by the FD3 method. The simulated synthetic data for a 2-D P-SV (elastodynamics problem computed using the modified scheme are 30 times more accurate than synthetics computed using a conventional scheme, at a cost of only 3.5 times as much CPU time. The FDM is of particular interest in the modeling of large scale (spatial dimension is more or equal to one thousand wave lengths or observation time interval is very high compared to reference time step wave propagation and scattering problems, for instance, in ultrasonic antenna and synthetic scattering data modeling for Non
Delivery of a national home safety equipment scheme in England: a survey of local scheme leaders.
Mulvaney, C A; Watson, M C; Hamilton, T; Errington, G
2013-11-01
Unintentional home injuries sustained by preschool children are a major cause of morbidity in the UK. Home safety equipment schemes may reduce home injury rates. In 2009, the Royal Society for the Prevention of Accidents was appointed as central coordinator of a two-year, £18m national home safety equipment scheme in England. This paper reports the findings from a national survey of all scheme leaders responsible for local scheme delivery. A questionnaire mailed to all local scheme leaders sought details of how the schemes were operated locally; barriers and facilitators to scheme implementation; evaluation of the local scheme and its sustainability. A response rate of 73% was achieved. Health visitors and family support workers played a key role in both the identification of eligible families and performing home safety checks. The majority of local scheme leaders (94.6%) reported that they thought their local scheme had been successful in including those families considered 'harder to engage'. Many scheme leaders (72.4%) reported that they had evaluated the provision of safety equipment in their scheme and over half (56.6%) stated that they would not be able to continue the scheme once funding ceased. Local schemes need support to effectively evaluate their scheme and to seek sustainability funding to ensure the future of the scheme. There remains a lack of evidence of whether the provision of home safety equipment reduces injuries in preschool children.
Numerical Modeling of Ablation Heat Transfer
Ewing, Mark E.; Laker, Travis S.; Walker, David T.
2013-01-01
A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.
Channel Aggregation Schemes for Cognitive Radio Networks
Lee, Jongheon; So, Jaewoo
This paper proposed three channel aggregation schemes for cognitive radio networks, a constant channel aggregation scheme, a probability distribution-based variable channel aggregation scheme, and a residual channel-based variable channel aggregation scheme. A cognitive radio network can have a wide bandwidth if unused channels in the primary networks are aggregated. Channel aggregation schemes involve either constant channel aggregation or variable channel aggregation. In this paper, a Markov chain is used to develop an analytical model of channel aggregation schemes; and the performance of the model is evaluated in terms of the average sojourn time, the average throughput, the forced termination probability, and the blocking probability. Simulation results show that channel aggregation schemes can reduce the average sojourn time of cognitive users by increasing the channel occupation rate of unused channels in a primary network.
Directory of Open Access Journals (Sweden)
Ku David N
2010-07-01
Full Text Available Abstract Background The finite volume solver Fluent (Lebanon, NH, USA is a computational fluid dynamics software employed to analyse biological mass-transport in the vasculature. A principal consideration for computational modelling of blood-side mass-transport is convection-diffusion discretisation scheme selection. Due to numerous discretisation schemes available when developing a mass-transport numerical model, the results obtained should either be validated against benchmark theoretical solutions or experimentally obtained results. Methods An idealised aneurysm model was selected for the experimental and computational mass-transport analysis of species concentration due to its well-defined recirculation region within the aneurysmal sac, allowing species concentration to vary slowly with time. The experimental results were obtained from fluid samples extracted from a glass aneurysm model, using the direct spectrophometric concentration measurement technique. The computational analysis was conducted using the four convection-diffusion discretisation schemes available to the Fluent user, including the First-Order Upwind, the Power Law, the Second-Order Upwind and the Quadratic Upstream Interpolation for Convective Kinetics (QUICK schemes. The fluid has a diffusivity of 3.125 × 10-10 m2/s in water, resulting in a Peclet number of 2,560,000, indicating strongly convection-dominated flow. Results The discretisation scheme applied to the solution of the convection-diffusion equation, for blood-side mass-transport within the vasculature, has a significant influence on the resultant species concentration field. The First-Order Upwind and the Power Law schemes produce similar results. The Second-Order Upwind and QUICK schemes also correlate well but differ considerably from the concentration contour plots of the First-Order Upwind and Power Law schemes. The computational results were then compared to the experimental findings. An average error of 140
Jiang, Jiamin; Younis, Rami M.
2017-10-01
In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.
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A. H. Bhrawy
2014-01-01
Full Text Available The shifted Jacobi-Gauss collocation (SJGC scheme is proposed and implemented to solve the fractional neutral functional-differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm.
Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model
Calatroni, L.; Estatico, C.; Garibaldi, N.; Parisotto, S.
2017-10-01
We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in [10] for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Scheme of thinking quantum systems
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Fragment separator momentum compression schemes
Energy Technology Data Exchange (ETDEWEB)
Bandura, Laura, E-mail: bandura@anl.gov [Facility for Rare Isotope Beams (FRIB), 1 Cyclotron, East Lansing, MI 48824-1321 (United States); National Superconducting Cyclotron Lab, Michigan State University, 1 Cyclotron, East Lansing, MI 48824-1321 (United States); Erdelyi, Bela [Argonne National Laboratory, Argonne, IL 60439 (United States); Northern Illinois University, DeKalb, IL 60115 (United States); Hausmann, Marc [Facility for Rare Isotope Beams (FRIB), 1 Cyclotron, East Lansing, MI 48824-1321 (United States); Kubo, Toshiyuki [RIKEN Nishina Center, RIKEN, Wako (Japan); Nolen, Jerry [Argonne National Laboratory, Argonne, IL 60439 (United States); Portillo, Mauricio [Facility for Rare Isotope Beams (FRIB), 1 Cyclotron, East Lansing, MI 48824-1321 (United States); Sherrill, Bradley M. [National Superconducting Cyclotron Lab, Michigan State University, 1 Cyclotron, East Lansing, MI 48824-1321 (United States)
2011-07-21
We present a scheme to use a fragment separator and profiled energy degraders to transfer longitudinal phase space into transverse phase space while maintaining achromatic beam transport. The first order beam optics theory of the method is presented and the consequent enlargement of the transverse phase space is discussed. An interesting consequence of the technique is that the first order mass resolving power of the system is determined by the first dispersive section up to the energy degrader, independent of whether or not momentum compression is used. The fragment separator at the Facility for Rare Isotope Beams is a specific application of this technique and is described along with simulations by the code COSY INFINITY.
Fragment separator momentum compression schemes.
Energy Technology Data Exchange (ETDEWEB)
Bandura, L.; Erdelyi, B.; Hausmann, M.; Kubo, T.; Nolen, J.; Portillo, M.; Sherrill, B.M. (Physics); (MSU); (Northern Illinois Univ.); (RIKEN)
2011-07-21
We present a scheme to use a fragment separator and profiled energy degraders to transfer longitudinal phase space into transverse phase space while maintaining achromatic beam transport. The first order beam optics theory of the method is presented and the consequent enlargement of the transverse phase space is discussed. An interesting consequence of the technique is that the first order mass resolving power of the system is determined by the first dispersive section up to the energy degrader, independent of whether or not momentum compression is used. The fragment separator at the Facility for Rare Isotope Beams is a specific application of this technique and is described along with simulations by the code COSY INFINITY.
Fragment separator momentum compression schemes
Bandura, Laura; Erdelyi, Bela; Hausmann, Marc; Kubo, Toshiyuki; Nolen, Jerry; Portillo, Mauricio; Sherrill, Bradley M.
2011-07-01
We present a scheme to use a fragment separator and profiled energy degraders to transfer longitudinal phase space into transverse phase space while maintaining achromatic beam transport. The first order beam optics theory of the method is presented and the consequent enlargement of the transverse phase space is discussed. An interesting consequence of the technique is that the first order mass resolving power of the system is determined by the first dispersive section up to the energy degrader, independent of whether or not momentum compression is used. The fragment separator at the Facility for Rare Isotope Beams is a specific application of this technique and is described along with simulations by the code COSY INFINITY.
Implicit Flux Limiting Schemes for Petroleum Reservoir Simulation
Blunt, Martin; Rubin, Barry
1992-09-01
Explicit total variation diminishing (TVD) numerical methods have been used in the past to give convergent, high order accurate solutions to hyperbolic conservation equations, such as those governing flow in oil reservoirs. To ensure stability there is a restriction on the size of time step that can be used. Many petroleum reservoir simulation problems have regions of fast flow away from sharp fronts, which means that this time step limitation makes explicit schemes less efficient than the best implicit methods. This work extends the theory of TVD schemes to both fully implicit and partially implicit methods. We use our theoretical results to construct schemes which are stable even for very large time steps. We show how to construct an adaptively implicit scheme which is nearly fully implicit in regions of fast flow, but which may be explicit at sharp fronts which are moving more slowly. In general these schemes are only first-order accurate in time overall, but locally may achieve second-order time accuracy. Results, presented for a one-dimensional Buckley-Leverett problem, demonstrate that these methods are more accurate than conventional implicit algorithms and more efficient than fully explicit methods, for which smaller time steps must be used. The theory is also extended to embrace mixed hyperbolic/parabolic (black oil) systems and example solutions to a radial flow equation are presented. In this case the time step is not limited by the high flow speeds at a small radius, as would be the case for an explicit solution. Moreover, the shock front is resolved more sharply than for a fully implicit method.
Novel coupling scheme to control dynamics of coupled discrete systems
Shekatkar, Snehal M.; Ambika, G.
2015-08-01
We present a new coupling scheme to control spatio-temporal patterns and chimeras on 1-d and 2-d lattices and random networks of discrete dynamical systems. The scheme involves coupling with an external lattice or network of damped systems. When the system network and external network are set in a feedback loop, the system network can be controlled to a homogeneous steady state or synchronized periodic state with suppression of the chaotic dynamics of the individual units. The control scheme has the advantage that its design does not require any prior information about the system dynamics or its parameters and works effectively for a range of parameters of the control network. We analyze the stability of the controlled steady state or amplitude death state of lattices using the theory of circulant matrices and Routh-Hurwitz criterion for discrete systems and this helps to isolate regions of effective control in the relevant parameter planes. The conditions thus obtained are found to agree well with those obtained from direct numerical simulations in the specific context of lattices with logistic map and Henon map as on-site system dynamics. We show how chimera states developed in an experimentally realizable 2-d lattice can be controlled using this scheme. We propose this mechanism can provide a phenomenological model for the control of spatio-temporal patterns in coupled neurons due to non-synaptic coupling with the extra cellular medium. We extend the control scheme to regulate dynamics on random networks and adapt the master stability function method to analyze the stability of the controlled state for various topologies and coupling strengths.
