Java technology for implementing efficient numerical analysis in intranet

International Nuclear Information System (INIS)

Song, Hee Yong; Ko, Sung Ho

2001-01-01

This paper introduces some useful Java technologies for utilizing the internet in numerical analysis, and suggests one architecture performing efficient numerical analysis in the intranet by using them. The present work has verified it's possibility by implementing some parts of this architecture with two easy examples. One is based on Servlet-Applet communication, JDBC and swing. The other is adding multi-threads, file transfer and Java remote method invocation to the former. Through this work it has been intended to make the base for the later advanced and practical research that will include efficiency estimates of this architecture and deal with advanced load balancing

Efficient numerical simulations of many-body localized systems

Energy Technology Data Exchange (ETDEWEB)

Pollmann, Frank [Max-Planck-Institut fuer Physik komplexer Systeme, 01187 Dresden (Germany); Khemani, Vedika; Sondhi, Shivaji [Physics Department, Princeton University, Princeton, NJ 08544 (United States)

2016-07-01

Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new, efficient numerical methods to find highly excited eigenstates is essential. We introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate-large disorder. This method explicitly takes advantage of the local spatial structure characterizing MBL eigenstates.

Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

KAUST Repository

Happola, Juho

2017-09-19

Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

KAUST Repository

Happola, Juho

2017-01-01

Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

Hybrid RANS-LES using high order numerical methods

Science.gov (United States)

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

2017-11-01

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

Numerical methods for characterization of synchrotron radiation based on the Wigner function method

Directory of Open Access Journals (Sweden)

Takashi Tanaka

2014-06-01

Full Text Available Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.

Numerical Methods for a Class of Differential Algebraic Equations

Directory of Open Access Journals (Sweden)

Lei Ren

2017-01-01

Full Text Available This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs. At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.

An Energy-Efficient Cluster-Based Vehicle Detection on Road Network Using Intention Numeration Method

Directory of Open Access Journals (Sweden)

Deepa Devasenapathy

2015-01-01

Full Text Available The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.

An energy-efficient cluster-based vehicle detection on road network using intention numeration method.

Science.gov (United States)

Devasenapathy, Deepa; Kannan, Kathiravan

2015-01-01

The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.

A Numerical and Experimental Study of Local Exhaust Capture Efficiency

DEFF Research Database (Denmark)

Madsen, U.; Breum, N. O.; Nielsen, Peter Vilhelm

1993-01-01

Direct capture efficiency of a local exhaust system is defined by introducing an imaginary control box surrounding the contaminant source and the exhaust opening. The imaginary box makes it possible to distinguish between contaminants directly captured and those that escape. Two methods for estim...... location is less important for the case studied. The choice of sampling strategy to obtain a representative background concentration is essential as substantial differences on direct capture efficiency are found. Recommendations are given......Direct capture efficiency of a local exhaust system is defined by introducing an imaginary control box surrounding the contaminant source and the exhaust opening. The imaginary box makes it possible to distinguish between contaminants directly captured and those that escape. Two methods...... for estimation of direct capture efficiency are given: (1) a numerical method based on the time-averaged Navier-Stokes equations for turbulent flows; and (2) a field method based on a representative background concentration. Direct capture efficiency is sensitive to the size of the control box, whereas its...

Deformation data modeling through numerical models: an efficient method for tracking magma transport

Science.gov (United States)

Charco, M.; Gonzalez, P. J.; Galán del Sastre, P.

2017-12-01

Nowadays, multivariate collected data and robust physical models at volcano observatories are becoming crucial for providing effective volcano monitoring. Nevertheless, the forecast of volcanic eruption is notoriously difficult. Wthin this frame one of the most promising methods to evaluate the volcano hazard is the use of surface ground deformation and in the last decades many developments in the field of deformation modeling has been achieved. In particular, numerical modeling allows realistic media features such as topography and crustal heterogeneities to be included, although it is still very time cosuming to solve the inverse problem for near-real time interpretations. Here, we present a method that can be efficiently used to estimate the location and evolution of magmatic sources base on real-time surface deformation data and Finite Element (FE) models. Generally, the search for the best-fitting magmatic (point) source(s) is conducted for an array of 3-D locations extending below a predefined volume region and the Green functions for all the array components have to be precomputed. We propose a FE model for the pre-computation of Green functions in a mechanically heterogeneous domain which eventually will lead to a better description of the status of the volcanic area. The number of Green functions is reduced here to the number of observational points by using their reciprocity relationship. We present and test this methodology with an optimization method base on a Genetic Algorithm. Following synthetic and sensitivity test to estimate the uncertainty of the model parameters, we apply the tool for magma tracking during 2007 Kilauea volcano intrusion and eruption. We show how data inversion with numerical models can speed up the source parameters estimations for a given volcano showing signs of unrest.

Numerical simulation of GEW equation using RBF collocation method

Directory of Open Access Journals (Sweden)

Hamid Panahipour

2012-08-01

Full Text Available The generalized equal width (GEW equation is solved numerically by a meshless method based on a global collocation with standard types of radial basis functions (RBFs. Test problems including propagation of single solitons, interaction of two and three solitons, development of the Maxwellian initial condition pulses, wave undulation and wave generation are used to indicate the efficiency and accuracy of the method. Comparisons are made between the results of the proposed method and some other published numerical methods.

Efficient Numerical Solution of Coupled Radial Differential Equations in Multichannel Scattering Problems

International Nuclear Information System (INIS)

Houfek, Karel

2008-01-01

Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.

Efficient numerical solution to vacuum decay with many fields

Energy Technology Data Exchange (ETDEWEB)

Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin, E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: shlaer@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

2017-01-01

Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.

A Fast Numerical Method for Max-Convolution and the Application to Efficient Max-Product Inference in Bayesian Networks.

Science.gov (United States)

Serang, Oliver

2015-08-01

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.

Implementation and assessment of high-resolution numerical methods in TRACE

Energy Technology Data Exchange (ETDEWEB)

Wang, Dean, E-mail: wangda@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley RD 6167, Oak Ridge, TN 37831 (United States); Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G. [U.S. Nuclear Regulatory Commission, Washington, DC 20555 (United States)

2013-10-15

Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency.

Implementation and assessment of high-resolution numerical methods in TRACE

International Nuclear Information System (INIS)

Wang, Dean; Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G.

2013-01-01

Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency

Numerical methods in multibody dynamics

CERN Document Server

Eich-Soellner, Edda

1998-01-01

Today computers play an important role in the development of complex mechanical systems, such as cars, railway vehicles or machines. Efficient simulation of these systems is only possible when based on methods that explore the strong link between numerics and computational mechanics. This book gives insight into modern techniques of numerical mathematics in the light of an interesting field of applications: multibody dynamics. The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck. Different versions of this mechanical model illustrate all key concepts in static and dynamic analysis as well as in parameter identification. The book focuses in particular on constrained mechanical systems. Their formulation in terms of differential-algebraic equations is the backbone of nearly all chapters. The book is written for students and teachers in numerical analysis and mechanical engineering as well as for engineers in industrial research labor...

Efficient and robust implementation of the TLISMNI method

Science.gov (United States)

Aboubakr, Ahmed K.; Shabana, Ahmed A.

2015-09-01

The dynamics of large scale and complex multibody systems (MBS) that include flexible bodies and contact/impact pairs is governed by stiff equations. Because explicit integration methods can be inefficient and often fail in the case of stiff problems, the use of implicit numerical integration methods is recommended in this case. This paper presents a new and efficient implementation of the two-loop implicit sparse matrix numerical integration (TLISMNI) method proposed for the solution of constrained rigid and flexible MBS differential and algebraic equations. The TLISMNI method has desirable features that include avoiding numerical differentiation of the forces, allowing for an efficient sparse matrix implementation, and ensuring that the kinematic constraint equations are satisfied at the position, velocity and acceleration levels. In this method, a sparse Lagrangian augmented form of the equations of motion that ensures that the constraints are satisfied at the acceleration level is used to solve for all the accelerations and Lagrange multipliers. The generalized coordinate partitioning or recursive methods can be used to satisfy the constraint equations at the position and velocity levels. In order to improve the efficiency and robustness of the TLISMNI method, the simple iteration and the Jacobian-Free Newton-Krylov approaches are used in this investigation. The new implementation is tested using several low order formulas that include Hilber-Hughes-Taylor (HHT), L-stable Park, A-stable Trapezoidal, and A-stable BDF methods. The HHT method allows for including numerical damping. Discussion on which method is more appropriate to use for a certain application is provided. The paper also discusses TLISMNI implementation issues including the step size selection, the convergence criteria, the error control, and the effect of the numerical damping. The use of the computer algorithm described in this paper is demonstrated by solving complex rigid and flexible tracked

Numerical methods for engine-airframe integration

International Nuclear Information System (INIS)

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

1986-01-01

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

Methods of numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1983-01-01

Numerical Relativity is an alternative to analytical methods for obtaining solutions for Einstein equations. Numerical methods are particularly useful for studying generation of gravitational radiation by potential strong sources. The author reviews the analytical background, the numerical analysis aspects and techniques and some of the difficulties involved in numerical relativity. (Auth.)

An efficient unstructured WENO method for supersonic reactive flows

Science.gov (United States)

Zhao, Wen-Geng; Zheng, Hong-Wei; Liu, Feng-Jun; Shi, Xiao-Tian; Gao, Jun; Hu, Ning; Lv, Meng; Chen, Si-Cong; Zhao, Hong-Da

2018-03-01

An efficient high-order numerical method for supersonic reactive flows is proposed in this article. The reactive source term and convection term are solved separately by splitting scheme. In the reaction step, an adaptive time-step method is presented, which can improve the efficiency greatly. In the convection step, a third-order accurate weighted essentially non-oscillatory (WENO) method is adopted to reconstruct the solution in the unstructured grids. Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids, while high order accuracy can be achieved in the smooth region. In addition, the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method.

Valve cam design using numerical step-by-step method

OpenAIRE

Vasilyev, Aleksandr; Bakhracheva, Yuliya; Kabore, Ousman; Zelenskiy, Yuriy

2014-01-01

This article studies the numerical step-by-step method of cam profile design. The results of the study are used for designing the internal combustion engine valve gear. This method allows to profile the peak efficiency of cams in view of many restrictions, connected with valve gear serviceability and reliability.

Quantitative Efficiency Evaluation Method for Transportation Networks

Directory of Open Access Journals (Sweden)

Jin Qin

2014-11-01

Full Text Available An effective evaluation of transportation network efficiency/performance is essential to the establishment of sustainable development in any transportation system. Based on a redefinition of transportation network efficiency, a quantitative efficiency evaluation method for transportation network is proposed, which could reflect the effects of network structure, traffic demands, travel choice, and travel costs on network efficiency. Furthermore, the efficiency-oriented importance measure for network components is presented, which can be used to help engineers identify the critical nodes and links in the network. The numerical examples show that, compared with existing efficiency evaluation methods, the network efficiency value calculated by the method proposed in this paper can portray the real operation situation of the transportation network as well as the effects of main factors on network efficiency. We also find that the network efficiency and the importance values of the network components both are functions of demands and network structure in the transportation network.

Semi-empirical γ-ray peak efficiency determination including self-absorption correction based on numerical integration

International Nuclear Information System (INIS)

Noguchi, M.; Takeda, K.; Higuchi, H.

1981-01-01

A method of γ-ray efficiency determination for extended (plane or bulk) samples based on numerical integration of point source efficiency is studied. The proposed method is widely applicable to samples of various shapes and materials. The geometrical factor in the peak efficiency can easily be corrected for by simply changing the integration region, and γ-ray self-absorption is also corrected by the absorption coefficients for the sample matrix. (author)

Numerical methods using Matlab

CERN Document Server

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

Spectral methods in numerical plasma simulation

International Nuclear Information System (INIS)

Coutsias, E.A.; Hansen, F.R.; Huld, T.; Knorr, G.; Lynov, J.P.

1989-01-01

An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed. (orig.)

An efficient method for solving fractional Sturm-Liouville problems

International Nuclear Information System (INIS)

Al-Mdallal, Qasem M.

2009-01-01

The numerical approximation of the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, is considered. The present results can be implemented on the numerical solution of the fractional diffusion-wave equation. The results show the simplicity and efficiency of the numerical method.

Numerical calculation of particle collection efficiency in an ...

Indian Academy of Sciences (India)

Theoretical and numerical research has been previously done on ESPs to predict the efficiency ... Lagrangian simulations of particle transport in wire–plate ESP were .... The collection efficiency can be defined as the ratio of the number of ...

Development of parallel implementation of adaptive numerical methods with industrial applications in fluid mechanics

International Nuclear Information System (INIS)

Laucoin, E.

2008-10-01

Numerical resolution of partial differential equations can be made reliable and efficient through the use of adaptive numerical methods.We present here the work we have done for the design, the implementation and the validation of such a method within an industrial software platform with applications in thermohydraulics. From the geometric point of view, this method can deal both with mesh refinement and mesh coarsening, while ensuring the quality of the mesh cells. Numerically, we use the mortar elements formalism in order to extend the Finite Volumes-Elements method implemented in the Trio-U platform and to deal with the non-conforming meshes arising from the adaptation procedure. Finally, we present an implementation of this method using concepts from domain decomposition methods for ensuring its efficiency while running in a parallel execution context. (author)

Advanced numerical methods for three dimensional two-phase flow calculations

Energy Technology Data Exchange (ETDEWEB)

Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)

1997-07-01

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

Advanced numerical methods for three dimensional two-phase flow calculations

International Nuclear Information System (INIS)

Toumi, I.; Caruge, D.

1997-01-01

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

Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

KAUST Repository

Wang, Yi

2016-07-21

Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.

Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

Energy Technology Data Exchange (ETDEWEB)

Safta, Cosmin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Najm, Habib N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Phipps, Eric Todd [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-09-01

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

New numerical method for solving the solute transport equation

International Nuclear Information System (INIS)

Ross, B.; Koplik, C.M.

1978-01-01

The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method

Directory of Open Access Journals (Sweden)

Hossein Aminikhah

2016-01-01

Full Text Available A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error L2-norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.

An efficient and general numerical method to compute steady uniform vortices

Science.gov (United States)

Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.

2011-07-01

Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.

High accuracy mantle convection simulation through modern numerical methods

KAUST Repository

Kronbichler, Martin

2012-08-21

Numerical simulation of the processes in the Earth\\'s mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth\\'s core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earth\\'s mantle, and discusses their implementation in the Open Source code Aspect (Advanced Solver for Problems in Earth\\'s ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large numbers of processors on compute clusters. Aspect relies on the numerical software packages deal.II and Trilinos, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs. © 2012 The Authors Geophysical Journal International © 2012 RAS.

Interleaved numerical renormalization group as an efficient multiband impurity solver

Science.gov (United States)

Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.

2016-06-01

Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

Introduction to precise numerical methods

CERN Document Server

Aberth, Oliver

2007-01-01

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.

A two-dimensional adaptive numerical grids generation method and its realization

International Nuclear Information System (INIS)

Xu Tao; Shui Hongshou

1998-12-01

A two-dimensional adaptive numerical grids generation method and its particular realization is discussed. This method is effective and easy to realize if the control functions are given continuously, and the grids for some regions is showed in this case. For Computational Fluid Dynamics, because the control values of adaptive grids-numerical solution is given in dispersed form, it is needed to interpolate these values to get the continuous control functions. These interpolation techniques are discussed, and some efficient adaptive grids are given. A two-dimensional fluid dynamics example was also given

Method for determining efficiency in a liquid scintillation system

International Nuclear Information System (INIS)

Laney, B.H.

1975-01-01

This invention relates to a method of counting radioactive events in a liquid scintillation radiation detecting and counting apparatus by utilizing pulses generated by a photomultiplying means resulting from scintillations caused by radioactive events. A counting efficiency value is assigned to each pulse generated in the photomultiplying means according to the height of the pulse. The numerical inverse of each assigned counting efficiency value is determined and each numerical inverse is recorded as an actual number of radioactive events with each having a pulse height identical to that of the corresponding pulse generated in the photomultiplying means. (Patent Office Record)

Advanced numerical methods for three dimensional two-phase flow calculations in PWR

International Nuclear Information System (INIS)

Toumi, I.; Gallo, D.; Royer, E.

1997-01-01

This paper is devoted to new numerical methods developed for three dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe's approximate Riemann solver to define convective fluxes versus mean cell quantities. To go forward in time, a linearized conservative implicit integrating step is used, together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three dimensional thermal-hydraulic code FLICA-4 which is mainly dedicated to core thermal-hydraulic transient and steady-state analysis. Hereafter, we will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with 3 pumps out of 4, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow steam-line-break conditions. (author)

Efficient 3D Volume Reconstruction from a Point Cloud Using a Phase-Field Method

Directory of Open Access Journals (Sweden)

Darae Jeong

2018-01-01

Full Text Available We propose an explicit hybrid numerical method for the efficient 3D volume reconstruction from unorganized point clouds using a phase-field method. The proposed three-dimensional volume reconstruction algorithm is based on the 3D binary image segmentation method. First, we define a narrow band domain embedding the unorganized point cloud and an edge indicating function. Second, we define a good initial phase-field function which speeds up the computation significantly. Third, we use a recently developed explicit hybrid numerical method for solving the three-dimensional image segmentation model to obtain efficient volume reconstruction from point cloud data. In order to demonstrate the practical applicability of the proposed method, we perform various numerical experiments.

On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

Directory of Open Access Journals (Sweden)

H. Montazeri

2012-01-01

Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

Solution methods for compartment models of transport through the environment using numerical inversion of Laplace transforms

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

Compartment models for the transport of radionuclides in the biosphere are conventionally solved using a numerical time-stepping procedure. This report examines an alternative method based on the numerical inversion of Laplace transforms, which is potentially more efficient and accurate for some classes of problem. The central problem considered is the most efficient and robust technique for solving the Laplace-transformed rate equations. The conclusion is that Gaussian elimination is the most efficient and robust solution method. A general compartment model has been implemented on a personal computer and used to solve a realistic case including radionuclide decay chains. (author)

Estimation of the drift eliminator efficiency using numerical and experimental methods

Directory of Open Access Journals (Sweden)

Stodůlka Jiří

2016-01-01

Full Text Available The purpose of the drift eliminators is to prevent water from escaping in significant amounts the cooling tower. They are designed to catch the droplets dragged by the tower draft and the efficiency given by the shape of the eliminator is the main evaluation criteria. The ability to eliminate the escaping water droplets is studied using CFD and using the experimental IPI method.

Flow Structures and Efficiency of Swimming Fish school: Numerical Study

Science.gov (United States)

Yatagai, Yuzuru; Hattori, Yuji

2013-11-01

The flow structure and energy-saving mechanism in fish school is numerically investigated by using the volume penalization method. We calculate the various patterns of configuration of fishes and investigate the relation between spatial arrangement and the performance of fish. It is found that the down-stream fish gains a hydrodynamic advantage from the upstream wake shed by the upstream fish. The most efficient configuration is that the downstream fish is placed in the wake. It reduces the drag force of the downstream fish in comparison with that in solo swimming.

An efficient approach to numerical study of the coupled-BBM system with B-spline collocation method

Directory of Open Access Journals (Sweden)

khalid ali

2016-11-01

Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with cubic trigonometric B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Efficient Numerical Simulation of Aerothermoelastic Hypersonic Vehicles

Science.gov (United States)

Klock, Ryan J.

speed and overall solution fidelity. A number of enhancements to this framework are made through 1. the implementation of a publish-subscribe code architecture for rapid prototyping of physics and process models. 2. the implementation of a selection of linearization and model identification methods including high-order pseudo-time forward difference, complex-step, and direct identification from ordinary differential equation inspection. 3. improvements to the aeroheating and thermal models with non-equilibrium gas dynamics and generalized temperature dependent material thermal properties. A variety of model reduction and surrogate model techniques are applied to a representative hypersonic vehicle on a terminal trajectory to enable complete aerothermoelastic flight simulations. Multiple terminal trajectories of various starting altitudes and Mach numbers are optimized to maximize final kinetic energy of the vehicle upon reaching the surface. Surrogate models are compared to represent the variation of material thermal properties with temperature. A new method is developed and shown to be both accurate and computationally efficient. While the numerically efficient simulation of high-speed vehicles is developed within the presented framework, the goal of real time simulation is hampered by the necessity of multiple nested convergence loops. An alternative all-in-one surrogate model method is developed based on singular-value decomposition and regression that is near real time. Finally, the aeroelastic stability of pressurized cylindrical shells is investigated in the context of a maneuvering axisymmetric high-speed vehicle. Moderate internal pressurization is numerically shown to decrease stability, as showed experimentally in the literature, yet not well reproduced analytically. Insights are drawn from time simulation results and used to inform approaches for future vehicle model development.

Experimental and Numerical Simulations Predictions Comparison of Power and Efficiency in Hydraulic Turbine

Directory of Open Access Journals (Sweden)

Laura Castro

2011-01-01

Full Text Available On-site power and mass flow rate measurements were conducted in a hydroelectric power plant (Mexico. Mass flow rate was obtained using Gibson's water hammer-based method. A numerical counterpart was carried out by using the commercial CFD software, and flow simulations were performed to principal components of a hydraulic turbine: runner and draft tube. Inlet boundary conditions for the runner were obtained from a previous simulation conducted in the spiral case. The computed results at the runner's outlet were used to conduct the subsequent draft tube simulation. The numerical results from the runner's flow simulation provided data to compute the torque and the turbine's power. Power-versus-efficiency curves were built, and very good agreement was found between experimental and numerical data.

A Broyden numerical Kutta condition for an unsteady panel method

International Nuclear Information System (INIS)

Liu, P.; Bose, N.; Colbourne, B.

2003-01-01

In panel methods, numerical Kutta conditions are applied in order to ensure that pressure differences between the surfaces at the trailing edges of lifting surface elements are close to zero. Previous numerical Kutta conditions for 3-D panel methods have focused on use of the Newton-Raphson iterative procedure. For extreme unsteady motions, such as for oscillating hydrofoils or for a propeller behind a blockage, the Newton-Raphson procedure can have severe convergence difficulties. The Broyden iteration, a modified Newton-Raphson iteration procedure, is applied here to obtain improved convergence behavior. Using the Broyden iteration increases the reliability, robustness and in many cases computing efficiency for unsteady, multi-body interactive flows. This method was tested in a time domain code for an ice class propeller in both open water flow and during interaction with a nearby ice blockage. Predictions showed that the method was effective in these extreme flows. (author)

Numerical methods in software and analysis

CERN Document Server

Rice, John R

1992-01-01

Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm

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

Science.gov (United States)

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

2017-08-01

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

The instanton method and its numerical implementation in fluid mechanics

Science.gov (United States)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-08-01

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.

The instanton method and its numerical implementation in fluid mechanics

International Nuclear Information System (INIS)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-01-01

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin–Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler–Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier–Stokes equations. (topical review)

Excel spreadsheet in teaching numerical methods

Science.gov (United States)

Djamila, Harimi

2017-09-01

One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.

Numerical quantification and minimization of perimeter losses in high-efficiency silicon solar cells

Energy Technology Data Exchange (ETDEWEB)

Altermatt, P.P.; Heiser, Gernot; Green, M.A. [New South Wales Univ., Kensington, NSW (Australia)

1996-09-01

This paper presents a quantitative analysis of perimeter losses in high-efficiency silicon solar cells. A new method of numerical modelling is used, which provides the means to simulate a full-sized solar cell, including its perimeter region. We analyse the reduction in efficiency due to perimeter losses as a function of the distance between the active cell area and the cut edge. It is shown how the optimum distance depends on whether the cells in the panel are shingled or not. The simulations also indicate that passivating the cut-face with a thermal oxide does not increase cell efficiency substantially. Therefore, doping schemes for the perimeter domain are suggested in order to increase efficiency levels above present standards. Finally, perimeter effects in cells that remain embedded in the wafer during the efficiency measurement are outlined. (author)

Real-time numerical simulation with high efficiency for an experimental reactor system

International Nuclear Information System (INIS)

Ding Shuling; Li Fu; Li Sifeng; Chu Xinyuan

2006-01-01

The paper presents a systematic and efficient method for numerical real-time simulation of an experimental reactor. The reactor models were built based on the physical characteristics of the experimental reactor, and several real-time simulation approaches were discussed and compared in the paper. How to implement the real-time reactor simulation system in Windows platform for the sake of hardware-in-loop experiment for the reactor power control system was discussed. (authors)

A comparison of efficient methods for the computation of Born gluon amplitudes

International Nuclear Information System (INIS)

Dinsdale, Michael; Ternick, Marko; Weinzierl, Stefan

2006-01-01

We compare four different methods for the numerical computation of the pure gluonic amplitudes in the Born approximation. We are in particular interested in the efficiency of the various methods as the number n of the external particles increases. In addition we investigate the numerical accuracy in critical phase space regions. The methods considered are based on (i) Berends-Giele recurrence relations, (ii) scalar diagrams, (iii) MHV vertices and (iv) BCF recursion relations

Improved numerical methods for quantum field theory (Outstanding junior investigator award)

International Nuclear Information System (INIS)

Sokal, A.D.

1992-01-01

We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo, Swendsen-Wang and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory

Improved numerical methods for quantum field theory (Outstanding junior investigator award)

International Nuclear Information System (INIS)

Sokal, A.D.

1993-01-01

We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo (MGMC), Swendsen-Wang (SW) and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory

Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

Numerical methods for hydrodynamic stability problems

International Nuclear Information System (INIS)

Fujimura, Kaoru

1985-11-01

Numerical methods for solving the Orr-Sommerfeld equation, which is the fundamental equation of the hydrodynamic stability theory for various shear flows, are reviewed and typical numerical results are presented. The methods of asymptotic solution, finite difference methods, initial value methods and expansions in orthogonal functions are compared. (author)

Development of CAD implementing the algorithm of boundary elements’ numerical analytical method

Directory of Open Access Journals (Sweden)

Yulia V. Korniyenko

2015-03-01

Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.

Numerical modelling of methane oxidation efficiency and coupled water-gas-heat reactive transfer in a sloping landfill cover.

Science.gov (United States)

Feng, S; Ng, C W W; Leung, A K; Liu, H W

2017-10-01

Microbial aerobic methane oxidation in unsaturated landfill cover involves coupled water, gas and heat reactive transfer. The coupled process is complex and its influence on methane oxidation efficiency is not clear, especially in steep covers where spatial variations of water, gas and heat are significant. In this study, two-dimensional finite element numerical simulations were carried out to evaluate the performance of unsaturated sloping cover. The numerical model was calibrated using a set of flume model test data, and was then subsequently used for parametric study. A new method that considers transient changes of methane concentration during the estimation of the methane oxidation efficiency was proposed and compared against existing methods. It was found that a steeper cover had a lower oxidation efficiency due to enhanced downslope water flow, during which desaturation of soil promoted gas transport and hence landfill gas emission. This effect was magnified as the cover angle and landfill gas generation rate at the bottom of the cover increased. Assuming the steady-state methane concentration in a cover would result in a non-conservative overestimation of oxidation efficiency, especially when a steep cover was subjected to rainfall infiltration. By considering the transient methane concentration, the newly-modified method can give a more accurate oxidation efficiency. Copyright © 2017. Published by Elsevier Ltd.

Numerical Investigations on Several Stabilized Finite Element Methods for the Stokes Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Pengzhan Huang

2011-01-01

Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.

Efficiency and stability of the DSBGK method

KAUST Repository

Li, Jun

2012-07-09

Recently, the DSBGK method (Note: the original name DS-BGK is changed to DSBGK for simplicity) was proposed to reduce the stochastic noise in simulating rarefied gas flows at low velocity. Its total computational time is almost independent of the magnitude of deviation from equilibrium state. It was verified by the DSMC method in different benchmark problems over a wide range of Kn number. Some simulation results of the closed lid-driven cavity flow, thermal transpiration flow and the open channel flow by the DSBGK method are given here to show its efficiency and numerical stability. In closed problems, the density distribution is subject to unphysical fluctuation due to the absence of density constraint at the boundary. Thus, many simulated molecules are employed by DSBGK simulations to improve the stability and reduce the magnitude of fluctuation. This increases the memory usage remarkably but has small influence to the efficiency of DSBGK simulations. In open problems, the DSBGK simulation remains stable when using about 10 simulated molecules per cell because the fixed number densities at open boundaries eliminate the unphysical fluctuation. Small modification to the CLL reflection model is introduced to further improve the efficiency slightly.