Kumari, Komal; Donzis, Diego
2017-11-01
Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.
Chaudhry, Shehzad Ashraf; Mahmood, Khalid; Naqvi, Husnain; Khan, Muhammad Khurram
2015-11-01
Telecare medicine information system (TMIS) offers the patients convenient and expedite healthcare services remotely anywhere. Patient security and privacy has emerged as key issues during remote access because of underlying open architecture. An authentication scheme can verify patient's as well as TMIS server's legitimacy during remote healthcare services. To achieve security and privacy a number of authentication schemes have been proposed. Very recently Lu et al. (J. Med. Syst. 39(3):1-8, 2015) proposed a biometric based three factor authentication scheme for TMIS to confiscate the vulnerabilities of Arshad et al.'s (J. Med. Syst. 38(12):136, 2014) scheme. Further, they emphasized the robustness of their scheme against several attacks. However, in this paper we establish that Lu et al.'s scheme is vulnerable to numerous attacks including (1) Patient anonymity violation attack, (2) Patient impersonation attack, and (3) TMIS server impersonation attack. Furthermore, their scheme does not provide patient untraceability. We then, propose an improvement of Lu et al.'s scheme. We have analyzed the security of improved scheme using popular automated tool ProVerif. The proposed scheme while retaining the plusses of Lu et al.'s scheme is also robust against known attacks.
Groß, Michael; Dietzsch, Julian
2017-07-01
In this paper, a new class of time-stepping schemes for structural dynamics is presented, which originally emanate from Gauss-Runge-Kutta schemes as traditional representatives of higher-order symplectic-momentum schemes. The presented time stepping schemes belong to the family of higher-order energy-momentum schemes, which represent Gauss-Runge-Kutta schemes with a physically motivated time approximation of the considered mechanical system. As higher-order energy-momentum schemes so far are not derived by using a straight-forward design method, a variational-based design of energy-momentum schemes is shown. Here, a differential variational principle of continuum mechanics, Jourdain's principle, is discretized, and energy-momentum schemes emanate as discrete Euler-Lagrange equations. This procedure is strong related, but is not identical, to the derivation of variational integrators (VI), which emanate from discretising a Lagrange function or Hamilton's principle, respectively. Furthermore, this design procedure is well suited to connect energy-momentum schemes with numerical modifications based on mixed variational principles, as the enhanced assumed strain elements for improving the spatial discretisation in direction of a locking-free discrete formulation. Therefore, a Q1/E9 energy-momentum scheme of higher order for the continuum formulation of fiber-reinforced materials is presented. This material formulation is important for simulating dynamics of light-weight structures.
Tanaka, Satoshi; Yoshikawa, Kohji; Minoshima, Takashi; Yoshida, Naoki
2017-11-01
We develop new numerical schemes for Vlasov–Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that the positivity of the distribution function is also preserved. We adopt an efficient semi-Lagrangian time integration scheme that is more accurate and computationally less expensive than the three-stage TVD Runge–Kutta integration. We apply our spatially fifth- and seventh-order schemes to a suite of simulations of collisionless self-gravitating systems and electrostatic plasma simulations, including linear and nonlinear Landau damping in one dimension and Vlasov–Poisson simulations in a six-dimensional phase space. The high-order schemes achieve a significantly improved accuracy in comparison with the third-order positive-flux-conserved scheme adopted in our previous study. With the semi-Lagrangian time integration, the computational cost of our high-order schemes does not significantly increase, but remains roughly the same as that of the third-order scheme. Vlasov–Poisson simulations on {128}3× {128}3 mesh grids have been successfully performed on a massively parallel computer.
The a(4) Scheme-A High Order Neutrally Stable CESE Solver
Chang, Sin-Chung
2009-01-01
The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3
Spurious sea ice formation caused by oscillatory ocean tracer advection schemes
Naughten, Kaitlin A.; Galton-Fenzi, Benjamin K.; Meissner, Katrin J.; England, Matthew H.; Brassington, Gary B.; Colberg, Frank; Hattermann, Tore; Debernard, Jens B.
2017-08-01
Tracer advection schemes used by ocean models are susceptible to artificial oscillations: a form of numerical error whereby the advected field alternates between overshooting and undershooting the exact solution, producing false extrema. Here we show that these oscillations have undesirable interactions with a coupled sea ice model. When oscillations cause the near-surface ocean temperature to fall below the freezing point, sea ice forms for no reason other than numerical error. This spurious sea ice formation has significant and wide-ranging impacts on Southern Ocean simulations, including the disappearance of coastal polynyas, stratification of the water column, erosion of Winter Water, and upwelling of warm Circumpolar Deep Water. This significantly limits the model's suitability for coupled ocean-ice and climate studies. Using the terrain-following-coordinate ocean model ROMS (Regional Ocean Modelling System) coupled to the sea ice model CICE (Community Ice CodE) on a circumpolar Antarctic domain, we compare the performance of three different tracer advection schemes, as well as two levels of parameterised diffusion and the addition of flux limiters to prevent numerical oscillations. The upwind third-order advection scheme performs better than the centered fourth-order and Akima fourth-order advection schemes, with far fewer incidents of spurious sea ice formation. The latter two schemes are less problematic with higher parameterised diffusion, although some supercooling artifacts persist. Spurious supercooling was eliminated by adding flux limiters to the upwind third-order scheme. We present this comparison as evidence of the problematic nature of oscillatory advection schemes in sea ice formation regions, and urge other ocean/sea-ice modellers to exercise caution when using such schemes.
Numerical study of MHD supersonic flow control
Ryakhovskiy, A. I.; Schmidt, A. A.
2017-11-01
Supersonic MHD flow around a blunted body with a constant external magnetic field has been simulated for a number of geometries as well as a range of the flow parameters. Solvers based on Balbas-Tadmor MHD schemes and HLLC-Roe Godunov-type method have been developed within the OpenFOAM framework. The stability of the solution varies depending on the intensity of magnetic interaction The obtained solutions show the potential of MHD flow control and provide insights into for the development of the flow control system. The analysis of the results proves the applicability of numerical schemes, that are being used in the solvers. A number of ways to improve both the mathematical model of the process and the developed solvers are proposed.
Supertasks and Numeral Systems
Rizza, Davide
2016-01-01
Physical supertasks are completed, infinite sequences of events or interactions that occur within a finite amount of time. Examples thereof have been constructed to show that infinite physical systems may violate conservation laws. It is shown in this paper that this conclusion may be critically sensitive to a selection of numeral system. Weaker numeral systems generate physical reports whose inaccuracy simulates the violation of a conservation law. Stronger numeral systems can confirm this e...
Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation
Directory of Open Access Journals (Sweden)
Yuxin Zhang
2014-01-01
scheme is unconditionally stable, and convergence order is O(τ+h4, where τ and h are the temporal and spatial step sizes, respectively. Finally, numerical results are given to confirm the theoretical analysis.
Supertasks and numeral systems
Rizza, Davide
2016-10-01
Physical supertasks are completed, infinite sequences of events or interactions that occur within a finite amount of time. Examples thereof have been constructed to show that infinite physical systems may violate conservation laws. It is shown in this paper that this conclusion may be critically sensitive to a selection of numeral system. Weaker numeral systems generate physical reports whose inaccuracy simulates the violation of a conservation law. Stronger numeral systems can confirm this effect by allowing a direct computation of the quantities conserved. The supertasks presented in [2], [4] are used to illustrate this phenomenon from the point of view of the new numeral system introduced in [6].
Numerical methods using Matlab
Lindfield, George
2012-01-01
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use
Sensitivity of Forecast Skill to Different Objective Analysis Schemes
Baker, W. E.
1979-01-01
Numerical weather forecasts are characterized by rapidly declining skill in the first 48 to 72 h. Recent estimates of the sources of forecast error indicate that the inaccurate specification of the initial conditions contributes substantially to this error. The sensitivity of the forecast skill to the initial conditions is examined by comparing a set of real-data experiments whose initial data were obtained with two different analysis schemes. Results are presented to emphasize the importance of the objective analysis techniques used in the assimilation of observational data.
Iterative Schemes for Time Parallelization with Application to Reservoir Simulation
Energy Technology Data Exchange (ETDEWEB)
Garrido, I; Fladmark, G E; Espedal, M S; Lee, B
2005-04-18
Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution. But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods. In this paper, they present several such algorithms that actually exploit the sequential nature of time evolution through a predictor-corrector procedure. This sequentialness ensures convergence of a parallel predictor-corrector scheme within a fixed number of iterations. The performance of these novel algorithms, which are derived from the classical alternating Schwarz method, are illustrated through several numerical examples using the reservoir simulator Athena.
Modified unified kinetic scheme for all flow regimes.
Liu, Sha; Zhong, Chengwen
2012-06-01
A modified unified kinetic scheme for the prediction of fluid flow behaviors in all flow regimes is described. The time evolution of macrovariables at the cell interface is calculated with the idea that both free transport and collision mechanisms should be considered. The time evolution of macrovariables is obtained through the conservation constraints. The time evolution of local Maxwellian distribution is obtained directly through the one-to-one mapping from the evolution of macrovariables. These improvements provide more physical realities in flow behaviors and more accurate numerical results in all flow regimes especially in the complex transition flow regime. In addition, the improvement steps introduce no extra computational complexity.
Improved Load Shedding Scheme considering Distributed Generation
DEFF Research Database (Denmark)
Das, Kaushik; Nitsas, Antonios; Altin, Müfit
2017-01-01
With high penetration of distributed generation (DG), the conventional under-frequency load shedding (UFLS) face many challenges and may not perform as expected. This article proposes new UFLS schemes, which are designed to overcome the shortcomings of traditional load shedding scheme. These sche......With high penetration of distributed generation (DG), the conventional under-frequency load shedding (UFLS) face many challenges and may not perform as expected. This article proposes new UFLS schemes, which are designed to overcome the shortcomings of traditional load shedding scheme....... These schemes utilize directional relays, power flow through feeders, wind and PV measurements to optimally select the feeders to be disconnected during load shedding such that DG disconnection is minimized while disconnecting required amount of consumption. These different UFLS schemes are compared in terms...
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-07
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
Resonance ionization scheme development for europium
Chrysalidis, K; Fedosseev, V N; Marsh, B A; Naubereit, P; Rothe, S; Seiffert, C; Kron, T; Wendt, K
2017-01-01
Odd-parity autoionizing states of europium have been investigated by resonance ionization spectroscopy via two-step, two-resonance excitations. The aim of this work was to establish ionization schemes specifically suited for europium ion beam production using the ISOLDE Resonance Ionization Laser Ion Source (RILIS). 13 new RILIS-compatible ionization schemes are proposed. The scheme development was the first application of the Photo Ionization Spectroscopy Apparatus (PISA) which has recently been integrated into the RILIS setup.
Resonance ionization scheme development for europium
Energy Technology Data Exchange (ETDEWEB)
Chrysalidis, K., E-mail: katerina.chrysalidis@cern.ch; Goodacre, T. Day; Fedosseev, V. N.; Marsh, B. A. [CERN (Switzerland); Naubereit, P. [Johannes Gutenberg-Universität, Institiut für Physik (Germany); Rothe, S.; Seiffert, C. [CERN (Switzerland); Kron, T.; Wendt, K. [Johannes Gutenberg-Universität, Institiut für Physik (Germany)
2017-11-15
Odd-parity autoionizing states of europium have been investigated by resonance ionization spectroscopy via two-step, two-resonance excitations. The aim of this work was to establish ionization schemes specifically suited for europium ion beam production using the ISOLDE Resonance Ionization Laser Ion Source (RILIS). 13 new RILIS-compatible ionization schemes are proposed. The scheme development was the first application of the Photo Ionization Spectroscopy Apparatus (PISA) which has recently been integrated into the RILIS setup.
SIGNCRYPTION BASED ON DIFFERENT DIGITAL SIGNATURE SCHEMES
Adrian Atanasiu; Laura Savu
2012-01-01
This article presents two new signcryption schemes. The first one is based on Schnorr digital signature algorithm and the second one is using Proxy Signature scheme introduced by Mambo. Schnorr Signcryption has been implemented in a program and here are provided the steps of the algorithm, the results and some examples. The Mambo’s Proxy Signature is adapted for Shortened Digital Signature Standard, being part of a new Proxy Signcryption scheme.
Optics design for CEPC double ring scheme
Wang, Yiwei; Su, Feng; Bai, Sha; Yu, Chenghui; Gao, Jie
2017-12-01
The CEPC is a future Circular Electron and Positron Collider proposed by China to mainly study the Higgs boson. Its baseline design is a double ring scheme and an alternative design is a partial double ring scheme. This paper will present the optics design for the main ring of the double ring scheme. The CEPC will also work as a W and Z factory. Compatible optics designs for a W and a Z modes will be presented as well.
Wavelet Denoising within the Lifting Scheme Framework
Directory of Open Access Journals (Sweden)
M. P. Paskaš
2012-11-01
Full Text Available In this paper, we consider an example of the lifting scheme and present the results of the simple lifting scheme implementation using lazy transform. The paper is tutorial-oriented. The results are obtained by testing several common test signals for the signal denoising problem and using different threshold values. The lifting scheme represents an effective and flexible tool that can be used for introducing signal dependence into the problem by improving the wavelet properties.
Numerical treatment of interfaces for second-order wave equations
Cécere, Mariana; Reula, Oscar
2011-01-01
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. In the spirit of the Simultaneous Approximation Term (SAT) schemes introduced in \\cite{Carpenter1999341}, information is passed among grids using the values of the fields only at the contact points between them (actually, in our case, just the values of the field corresponding to the time derivative of the field). The scheme seems to be as accurate as the space and time discretizations used for the corresponding derivatives. The semi-discrete approximation preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge-Kutta method. This is crucial for, otherwise, the methods will be impractical given the severe restrictions its stiff parts would put on totally explicit integrators.
On the numerical stability for some symplectic integrators
Liu, F. Y.; Wu, X.; Lu, B. K.
2006-10-01
This research deals mainly with an analysis of the linear stability of several symplectic integrators for a linear Hamiltonian system, which involve the first-order implicit symplectic Euler scheme, the second-order implicit centered Euler difference scheme, the first-order explicit symplectic Euler scheme and the second-order explicit leapfrog symplectic integrator. Meantime, a stable region for each integrator is found. The fact is also checked by numerical tests. Especially for a system with a real symmetric quadratic form, a simpler way to study the numerical stability is to use diagonalizing transformations. As an emphasis, a rather larger stable time step of each algorithm is admissible for either a linear or nonlinear system with integrable separations of one main piece and another petty piece rather than a kinetic energy and a potential energy.
Numerical simulations and mathematical models of flows in complex geometries
DEFF Research Database (Denmark)
Hernandez Garcia, Anier
The research work of the present thesis was mainly aimed at exploiting one of the strengths of the Lattice Boltzmann methods, namely, the ability to handle complicated geometries to accurately simulate flows in complex geometries. In this thesis, we perform a very detailed theoretical analysis...... and through the Chapman-Enskog multi-scale expansion technique the dependence of the kinetic viscosity on each scheme is investigated. Seeking for optimal numerical schemes to eciently simulate a wide range of complex flows a variant of the finite element, off-lattice Boltzmann method [5], which uses...... the characteristic based integration is also implemented. Using the latter scheme, numerical simulations are conducted in flows of different complexities: flow in a (real) porous network and turbulent flows in ducts with wall irregularities. From the simulations of flows in porous media driven by pressure gradients...
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano
2017-03-22
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
THEORETICAL AND NUMERICAL OBSERVABILITY OF THE BRESSE BEAM
El Arwadi, Toufic; Youssef, Wael; Wehbeh, Ali
2017-01-01
The aim of this paper is to study the observability of the elastic type of Bresse systems in one-dimensional bounded domain. We rst study the observability of this systems by observing the displacement. The multiplier techniques are applied. In numerical point vue, an implicit Euler scheme is proposed and studied. This allow us to introduce a discrete observability.
A Numerical Study of Reaction Kinetics Model of Polymerization In ...
African Journals Online (AJOL)
The model which is a system of partial differential equations is analyzed numerically using the finite difference scheme to obtain results for1, 2, 3, 4, 10, 100, 1000 (where p is the order of reaction). Keywords: Frontal polymerization, Material diffusion. Journal of the Nigerian Association of Mathematical Physics, Volume 19 ...
Mixed ultrasoft/norm-conserved pseudopotential scheme
DEFF Research Database (Denmark)
Stokbro, Kurt
1996-01-01
A variant of the Vanderbilt ultrasoft pseudopotential scheme, where the norm conservation is released for only one or a few angular channels, is presented. Within this scheme some difficulties of the truly ultrasoft pseudopotentials are overcome without sacrificing the pseudopotential softness. (i......) Ghost states are easily avoided without including semicore shells. (ii) The ultrasoft pseudo-charge-augmentation functions can be made softer. (iii) The number of nonlocal operators is reduced. The scheme will be most useful for transition metals, and the feasibility and accuracy of the scheme...
Numerical Investigation of a Model Scramjet Combustor Using DDES
Shin, Junsu; Sung, Hong-Gye
2017-04-01
Non-reactive flows moving through a model scramjet were investigated using a delayed detached eddy simulation (DDES), which is a hybrid scheme combining Reynolds averaged Navier-Stokes scheme and a large eddy simulation. The three dimensional Navier-Stokes equations were solved numerically on a structural grid using finite volume methods. An in-house was developed. This code used a monotonic upstream-centered scheme for conservation laws (MUSCL) with an advection upstream splitting method by pressure weight function (AUSMPW+) for space. In addition, a 4th order Runge-Kutta scheme was used with preconditioning for time integration. The geometries and boundary conditions of a scramjet combustor operated by DLR, a German aerospace center, were considered. The profiles of the lower wall pressure and axial velocity obtained from a time-averaged solution were compared with experimental results. Also, the mixing efficiency and total pressure recovery factor were provided in order to inspect the performance of the combustor.
Numerical Modelling of Streams
DEFF Research Database (Denmark)
Vestergaard, Kristian
In recent years there has been a sharp increase in the use of numerical water quality models. Numeric water quality modeling can be divided into three steps: Hydrodynamic modeling for the determination of stream flow and water levels. Modelling of transport and dispersion of a conservative dissol...... dissolved substance. Modeling of chemical and biological turnover of substances....
Analysis of a HMM time-discretization scheme for a system of Stochastic PDE's
Bréhier, Charles-Edouard
2012-01-01
International audience; We consider the discretization in time of a system of parabolic stochastic partial differential equations with slow and fast components; the fast equation is driven by an additive space-time white noise. The numerical method is inspired by the Averaging Principle satisfied by this system, and fits to the framework of Heterogeneous Multiscale Methods.The slow and the fast components are approximated with two coupled numerical semi-implicit Euler schemes depending on two...
Wu, Hai-Dan; Zhou, Tao
2017-11-01
We propose theoretically an effective scheme for braiding Majorana bound states by manipulating the point potential. The vortex pinning effect is carefully elucidated. This effect can be used to control the vortices and Majorana bound states in topological superconductors. The exchange of two vortices induced by moving the potentials is simulated numerically. The zero-energy state in the vortex core is robust with respect to the strength of the potential. The Majorana bound states in a pinned vortex are identified numerically.
Numerical Verification of Industrial Numerical Codes
Directory of Open Access Journals (Sweden)
Montan Sethy
2012-04-01
Full Text Available Several approximations occur during a numerical simulation: physical effects mapy be discarded, continuous functions replaced by discretized ones and real numbers replaced by finite-precision representations. The use of the floating point arithmetic generates round-off errors at each arithmetical expression and some mathematical properties are lost. The aim of the numerical verification activity at EDF R&D is to study the effect of the round-off error propagation on the results of a numerical simulation. It is indeed crucial to perform a numerical verification of industrial codes such as developped at EDF R&D even more for code running in HPC environments. This paper presents some recent studies around the numerical verification at EDF R&D. Le résultat d’un code de simulation numérique subit plusieurs approximations effectuées lors de la modélisation mathématique du problème physique, de la discrétisation du modèle mathématique et de la résolution numérique en arithmétique flottante. L’utilisation de l’arithmétique flottante génère en effet des erreurs d’arrondi lors de chaque opération flottante et des propriétés mathématiques sont perdues. Il existe à EDF R&D une activité transverse de vérification numérique consistant à étudier l’effet de la propagation des erreurs d’arrondi sur les résultats des simulations. Il est en effet important de vérifier numériquement des codes industriels et ce d’autant plus s’ils sont éxécutés dans environnements de calcul haute performance. Ce papier présente des études récentes autour de la vérification numérique à EDF R&D.
Arakawa, A.; Lamb, V. R.
1979-01-01
A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.
Pötz, Walter
2017-11-01
A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.