Efficiency and stability of the DSBGK method

KAUST Repository

Li, Jun

2012-01-01

Recently, the DSBGK method (Note: the original name DS-BGK is changed to DSBGK for simplicity) was proposed to reduce the stochastic noise in simulating rarefied gas flows at low velocity. Its total computational time is almost independent of the magnitude of deviation from equilibrium state. It was verified by the DSMC method in different benchmark problems over a wide range of Kn number. Some simulation results of the closed lid-driven cavity flow, thermal transpiration flow and the open channel flow by the DSBGK method are given here to show its efficiency and numerical stability. In closed problems, the density distribution is subject to unphysical fluctuation due to the absence of density constraint at the boundary. Thus, many simulated molecules are employed by DSBGK simulations to improve the stability and reduce the magnitude of fluctuation. This increases the memory usage remarkably but has small influence to the efficiency of DSBGK simulations. In open problems, the DSBGK simulation remains stable when using about 10 simulated molecules per cell because the fixed number densities at open boundaries eliminate the unphysical fluctuation. Small modification to the CLL reflection model is introduced to further improve the efficiency slightly.

Parallel scalability and efficiency of vortex particle method for aeroelasticity analysis of bluff bodies

Science.gov (United States)

Tolba, Khaled Ibrahim; Morgenthal, Guido

2018-01-01

This paper presents an analysis of the scalability and efficiency of a simulation framework based on the vortex particle method. The code is applied for the numerical aerodynamic analysis of line-like structures. The numerical code runs on multicore CPU and GPU architectures using OpenCL framework. The focus of this paper is the analysis of the parallel efficiency and scalability of the method being applied to an engineering test case, specifically the aeroelastic response of a long-span bridge girder at the construction stage. The target is to assess the optimal configuration and the required computer architecture, such that it becomes feasible to efficiently utilise the method within the computational resources available for a regular engineering office. The simulations and the scalability analysis are performed on a regular gaming type computer.

A variable timestep generalized Runge-Kutta method for the numerical integration of the space-time diffusion equations

International Nuclear Information System (INIS)

Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.

1991-09-01

A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs

Vectorization on the star computer of several numerical methods for a fluid flow problem

Science.gov (United States)

Lambiotte, J. J., Jr.; Howser, L. M.

1974-01-01

A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

Numerical methods and inversion algorithms in reservoir simulation based on front tracking

Energy Technology Data Exchange (ETDEWEB)

Haugse, Vidar

1999-04-01

This thesis uses front tracking to analyse laboratory experiments on multiphase flow in porous media. New methods for parameter estimation for two- and three-phase relative permeability experiments have been developed. Up scaling of heterogeneous and stochastic porous media is analysed. Numerical methods based on front tracking is developed and analysed. Such methods are efficient for problems involving steep changes in the physical quantities. Multi-dimensional problems are solved by combining front tracking with dimensional splitting. A method for adaptive grid refinement is developed.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

Science.gov (United States)

Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

2012-07-02

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of

Numerical Methods for Partial Differential Equations

CERN Document Server

Guo, Ben-yu

1987-01-01

These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

Numerical conversion efficiency of thermally isolated Seebeck nanoantennas

Directory of Open Access Journals (Sweden)

Edgar Briones

2016-11-01

Full Text Available In this letter, we evaluate the conversion efficiency of thermally isolated Seebeck nanoantennas by numerical simulations and discuss their uses and scope for energy harvesting applications. This analysis includes the simple case of titanium-nickel dipoles suspended in air above the substrate by a 200 nm silicon dioxide membrane to isolate the heat dissipation. Results show that substantially thermal gradients are induced along the devices leading to a harvesting efficiency around 10-4 %, 400 % higher than the previously reported Seebeck nanoantennas. In the light of these results, different optimizing strategies should be considered in order to make the Seebeck nanoantennas useful for harvesting applications.

Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

International Nuclear Information System (INIS)

Zhou, Xiafeng; Guo, Jiong; Li, Fu

2015-01-01

Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn

2015-12-15

Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

Numerical method of lines for the relaxational dynamics of nematic liquid crystals.

Science.gov (United States)

Bhattacharjee, A K; Menon, Gautam I; Adhikari, R

2008-08-01

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase, and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic-nematic interface, illustrate the anisotropic character of droplets in the nucleation regime, and validate dynamical scaling in the coarsening regime.

Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects

Directory of Open Access Journals (Sweden)

Mahmoud A. Eissa

2017-01-01

Full Text Available Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES. The RES investment is characterized by uncertainty, which is long-term, costly and depends on feed-in tariff and support schemes. In this paper, we address the real option valuation (ROV of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price and, further, the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assessing the value of the deferred option are discussed. The new three-stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM methods. The numerical methods are integrated with the concept of Black–Scholes option pricing theory and applied in option valuation for solar energy investment with uncertainty. The numerical results of the L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our dataset refers to the Arab Republic of Egypt.

Efficient modeling of chiral media using SCN-TLM method

Directory of Open Access Journals (Sweden)

Yaich M.I.

2004-01-01

Full Text Available An efficient approach allowing to include linear bi-isotropic chiral materials in time-domain transmission line matrix (TLM calculations by employing recursive evaluation of the convolution of the electric and magnetic fields and susceptibility functions is presented. The new technique consists to add both voltage and current sources in supplementary stubs of the symmetrical condensed node (SCN of the TLM method. In this article, the details and the complete description of this approach are given. A comparison of the obtained numerical results with those of the literature reflects its validity and efficiency.

Study on numerical methods for transient flow induced by speed-changing impeller of fluid machinery

International Nuclear Information System (INIS)

Wu, Dazhuan; Chen, Tao; Wang, Leqin; Cheng, Wentao; Sun, Youbo

2013-01-01

In order to establish a reliable numerical method for solving the transient rotating flow induced by a speed-changing impeller, two numerical methods based on finite volume method (FVM) were presented and analyzed in this study. Two-dimensional numerical simulations of incompressible transient unsteady flow induced by an impeller during starting process were carried out respectively by using DM and DSR methods. The accuracy and adaptability of the two methods were evaluated by comprehensively comparing the calculation results. Moreover, an intensive study on the application of DSR method was conducted subsequently. The results showed that transient flow structure evolution and transient characteristics of the starting impeller are obviously affected by the starting process. The transient flow can be captured by both two methods, and the DSR method shows a higher computational efficiency. As an application example, the starting process of a mixed-flow pump was simulated by using DSR method. The calculation results were analyzed by comparing with the experiment data.

Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Karlsen, K.H.; Risebro, N.H.; Towers, J.D.

2001-10-01

We consider a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a nonlinear hyperbolic partial differential equation with a flux function that depends discontinuously on height. The purpose of this contribution is to present and demonstrate two numerical methods for simulating continuous sedimentation: a front tracking method and a finite finite difference method. The basic building blocks in the front tracking method are the solutions of a finite number of certain Riemann problems and a procedure for tracking local collisions of shocks. The solutions of the Riemann problems are recalled herein and the front tracking algorithm is described. As an alternative to the front tracking method, a simple scalar finite difference algorithm is proposed. This method is based on discretizing the spatially varying flux parameters on a mesh that is staggered with respect to that of the conserved variable, resulting in a straightforward generalization of the well-known Engquist-Osher upwind finite difference method. The result is an easily implemented upwind shock capturing method. Numerical examples demonstrate that the front tracking and finite difference methods can be used as efficient and accurate simulation tools for continuous sedimentation. The numerical results for the finite difference method indicate that discontinuities in the local solids concentration are resolved sharply and agree with those produced by the front tracking method. The latter is free of numerical dissipation, which leads to sharply resolved concentration discontinuities, but is more complicated to implement than the former. Available mathematical results for the proposed numerical methods are also briefly reviewed. (author)

Numerical prediction of Pelton turbine efficiency

Energy Technology Data Exchange (ETDEWEB)

Jott, D; Mez' nar, P; Lipej, A, E-mail: dragicajost@turboinstitut.s [Turbointtitut, Rovtnikova 7, Ljubljana, 1210 (Slovenia)

2010-08-15

This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-{omega} SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.

Numerical prediction of Pelton turbine efficiency

Science.gov (United States)

Jošt, D.; Mežnar, P.; Lipej, A.

2010-08-01

This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-ω SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.

Numerical prediction of Pelton turbine efficiency

International Nuclear Information System (INIS)

Jott, D; Mez'nar, P; Lipej, A

2010-01-01

This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-ω SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.

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

Science.gov (United States)

Song, Haiming; Zhang, Qi; Zhang, Ran

2015-10-01

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

An outline review of numerical transport methods

International Nuclear Information System (INIS)

Budd, C.

1981-01-01

A brief review is presented of numerical methods for solving the neutron transport equation in the context of reactor physics. First the various forms of transport equation are given. Second, the various ways of classifying numerical transport methods are discussed. Finally each method (or class of methods) is outlined in turn. (U.K.)

A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems

International Nuclear Information System (INIS)

Anastassi, Z. A.; Simos, T. E.

2010-01-01

We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.

Status and future prospects of using numerical methods to study complex flows at High Reynolds numbers

Science.gov (United States)

Maccormack, R. W.

1978-01-01

The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.

An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

A. H. Bhrawy

2014-01-01

Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

Numerical Simulation of Plasma Antenna with FDTD Method

International Nuclear Information System (INIS)

Chao, Liang; Yue-Min, Xu; Zhi-Jiang, Wang

2008-01-01

We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the characteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconBgurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design

Numerical simulation of plasma antenna with FDTD method

International Nuclear Information System (INIS)

Liang Chao; Xu Yuemin; Wang Zhijiang

2008-01-01

We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the characteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconfigurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design. (authors)

Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods

Directory of Open Access Journals (Sweden)

Frank Weichert

2013-01-01

Full Text Available The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs and lattice Boltzmann methods (LBMs. The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms.

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

Science.gov (United States)

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

2018-05-01

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

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

Science.gov (United States)

Verhoff, Ashley Marie

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

Efficient numerical simulation of heat storage in subsurface georeservoirs

Science.gov (United States)

Boockmeyer, A.; Bauer, S.

2015-12-01

The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and

A New Numerical Method for Z2 Topological Insulators with Strong Disorder

Science.gov (United States)

Akagi, Yutaka; Katsura, Hosho; Koma, Tohru

2017-12-01

We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.

Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning

Science.gov (United States)

Bradley, Ben K.

Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and

Numerical methods and modelling for engineering

CERN Document Server

Khoury, Richard

2016-01-01

This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...

On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

KAUST Repository

Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

2014-01-01

SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.

On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

KAUST Repository

Collier, Nathan

2014-09-17

SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.

Numerical Study on Several Stabilized Finite Element Methods for the Steady Incompressible Flow Problem with Damping

Directory of Open Access Journals (Sweden)

Jilian Wu

2013-01-01

Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.

An Efficient Evolutionary Based Method For Image Segmentation

OpenAIRE

Aslanzadeh, Roohollah; Qazanfari, Kazem; Rahmati, Mohammad

2017-01-01

The goal of this paper is to present a new efficient image segmentation method based on evolutionary computation which is a model inspired from human behavior. Based on this model, a four layer process for image segmentation is proposed using the split/merge approach. In the first layer, an image is split into numerous regions using the watershed algorithm. In the second layer, a co-evolutionary process is applied to form centers of finals segments by merging similar primary regions. In the t...

An introduction to numerical methods and analysis

CERN Document Server

Epperson, James F

2013-01-01

Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentralblatt MATH "". . . carefully structured with many detailed worked examples.""-The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to

Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

Energy Technology Data Exchange (ETDEWEB)

Klein, R I; Stone, J M

2007-11-20

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

Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

International Nuclear Information System (INIS)

Klein, R I; Stone, J M

2007-01-01

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

Efficient parallel implicit methods for rotary-wing aerodynamics calculations

Science.gov (United States)

Wissink, Andrew M.

Euler/Navier-Stokes Computational Fluid Dynamics (CFD) methods are commonly used for prediction of the aerodynamics and aeroacoustics of modern rotary-wing aircraft. However, their widespread application to large complex problems is limited lack of adequate computing power. Parallel processing offers the potential for dramatic increases in computing power, but most conventional implicit solution methods are inefficient in parallel and new techniques must be adopted to realize its potential. This work proposes alternative implicit schemes for Euler/Navier-Stokes rotary-wing calculations which are robust and efficient in parallel. The first part of this work proposes an efficient parallelizable modification of the Lower Upper-Symmetric Gauss Seidel (LU-SGS) implicit operator used in the well-known Transonic Unsteady Rotor Navier Stokes (TURNS) code. The new hybrid LU-SGS scheme couples a point-relaxation approach of the Data Parallel-Lower Upper Relaxation (DP-LUR) algorithm for inter-processor communication with the Symmetric Gauss Seidel algorithm of LU-SGS for on-processor computations. With the modified operator, TURNS is implemented in parallel using Message Passing Interface (MPI) for communication. Numerical performance and parallel efficiency are evaluated on the IBM SP2 and Thinking Machines CM-5 multi-processors for a variety of steady-state and unsteady test cases. The hybrid LU-SGS scheme maintains the numerical performance of the original LU-SGS algorithm in all cases and shows a good degree of parallel efficiency. It experiences a higher degree of robustness than DP-LUR for third-order upwind solutions. The second part of this work examines use of Krylov subspace iterative solvers for the nonlinear CFD solutions. The hybrid LU-SGS scheme is used as a parallelizable preconditioner. Two iterative methods are tested, Generalized Minimum Residual (GMRES) and Orthogonal s-Step Generalized Conjugate Residual (OSGCR). The Newton method demonstrates good

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2014-01-01

Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow...... equations. We present new detailed fundamental analysis using finite-amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high-order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow...

Methods to determine stratification efficiency of thermal energy storage processes–Review and theoretical comparison

DEFF Research Database (Denmark)

Haller, Michel; Cruickshank, Chynthia; Streicher, Wolfgang

2009-01-01

This paper reviews different methods that have been proposed to characterize thermal stratification in energy storages from a theoretical point of view. Specifically, this paper focuses on the methods that can be used to determine the ability of a storage to promote and maintain stratification...... during charging, storing and discharging, and represent this ability with a single numerical value in terms of a stratification efficiency for a given experiment or under given boundary conditions. Existing methods for calculating stratification efficiencies have been applied to hypothetical storage...

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

Science.gov (United States)

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

The differential method for grating efficiencies implemented in mathematica

Energy Technology Data Exchange (ETDEWEB)

Valdes, V.; McKinney, W. [Lawrence Berkeley Lab., CA (United States); Palmer, C. [Milton Co., Rochester, NY (United States). Roy Analytical Products Div.