DEFF Research Database (Denmark)
Henriquez, Vicente Cutanda
This thesis describes the development of a numerical model of the propagation of sound waves in fluids with viscous and thermal losses, with application to the simulation of acoustic transducers, in particular condenser microphones for measurement. The theoretical basis is presented, numerical...... with very close surfaces, as found in condenser microphones, where the membrane has a backplate very close behind. This improvement could be useful for many other problems where the BEM is applied. The numerical implementation that includes both viscous and thermal effects is then worked out. Some numerical...... that are allowable in this case: linear variations, absence of flow, harmonic time variation, thermodynamical equilibrium and physical dimensions much larger than the molecular mean free path. A formulation of the BEM is also developed with an improvement designed to cope with the numerical difficulty associated...
Convergence of the Graph Allen-Cahn Scheme
Luo, Xiyang; Bertozzi, Andrea L.
2017-05-01
The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The diffuse interface model is widely used for modeling in material science, and can also be used as a proxy to total variation minimization. In Bertozzi and Flenner (Multiscale Model Simul 10(3):1090-1118, 2012), an algorithm was developed to generalize the diffuse interface model to graphs to solve the graph cut problem. This work analyzes the conditions for the graph diffuse interface algorithm to converge. Using techniques from numerical PDE and convex optimization, monotonicity in function value and convergence under an a posteriori condition are shown for a class of schemes under a graph-independent stepsize condition. We also generalize our results to incorporate spectral truncation, a common technique used to save computation cost, and also to the case of multiclass classification. Various numerical experiments are done to compare theoretical results with practical performance.
Upscaling scheme for long-term ion diffusion in charged porous media
Yang, Yuankai; Wang, Moran
2017-08-01
Description of long-term (over years) ion diffusion at the pore scale is a huge challenge since the characteristic time of diffusion in a typical representative elementary volume is around microseconds, generally ten orders of magnitude lower than the time we were concerned with. This paper presents a numerical upscaling scheme for ion diffusion with electrical double-layer effects (electrodiffusion) considered in charged porous media. After a scaling analysis for the nondimensional governing equations of ion transport at the pore scale, we identify the conditions for decoupling of electrical effect and diffusion, and therefore are able to choose apposite temporal and spatial scales for corresponding directions of the electrodiffusion process. The upscaling scheme is therefore proposed based on a numerical framework for governing equations using a lattice Boltzmann method. The electrical potential or concentration profiles from steady- or unsteady-state electrodiffusion in the long, straight channel, calculated by this upscaling scheme, are compared with the well-meshed full-sized simulations with good agreement. Furthermore, this scheme is used to predict tracer-ion throughdiffusion and outdiffusion in hardened cement pastes. All numerical results show good agreement with the full-sized simulations or experiment data without any fitting parameters. This upscaling scheme bridges the ion diffusion behaviors in different time scales, and may help to improve the understanding of long-term ion transport mechanisms in charged porous media.
Central upwind scheme for a compressible two-phase flow model.
Directory of Open Access Journals (Sweden)
Munshoor Ahmed
Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.
A new third order finite volume weighted essentially non-oscillatory scheme on tetrahedral meshes
Zhu, Jun; Qiu, Jianxian
2017-11-01
In this paper a third order finite volume weighted essentially non-oscillatory scheme is designed for solving hyperbolic conservation laws on tetrahedral meshes. Comparing with other finite volume WENO schemes designed on tetrahedral meshes, the crucial advantages of such new WENO scheme are its simplicity and compactness with the application of only six unequal size spatial stencils for reconstructing unequal degree polynomials in the WENO type spatial procedures, and easy choice of the positive linear weights without considering the topology of the meshes. The original innovation of such scheme is to use a quadratic polynomial defined on a big central spatial stencil for obtaining third order numerical approximation at any points inside the target tetrahedral cell in smooth region and switch to at least one of five linear polynomials defined on small biased/central spatial stencils for sustaining sharp shock transitions and keeping essentially non-oscillatory property simultaneously. By performing such new procedures in spatial reconstructions and adopting a third order TVD Runge-Kutta time discretization method for solving the ordinary differential equation (ODE), the new scheme's memory occupancy is decreased and the computing efficiency is increased. So it is suitable for large scale engineering requirements on tetrahedral meshes. Some numerical results are provided to illustrate the good performance of such scheme.
On the modelling of compressible inviscid flow problems using AUSM schemes
Directory of Open Access Journals (Sweden)
Hajžman M.
2007-11-01
Full Text Available During last decades, upwind schemes have become a popular method in the field of computational fluid dynamics. Although they are only first order accurate, AUSM (Advection Upstream Splitting Method schemes proved to be well suited for modelling of compressible flows due to their robustness and ability of capturing shock discontinuities. In this paper, we review the composition of the AUSM flux-vector splitting scheme and its improved version noted AUSM+, proposed by Liou, for the solution of the Euler equations. Mach number splitting functions operating with values from adjacent cells are used to determine numerical convective fluxes and pressure splitting is used for the evaluation of numerical pressure fluxes. Both versions of the AUSM scheme are applied for solving some test problems such as one-dimensional shock tube problem and three dimensional GAMM channel. Features of the schemes are discussed in comparison with some explicit central schemes of the first order accuracy (Lax-Friedrichs and of the second order accuracy (MacCormack.
A gradient stable scheme for a phase field model for the moving contact line problem
Gao, Min
2012-02-01
In this paper, an efficient numerical scheme is designed for a phase field model for the moving contact line problem, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition [1,2,4]. The nonlinear version of the scheme is semi-implicit in time and is based on a convex splitting of the Cahn-Hilliard free energy (including the boundary energy) together with a projection method for the Navier-Stokes equations. We show, under certain conditions, the scheme has the total energy decaying property and is unconditionally stable. The linearized scheme is easy to implement and introduces only mild CFL time constraint. Numerical tests are carried out to verify the accuracy and stability of the scheme. The behavior of the solution near the contact line is examined. It is verified that, when the interface intersects with the boundary, the consistent splitting scheme [21,22] for the Navier Stokes equations has the better accuracy for pressure. © 2011 Elsevier Inc.
White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.
2012-01-01
The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.
A subtraction scheme for double-real radiation at NNLO
Energy Technology Data Exchange (ETDEWEB)
Heymes, David; Czakon, Michal [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany)
2013-07-01
Higher order perturbative calculations for QCD observables are indispensable to make precise predictions for the LHC. In each part of the calculation unphysical infrared divergences appear that cancel between real and virtual corrections to the cross section. While at next-to-leading order (NLO) general algorithms exist to subtract these singularities, further difficulties arise at next-to-next-to-leading order (NNLO) accuracy. A trivial generalization to this case is not possible. We present STRIPPER, a subtraction scheme for real radiation at NNLO. The main idea is to split the double-real radiation phase-space into sectors to obtain a Laurent series in the dimensional regulator ε. The coefficients can be integrated numerically. This is achieved by parameterizing each sector adequately as well as exploiting the universal soft and collinear factorization properties of QCD tree-level matrix elements. This subtraction scheme can be implemented in the t'Hooft-Veltman regularization scheme, which is discussed in this presentation.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Kumar, Vivek; Raghurama Rao, S. V.
2008-04-01
Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally
Finite difference Hermite WENO schemes for the Hamilton-Jacobi equations
Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian
2017-05-01
In this paper, a new type of finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes are constructed for solving Hamilton-Jacobi (HJ) equations. Point values of both the solution and its first derivatives are used in the HWENO reconstruction and evolved via time advancing. While the evolution of the solution is still through the classical numerical fluxes to ensure convergence to weak solutions, the evolution of the first derivatives of the solution is through a simple dimension-by-dimension non-conservative procedure to gain efficiency. The main advantages of this new scheme include its compactness in the spatial field and its simplicity in the reconstructions. Extensive numerical experiments in one and two dimensional cases are performed to verify the accuracy, high resolution and efficiency of this new scheme.
CSIR Research Space (South Africa)
Jovanovic, Nebo
2017-01-01
Full Text Available The Atlantis Water Supply Scheme (AWSS, Western Cape, South Africa) has been in operation for about 40 years as a means to supply and augment drinking water to the town of Atlantis via managed aquifer recharge (MAR). In this study, the numerical...
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi
2010-08-01
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.
Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
Directory of Open Access Journals (Sweden)
Walter H. Aschbacher
2009-01-01
Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.
Optimization of pumping schemes for 160-Gb/s single channel Raman amplified systems
DEFF Research Database (Denmark)
Xu, Lin; Rottwitt, Karsten; Peucheret, Christophe
2004-01-01
Three different distributed Raman amplification schemes-backward pumping, bidirectional pumping, and second-order pumping-are evaluated numerically for 160-Gb/s single-channel transmission. The same longest transmission distance of 2500 km is achieved for all three pumping methods with a 105-km...
Chai, Zhenhua; Zhao, T S
2014-07-01
In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.
Privacy Preserving Mapping Schemes Supporting Comparison
Tang, Qiang
2010-01-01
To cater to the privacy requirements in cloud computing, we introduce a new primitive, namely Privacy Preserving Mapping (PPM) schemes supporting comparison. An PPM scheme enables a user to map data items into images in such a way that, with a set of images, any entity can determine the <, =, >
Sampling scheme optimization from hyperspectral data
Debba, P.
2006-01-01
This thesis presents statistical sampling scheme optimization for geo-environ-menta] purposes on the basis of hyperspectral data. It integrates derived products of the hyperspectral remote sensing data into individual sampling schemes. Five different issues are being dealt with.First, the optimized
Consolidation of the health insurance scheme
Association du personnel
2009-01-01
In the last issue of Echo, we highlighted CERN’s obligation to guarantee a social security scheme for all employees, pensioners and their families. In that issue we talked about the first component: pensions. This time we shall discuss the other component: the CERN Health Insurance Scheme (CHIS).
A hierarchical classification scheme of psoriasis images
DEFF Research Database (Denmark)
Maletti, Gabriela Mariel; Ersbøll, Bjarne Kjær
2003-01-01
A two-stage hierarchical classification scheme of psoriasis lesion images is proposed. These images are basically composed of three classes: normal skin, lesion and background. The scheme combines conventional tools to separate the skin from the background in the first stage, and the lesion from...
Mobile Machine for E-payment Scheme
Sattar J Aboud
2010-01-01
In this article e-payment scheme by mobile machine is considered. The requirements for a mobile machine in e-payment are presented, particularly when merchant employing accounts for payments and when using advertising. In the proposed scheme we will use the public key infrastructure and certificate for authenticate purchaser and merchant and to secure the communication between them.
THROUGHPUT ANALYSIS OF EXTENDED ARQ SCHEMES
African Journals Online (AJOL)
PUBLICATIONS1
formation transmitted in digital communication systems. Such schemes ... Department of Electronics and Telecommunications Engineering,. University of Dar es ...... (2): 165-176. Kundaeli, H. N. (2013). Throughput-Delay. Analysis of the SR-ST-GBN ARQ Scheme. Mediterranean Journal of Electronics and. Communication.
Ziegler, Gerhard
2011-01-01
Distance protection provides the basis for network protection in transmission systems and meshed distribution systems. This book covers the fundamentals of distance protection and the special features of numerical technology. The emphasis is placed on the application of numerical distance relays in distribution and transmission systems.This book is aimed at students and engineers who wish to familiarise themselves with the subject of power system protection, as well as the experienced user, entering the area of numerical distance protection. Furthermore it serves as a reference guide for s
Singh, Devraj
2015-01-01
Numerical Problems in Physics, Volume 1 is intended to serve the need of the students pursuing graduate and post graduate courses in universities with Physics and Materials Science as subject including those appearing in engineering, medical, and civil services entrance examinations. KEY FEATURES: * 29 chapters on Optics, Wave & Oscillations, Electromagnetic Field Theory, Solid State Physics & Modern Physics * 540 solved numerical problems of various universities and ompetitive examinations * 523 multiple choice questions for quick and clear understanding of subject matter * 567 unsolved numerical problems for grasping concepts of the various topic in Physics * 49 Figures for understanding problems and concept
Numerical Solution of Turbulence Problems by Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Alicia Cordero
2015-05-01
Full Text Available In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.
Numerical simulation of fractional Cable equation of spiny neuronal dendrites.
Sweilam, N H; Khader, M M; Adel, M
2014-03-01
In this article, numerical study for the fractional Cable equation which is fundamental equations for modeling neuronal dynamics is introduced by using weighted average of finite difference methods. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. A simple and an accurate stability criterion valid for different discretization schemes of the fractional derivative and arbitrary weight factor is introduced and checked numerically. Numerical results, figures, and comparisons have been presented to confirm the theoretical results and efficiency of the proposed method.
Numerical simulation of fractional Cable equation of spiny neuronal dendrites
Directory of Open Access Journals (Sweden)
N.H. Sweilam
2014-03-01
Full Text Available In this article, numerical study for the fractional Cable equation which is fundamental equations for modeling neuronal dynamics is introduced by using weighted average of finite difference methods. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. A simple and an accurate stability criterion valid for different discretization schemes of the fractional derivative and arbitrary weight factor is introduced and checked numerically. Numerical results, figures, and comparisons have been presented to confirm the theoretical results and efficiency of the proposed method.
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
Energy Technology Data Exchange (ETDEWEB)
FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory
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.
NUMERICAL SIMULATION OF SHOCK WAVE REFRACTION ON INCLINED CONTACT DISCONTINUITY
Directory of Open Access Journals (Sweden)
P. V. Bulat
2016-05-01
Full Text Available We consider numerical simulation of shock wave refraction on plane contact discontinuity, separating two gases with different density. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes, implemented on unstructured meshes. Integration over time is performed with the use of the third-order Runge–Kutta stepping procedure. The procedure of identification and classification of gas dynamic discontinuities based on conditions of dynamic consistency and image processing methods is applied to visualize and interpret the results of numerical calculations. The flow structure and its quantitative characteristics are defined. The results of numerical and experimental visualization (shadowgraphs, schlieren images, and interferograms are compared.
An information-guided channel-hopping scheme for block-fading channels with estimation errors
Yang, Yuli
2010-12-01
Information-guided channel-hopping technique employing multiple transmit antennas was previously proposed for supporting high data rate transmission over fading channels. This scheme achieves higher data rates than some mature schemes, such as the well-known cyclic transmit antenna selection and space-time block coding, by exploiting the independence character of multiple channels, which effectively results in having an additional information transmitting channel. Moreover, maximum likelihood decoding may be performed by simply decoupling the signals conveyed by the different mapping methods. In this paper, we investigate the achievable spectral efficiency of this scheme in the case of having channel estimation errors, with optimum pilot overhead for minimum meansquare error channel estimation, when transmitting over blockfading channels. Our numerical results further substantiate the robustness of the presented scheme, even with imperfect channel state information. ©2010 IEEE.
Bates, Alice P; Kennedy, Rodney A
2015-01-01
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.
An almost symmetric Strang splitting scheme for nonlinear evolution equations.
Einkemmer, Lukas; Ostermann, Alexander
2014-07-01
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.
A Variable Frequency Tuning Scheme for Inductive Plasma Sources
Niazi, Kaveh; Chen, Zhan; Karpenko, Oleh
2003-10-01
A common approach for the efficient coupling of RF power to an inductive plasma source consists of a matching network with variable capacitive components that adjust in response to the varying load conditions of the plasma source. The use of variable capacitances in industrial applications such as semiconductor equipment is non-trivial, however. The high voltage ratings often required for semiconductor equipment result in capacitors that are expensive and quite bulky. In addition the motors that are used to adjust the capacitances often have a slower response time than desired. An alternate approach, the use of fixed capacitors and a variable frequency source signal to reduce the reflection coefficient, ñ, to an acceptable level, addresses both these concerns and is discussed in this paper. By using a circuit model for the plasma source and matching network, it is possible to predict an optimal frequency and corresponding reflection coefficient for a given plasma load condition. In this paper numerical predictions of the reflection coefficient for the variable frequency matching scheme are presented for common inductive plasma source impedance parameters. In addition if the limits on the allowed VSWR and the plasma source impedance are specified, the numerical model presented provides a simple scheme for specifying the required frequency range and fixed capacitance values for the matching network.
Generating Unstable Resonances for Extraction Schemes Based on Transverse Splitting
Giovannozzi, M; Turchetti, G
2009-01-01
A few years ago, a novel multi-turn extraction scheme was proposed, based on particle trapping inside stable resonances. Numerical simulations and experimental tests have confirmed the feasibility of such a scheme for low order resonances. While the third-order resonance is generically unstable and those higher than fourth-order are generically stable, the fourth-order resonance can be either stable or unstable depending on the specifics of the system under consideration. By means of the Normal Form a general approach to control the stability of the fourth-order resonance has been derived. This approach is based on the control of the amplitude detuning and the general form for a lattice with an arbitrary number of sextupole and octupole families is derived in this paper. Numerical simulations have confirmed the analytical results and have shown that, when crossing the unstable fourth-order resonance, the region around the centre of the phase space is depleted and particles are trapped in only the four stable ...
Numerical Simulation of Oil Spill in Ocean
Directory of Open Access Journals (Sweden)
Yong-Sik Cho
2012-01-01
Full Text Available The spreading of oil in an open ocean may cause serious damage to a marine environmental system. Thus, an accurate prediction of oil spill is very important to minimize coastal damage due to unexpected oil spill accident. The movement of oil may be represented with a numerical model that solves an advection-diffusion-reaction equation with a proper numerical scheme. In this study, the spilled oil dispersion model has been established in consideration of tide and tidal currents simultaneously. The velocity components in the advection-diffusion-reaction equation are obtained from the shallow-water equations. The accuracy of the model is verified by applying it to a simple but significant problem. The results produced by the model agree with corresponding analytical solutions and field-observed data. The model is then applied to predict the spreading of an oil spill in a real coastal environment.
Numerical modeling process of embolization arteriovenous malformation
Cherevko, A. A.; Gologush, T. S.; Petrenko, I. A.; Ostapenko, V. V.
2017-10-01
Cerebral arteriovenous malformation is a difficult, dangerous, and most frequently encountered vascular failure of development. It consists of vessels of very small diameter, which perform a discharge of blood from the artery to the vein. In this regard it can be adequately modeled using porous medium. Endovascular embolization of arteriovenous malformation is effective treatment of such pathologies. However, the danger of intraoperative rupture during embolization still exists. The purpose is to model this process and build an optimization algorithm for arteriovenous malformation embolization. To study the different embolization variants, the initial-boundary value problems, describing the process of embolization, were solved numerically by using a new modification of CABARET scheme. The essential moments of embolization process were modeled in our numerical experiments. This approach well reproduces the essential features of discontinuous two-phase flows, arising in the embolization problems. It can be used for further study on the process of embolization.
Numerical optimization design by computational fluid dynamics
Energy Technology Data Exchange (ETDEWEB)
Lee, J.W.; Moon, Y.J. [Korea University, Seoul (Korea, Republic of)
1996-07-01
Purpose of the present study is to develop a computational design program for shape optimization, combining the numerical optimization technique with the flow analysis code. The present methodology is then validated in three cases of aerodynamic shape optimization. In the numerical optimization, a feasible direction optimization algorithm and shape functions are considered. In the flow analysis, the Navier-Stokes equations are discretized by a cell-centered finite volume method, and Roe`s flux difference splitting TVD scheme and ADI method are used. The developed design code is applied to a transonic channel flow over a bump, and an external flow over a NACA0012 airfoil to minimize the wave drag induced by shock waves. Also a separated subsonic flow over a NACA0024 airfoil is considered to determine a maximum allowable thickness of the airfoil without separation. (author). 7 refs., 17 figs.
7th International Conference on Hyperbolic Problems Theory, Numerics, Applications
Jeltsch, Rolf
1999-01-01
These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phe...
Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion
Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun
2016-05-01
Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion.
A Hybrid Cooperative Coding Scheme for the Relay-Eavesdropper Channel
Directory of Open Access Journals (Sweden)
Peng Xu
2014-03-01
Full Text Available This paper considers the four-node relay-eavesdropper channel, where a relay node helps the source to send secret messages to the destination in the presence of a passive eavesdropper. For the discrete memoryless case, we propose a hybrid cooperative coding scheme, which is based on the combination of the partial decode-forward scheme, the noise-forward scheme and the random binning scheme. The key feature of the proposed hybrid cooperative scheme is that the relay integrates the explicit cooperation strategy and the implicit cooperation strategy by forwarding source messages and additional interference at the same time. The derived achievable secrecy rate shows that some existing works can be viewed as special cases of the proposed scheme. Then, the achievable secrecy rate is extended to the Gaussian channel based on Gaussian codebooks, and the optimal power policy is also identified in the high power region. Both the analysis and numerical results are provided to demonstrate that the proposed hybrid cooperative coding scheme outperforms the comparable ones, especially in the high power region.
Joint multiuser switched diversity and adaptive modulation schemes for spectrum sharing systems
Qaraqe, Marwa
2012-12-01
In this paper, we develop multiuser access schemes for spectrum sharing systems whereby secondary users are allowed to share the spectrum with primary users under the condition that the interference observed at the primary receiver is below a predetermined threshold. In particular, we devise two schemes for selecting a user among those that satisfy the interference constraint and achieve an acceptable signal-to-noise ratio level. The first scheme selects the user that reports the best channel quality. In order to alleviate the high feedback load associated with the first scheme, we develop a second scheme based on the concept of switched diversity where the base station scans the users in a sequential manner until an acceptable user is found. In addition to these two selection schemes, we consider two power adaptive settings at the secondary users based on the amount of interference available at the secondary transmitter. In the On/Off power setting, users are allowed to transmit based on whether the interference constraint is met or not, while in the full power adaptive setting, the users are allowed to vary their transmission power to satisfy the interference constraint. Finally, we present numerical results for our proposed algorithms where we show the trade-off between the average spectral efficiency and average feedback load for both schemes. © 2012 IEEE.