1993-08-01

In order to facilitate the accurate calculation of diffraction grating efficiencies in the soft x-ray region, we have implemented the differential method of Neviere and Vincent in Mathematica [1]. This simplifies the programming to maximize the transparency of the theory for the user. We alleviate some of the overhead burden of the Mathematica program by coding the time-consuming numerical integration in C subprograms. We recall the differential method directly from Maxwell`s equations. The pseudo-periodicity of the grating profile and the electromagnetic fields allows us to use their Fourier series expansions to formulate an infinite set of coupled differential equations. A finite subset of the equations are then numerically integrated using the Numerov method for the transverse electric (TE) case and a fourth-order Runge-Kutta algorithm for the transverse magnetic (TM) case. We have tested our program by comparisons with the scalar theory and with published theoretical results for the blazed, sinusoidal and square wave profiles. The Reciprocity Theorem has also been used as a means to verify the method. We have found it to be verified for several cases to within the computational accuracy of the method.

Analysis of numerical methods

CERN Document Server

Isaacson, Eugene

1994-01-01

This excellent text for advanced undergraduates and graduate students covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, and other topics. It offers a careful analysis and stresses techniques for developing new methods, plus many examples and problems. 1966 edition.

Hybrid methods for airframe noise numerical prediction

Energy Technology Data Exchange (ETDEWEB)

Terracol, M.; Manoha, E.; Herrero, C.; Labourasse, E.; Redonnet, S. [ONERA, Department of CFD and Aeroacoustics, BP 72, Chatillon (France); Sagaut, P. [Laboratoire de Modelisation en Mecanique - UPMC/CNRS, Paris (France)

2005-07-01

This paper describes some significant steps made towards the numerical simulation of the noise radiated by the high-lift devices of a plane. Since the full numerical simulation of such configuration is still out of reach for present supercomputers, some hybrid strategies have been developed to reduce the overall cost of such simulations. The proposed strategy relies on the coupling of an unsteady nearfield CFD with an acoustic propagation solver based on the resolution of the Euler equations for midfield propagation in an inhomogeneous field, and the use of an integral solver for farfield acoustic predictions. In the first part of this paper, this CFD/CAA coupling strategy is presented. In particular, the numerical method used in the propagation solver is detailed, and two applications of this coupling method to the numerical prediction of the aerodynamic noise of an airfoil are presented. Then, a hybrid RANS/LES method is proposed in order to perform some unsteady simulations of complex noise sources. This method allows for significant reduction of the cost of such a simulation by considerably reducing the extent of the LES zone. This method is described and some results of the numerical simulation of the three-dimensional unsteady flow in the slat cove of a high-lift profile are presented. While these results remain very difficult to validate with experiments on similar configurations, they represent up to now the first 3D computations of this kind of flow. (orig.)

Numerical analysis in electromagnetics the TLM method

CERN Document Server

Saguet, Pierre

2013-01-01

The aim of this book is to give a broad overview of the TLM (Transmission Line Matrix) method, which is one of the "time-domain numerical methods". These methods are reputed for their significant reliance on computer resources. However, they have the advantage of being highly general.The TLM method has acquired a reputation for being a powerful and effective tool by numerous teams and still benefits today from significant theoretical developments. In particular, in recent years, its ability to simulate various situations with excellent precision, including complex materials, has been

Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices

Directory of Open Access Journals (Sweden)

Alicia Cordero

2018-01-01

Full Text Available We construct a family of derivative-free optimal iterative methods without memory to approximate a simple zero of a nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable to with-memory class. The extension of new family to the with-memory one is also presented which attains the convergence order 15.5156 and a very high efficiency index 15.51561/4≈1.9847. Some particular schemes of the with-memory family are also described. Numerical examples and some dynamical aspects of the new schemes are given to support theoretical results.

Numerical and adaptive grid methods for ideal magnetohydrodynamics

Science.gov (United States)

Loring, Burlen

2008-02-01

In this thesis numerical finite difference methods for ideal magnetohydrodynamics(MHD) are investigated. A review of the relevant physics, essential for interpreting the results of numerical solutions and constructing validation cases, is presented. This review includes a discusion of the propagation of small amplitude waves in the MHD system as well as a thorough discussion of MHD shocks, contacts and rarefactions and how they can be piece together to obtain a solutions to the MHD Riemann problem. Numerical issues relevant to the MHD system such as: the loss of nonlinear numerical stability in the presence of discontinuous solutions, the introduction of spurious forces due to the growth of the divergence of the magnetic flux density, the loss of pressure positivity, and the effects of non-conservative numerical methods are discussed, along with the practical approaches which can be used to remedy or minimize the negative consequences of each. The use of block structured adaptive mesh refinement is investigated in the context of a divergence free MHD code. A new method for conserving magnetic flux across AMR grid interfaces is developed and a detailed discussion of our implementation of this method using the CHOMBO AMR framework is given. A preliminary validation of the new method for conserving magnetic flux density across AMR grid interfaces illustrates that the method works. Finally a number of code validation cases are examined spurring a discussion of the strengths and weaknesses of the numerics employed.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

Science.gov (United States)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Investigation of Schottky-Barrier carbon nanotube field-effect transistor by an efficient semi-classical numerical modeling

International Nuclear Information System (INIS)

Chen Changxin; Zhang Wei; Zhao Bo; Zhang Yafei

2009-01-01

An efficient semi-classical numerical modeling approach has been developed to simulate the coaxial Schottky-barrier carbon nanotube field-effect transistor (SB-CNTFET). In the modeling, the electrostatic potential of the CNT is obtained by self-consistently solving the analytic expression of CNT carrier distribution and the cylindrical Poisson equation, which significantly enhances the computational efficiency and simultaneously present a result in good agreement to that obtained from the non-equilibrium Green's function (NEGF) formalism based on the first principle. With this method, the effects of the CNT diameter, power supply voltage, thickness and dielectric constant of gate insulator on the device performance are investigated.

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

Science.gov (United States)

Chang, Ching-Yuan; Ma, Chien-Ching

2017-08-01

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

Multi-hump potentials for efficient wave absorption in the numerical solution of the time-dependent Schrödinger equation

Science.gov (United States)

Silaev, A. A.; Romanov, A. A.; Vvedenskii, N. V.

2018-03-01

In the numerical solution of the time-dependent Schrödinger equation by grid methods, an important problem is the reflection and wrap-around of the wave packets at the grid boundaries. Non-optimal absorption of the wave function leads to possible large artifacts in the results of numerical simulations. We propose a new method for the construction of the complex absorbing potentials for wave suppression at the grid boundaries. The method is based on the use of the multi-hump imaginary potential which contains a sequence of smooth and symmetric humps whose widths and amplitudes are optimized for wave absorption in different spectral intervals. We show that this can ensure a high efficiency of absorption in a wide range of de Broglie wavelengths, which includes wavelengths comparable to the width of the absorbing layer. Therefore, this method can be used for high-precision simulations of various phenomena where strong spreading of the wave function takes place, including the phenomena accompanying the interaction of strong fields with atoms and molecules. The efficiency of the proposed method is demonstrated in the calculation of the spectrum of high-order harmonics generated during the interaction of hydrogen atoms with an intense infrared laser pulse.

Talbot's method for the numerical inversion of Laplace transforms: an implementation for personal computers

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

Safety assessments of radioactive waste disposal require efficient computer models for the important processes. The present paper is based on an efficient computational technique which can be used to solve a wide variety of safety assessment models. It involves the numerical inversion of analytical solutions to the Laplace-transformed differential equations using a method proposed by Talbot. This method has been implemented on a personal computer in a user-friendly manner. The steps required to implement a particular transform and run the program are outlined. Four examples are described which illustrate the flexibility, accuracy and efficiency of the program. The improvements in computational efficiency described in this paper have application to the probabilistic safety assessment codes ESCORT and MASCOT which are currently under development. Also, it is hoped that the present work will form the basis of software for personal computers which could be used to demonstrate safety assessment procedures to a wide audience. (author)

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

Science.gov (United States)

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

A numerical method for resonance integral calculations

International Nuclear Information System (INIS)

Tanbay, Tayfun; Ozgener, Bilge

2013-01-01

A numerical method has been proposed for resonance integral calculations and a cubic fit based on least squares approximation to compute the optimum Bell factor is given. The numerical method is based on the discretization of the neutron slowing down equation. The scattering integral is approximated by taking into account the location of the upper limit in energy domain. The accuracy of the method has been tested by performing computations of resonance integrals for uranium dioxide isolated rods and comparing the results with empirical values. (orig.)

Design of heat exchangers by numerical methods

International Nuclear Information System (INIS)

Konuk, A.A.

1981-01-01

Differential equations describing the heat tranfer in shell - and tube heat exchangers are derived and solved numerically. The method of ΔT sub(lm) is compared with the proposed method in cases where the specific heat at constant pressure, Cp and the overall heat transfer coefficient, U, vary with temperature. The error of the method of ΔT sub (lm) for the computation of the exchanger lenght is less than + 10%. However, the numerical method, being more accurate and at the same time easy to use and economical, is recommended for the design of shell-and-tube heat exchangers. (Author) [pt

Numerical methods for semiconductor heterostructures with band nonparabolicity

International Nuclear Information System (INIS)

Wang Weichung; Hwang Tsungmin; Lin Wenwei; Liu Jinnliang

2003-01-01

This article presents numerical methods for computing bound state energies and associated wave functions of three-dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity. A nonuniform finite difference method is presented to approximate a model of a cylindrical-shaped semiconductor quantum dot embedded in another semiconductor matrix. A matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems. Moreover, the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic Jacobi-Davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs. Numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail

Numerical implementation of the loop-tree duality method

Energy Technology Data Exchange (ETDEWEB)

Buchta, Sebastian; Rodrigo, German [Universitat de Valencia-Consejo Superior de Investigaciones Cientificas, Parc Cientific, Instituto de Fisica Corpuscular, Valencia (Spain); Chachamis, Grigorios [Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Draggiotis, Petros [Institute of Nuclear and Particle Physics, NCSR ' ' Demokritos' ' , Agia Paraskevi (Greece)

2017-05-15

We present a first numerical implementation of the loop-tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs. (orig.)

Numerical methods for metamaterial design

CERN Document Server

2013-01-01

This book describes a relatively new approach for the design of electromagnetic metamaterials.  Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths. After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered.  Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies.  Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization.  Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromag...

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

Science.gov (United States)

Katsaounis, T. D.

2005-02-01

equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical

Lagrangian numerical methods for ocean biogeochemical simulations

Science.gov (United States)

Paparella, Francesco; Popolizio, Marina

2018-05-01

We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.

Kinetic Energy Losses and Efficiency of an Axial Turbine Stage in Numerical Modeling of Unsteady Flows

Directory of Open Access Journals (Sweden)

A. S. Laskin

2015-01-01

Full Text Available The article presents the results of numerical investigation of kinetic energy (KE loss and blading efficiency of the single-stage axial turbine under different operating conditions, characterized by the ratio u/C0. The calculations are performed by stationary (Stage method and nonstationary (Transient method methods using ANSYS CFX. The novelty of this work lies in the fact that the numerical simulation of steady and unsteady flows in a turbine stage is conducted, and the results are obtained to determine the loss of KE, both separately by the elements of the flow range and their total values, in the stage efficiency as well. The results obtained are compared with the calculated efficiency according to one-dimensional theory.To solve these problems was selected model of axial turbine stage with D/l = 13, blade profiles of rotor and stator of constant cross-section, similar to tested ones in inverted turbine when = 0.3. The degree of reactivity ρ = 0.27, the rotor speed was varied within the range 1000 ÷ 1800 rev/min.Results obtained allow us to draw the following conclusions:1. The level of averaged coefficients of total KE losses in the range of from 0.48 to 0.75 is from 18% to 21% when calculating by the Stage method and from 21% to 25% by the Transient one.2. The level of averaged coefficients of KE losses with the output speed of in the specified range is from 9% to 13%, and almost the same when in calculating by Stage and Transient methods.3. Levels of averaged coefficients of KE loss in blade tips (relative to the differential enthalpies per stage are changed in the range: from 4% to 3% (Stage and are stored to be equal to 5% (Transient; from 5% to 6% (Stage and from 6% to 8% (Transient.4. Coefficients of KE losses in blade tips GV and RB are higher in calculations of the model stage using the Transient method than the Stage one, respectively, by = 1.5 ÷ 2.5% and = 4 ÷ 5% of the absolute values. These are values to characterize the KE

Application of Numerical Integration and Data Fusion in Unit Vector Method

Science.gov (United States)

Zhang, J.

2012-01-01

The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of

Numerical simulation of the flow field in pump intakes by means of Lattice Boltzmann methods

International Nuclear Information System (INIS)

Schneider, A; Conrad, D; Böhle, M

2013-01-01

Lattice Boltzmann Methods are nowadays popular schemes for solving fluid flow problems of engineering interest. This popularity is due to the advantages of these schemes: For example, the meshing of the fluid domain can be performed fully automatically which results in great simplicity in handling complex geometries. In this paper a numerical scheme for the flow simulation in pump intakes based on a Lattice Boltzmann large eddy approach is presented. The ability of this scheme to capture the flow phenomena of the intake flow at different operating conditions is analysed. For the operational reliability and efficiency of pumps and pump systems, the incoming flow conditions are crucial. Since the efficiency and reliability requirements of pumps are rising and must be guaranteed, the flow conditions in pump intakes have to be evaluated during plant planning. Recent trends show that pump intakes are built more and more compact, which makes the flow in the intake even more complex. Numerical methods are a promising technique for conduction flow analysis in pump intakes, because they can be realised rapidly and cheaply

Efficient evaluation of influence coefficients in three-dimensional extended boundary-node method for potential problems

International Nuclear Information System (INIS)

Itoh, Taku; Saitoh, Ayumu; Kamitani, Atsushi; Nakamura, Hiroaki

2011-01-01

For the purpose of speed-up of the three-dimensional eXtended Boundary-Node Method (X-BNM), an efficient algorithm for evaluating influence coefficients has been developed. The algorithm can be easily implemented into the X-BNM without using any integration cells. By applying the resulting X-BNM to the Laplace problem, the performance of the algorithm is numerically investigated. The numerical experiments show that, by using the algorithm, computational costs for evaluating influence coefficients in the X-BNM are reduced considerably. Especially for a large-sized problem, the algorithm is efficiently performed, and the computational costs of the X-BNM are close to those of the Boundary-Element Method (BEM). In addition, for the problem, the X-BNM shows almost the same accuracy as that of the BEM. (author)

Tensor viscosity method for convection in numerical fluid dynamics

International Nuclear Information System (INIS)

Dukowicz, J.K.; Ramshaw, J.D.