Directory of Open Access Journals (Sweden)
Chenyu Wang
2017-12-01
Full Text Available As an essential part of Internet of Things (IoT, wireless sensor networks (WSNs have touched every aspect of our lives, such as health monitoring, environmental monitoring and traffic monitoring. However, due to its openness, wireless sensor networks are vulnerable to various security threats. User authentication, as the first fundamental step to protect systems from various attacks, has attracted much attention. Numerous user authentication protocols armed with formal proof are springing up. Recently, two biometric-based schemes were proposed with confidence to be resistant to the known attacks including offline dictionary attack, impersonation attack and so on. However, after a scrutinization of these two schemes, we found them not secure enough as claimed, and then demonstrated that these schemes suffer from various attacks, such as offline dictionary attack, impersonation attack, no user anonymity, no forward secrecy, etc. Furthermore, we proposed an enhanced scheme to overcome the identified weaknesses, and proved its security via Burrows–Abadi–Needham (BAN logic and the heuristic analysis. Finally, we compared our scheme with other related schemes, and the results showed the superiority of our scheme.
Wang, Chenyu; Xu, Guoai; Sun, Jing
2017-12-19
As an essential part of Internet of Things (IoT), wireless sensor networks (WSNs) have touched every aspect of our lives, such as health monitoring, environmental monitoring and traffic monitoring. However, due to its openness, wireless sensor networks are vulnerable to various security threats. User authentication, as the first fundamental step to protect systems from various attacks, has attracted much attention. Numerous user authentication protocols armed with formal proof are springing up. Recently, two biometric-based schemes were proposed with confidence to be resistant to the known attacks including offline dictionary attack, impersonation attack and so on. However, after a scrutinization of these two schemes, we found them not secure enough as claimed, and then demonstrated that these schemes suffer from various attacks, such as offline dictionary attack, impersonation attack, no user anonymity, no forward secrecy, etc. Furthermore, we proposed an enhanced scheme to overcome the identified weaknesses, and proved its security via Burrows-Abadi-Needham (BAN) logic and the heuristic analysis. Finally, we compared our scheme with other related schemes, and the results showed the superiority of our scheme.
Hossain, Md Jahangir
2010-07-01
In our earlier works, we proposed rate adaptive hierarchical modulation-assisted two-best user opportunistic scheduling (TBS) and hybrid two-user scheduling (HTS) schemes. The proposed schemes are innovative in the sense that they include a second user in the transmission opportunistically using hierarchical modulations. As such the frequency of information access of the users increases without any degradation of the system spectral efficiency (SSE) compared to the classical opportunistic scheduling scheme. In this paper, we analyze channel access delay of an incoming packet at the base station (BS) buffer when our proposed TBS and HTS schemes are employed at the BS. Specifically, using a queuing analytic model we derive channel access delay as well as buffer distribution of the packets that wait at BS buffer for down-link (DL) transmission. We compare performance of the TBS and HTS schemes with that of the classical single user opportunistic schemes namely, absolute carrier-to-noise ratio (CNR)-based single user scheduling (ASS) and normalized CNR-based single user scheduling (NSS). For an independent and identically distributed (i.i.d.) fading environment, our proposed scheme can improve packet\\'s access delay performance compared to the ASS. Selected numerical results in an independent but non-identically distributed (i.n.d.) fading environment show that our proposed HTS achieves overall good channel access delay performance. © 2010 IEEE.
Introduction to numerical analysis
Hildebrand, F B
1987-01-01
Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, other topics in lucid presentation. Includes 150 additional problems in this edition. Bibliography.
Introductory numerical analysis
Pettofrezzo, Anthony J
2006-01-01
Written for undergraduates who require a familiarity with the principles behind numerical analysis, this classical treatment encompasses finite differences, least squares theory, and harmonic analysis. Over 70 examples and 280 exercises. 1967 edition.
Farmer, Jeff D.; Powers, Robert A.
2005-01-01
This article describes an exploration activity involving Mayan numerals, which can be adapted by teachers at various levels to help students better understand the concept of place value and appreciate contributions to mathematics made by an indigenous Central American culture.
An implicit evolution scheme for active contours and surfaces based on IIR filtering.
Delibasis, Konstantinos K; Asvestas, Pantelis A; Kechriniotis, Aristides I; Matsopoulos, George K
2014-05-01
In this work, we present an approach for implementing an implicit scheme for the numerical solution of the partial differential equation of the evolution of an active contour/surface. The proposed scheme is applicable to any variant of the traditional active contour (AC), irrespectively of the calculation of the image-based force field and it is readily applicable to explicitly parameterized active surfaces (AS). The proposed approach is formulated as an infinite impulse response (IIR) filtering of the coordinates of the contour/surface points. The poles of the filter are determined by the parameters controlling the shape of the active contour/surface. We show that the proposed IIR-based implicit evolution scheme has very low complexity. Furthermore, the proposed scheme is numerically stable, thus it allows the convergence of the AC/AS with significantly fewer iterations than the explicit evolution scheme. It also possesses the separability property along the two parameters of the AS, thus it may be applied to deformable surfaces, without the need to store and invert large sparse matrices. We implemented the proposed IIR-based implicit evolution scheme in the Vector Field Convolution (VFC) AC/AS using synthetic and clinical volumetric data. We compared the segmentation results with those of the explicit AC/AS evolution, in terms of accuracy and efficiency. Results show that the VFC AC/AS with the proposed IIR-based implicit evolution scheme achieves the same segmentation results with the explicit scheme, with considerably less computation time. Copyright © 2014 Elsevier Ltd. All rights reserved.
Assimilation scheme of the Mediterranean Forecasting System: operational implementation
Directory of Open Access Journals (Sweden)
E. Demirov
2003-01-01
Full Text Available This paper describes the operational implementation of the data assimilation scheme for the Mediterranean Forecasting System Pilot Project (MFSPP. The assimilation scheme, System for Ocean Forecast and Analysis (SOFA, is a reduced order Optimal Interpolation (OI scheme. The order reduction is achieved by projection of the state vector into vertical Empirical Orthogonal Functions (EOF. The data assimilated are Sea Level Anomaly (SLA and temperature profiles from Expandable Bathy Termographs (XBT. The data collection, quality control, assimilation and forecast procedures are all done in Near Real Time (NRT. The OI is used intermittently with an assimilation cycle of one week so that an analysis is produced once a week. The forecast is then done for ten days following the analysis day. The root mean square (RMS between the model forecast and the analysis (the forecast RMS is below 0.7°C in the surface layers and below 0.2°C in the layers deeper than 200 m for all the ten forecast days. The RMS between forecast and initial condition (persistence RMS is higher than forecast RMS after the first day. This means that the model improves forecast with respect to persistence. The calculation of the misfit between the forecast and the satellite data suggests that the model solution represents well the main space and time variability of the SLA except for a relatively short period of three – four weeks during the summer when the data show a fast transition between the cyclonic winter and anti-cyclonic summer regimes. This occurs in the surface layers that are not corrected by our assimilation scheme hypothesis. On the basis of the forecast skill scores analysis, conclusions are drawn about future improvements. Key words. Oceanography; general (marginal and semi-enclosed seas; numerical modeling; ocean prediction
Assimilation scheme of the Mediterranean Forecasting System: operational implementation
Directory of Open Access Journals (Sweden)
E. Demirov
Full Text Available This paper describes the operational implementation of the data assimilation scheme for the Mediterranean Forecasting System Pilot Project (MFSPP. The assimilation scheme, System for Ocean Forecast and Analysis (SOFA, is a reduced order Optimal Interpolation (OI scheme. The order reduction is achieved by projection of the state vector into vertical Empirical Orthogonal Functions (EOF. The data assimilated are Sea Level Anomaly (SLA and temperature profiles from Expandable Bathy Termographs (XBT. The data collection, quality control, assimilation and forecast procedures are all done in Near Real Time (NRT. The OI is used intermittently with an assimilation cycle of one week so that an analysis is produced once a week. The forecast is then done for ten days following the analysis day. The root mean square (RMS between the model forecast and the analysis (the forecast RMS is below 0.7°C in the surface layers and below 0.2°C in the layers deeper than 200 m for all the ten forecast days. The RMS between forecast and initial condition (persistence RMS is higher than forecast RMS after the first day. This means that the model improves forecast with respect to persistence. The calculation of the misfit between the forecast and the satellite data suggests that the model solution represents well the main space and time variability of the SLA except for a relatively short period of three – four weeks during the summer when the data show a fast transition between the cyclonic winter and anti-cyclonic summer regimes. This occurs in the surface layers that are not corrected by our assimilation scheme hypothesis. On the basis of the forecast skill scores analysis, conclusions are drawn about future improvements.
Key words. Oceanography; general (marginal and semi-enclosed seas; numerical modeling; ocean prediction
Numerical computations with GPUs
Kindratenko, Volodymyr
2014-01-01
This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to
Numerical transducer modelling
DEFF Research Database (Denmark)
Cutanda, Vicente
1999-01-01
Numerical modelling is of importance for the design, improvement and study of acoustic transducers such as microphones and accelerometers. Techniques like the boundary element method and the finite element method are the most common supplement to the traditional empirical and analytical approaches...... errors and instabilities in the computations of numerical solutions. An investigation to deal with this narrow-gap problem has been carried out....
Zhang, Xiaoping; Su, Shuai; Wu, Jiming
2017-09-01
We suggest a new positivity-preserving finite volume scheme for anisotropic diffusion problems on arbitrary polygonal grids. The scheme has vertex-centered, edge-midpoint and cell-centered unknowns. The vertex-centered unknowns are primary and have finite volume equations associated with them. The edge-midpoint and cell-centered unknowns are treated as auxiliary ones and are interpolated by the primary unknowns, which makes the final scheme a pure vertex-centered one. Unlike most existing positivity-preserving schemes, the construction of the scheme is based on a special nonlinear two-point flux approximation that has a fixed stencil and does not require the convex decomposition of the co-normal. In order to solve efficiently the nonlinear systems resulting from the nonlinear scheme, Picard method and its Anderson acceleration are discussed. Numerical experiments demonstrate the second-order accuracy and well positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids. The high efficiency of the Anderson acceleration is also shown on reduction of the number of nonlinear iterations. Moreover, the proposed scheme does not have the so-called numerical heat-barrier issue suffered by most existing cell-centered and hybrid schemes. However, further improvements have to be made if the solution is very close to the machine precision and the mesh distortion is very severe.
On Spurious Numerics in Solving Reactive Equations
Kotov, D. V; Yee, H. C.; Wang, W.; Shu, C.-W.
2013-01-01
The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here "coarse grids" means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed.
Optimal Face-Iris Multimodal Fusion Scheme
Directory of Open Access Journals (Sweden)
Omid Sharifi
2016-06-01
Full Text Available Multimodal biometric systems are considered a way to minimize the limitations raised by single traits. This paper proposes new schemes based on score level, feature level and decision level fusion to efficiently fuse face and iris modalities. Log-Gabor transformation is applied as the feature extraction method on face and iris modalities. At each level of fusion, different schemes are proposed to improve the recognition performance and, finally, a combination of schemes at different fusion levels constructs an optimized and robust scheme. In this study, CASIA Iris Distance database is used to examine the robustness of all unimodal and multimodal schemes. In addition, Backtracking Search Algorithm (BSA, a novel population-based iterative evolutionary algorithm, is applied to improve the recognition accuracy of schemes by reducing the number of features and selecting the optimized weights for feature level and score level fusion, respectively. Experimental results on verification rates demonstrate a significant improvement of proposed fusion schemes over unimodal and multimodal fusion methods.
Ponzi scheme diffusion in complex networks
Zhu, Anding; Fu, Peihua; Zhang, Qinghe; Chen, Zhenyue
2017-08-01
Ponzi schemes taking the form of Internet-based financial schemes have been negatively affecting China's economy for the last two years. Because there is currently a lack of modeling research on Ponzi scheme diffusion within social networks yet, we develop a potential-investor-divestor (PID) model to investigate the diffusion dynamics of Ponzi scheme in both homogeneous and inhomogeneous networks. Our simulation study of artificial and real Facebook social networks shows that the structure of investor networks does indeed affect the characteristics of dynamics. Both the average degree of distribution and the power-law degree of distribution will reduce the spreading critical threshold and will speed up the rate of diffusion. A high speed of diffusion is the key to alleviating the interest burden and improving the financial outcomes for the Ponzi scheme operator. The zero-crossing point of fund flux function we introduce proves to be a feasible index for reflecting the fast-worsening situation of fiscal instability and predicting the forthcoming collapse. The faster the scheme diffuses, the higher a peak it will reach and the sooner it will collapse. We should keep a vigilant eye on the harm of Ponzi scheme diffusion through modern social networks.
Secure Electronic Cash Scheme with Anonymity Revocation
Directory of Open Access Journals (Sweden)
Baoyuan Kang
2016-01-01
Full Text Available In a popular electronic cash scheme, there are three participants: the bank, the customer, and the merchant. First, a customer opens an account in a bank. Then, he withdraws an e-cash from his account and pays it to a merchant. After checking the electronic cash’s validity, the merchant accepts it and deposits it to the bank. There are a number of requirements for an electronic cash scheme, such as, anonymity, unforgeability, unreusability, divisibility, transferability, and portability. Anonymity property of electronic cash schemes can ensure the privacy of payers. However, this anonymity property is easily abused by criminals. In 2011, Chen et al. proposed a novel electronic cash system with trustee-based anonymity revocation from pairing. On demand, the trustee can disclose the identity for e-cash. But, in this paper we point out that Chen et al.’s scheme is subjected to some drawbacks. To contribute secure electronic cash schemes, we propose a new offline electronic cash scheme with anonymity revocation. We also provide the formally security proofs of the unlinkability and unforgeability. Furthermore, the proposed scheme ensures the property of avoiding merchant frauds.
Upwind scheme for acoustic disturbances generated by low-speed flows
DEFF Research Database (Denmark)
Ekaterinaris, J.A.
1997-01-01
, compressible how equations, A numerical method for the solution of the equations governing the acoustic field is presented. The primitive variable form of the governing equations is used for the numerical solution. Time integration is performed with a fourth-order, Runge-Kutta method, Discretization...... of the primitive variables space derivatives is obtained with a high-order, upwind-biased numerical scheme. Upwinding of these convective fluxes is performed according to the eigenvalue sign of the coefficient matrices. Nonreflecting boundary conditions are applied to properly convect outgoing waves away from...
Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers
Kennedy, Christopher A.; Carpenter, Mark H.
1997-01-01
An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.
Deitmar schemes, graphs and zeta functions
Mérida-Angulo, Manuel; Thas, Koen
2017-07-01
In Thas (2014) it was explained how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, F1) to a so-called ;loose graph; (which is a generalization of a graph). Several properties of the Deitmar scheme can be proven easily from the combinatorics of the (loose) graph, and known realizations of objects over F1 such as combinatorial F1-projective and F1-affine spaces exactly depict the loose graph which corresponds to the associated Deitmar scheme. In this paper, we first modify the construction of loc. cit., and show that Deitmar schemes which are defined by finite trees (with possible end points) are ;defined over F1; in Kurokawa's sense; we then derive a precise formula for the Kurokawa zeta function for such schemes (and so also for the counting polynomial of all associated Fq-schemes). As a corollary, we find a zeta function for all such trees which contains information such as the number of inner points and the spectrum of degrees, and which is thus very different than Ihara's zeta function (which is trivial in this case). Using a process called ;surgery,; we show that one can determine the zeta function of a general loose graph and its associated {Deitmar, Grothendieck}-schemes in a number of steps, eventually reducing the calculation essentially to trees. We study a number of classes of examples of loose graphs, and introduce the Grothendieck ring ofF1-schemes along the way in order to perform the calculations. Finally, we include a computer program for performing more tedious calculations, and compare the new zeta function to Ihara's zeta function for graphs in a number of examples.
Vector domain decomposition schemes for parabolic equations
Vabishchevich, P. N.
2017-09-01
A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.
Algebraic K-theory of generalized schemes
DEFF Research Database (Denmark)
Anevski, Stella Victoria Desiree
and geometry over the field with one element. It also permits the construction of important Arakelov theoretical objects, such as the completion \\Spec Z of Spec Z. In this thesis, we prove a projective bundle theorem for the eld with one element and compute the Chow rings of the generalized schemes Sp\\ec ZN......Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry......, appearing in the construction of \\Spec Z....
Galilean invariant resummation schemes of cosmological perturbations
Peloso, Marco; Pietroni, Massimo
2017-01-01
Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.
Finite-volume scheme for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)
2016-02-01
In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.
Cognitive radio networks dynamic resource allocation schemes
Wang, Shaowei
2014-01-01
This SpringerBrief presents a survey of dynamic resource allocation schemes in Cognitive Radio (CR) Systems, focusing on the spectral-efficiency and energy-efficiency in wireless networks. It also introduces a variety of dynamic resource allocation schemes for CR networks and provides a concise introduction of the landscape of CR technology. The author covers in detail the dynamic resource allocation problem for the motivations and challenges in CR systems. The Spectral- and Energy-Efficient resource allocation schemes are comprehensively investigated, including new insights into the trade-off
Graph state-based quantum authentication scheme
Liao, Longxia; Peng, Xiaoqi; Shi, Jinjing; Guo, Ying
2017-04-01
Inspired by the special properties of the graph state, a quantum authentication scheme is proposed in this paper, which is implemented with the utilization of the graph state. Two entities, a reliable party, Trent, as a verifier and Alice as prover are included. Trent is responsible for registering Alice in the beginning and confirming Alice in the end. The proposed scheme is simple in structure and convenient to realize in the realistic physical system due to the use of the graph state in a one-way quantum channel. In addition, the security of the scheme is extensively analyzed and accordingly can resist the general individual attack strategies.
Autonomous Droop Scheme With Reduced Generation Cost
DEFF Research Database (Denmark)
Nutkani, Inam Ullah; Loh, Poh Chiang; Wang, Peng
2014-01-01
. This objective might, however, not suit microgrids well since DGs are usually of different types, unlike synchronous generators. Other factors like cost, efficiency, and emission penalty of each DG at different loading must be considered since they contribute directly to the total generation cost (TGC......) of the microgrid. To reduce this TGC without relying on fast communication links, an autonomous droop scheme is proposed here, whose resulting power sharing is decided by the individual DG generation costs. Comparing it with the traditional scheme, the proposed scheme retains its simplicity and it is hence more...
Energy Technology Data Exchange (ETDEWEB)
Furumura, T. [Hokkaido Univ. of Education, Sapporo (Japan); Koketsu, K. [The University of Tokyo, Tokyo (Japan). Earthquake Research Institute
1996-10-01
Hyogo-ken Nanbu earthquake with a focus in the Akashi straits has given huge earthquake damages in and around Awaji Island and Kobe City in 1995. It is clear that the basement structure, which is steeply deepened at Kobe City from Rokko Mountains towards the coast, and the focus under this related closely to the local generation of strong ground motion. Generation process of the strong ground motion was discussed using 2D and 3D numerical simulation methods. The 3D pseudospectral method was used for the calculation. Space of 51.2km{times}25.6km{times}25.6km was selected for the calculation. This space was discretized with the lattice interval of 200m. Consequently, it was found that the basement structure with a steeply deepened basement, soft and weak geological structure thickly deposited on the basement, and earthquake faults running under the boundary of base rock and sediments related greatly to the generation of strong ground motion. Numerical simulation can be expected to predict the strong ground motion by shallow earthquakes. 9 refs., 7 figs.
Mathematical theory of compressible viscous fluids analysis and numerics
Feireisl, Eduard; Pokorný, Milan
2016-01-01
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...
Extended Hamiltonian learning on Riemannian manifolds: numerical aspects.
Fiori, Simone
2012-01-01
This paper is the second part of a study initiated with the paper S. Fiori, "Extended Hamiltonian learning on Riemannian manifolds: Theoretical aspects," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 687-700, May 2011, which aimed at introducing a general framework to develop a theory of learning on differentiable manifolds by extended Hamiltonian stationary-action principle. This paper discusses the numerical implementation of the extended Hamiltonian learning paradigm by making use of notions from geometric numerical integration to numerically solve differential equations on manifolds. The general-purpose integration schemes and the discussion of several cases of interest show that the implementation of the dynamical learning equations exhibits a rich structure. The behavior of the discussed learning paradigm is illustrated via several numerical examples and discussions of case studies. The numerical examples confirm the theoretical developments presented in this paper as well as in its first part.
Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
Carrillo, José A.
2016-09-22
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient flow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this property with various examples in spatial dimension one and two.
Performance analysis of joint diversity combining, adaptive modulation, and power control schemes
Qaraqe, Khalid A.