1979-01-01

A new method, called the tensor viscosity method, is described for differencing the convective terms in multidimensional numerical fluid dynamics. The method is the proper generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping. It is a single-step method that is distinguished by simplicity and case of implementation, even in the case of an arbitrary non-rectangular mesh. It should therefore be useful in finite-element as well as finite-difference formulations

Numerical simulation methods for phase-transitional flow

NARCIS (Netherlands)

Pecenko, A.

2010-01-01

The object of the present dissertation is a numerical study of multiphase flow of one fluid component. In particular, the research described in this thesis focuses on the development of numerical methods that are based on a diffuse-interface model (DIM). With this approach, the modeling problem

Fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles

International Nuclear Information System (INIS)

Fogelson, A.L.; Peskin, C.S.

1988-01-01

A new fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles is presented. The fluid dynamics equations are solved on a lattice. A particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice. These points are coupled by forces which resist deformation of the particle. These forces contribute to the force density in the Stokes' equations. As a result, a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries. Particles size, shape, and deformability may be prescribed. Computational work increases only linearly with the number of particles, so large numbers (500--1000) of particles may be studied efficiently. The numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite-difference approximation to the Stokes' equations using the Fourier--Toeplitz method. The numerical method has been implemented to run on all CRAY computers: the implementation exploits the CRAY's vectorized arithmetic, and on machines with insufficient central memory, it performs efficient disk I/O while storing most of the data on disk. Applications of the method to sedimentation of one-, two-, and many-particle systems are described. Trajectories and settling speeds for two-particle sedimentation, and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories. copyright 1988 Academic Press, Inc

A New Efficient Algorithm for the 2D WLP-FDTD Method Based on Domain Decomposition Technique

Directory of Open Access Journals (Sweden)

Bo-Ao Xu

2016-01-01

Full Text Available This letter introduces a new efficient algorithm for the two-dimensional weighted Laguerre polynomials finite difference time-domain (WLP-FDTD method based on domain decomposition scheme. By using the domain decomposition finite difference technique, the whole computational domain is decomposed into several subdomains. The conventional WLP-FDTD and the efficient WLP-FDTD methods are, respectively, used to eliminate the splitting error and speed up the calculation in different subdomains. A joint calculation scheme is presented to reduce the amount of calculation. Through our work, the iteration is not essential to obtain the accurate results. Numerical example indicates that the efficiency and accuracy are improved compared with the efficient WLP-FDTD method.

Assessing numerical methods used in nuclear aerosol transport models

International Nuclear Information System (INIS)

McDonald, B.H.

1987-01-01

Several computer codes are in use for predicting the behaviour of nuclear aerosols released into containment during postulated accidents in water-cooled reactors. Each of these codes uses numerical methods to discretize and integrate the equations that govern the aerosol transport process. Computers perform only algebraic operations and generate only numbers. It is in the numerical methods that sense can be made of these numbers and where they can be related to the actual solution of the equations. In this report, the numerical methods most commonly used in the aerosol transport codes are examined as special cases of a general solution procedure, the Method of Weighted Residuals. It would appear that the numerical methods used in the codes are all capable of producing reasonable answers to the mathematical problem when used with skill and care. 27 refs

Nonlinear ordinary differential equations analytical approximation and numerical methods

CERN Document Server

Hermann, Martin

2016-01-01

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

Efficient generalized Golub-Kahan based methods for dynamic inverse problems

Science.gov (United States)

Chung, Julianne; Saibaba, Arvind K.; Brown, Matthew; Westman, Erik

2018-02-01

We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately 43 000 measurements and 7.8 million unknowns in under 40 s on a standard desktop.

METRIC CHARACTERISTICS OF VARIOUS METHODS FOR NUMERICAL DENSITY ESTIMATION IN TRANSMISSION LIGHT MICROSCOPY – A COMPUTER SIMULATION

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Miroslav Kališnik

2011-05-01

Full Text Available In the introduction the evolution of methods for numerical density estimation of particles is presented shortly. Three pairs of methods have been analysed and compared: (1 classical methods for particles counting in thin and thick sections, (2 original and modified differential counting methods and (3 physical and optical disector methods. Metric characteristics such as accuracy, efficiency, robustness, and feasibility of methods have been estimated and compared. Logical, geometrical and mathematical analysis as well as computer simulations have been applied. In computer simulations a model of randomly distributed equal spheres with maximal contrast against surroundings has been used. According to our computer simulation all methods give accurate results provided that the sample is representative and sufficiently large. However, there are differences in their efficiency, robustness and feasibility. Efficiency and robustness increase with increasing slice thickness in all three pairs of methods. Robustness is superior in both differential and both disector methods compared to both classical methods. Feasibility can be judged according to the additional equipment as well as to the histotechnical and counting procedures necessary for performing individual counting methods. However, it is evident that not all practical problems can efficiently be solved with models.

A method for data handling numerical results in parallel OpenFOAM simulations

International Nuclear Information System (INIS)

nd Vasile Pârvan Ave., 300223, TM Timişoara, Romania, alin.anton@cs.upt.ro (Romania))" data-affiliation=" (Faculty of Automatic Control and Computing, Politehnica University of Timişoara, 2nd Vasile Pârvan Ave., 300223, TM Timişoara, Romania, alin.anton@cs.upt.ro (Romania))" >Anton, Alin; th Mihai Viteazu Ave., 300221, TM Timişoara (Romania))" data-affiliation=" (Center for Advanced Research in Engineering Science, Romanian Academy – Timişoara Branch, 24th Mihai Viteazu Ave., 300221, TM Timişoara (Romania))" >Muntean, Sebastian

2015-01-01

Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit ® [1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms

A method for data handling numerical results in parallel OpenFOAM simulations

Energy Technology Data Exchange (ETDEWEB)

Anton, Alin [Faculty of Automatic Control and Computing, Politehnica University of Timişoara, 2" n" d Vasile Pârvan Ave., 300223, TM Timişoara, Romania, alin.anton@cs.upt.ro (Romania); Muntean, Sebastian [Center for Advanced Research in Engineering Science, Romanian Academy – Timişoara Branch, 24" t" h Mihai Viteazu Ave., 300221, TM Timişoara (Romania)

2015-12-31

Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit{sup ®}[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.

Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

KAUST Repository

Kou, Jisheng

2015-07-16

In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton\\'s method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.

Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2015-01-01

In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

Science.gov (United States)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow

Efficient implicit LES method for the simulation of turbulent cavitating flows

International Nuclear Information System (INIS)

Egerer, Christian P.; Schmidt, Steffen J.; Hickel, Stefan; Adams, Nikolaus A.

2016-01-01

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flow field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.

A Fortran program for the numerical integration of the one-dimensional Schroedinger equation using exponential and Bessel fitting methods

International Nuclear Information System (INIS)

Cash, J.R.; Raptis, A.D.; Simos, T.E.

1990-01-01

An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)

Efficient kinetic Monte Carlo method for reaction-diffusion problems with spatially varying annihilation rates

Science.gov (United States)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

Numerical methods and analysis of multiscale problems

CERN Document Server

Madureira, Alexandre L

2017-01-01

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

Spectral Methods in Numerical Plasma Simulation

DEFF Research Database (Denmark)

Coutsias, E.A.; Hansen, F.R.; Huld, T.

1989-01-01

An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...

Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods

Science.gov (United States)

Zhu, Honggeng; Zhang, Rentian; Deng, Dongsheng; Feng, Xusong; Yao, Linbi

2010-06-01

Since the flow in tubular pumping systems is basically along axial direction and passes symmetrically through the impeller, most satisfying the basic hypotheses in the design of impeller and having higher pumping system efficiency in comparison with vertical pumping system, they are being widely applied to low-head pumping engineering. In a pumping station, the fluctuation of water levels in the sump and discharge pool is most common and at most time the pumping system runs under off-design conditions. Hence, the operation of pump has to be flexibly regulated to meet the needs of flow rates, and the selection of regulation method is as important as that of pump to reduce operation cost and achieve economic operation. In this paper, the three dimensional time-averaged Navier-Stokes equations are closed by RNG κ-ɛ turbulent model, and two tubular pumping systems with different regulation methods, equipped with the same pump model but with different designed system structures, are numerically simulated respectively to predict the pumping system performances and analyze the influence of regulation device and help designers make final decision in the selection of design schemes. The computed results indicate that the pumping system with blade-adjusting device needs longer suction box, and the increased hydraulic loss will lower the pumping system efficiency in the order of 1.5%. The pumping system with permanent magnet motor, by means of variable speed regulation, obtains higher system efficiency partly for shorter suction box and partly for different structure design. Nowadays, the varied speed regulation is realized by varied frequency device, the energy consumption of which is about 3˜4% of output power of the motor. Hence, when the efficiency of variable frequency device is considered, the total pumping system efficiency will probably be lower.

Essential numerical computer methods

CERN Document Server

Johnson, Michael L

2010-01-01

The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide ...

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Numerical methods and optimization a consumer guide

CERN Document Server

Walter, Éric

2014-01-01

Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to ·         discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; ·         understand the principles behind recognized algorithms used in state-of-the-art numerical software; ·         learn the advantag...

Operator theory and numerical methods

CERN Document Server

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.

Numerical methods for scientists and engineers

CERN Document Server

Antia, H M

2012-01-01

This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

2015-01-01

Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

Numerical methods for stochastic partial differential equations with white noise

CERN Document Server

Zhang, Zhongqiang

2017-01-01

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...

Numerical method of singular problems on singular integrals

International Nuclear Information System (INIS)

Zhao Huaiguo; Mou Zongze

1992-02-01

As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily

A numerically efficient damping model for acoustic resonances in microfluidic cavities

Energy Technology Data Exchange (ETDEWEB)

Hahn, P., E-mail: hahnp@ethz.ch; Dual, J. [Institute of Mechanical Systems (IMES), Department of Mechanical and Process Engineering, ETH Zurich, Tannenstrasse 3, CH-8092 Zurich (Switzerland)

2015-06-15

Bulk acoustic wave devices are typically operated in a resonant state to achieve enhanced acoustic amplitudes and high acoustofluidic forces for the manipulation of microparticles. Among other loss mechanisms related to the structural parts of acoustofluidic devices, damping in the fluidic cavity is a crucial factor that limits the attainable acoustic amplitudes. In the analytical part of this study, we quantify all relevant loss mechanisms related to the fluid inside acoustofluidic micro-devices. Subsequently, a numerical analysis of the time-harmonic visco-acoustic and thermo-visco-acoustic equations is carried out to verify the analytical results for 2D and 3D examples. The damping results are fitted into the framework of classical linear acoustics to set up a numerically efficient device model. For this purpose, all damping effects are combined into an acoustofluidic loss factor. Since some components of the acoustofluidic loss factor depend on the acoustic mode shape in the fluid cavity, we propose a two-step simulation procedure. In the first step, the loss factors are deduced from the simulated mode shape. Subsequently, a second simulation is invoked, taking all losses into account. Owing to its computational efficiency, the presented numerical device model is of great relevance for the simulation of acoustofluidic particle manipulation by means of acoustic radiation forces or acoustic streaming. For the first time, accurate 3D simulations of realistic micro-devices for the quantitative prediction of pressure amplitudes and the related acoustofluidic forces become feasible.

Numerical modeling of contaminant transport in fractured porous media using mixed finite-element and finitevolume methods

KAUST Repository

Dong, Chen

2011-01-01

A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods; i.e., the mixed finite-element (MFE) method and the finite-volume method. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocity fields for both the fractures and matrix, which are crucial to the convection part of the transport equation. The finite-volume method and the standard MFE method are used to approximate the convection and dispersion terms, respectively. The temporary evolution for the pressure distributions, streamline fields, and concentration profiles are obtained for six different arrangements of fractures. The results clearly show the distorted concentration effects caused by the ordered and disordered (random) patterns of the fractures and illustrate the robustness and efficiency of the proposed numerical model. © 2011 by Begell House Inc.

Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki

2007-01-01

The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)

Use of exact albedo conditions in numerical methods for one-dimensional one-speed discrete ordinates eigenvalue problems

International Nuclear Information System (INIS)

Abreu, M.P. de

1994-01-01

The use of exact albedo boundary conditions in numerical methods applied to one-dimensional one-speed discrete ordinates (S n ) eigenvalue problems for nuclear reactor global calculations is described. An albedo operator that treats the reflector region around a nuclear reactor core implicitly is described and exactly was derived. To illustrate the method's efficiency and accuracy, it was used conventional linear diamond method with the albedo option to solve typical model problems. (author)

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

Full Text Available An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

NUMERICAL AND ANALYTIC METHODS OF ESTIMATION BRIDGES’ CONSTRUCTIONS

Directory of Open Access Journals (Sweden)

Y. Y. Luchko

2010-03-01

Full Text Available In this article the numerical and analytical methods of calculation of the stressed-and-strained state of bridge constructions are considered. The task on increasing of reliability and accuracy of the numerical method and its solution by means of calculations in two bases are formulated. The analytical solution of the differential equation of deformation of a ferro-concrete plate under the action of local loads is also obtained.

A Numerical Method for Blast Shock Wave Analysis of Missile Launch from Aircraft

Directory of Open Access Journals (Sweden)

Sebastian Heimbs

2015-01-01

Full Text Available An efficient empirical approach was developed to accurately represent the blast shock wave loading resulting from the launch of a missile from a military aircraft to be used in numerical analyses. Based on experimental test series of missile launches in laboratory environment and from a helicopter, equations were derived to predict the time- and position-dependent overpressure. The method was finally applied and validated in a structural analysis of a helicopter tail boom under missile launch shock wave loading.

Multilevel summation methods for efficient evaluation of long-range pairwise interactions in atomistic and coarse-grained molecular simulation.

Energy Technology Data Exchange (ETDEWEB)

Bond, Stephen D.

2014-01-01

The availability of efficient algorithms for long-range pairwise interactions is central to the success of numerous applications, ranging in scale from atomic-level modeling of materials to astrophysics. This report focuses on the implementation and analysis of the multilevel summation method for approximating long-range pairwise interactions. The computational cost of the multilevel summation method is proportional to the number of particles, N, which is an improvement over FFTbased methods whos cost is asymptotically proportional to N logN. In addition to approximating electrostatic forces, the multilevel summation method can be use to efficiently approximate convolutions with long-range kernels. As an application, we apply the multilevel summation method to a discretized integral equation formulation of the regularized generalized Poisson equation. Numerical results are presented using an implementation of the multilevel summation method in the LAMMPS software package. Preliminary results show that the computational cost of the method scales as expected, but there is still a need for further optimization.

Application of a space-time CE/SE (Conversation Element/Solution Element) method to the numerical solution of chromatographic separation processes

DEFF Research Database (Denmark)

including convection-difmsion-reaction PDEs are numerically solved using the two methods on the same spatial grid. Even though the CE/SE method uses a simple stencil structure and is developed on a simple mathematical basis (i.e., Gauss' divergence theorem), accurate and computationally-efficient solutions...

Composite magnetic refrigerants for an Ericsson cycle: New method of selection using a numerical approach

International Nuclear Information System (INIS)

Smaieli, A.; Chahine, R.

1997-01-01

The efficient operation of an Ericsson cycle requires the magnetic entropy change (AS) be constant as a function of temperature. To realize this condition using composite materials, a numerical method has been developed to determine the optimum proportions of the components. The Gd x Er 1-x (x = 0.69, 0.90) alloys have been used to investigate the validity of the numerical method. The values of ΔS have been determined from experimental magnetization curves of these alloys, in the 0.1-9 T magnetic field and the 200-290 K range. The calculations have led to the mass ratio y = 0.56 for the composite (Gd 0.90 Er 0.10 ) y (Gd 0.69 Er 0.31 ) 1-y . The ΔS of this composite is fairly constant in the 225-280 K range. To confirm this result, the magnetization curves of the composite material have been determined experimentally, and the corresponding ΔS was compared with the one predicted numerically. A good agreement was found proving the method's ability to properly determine the required fractions of the refrigerant's constituent materials

Theoretical and numerical method in aeroacoustics

Directory of Open Access Journals (Sweden)

Nicuşor ALEXANDRESCU

2010-06-01

Full Text Available The paper deals with the mathematical and numerical modeling of the aerodynamic noisegenerated by the fluid flow interaction with the solid structure of a rotor blade.Our analysis use Lighthill’s acoustic analogy. Lighthill idea was to express the fundamental equationsof motion into a wave equation for acoustic fluctuation with a source term on the right-hand side. Theobtained wave equation is solved numerically by the spatial discretization. The method is applied inthe case of monopole source placed in different points of blade surfaces to find this effect of noisepropagation.

Numerical analyses for efficient photoionization by nonmonochromatic fields

International Nuclear Information System (INIS)

Hasegawa, Shuichi; Suzuki, Atsuyuki

2000-01-01

Numerical analyses on excitation and ionization probabilities of atoms with hyperfine structures were performed in order to compare two different excitation methods, adiabatic excitation and broadband excitation. The lifetime of the intermediate states was considered in order to investigate the effect of the absorption line broadening. The dependences of the two excitation methods on the lifetime were found to be quite different. The ionization probability by the adiabatic excitation is higher than that by the broadband excitation for identical excitation laser intensity. (author)

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 com...... to the fully implicit scheme, the proposed scheme achieves more accurate results, prevents numerical errors and requires less computational effort. In AMR simulations the new scheme can reduce the computational time by 88%....

Numerical methods in finance and economics a MATLAB-based introduction

CERN Document Server

Brandimarte, Paolo

2006-01-01

A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of financeThe use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications.The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions.Among this book''s most outstanding features is the...

Two numerical methods for an inverse problem for the 2-D Helmholtz equation

CERN Document Server

Gryazin, Y A; Lucas, T R

2003-01-01

Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.

Stochastic numerical methods an introduction for students and scientists

CERN Document Server

Toral, Raul

2014-01-01

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability ConceptsMonte Carlo IntegrationGeneration of Uniform and Non-uniformRandom Numbers: Non-correlated ValuesDynamical MethodsApplications to Statistical MechanicsIn...

Numerical methods design, analysis, and computer implementation of algorithms

CERN Document Server

Greenbaum, Anne

2012-01-01

Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book a...

A modified phase-fitted and amplification-fitted Runge-Kutta-Nyström method for the numerical solution of the radial Schrödinger equation

OpenAIRE

Papadopoulos , D. F.; Anastassi , Z. A.; Simos , T. E.

2010-01-01

Abstract A new Runge-Kutta-Nystrom method, with phase-lag and amplification error of order infinity, for the numerical solution of the Schrodinger equation is developed in this paper. The new method is based on the Runge-Kutta-Nystrom method with fourth algebraic order, developed by Dormand, El-Mikkawy and Prince. Numerical illustrations indicate that the new method is much more efficient than other methods derived for the same purpose. phone: +30-210-9421510 (Simos, T. E.) ...

A student's guide to numerical methods

CERN Document Server

Hutchinson, Ian H

2015-01-01

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introdu...

Partial differential equations with numerical methods

CERN Document Server

Larsson, Stig

2003-01-01

The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.

Improved DEA Cross Efficiency Evaluation Method Based on Ideal and Anti-Ideal Points

Directory of Open Access Journals (Sweden)

Qiang Hou

2018-01-01

Full Text Available A new model is introduced in the process of evaluating efficiency value of decision making units (DMUs through data envelopment analysis (DEA method. Two virtual DMUs called ideal point DMU and anti-ideal point DMU are combined to form a comprehensive model based on the DEA method. The ideal point DMU is taking self-assessment system according to efficiency concept. The anti-ideal point DMU is taking other-assessment system according to fairness concept. The two distinctive ideal point models are introduced to the DEA method and combined through using variance ration. From the new model, a reasonable result can be obtained. Numerical examples are provided to illustrate the new constructed model and certify the rationality of the constructed model through relevant analysis with the traditional DEA model.

Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions

International Nuclear Information System (INIS)

Havu, V.; Blum, V.; Havu, P.; Scheffler, M.

2009-01-01

We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.

Study on Parallel Processing for Efficient Flexible Multibody Analysis based on Subsystem Synthesis Method

Energy Technology Data Exchange (ETDEWEB)

Han, Jong-Boo; Song, Hajun; Kim, Sung-Soo [Chungnam Nat’l Univ., Daejeon (Korea, Republic of)

2017-06-15

Flexible multibody simulations are widely used in the industry to design mechanical systems. In flexible multibody dynamics, deformation coordinates are described either relatively in the body reference frame that is floating in the space or in the inertial reference frame. Moreover, these deformation coordinates are generated based on the discretization of the body according to the finite element approach. Therefore, the formulation of the flexible multibody system always deals with a huge number of degrees of freedom and the numerical solution methods require a substantial amount of computational time. Parallel computational methods are a solution for efficient computation. However, most of the parallel computational methods are focused on the efficient solution of large-sized linear equations. For multibody analysis, we need to develop an efficient formulation that could be suitable for parallel computation. In this paper, we developed a subsystem synthesis method for a flexible multibody system and proposed efficient parallel computational schemes based on the OpenMP API in order to achieve efficient computation. Simulations of a rotating blade system, which consists of three identical blades, were carried out with two different parallel computational schemes. Actual CPU times were measured to investigate the efficiency of the proposed parallel schemes.

Application of the photoelastic experimental hybrid method with new numerical method to the high stress distribution

International Nuclear Information System (INIS)

Hawong, Jai Sug; Lee, Dong Hun; Lee, Dong Ha; Tche, Konstantin

2004-01-01

In this research, the photoelastic experimental hybrid method with Hook-Jeeves numerical method has been developed: This method is more precise and stable than the photoelastic experimental hybrid method with Newton-Rapson numerical method with Gaussian elimination method. Using the photoelastic experimental hybrid method with Hook-Jeeves numerical method, we can separate stress components from isochromatics only and stress intensity factors and stress concentration factors can be determined. The photoelastic experimental hybrid method with Hook-Jeeves had better be used in the full field experiment than the photoelastic experimental hybrid method with Newton-Rapson with Gaussian elimination method

On the efficient numerical solution of lattice systems with low-order couplings

International Nuclear Information System (INIS)

Ammon, A.; Genz, A.; Hartung, T.; Jansen, K.; Volmer, J.; Leoevey, H.

2015-10-01

We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.

Teaching numerical methods with IPython notebooks and inquiry-based learning

KAUST Repository

Ketcheson, David I.

2014-01-01

A course in numerical methods should teach both the mathematical theory of numerical analysis and the craft of implementing numerical algorithms. The IPython notebook provides a single medium in which mathematics, explanations, executable code, and visualizations can be combined, and with which the student can interact in order to learn both the theory and the craft of numerical methods. The use of notebooks also lends itself naturally to inquiry-based learning methods. I discuss the motivation and practice of teaching a course based on the use of IPython notebooks and inquiry-based learning, including some specific practical aspects. The discussion is based on my experience teaching a Masters-level course in numerical analysis at King Abdullah University of Science and Technology (KAUST), but is intended to be useful for those who teach at other levels or in industry.

Two numerical methods for mean-field games

KAUST Repository

Gomes, Diogo A.

2016-01-01

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

Two numerical methods for mean-field games

KAUST Repository

Gomes, Diogo A.

2016-01-09

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem

Directory of Open Access Journals (Sweden)

Won-Tak Hong

2016-01-01

Full Text Available We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1 as well as oscillating singularities (of type rαsin⁡(ϵlog⁡r. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.

Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems

International Nuclear Information System (INIS)

Haber, E; Horesh, L; Tenorio, L

2010-01-01

Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data

Numerical methods in electron magnetic resonance

International Nuclear Information System (INIS)

Soernes, A.R.

1998-01-01

The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system

Numerical methods in electron magnetic resonance

Energy Technology Data Exchange (ETDEWEB)

Soernes, A.R

1998-07-01

The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system.

Study on highly efficient seismic data acquisition and processing methods based on sparsity constraint

Science.gov (United States)

Wang, H.; Chen, S.; Tao, C.; Qiu, L.

2017-12-01

High-density, high-fold and wide-azimuth seismic data acquisition methods are widely used to overcome the increasingly sophisticated exploration targets. The acquisition period is longer and longer and the acquisition cost is higher and higher. We carry out the study of highly efficient seismic data acquisition and processing methods based on sparse representation theory (or compressed sensing theory), and achieve some innovative results. The theoretical principles of highly efficient acquisition and processing is studied. We firstly reveal sparse representation theory based on wave equation. Then we study the highly efficient seismic sampling methods and present an optimized piecewise-random sampling method based on sparsity prior information. At last, a reconstruction strategy with the sparsity constraint is developed; A two-step recovery approach by combining sparsity-promoting method and hyperbolic Radon transform is also put forward. The above three aspects constitute the enhanced theory of highly efficient seismic data acquisition. The specific implementation strategies of highly efficient acquisition and processing are studied according to the highly efficient acquisition theory expounded in paragraph 2. Firstly, we propose the highly efficient acquisition network designing method by the help of optimized piecewise-random sampling method. Secondly, we propose two types of highly efficient seismic data acquisition methods based on (1) single sources and (2) blended (or simultaneous) sources. Thirdly, the reconstruction procedures corresponding to the above two types of highly efficient seismic data acquisition methods are proposed to obtain the seismic data on the regular acquisition network. A discussion of the impact on the imaging result of blended shooting is discussed. In the end, we implement the numerical tests based on Marmousi model. The achieved results show: (1) the theoretical framework of highly efficient seismic data acquisition and processing

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

Science.gov (United States)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Analysis of recovery efficiency in high-temperature aquifer thermal energy storage: a Rayleigh-based method

Science.gov (United States)

Schout, Gilian; Drijver, Benno; Gutierrez-Neri, Mariene; Schotting, Ruud

2014-01-01

High-temperature aquifer thermal energy storage (HT-ATES) is an important technique for energy conservation. A controlling factor for the economic feasibility of HT-ATES is the recovery efficiency. Due to the effects of density-driven flow (free convection), HT-ATES systems applied in permeable aquifers typically have lower recovery efficiencies than conventional (low-temperature) ATES systems. For a reliable estimation of the recovery efficiency it is, therefore, important to take the effect of density-driven flow into account. A numerical evaluation of the prime factors influencing the recovery efficiency of HT-ATES systems is presented. Sensitivity runs evaluating the effects of aquifer properties, as well as operational variables, were performed to deduce the most important factors that control the recovery efficiency. A correlation was found between the dimensionless Rayleigh number (a measure of the relative strength of free convection) and the calculated recovery efficiencies. Based on a modified Rayleigh number, two simple analytical solutions are proposed to calculate the recovery efficiency, each one covering a different range of aquifer thicknesses. The analytical solutions accurately reproduce all numerically modeled scenarios with an average error of less than 3 %. The proposed method can be of practical use when considering or designing an HT-ATES system.

Numerical analysis of bifurcations

International Nuclear Information System (INIS)

Guckenheimer, J.

1996-01-01

This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics

Screening of groundwater remedial alternatives for brownfield sites: a comprehensive method integrated MCDA with numerical simulation.

Science.gov (United States)

Li, Wei; Zhang, Min; Wang, Mingyu; Han, Zhantao; Liu, Jiankai; Chen, Zhezhou; Liu, Bo; Yan, Yan; Liu, Zhu

2018-06-01

Brownfield sites pollution and remediation is an urgent environmental issue worldwide. The screening and assessment of remedial alternatives is especially complex owing to its multiple criteria that involves technique, economy, and policy. To help the decision-makers selecting the remedial alternatives efficiently, the criteria framework conducted by the U.S. EPA is improved and a comprehensive method that integrates multiple criteria decision analysis (MCDA) with numerical simulation is conducted in this paper. The criteria framework is modified and classified into three categories: qualitative, semi-quantitative, and quantitative criteria, MCDA method, AHP-PROMETHEE (analytical hierarchy process-preference ranking organization method for enrichment evaluation) is used to determine the priority ranking of the remedial alternatives and the solute transport simulation is conducted to assess the remedial efficiency. A case study was present to demonstrate the screening method in a brownfield site in Cangzhou, northern China. The results show that the systematic method provides a reliable way to quantify the priority of the remedial alternatives.

Numerical Algorithm for Delta of Asian Option

Directory of Open Access Journals (Sweden)

Boxiang Zhang

2015-01-01

Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.

Numerical methods for the Lévy LIBOR model

DEFF Research Database (Denmark)

Papapantoleon, Antonis; Skovmand, David

2010-01-01

but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure....... This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\\'evy LIBOR model of Eberlein and \\"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates...