2011-01-01
Adaptive modulation and diversity combining represent very important adaptive solutions for future generations of wireless communication systems. Indeed, in order to improve the performance and the efficiency of these systems, these two techniques have been recently used jointly in new schemes named joint adaptive modulation and diversity combining (JAMDC) schemes. Considering the problem of finding low hardware complexity, bandwidth-efficient, and processing-power efficient transmission schemes for a downlink scenario and capitalizing on some of these recently proposed JAMDC schemes, we propose and analyze in this paper three joint adaptive modulation, diversity combining, and power control (JAMDCPC) schemes where a constant-power variable-rate adaptive modulation technique is used with an adaptive diversity combining scheme and a common power control process. More specifically, the modulation constellation size, the number of combined diversity paths, and the needed power level are jointly determined to achieve the highest spectral efficiency with the lowest possible processing power consumption quantified in terms of the average number of combined paths, given the fading channel conditions and the required bit error rate (BER) performance. In this paper, the performance of these three JAMDCPC schemes is analyzed in terms of their spectral efficiency, processing power consumption, and error-rate performance. Selected numerical examples show that these schemes considerably increase the spectral efficiency of the existing JAMDC schemes with a slight increase in the average number of combined paths for the low signal-to-noise ratio range while maintaining compliance with the BER performance and a low radiated power which yields to a substantial decrease in interference to co-existing users and systems. © 2011 IEEE.
Impact of WRF model PBL schemes on air quality simulations over Catalonia, Spain.
Banks, R F; Baldasano, J M
2016-12-01
Here we analyze the impact of four planetary boundary-layer (PBL) parametrization schemes from the Weather Research and Forecasting (WRF) numerical weather prediction model on simulations of meteorological variables and predicted pollutant concentrations from an air quality forecast system (AQFS). The current setup of the Spanish operational AQFS, CALIOPE, is composed of the WRF-ARW V3.5.1 meteorological model tied to the Yonsei University (YSU) PBL scheme, HERMES v2 emissions model, CMAQ V5.0.2 chemical transport model, and dust outputs from BSC-DREAM8bv2. We test the performance of the YSU scheme against the Assymetric Convective Model Version 2 (ACM2), Mellor-Yamada-Janjic (MYJ), and Bougeault-Lacarrère (BouLac) schemes. The one-day diagnostic case study is selected to represent the most frequent synoptic condition in the northeast Iberian Peninsula during spring 2015; regional recirculations. It is shown that the ACM2 PBL scheme performs well with daytime PBL height, as validated against estimates retrieved using a micro-pulse lidar system (mean bias=-0.11km). In turn, the BouLac scheme showed WRF-simulated air and dew point temperature closer to METAR surface meteorological observations. Results are more ambiguous when simulated pollutant concentrations from CMAQ are validated against network urban, suburban, and rural background stations. The ACM2 scheme showed the lowest mean bias (-0.96μgm(-3)) with respect to surface ozone at urban stations, while the YSU scheme performed best with simulated nitrogen dioxide (-6.48μgm(-3)). The poorest results were with simulated particulate matter, with similar results found with all schemes tested. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.
Saqib, Muhammad; Hasnain, Shahid; Mashat, Daoud Suleiman
2017-08-01
To develop an efficient numerical scheme for three-dimensional advection diffusion equation, higher order ADI method was proposed. 2nd and fourth order ADI schemes were used to handle such problem. Von Neumann stability analysis shows that Alternating Direction Implicit scheme is unconditionally stable. The accuracy and efficiency of such schemes was depicted by two test problems. Numerical results for two test problems were carried out to establish the performance of the given method and to compare it with the others Typical methods. Fourth order ADI method were found to be very efficient and stable for solving three dimensional Advection Diffusion Equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.
On the All-Speed Roe-type Scheme for Large Eddy Simulation of Homogeneous Decaying Turbulence
Li, Xue-song
2015-01-01
As the representative of the shock-capturing scheme, the Roe scheme fails to LES because important turbulent characteristics cannot be reproduced such as the famous k-5/3 spectral law owing to large numerical dissipation. In this paper, the Roe scheme is divided into five parts: , , , , and , which means basic upwind dissipation, pressure-difference-driven and velocity-difference-driven modification of the interface fluxes and pressure, respectively. Then, the role of each part on LES is investigated by homogeneous decaying turbulence. The results show that the parts , , and have little effect on LES. It is important especially for because it is necessary for computation stability. The large numerical dissipation is due to and , and each of them has much larger dissipation than SGS dissipation. According to these understanding, an improved all-speed LES-Roe scheme is proposed, which can give enough good LES results for even coarse grid resolution with usually adopted reconstruction.
Directory of Open Access Journals (Sweden)
Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
Password authentication scheme based on the quadratic residue problem
Ali, Muhammad Helmi; Ismail, Eddie Shahril
2017-04-01
In this paper, we propose a new password-authentication scheme based on quadratic residue problem with the following advantages: the scheme does not require a verification file, and the scheme can withstand replay attacks and resist from the guessing and impersonation attacks. We next discuss the advantages of our designated scheme over other schemes in terms of security and efficiency.
A survey of Strong Convergent Schemes for the Simulation of ...
African Journals Online (AJOL)
We considered strong convergent stochastic schemes for the simulation of stochastic differential equations. The stochastic Taylor's expansion, which is the main tool used for the derivation of strong convergent schemes; the Euler Maruyama, Milstein scheme, stochastic multistep schemes, Implicit and Explicit schemes were ...
Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging
Desmal, Abdulla
2016-03-01
Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using
Modelling of Two-Phase Flow with Second-Order Accurate Scheme
Tiselj, Iztok; Petelin, Stojan
1997-09-01
A second-order accurate scheme based on high-resolution shock-capturing methods was used with a typical two-phase flow model which is used in the computer codes for simulation of nuclear power plant accidents. The two-fluid model, which has been taken from the computer code RELAP5, consists of six first-order partial differential equations that represent 1D mass, momentum, and energy balances for vapour and liquid. The partial differential equations are ill-posed-nonhyperbolic. The hyperbolicity required by the presented numerical scheme was obtained in the practical range of the physical parameters by minor modification of the virtual mass term. No conservative form of the applied equations exists, therefore, instead of the Riemann solver, more basic averaging was used for the evaluation of the Jacobian matrix. The equations were solved using nonconservative and conservative basic variables. Since the source terms are stiff, they were integrated with time steps which were shorter than or equal to the convection time step. The sources were treated with Strang splitting to retain the second-order accuracy of the scheme. The numerical scheme has been used for the simulations of the two-phase shock tube problem and the Edwards pipe experiment. Results show the importance of the closure laws which have a crucial impact on the accuracy of two-fluid models. Advantages of the second-order accurate schemes are evident especially in the area of fast transients dominated by acoustic phenomena.
Qaraqe, Marwa
2014-04-01
This paper focuses on the development of multiuser access schemes for spectrum sharing systems whereby secondary users are allowed to share the spectrum with primary users under the condition that the interference observed at the primary receiver is below a predetermined threshold. In particular, two scheduling schemes are proposed for selecting a user among those that satisfy the interference constraint and achieve an acceptable signal-to-noise ratio level. The first scheme focuses on optimizing the average spectral efficiency by selecting the user that reports the best channel quality. In order to alleviate the relatively high feedback required by the first scheme, a second scheme based on the concept of switched diversity is proposed, where the base station (BS) scans the secondary users in a sequential manner until a user whose channel quality is above an acceptable predetermined threshold is found. We develop expressions for the statistics of the signal-to-interference and noise ratio as well as the average spectral efficiency, average feedback load, and the delay at the secondary BS. We then present numerical results for the effect of the number of users and the interference constraint on the optimal switching threshold and the system performance and show that our analysis results are in perfect agreement with the numerical results. © 2014 John Wiley & Sons, Ltd.
Kent, James; Holdaway, Daniel
2015-01-01
A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.
Watson, Wendy L; Kelly, Bridget; Hector, Debra; Hughes, Clare; King, Lesley; Crawford, Jennifer; Sergeant, John; Chapman, Kathy
2014-01-01
There is evidence that easily accessible, comprehensible and consistent nutrient information on the front of packaged foods could assist shoppers to make healthier food choices. This study used an online questionnaire of 4357 grocery shoppers to examine Australian shoppers' ability to use a range of front-of-pack labels to identify healthier food products. Seven different front-of-pack labelling schemes comprising variants of the Traffic Light labelling scheme and the Percentage Daily Intake scheme, and a star rating scheme, were applied to nine pairs of commonly purchased food products. Participants could also access a nutrition information panel for each product. Participants were able to identify the healthier product in each comparison over 80% of the time using any of the five schemes that provided information on multiple nutrients. No individual scheme performed significantly better in terms of shoppers' ability to determine the healthier product, shopper reliance on the 'back-of-pack' nutrition information panel, and speed of use. The scheme that provided information about energy only and a scheme with limited numerical information of nutrient type or content performed poorly, as did the nutrition information panel alone (control). Further consumer testing is necessary to determine the optimal format and content of an interpretive front-of-pack nutrition labelling scheme. Copyright © 2013 Elsevier Ltd. All rights reserved.
Introduction to Numerical Methods
Energy Technology Data Exchange (ETDEWEB)
Schoonover, Joseph A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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.
Designing optimal sampling schemes for field visits
CSIR Research Space (South Africa)
Debba, Pravesh
2008-10-01
Full Text Available This is a presentation of a statistical method for deriving optimal spatial sampling schemes. The research focuses on ground verification of minerals derived from hyperspectral data. Spectral angle mapper (SAM) and spectral feature fitting (SFF...
A Climate Classification Scheme for Habitable Worlds
Byrne, J. F.
2017-11-01
This presentation will include an exploration of the internal/external forcings and variability associated with climate using Earth as a reference model in addition to a classification scheme consisting of five categories.
Secure Wake-Up Scheme for WBANs
Liu, Jing-Wei; Ameen, Moshaddique Al; Kwak, Kyung-Sup
Network life time and hence device life time is one of the fundamental metrics in wireless body area networks (WBAN). To prolong it, especially those of implanted sensors, each node must conserve its energy as much as possible. While a variety of wake-up/sleep mechanisms have been proposed, the wake-up radio potentially serves as a vehicle to introduce vulnerabilities and attacks to WBAN, eventually resulting in its malfunctions. In this paper, we propose a novel secure wake-up scheme, in which a wake-up authentication code (WAC) is employed to ensure that a BAN Node (BN) is woken up by the correct BAN Network Controller (BNC) rather than unintended users or malicious attackers. The scheme is thus particularly implemented by a two-radio architecture. We show that our scheme provides higher security while consuming less energy than the existing schemes.