Numerical Methods for the Lévy LIBOR Model

DEFF Research Database (Denmark)

Papapantoleon, Antonis; Skovmand, David

are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables...... simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods...

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2012-01-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish. PMID:23564971

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2011-08-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Classical and modern numerical analysis theory, methods and practice

CERN Document Server

Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan

2009-01-01

Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...

Numerical method for the nonlinear Fokker-Planck equation

International Nuclear Information System (INIS)

Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.

1997-01-01

A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society

Efficient approximation of random fields for numerical applications

KAUST Repository

Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus

2015-01-01

We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

Efficient approximation of random fields for numerical applications

KAUST Repository

Harbrecht, Helmut

2015-01-07

We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

Efficient Numerical Methods for Nonequilibrium Re-Entry Flows

Science.gov (United States)

2014-01-14

right-hand side is the only quadratic operation). The number of sub- iterations , kmax, used in this update needs to be chosen for optimal convergence and...Upper Symmetric Gauss - Seidel Method for the Euler and Navier-Stokes Equations,”, AIAA Journal, Vol. 26, No. 9, pp. 1025-1026, Sept. 1988. 11Edwards, J.R...Candler, “The Solution of the Navier-Stokes Equations Using Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, pp. 135-150, 1989

A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

Directory of Open Access Journals (Sweden)

Changqing Yang

2012-01-01

Full Text Available A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Computer prediction of subsurface radionuclide transport: an adaptive numerical method

International Nuclear Information System (INIS)

Neuman, S.P.

1983-01-01

Radionuclide transport in the subsurface is often modeled with the aid of the advection-dispersion equation. A review of existing computer methods for the solution of this equation shows that there is need for improvement. To answer this need, a new adaptive numerical method is proposed based on an Eulerian-Lagrangian formulation. The method is based on a decomposition of the concentration field into two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single-step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices. Preliminary tests against analytical solutions of ne- and two-dimensional dispersion in a uniform steady state velocity field suggest that the proposed adaptive method can handle the entire range of Peclet numbers from 0 to infinity, with Courant numbers well in excess of 1

Numerical methods for modeling photonic-crystal VCSELs

DEFF Research Database (Denmark)

Dems, Maciej; Chung, Il-Sug; Nyakas, Peter

2010-01-01

We show comparison of four different numerical methods for simulating Photonic-Crystal (PC) VCSELs. We present the theoretical basis behind each method and analyze the differences by studying a benchmark VCSEL structure, where the PC structure penetrates all VCSEL layers, the entire top-mirror DBR...... to the effective index method. The simulation results elucidate the strength and weaknesses of the analyzed methods; and outline the limits of applicability of the different models....

Energy efficient process planning based on numerical simulations

OpenAIRE

Neugebauer, Reimund; Hochmuth, C.; Schmidt, G.; Dix, M.

2011-01-01

The main goal of energy-efficient manufacturing is to generate products with maximum value-added at minimum energy consumption. To this end, in metal cutting processes, it is necessary to reduce the specific cutting energy while, at the same time, precision requirements have to be ensured. Precision is critical in metal cutting processes because they often constitute the final stages of metalworking chains. This paper presents a method for the planning of energy-efficient machining processes ...

A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models

International Nuclear Information System (INIS)

Echard, B.; Gayton, N.; Lemaire, M.; Relun, N.

2013-01-01

Applying reliability methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling. This new method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the method is, first, proved on two academic applications. It is then conducted for assessing the reliability of a challenging aerospace case study submitted to fatigue.

Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method

Science.gov (United States)

Zhang, Hong; Zegeling, Paul Andries

2017-09-01

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow in porous media incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behavior. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-02-01

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

A numerical method for transient gas-liquid two-phase flow using a general curvilinear coordinate system. 1. Governing equations and numerical method

International Nuclear Information System (INIS)

Tomiyama, Akio; Matsuoka, Toshiyuki.

1995-01-01

A simple numerical method for solving a transient incompressible two-fluid model was proposed in the present study. A general curvilinear coordinate system was adopted in this method for predicting transient flows in practical engineering devices. The simplicity of the present method is due to the fact that the field equations and constitutive equations were expressed in a tensor form in the general curvilinear coordinate system. When a conventional rectangular mesh is adopted in a calculation, the method reduces to a numerical method for a Cartesian coordinate system. As an example, the present method was applied to transient air-water bubbly flow in a vertical U-tube. It was confirmed that the effects of centrifugal and gravitational forces on the phase distribution in the U-tube were reasonably predicted. (author)

Numerical methods: Analytical benchmarking in transport theory

International Nuclear Information System (INIS)

Ganapol, B.D.

1988-01-01

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

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

Science.gov (United States)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

A numerical method for a transient two-fluid model

International Nuclear Information System (INIS)

Le Coq, G.; Libmann, M.

1978-01-01

The transient boiling two-phase flow is studied. In nuclear reactors, the driving conditions for the transient boiling are a pump power decay or/and an increase in heating power. The physical model adopted for the two-phase flow is the two fluid model with the assumption that the vapor remains at saturation. The numerical method for solving the thermohydraulics problems is a shooting method, this method is highly implicit. A particular problem exists at the boiling and condensation front. A computer code using this numerical method allow the calculation of a transient boiling initiated by a steady state for a PWR or for a LMFBR

Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows

Science.gov (United States)

Moitra, Stuti; Gatski, Thomas B.

1997-01-01

A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.

Method for numerical simulation of two-term exponentially correlated colored noise

International Nuclear Information System (INIS)

Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.

2006-01-01

A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

International Nuclear Information System (INIS)

Khotylev, V.A.; Hoogenboom, J.E.

1996-01-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

Energy Technology Data Exchange (ETDEWEB)

Khotylev, V.A.; Hoogenboom, J.E. [Delft Univ. of Technology, Interfaculty Reactor Inst., Delft (Netherlands)

1996-07-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

Mathematica with a Numerical Methods Course

Science.gov (United States)

Varley, Rodney

2003-04-01

An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.

Numerical perturbative methods in the quantum theory of physical systems

International Nuclear Information System (INIS)

Adam, G.

1980-01-01

During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)

A Computationally-Efficient Numerical Model to Characterize the Noise Behavior of Metal-Framed Walls

Directory of Open Access Journals (Sweden)

Arun Arjunan

2015-08-01

Full Text Available Architects, designers, and engineers are making great efforts to design acoustically-efficient metal-framed walls, minimizing acoustic bridging. Therefore, efficient simulation models to predict the acoustic insulation complying with ISO 10140 are needed at a design stage. In order to achieve this, a numerical model consisting of two fluid-filled reverberation chambers, partitioned using a metal-framed wall, is to be simulated at one-third-octaves. This produces a large simulation model consisting of several millions of nodes and elements. Therefore, efficient meshing procedures are necessary to obtain better solution times and to effectively utilise computational resources. Such models should also demonstrate effective Fluid-Structure Interaction (FSI along with acoustic-fluid coupling to simulate a realistic scenario. In this contribution, the development of a finite element frequency-dependent mesh model that can characterize the sound insulation of metal-framed walls is presented. Preliminary results on the application of the proposed model to study the geometric contribution of stud frames on the overall acoustic performance of metal-framed walls are also presented. It is considered that the presented numerical model can be used to effectively visualize the noise behaviour of advanced materials and multi-material structures.

Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods

International Nuclear Information System (INIS)

Reynolds, J. M.; Lopez-Bruna, D.

2009-01-01

In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs

Towards numerical simulations of supersonic liquid jets using ghost fluid method

International Nuclear Information System (INIS)

Majidi, Sahand; Afshari, Asghar

2015-01-01

Highlights: • A ghost fluid method based solver is developed for numerical simulation of compressible multiphase flows. • The performance of the numerical tool is validated via several benchmark problems. • Emergence of supersonic liquid jets in quiescent gaseous environment is simulated using ghost fluid method for the first time. • Bow-shock formation ahead of the liquid jet is clearly observed in the obtained numerical results. • Radiation of mach waves from the phase-interface witnessed experimentally is evidently captured in our numerical simulations. - Abstract: A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid

Numerical functional integration method for studying the properties of the physical vacuum

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.

1998-01-01

The new approach to investigate the physical vacuum in quantum theories including its nonperturbative topological structure is discussed. This approach is based on the representation of the matrix element of the evolution operator in Euclidean metrics in a form of the functional integral with a certain measure in the corresponding space and on the use of approximation formulas which we constructed for this kind of integral. No preliminary discretization of space and time is required, as well as no simplifying assumptions like semiclassical approximation, collective excitations, introduction of ''short-time'' propagators, etc. are necessary in this approach. The method allows to use the more preferable deterministic algorithms instead of the traditional stochastic technique. It has been proven that our approach has important advantages over the other known methods, including the higher efficiency of computations. Examples of application of the method to the numerical study of some potential nuclear models and to the computation of the topological susceptibility and the θ-vacua energy are presented. (author)

A Numerical Study on the Improvement of Suction Performance and Hydraulic Efficiency for a Mixed-Flow Pump Impeller

Directory of Open Access Journals (Sweden)

Sung Kim

2014-01-01

Full Text Available This paper describes a numerical study on the improvement of suction performance and hydraulic efficiency of a mixed-flow pump by impellers. The design of these impellers was optimized using a commercial CFD (computational fluid dynamics code and DOE (design of experiments. The design variables of meridional plane and vane plane development were defined for impeller design. In DOE, variables of inlet part were selected as main design variables in meridional plane, and incidence angle was selected in vane plane development. The verification of the experiment sets that were generated by 2k factorial was done by numerical analysis. The objective functions were defined as the NPSHre (net positive suction head required, total efficiency, and total head of the impellers. The importance of the geometric design variables was analyzed using 2k factorial designs. The interaction between the NPSHre and total efficiency, according to the meridional plane and incidence angle, was discussed by analyzing the 2k factorial design results. The performance of optimally designed model was verified by experiments and numerical analysis and the reliability of the model was retained by comparison of numerical analysis and comparative analysis with the reference model.

Development of efficient time-evolution method based on three-term recurrence relation

International Nuclear Information System (INIS)

Akama, Tomoko; Kobayashi, Osamu; Nanbu, Shinkoh

2015-01-01

The advantage of the real-time (RT) propagation method is a direct solution of the time-dependent Schrödinger equation which describes frequency properties as well as all dynamics of a molecular system composed of electrons and nuclei in quantum physics and chemistry. Its applications have been limited by computational feasibility, as the evaluation of the time-evolution operator is computationally demanding. In this article, a new efficient time-evolution method based on the three-term recurrence relation (3TRR) was proposed to reduce the time-consuming numerical procedure. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function. Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. The formula was adapted to assess the performance of the RT time-dependent Hartree-Fock (RT-TDHF) method and the time-dependent density functional theory. Compared to the commonly used fourth-order Runge-Kutta method, our new approach decreased computational time of the RT-TDHF calculation by about factor of four, showing the 3TRR formula to be an efficient time-evolution method for reducing computational cost

Numerical methods in matrix computations

CERN Document Server

Björck, Åke

2015-01-01

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

An efficient implicit direct forcing immersed boundary method for incompressible flows

International Nuclear Information System (INIS)

Cai, S-G; Ouahsine, A; Smaoui, H; Favier, J; Hoarau, Y

2015-01-01

A novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature

Hybrid numerical calculation method for bend waveguides

OpenAIRE

Garnier , Lucas; Saavedra , C.; Castro-Beltran , Rigoberto; Lucio , José Luis; Bêche , Bruno

2017-01-01

National audience; The knowledge of how the light will behave in a waveguide with a radius of curvature becomes more and more important because of the development of integrated photonics, which include ring micro-resonators, phasars, and other devices with a radius of curvature. This work presents a numerical calculation method to determine the eigenvalues and eigenvectors of curved waveguides. This method is a hybrid method which uses at first conform transformation of the complex plane gene...

Intelligent numerical methods applications to fractional calculus

CERN Document Server

Anastassiou, George A

2016-01-01

In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

Development of an efficient retrotransposon-based fingerprinting method for rapid pea variety identification.

Science.gov (United States)

Smýkal, Petr

2006-01-01

Fast and efficient DNA fingerprinting of crop cultivars and individuals is frequently used in both theoretical population genetics and in practical breeding. Numerous DNA marker technologies exist and the ratio of speed, cost and accuracy are of importance. Therefore even in species where highly accurate and polymorphic marker systems are available, such as microsatellite SSR (simple sequence repeats), also alternative methods may be of interest. Thanks to their high abundance and ubiquity, temporary mobile retrotransposable elements come into recent focus. Their properties, such as genome wide distribution and well-defined origin of individual insertions by descent, predetermine them for use as molecular markers. In this study, several Ty3-gypsy type retrotransposons have been developed and adopted for the inter-retrotransposon amplified polymorphism (IRAP) method, which is suitable for fast and efficient pea cultivar fingerprinting. The method can easily distinguish even between genetically closely related pea cultivars and provide high polymorphic information content (PIC) in a single PCR analysis.

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

Science.gov (United States)

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

2013-01-01

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

A Numerical Matrix-Based method in Harmonic Studies in Wind Power Plants

DEFF Research Database (Denmark)

Dowlatabadi, Mohammadkazem Bakhshizadeh; Hjerrild, Jesper; Kocewiak, Łukasz Hubert

2016-01-01

In the low frequency range, there are some couplings between the positive- and negative-sequence small-signal impedances of the power converter due to the nonlinear and low bandwidth control loops such as the synchronization loop. In this paper, a new numerical method which also considers...... these couplings will be presented. The numerical data are advantageous to the parametric differential equations, because analysing the high order and complex transfer functions is very difficult, and finally one uses the numerical evaluation methods. This paper proposes a numerical matrix-based method, which...

Interdisciplinary Study of Numerical Methods and Power Plants Engineering

Directory of Open Access Journals (Sweden)

Ioana OPRIS

2014-08-01

Full Text Available The development of technology, electronics and computing opened the way for a cross-disciplinary research that brings benefits by combining the achievements of different fields. To prepare the students for their future interdisciplinary approach,aninterdisciplinary teaching is adopted. This ensures their progress in knowledge, understanding and ability to navigate through different fields. Aiming these results, the Universities introduce new interdisciplinary courses which explore complex problems by studying subjects from different domains. The paper presents a problem encountered in designingpower plants. The method of solvingthe problem isused to explain the numerical methods and to exercise programming.The goal of understanding a numerical algorithm that solves a linear system of equations is achieved by using the knowledge of heat transfer to design the regenerative circuit of a thermal power plant. In this way, the outcomes from the prior courses (mathematics and physics are used to explain a new subject (numerical methods and to advance future ones (power plants.

Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method

Directory of Open Access Journals (Sweden)

T. Jayakumar

2015-01-01

Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

Numerical methods for Bayesian inference in the face of aging

International Nuclear Information System (INIS)

Clarotti, C.A.; Villain, B.; Procaccia, H.

1996-01-01

In recent years, much attention has been paid to Bayesian methods for Risk Assessment. Until now, these methods have been studied from a theoretical point of view. Researchers have been mainly interested in: studying the effectiveness of Bayesian methods in handling rare events; debating about the problem of priors and other philosophical issues. An aspect central to the Bayesian approach is numerical computation because any safety/reliability problem, in a Bayesian frame, ends with a problem of numerical integration. This aspect has been neglected until now because most Risk studies assumed the Exponential model as the basic probabilistic model. The existence of conjugate priors makes numerical integration unnecessary in this case. If aging is to be taken into account, no conjugate family is available and the use of numerical integration becomes compulsory. EDF (National Board of Electricity, of France) and ENEA (National Committee for Energy, New Technologies and Environment, of Italy) jointly carried out a research program aimed at developing quadrature methods suitable for Bayesian Interference with underlying Weibull or gamma distributions. The paper will illustrate the main results achieved during the above research program and will discuss, via some sample cases, the performances of the numerical algorithms which on the appearance of stress corrosion cracking in the tubes of Steam Generators of PWR French power plants. (authors)

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

Science.gov (United States)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Numerical methods for image registration

CERN Document Server

Modersitzki, Jan

2003-01-01

Based on the author's lecture notes and research, this well-illustrated and comprehensive text is one of the first to provide an introduction to image registration with particular emphasis on numerical methods in medical imaging. Ideal for researchers in industry and academia, it is also a suitable study guide for graduate mathematicians, computer scientists, engineers, medical physicists, and radiologists.Image registration is utilised whenever information obtained from different viewpoints needs to be combined or compared and unwanted distortion needs to be eliminated. For example, CCTV imag

Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.; Saude, Joao

2017-01-01

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.

2017-04-29

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

Susy theories and QCD: numerical approaches

International Nuclear Information System (INIS)

Ita, Harald

2011-01-01

We review on-shell and unitarity methods and discuss their application to precision predictions for Large Hadron Collider (LHC) physics. Being universal and numerically robust, these methods are straightforward to automate for next-to-leading-order computations within standard model and beyond. Several state-of-the-art results including studies of (W/Z+3)-jet and (W+4)-jet production have explicitly demonstrated the effectiveness of the unitarity method for describing multi-parton scattering. Here we review central ideas needed to obtain efficient numerical implementations. This includes on-shell loop-level recursions, the unitarity method, color management and further refined tricks. (review)

Developing Teaching Material Software Assisted for Numerical Methods

Science.gov (United States)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

Introduction to numerical methods for time dependent differential equations

CERN Document Server

Kreiss, Heinz-Otto

2014-01-01

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method

International Nuclear Information System (INIS)

Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke

2012-01-01

Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.

Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method

Directory of Open Access Journals (Sweden)

Jun He

2018-05-01

Full Text Available One significant factor influencing geothermal energy exploitation is the variation of the mechanical properties of rock in high temperature environments. Since rock is typically a heterogeneous granular material, thermal fracturing frequently occurs in the rock when the ambient temperature changes, which can greatly influence the geothermal energy exploitation. A numerical method based on the numerical manifold method (NMM is developed in this study to simulate the thermo-elastic fracturing of rocklike granular materials. The Voronoi tessellation is incorporated into the pre-processor of NMM to represent the grain structure. A contact-based heat transfer model is developed to reflect heat interaction among grains. Based on the model, the transient thermal conduction algorithm for granular materials is established. To simulate the cohesion effects among grains and the fracturing process between grains, a damage-based contact fracture model is developed to improve the contact algorithm of NMM. In the developed numerical method, the heat interaction among grains as well as the heat transfer inside each solid grain are both simulated. Additionally, as damage evolution and fracturing at grain interfaces are also considered, the developed numerical method is applicable to simulate the geothermal-related thermal fracturing process.

Rigid inclusions-Comparison between analytical and numerical methods

International Nuclear Information System (INIS)

Gomez Perez, R.; Melentijevic, S.

2014-01-01

This paper compares different analytical methods for analysis of rigid inclusions with finite element modeling. First of all, the load transfer in the distribution layer is analyzed for its different thicknesses and different inclusion grids to define the range between results obtained by analytical and numerical methods. The interaction between the soft soil and the inclusion in the estimation of settlements is studied as well. Considering different stiffness of the soft soil, settlements obtained analytical and numerically are compared. The influence of the soft soil modulus of elasticity on the neutral point depth was also performed by finite elements. This depth has a great importance for the definition of the total length of rigid inclusion. (Author)

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

Science.gov (United States)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute

Numerical methods in nuclear engineering. Part 1

International Nuclear Information System (INIS)

Phillips, G.J.

1983-08-01

These proceedings, published in two parts contain the full text of 56 papers and summaries of six papers presented at the conference. They cover the use of numerical methods in thermal hydraulics, reactor physics, neutron diffusion, subchannel analysis, risk assessment, transport theory, and fuel behaviour

A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

Science.gov (United States)

Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

2018-01-01

In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

Highly efficient strong stability preserving Runge-Kutta methods with Low-Storage Implementations

KAUST Repository

Ketcheson, David I.

2008-01-01

Strong stability-preserving (SSP) Runge–Kutta methods were developed for time integration of semidiscretizations of partial differential equations. SSP methods preserve stability properties satisfied by forward Euler time integration, under a modified time-step restriction. We consider the problem of finding explicit Runge–Kutta methods with optimal SSP time-step restrictions, first for the case of linear autonomous ordinary differential equations and then for nonlinear or nonautonomous equations. By using alternate formulations of the associated optimization problems and introducing a new, more general class of low-storage implementations of Runge–Kutta methods, new optimal low-storage methods and new low-storage implementations of known optimal methods are found. The results include families of low-storage second and third order methods that achieve the maximum theoretically achievable effective SSP coefficient (independent of stage number), as well as low-storage fourth order methods that are more efficient than current full-storage methods. The theoretical properties of these methods are confirmed by numerical experiment.

Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method

Science.gov (United States)

Krasnov, M. M.; Kuchugov, P. A.; E Ladonkina, M.; E Lutsky, A.; Tishkin, V. F.

2017-02-01

Detailed unstructured grids and numerical methods of high accuracy are frequently used in the numerical simulation of gasdynamic flows in areas with complex geometry. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach offers a number of advantages inherent to both finite-element and finite-difference approximations. Moreover, the present paper shows that DGM schemes can be viewed as Godunov method extension to piecewise-polynomial functions. As is known, DGM involves significant computational complexity, and this brings up the question of ensuring the most effective use of all the computational capacity available. In order to speed up the calculations, operator programming method has been applied while creating the computational module. This approach makes possible compact encoding of mathematical formulas and facilitates the porting of programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. With the software package, based on DGM, numerical simulations of supersonic flow past solid bodies has been carried out. The numerical results are in good agreement with the experimental ones.

Numerical methods to solve the two-dimensional heat conduction equation

International Nuclear Information System (INIS)

Santos, R.S. dos.

1981-09-01

A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt

Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method

OpenAIRE

Jun He; Quansheng Liu; Zhijun Wu; Yalong Jiang

2018-01-01

One significant factor influencing geothermal energy exploitation is the variation of the mechanical properties of rock in high temperature environments. Since rock is typically a heterogeneous granular material, thermal fracturing frequently occurs in the rock when the ambient temperature changes, which can greatly influence the geothermal energy exploitation. A numerical method based on the numerical manifold method (NMM) is developed in this study to simulate the thermo-elastic fracturing ...

A hybrid numerical method for orbit correction

International Nuclear Information System (INIS)

White, G.; Himel, T.; Shoaee, H.

1997-09-01

The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings

Conservative numerical methods for solitary wave interactions

Energy Technology Data Exchange (ETDEWEB)

Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)

2003-07-18

The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.

FORECASTING PILE SETTLEMENT ON CLAYSTONE USING NUMERICAL AND ANALYTICAL METHODS

Directory of Open Access Journals (Sweden)

Ponomarev Andrey Budimirovich

2016-06-01

Full Text Available In the article the problem of designing pile foundations on claystones is reviewed. The purpose of this paper is comparative analysis of the analytical and numerical methods for forecasting the settlement of piles on claystones. The following tasks were solved during the study: 1 The existing researches of pile settlement are analyzed; 2 The characteristics of experimental studies and the parameters for numerical modeling are presented, methods of field research of single piles’ operation are described; 3 Calculation of single pile settlement is performed using numerical methods in the software package Plaxis 2D and analytical method according to the requirements SP 24.13330.2011; 4 Experimental data is compared with the results of analytical and numerical calculations; 5 Basing on these results recommendations for forecasting pile settlement on claystone are presented. Much attention is paid to the calculation of pile settlement considering the impacted areas in ground space beside pile and the comparison with the results of field experiments. Basing on the obtained results, for the prediction of settlement of single pile on claystone the authors recommend using the analytical method considered in SP 24.13330.2011 with account for the impacted areas in ground space beside driven pile. In the case of forecasting the settlement of single pile on claystone by numerical methods in Plaxis 2D the authors recommend using the Hardening Soil model considering the impacted areas in ground space beside the driven pile. The analyses of the results and calculations are presented for examination and verification; therefore it is necessary to continue the research work of deep foundation at another experimental sites to improve the reliability of the calculation of pile foundation settlement. The work is of great interest for geotechnical engineers engaged in research, design and construction of pile foundations.

Application of numerical analysis methods to thermoluminescence dosimetry

International Nuclear Information System (INIS)

Gomez Ros, J. M.; Delgado, A.

1989-01-01

This report presents the application of numerical methods to thermoluminescence dosimetry (TLD), showing the advantages obtained over conventional evaluation systems. Different configurations of the analysis method are presented to operate in specific dosimetric applications of TLD, such as environmental monitoring and mailed dosimetry systems for quality assurance in radiotherapy facilities. (Author) 10 refs

Numerical method for three dimensional steady-state two-phase flow calculations

International Nuclear Information System (INIS)

Raymond, P.; Toumi, I.

1992-01-01

This paper presents the numerical scheme which was developed for the FLICA-4 computer code to calculate three dimensional steady state two phase flows. This computer code is devoted to steady state and transient thermal hydraulics analysis of nuclear reactor cores 1,3 . The first section briefly describes the FLICA-4 flow modelling. Then in order to introduce the numerical method for steady state computations, some details are given about the implicit numerical scheme based upon an approximate Riemann solver which was developed for calculation of flow transients. The third section deals with the numerical method for steady state computations, which is derived from this previous general scheme and its optimization. We give some numerical results for steady state calculations and comparisons on required CPU time and memory for various meshing and linear system solvers

Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method

Directory of Open Access Journals (Sweden)

J. Prakash

2016-03-01

Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.

Numerical methods of mathematical optimization with Algol and Fortran programs

CERN Document Server

Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner

1971-01-01

Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition

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.

Numerical Analysis of Partial Differential Equations

CERN Document Server

Lui, S H

2011-01-01

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis

A computationally efficient moment-preserving Monte Carlo electron transport method with implementation in Geant4

Energy Technology Data Exchange (ETDEWEB)

Dixon, D.A., E-mail: ddixon@lanl.gov [Los Alamos National Laboratory, P.O. Box 1663, MS P365, Los Alamos, NM 87545 (United States); Prinja, A.K., E-mail: prinja@unm.edu [Department of Nuclear Engineering, MSC01 1120, 1 University of New Mexico, Albuquerque, NM 87131-0001 (United States); Franke, B.C., E-mail: bcfrank@sandia.gov [Sandia National Laboratories, Albuquerque, NM 87123 (United States)

2015-09-15

This paper presents the theoretical development and numerical demonstration of a moment-preserving Monte Carlo electron transport method. Foremost, a full implementation of the moment-preserving (MP) method within the Geant4 particle simulation toolkit is demonstrated. Beyond implementation details, it is shown that the MP method is a viable alternative to the condensed history (CH) method for inclusion in current and future generation transport codes through demonstration of the key features of the method including: systematically controllable accuracy, computational efficiency, mathematical robustness, and versatility. A wide variety of results common to electron transport are presented illustrating the key features of the MP method. In particular, it is possible to achieve accuracy that is statistically indistinguishable from analog Monte Carlo, while remaining up to three orders of magnitude more efficient than analog Monte Carlo simulations. Finally, it is shown that the MP method can be generalized to any applicable analog scattering DCS model by extending previous work on the MP method beyond analytical DCSs to the partial-wave (PW) elastic tabulated DCS data.

A numerical method for solving singular De`s

Energy Technology Data Exchange (ETDEWEB)

Mahaver, W.T.

1996-12-31

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

Preface of "The Second Symposium on Border Zones Between Experimental and Numerical Application Including Solution Approaches By Extensions of Standard Numerical Methods"

Science.gov (United States)

Ortleb, Sigrun; Seidel, Christian

2017-07-01

In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.

A method for the direct generation of comprehensive numerical solar building transfer functions

Energy Technology Data Exchange (ETDEWEB)

Chen, T.Y. [The Hong Kong Polytechnic University (China). Dept. of Building Services Engineering

2003-02-01

This paper describes a method for the direct generation of comprehensive numerical room transfer functions with any derived parameters as output, such as operative temperature or thermal load. Complex conductive, convective and radiant heat transfer processes, or any derived thermal parameters in buildings can be explicitly and precisely described by a generalized thermal network. This allows the s-transfer and z-transfer functions to be directly generated, using semi-symbolic analysis techniques, Cayley's expansion of determinant and Heaviside's expansion theorem. A simple algorithm is developed for finding the roots of the denominator in the inverse transform of the s-transfer functions, which ensures that no single root is missing. The techniques have been applied to generating the transfer functions of a passive solar room with floor heating. The example calculation demonstrates the high efficiency of the computational method. (author)

A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line

KAUST Repository

He, Qiaolin

2011-06-01

In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.

Efficiency profile method to study the hit efficiency of drift chambers

International Nuclear Information System (INIS)

Abyzov, A.; Bel'kov, A.; Lanev, A.; Spiridonov, A.; Walter, M.; Hulsbergen, W.

2002-01-01

A method based on the usage of efficiency profile is proposed to estimate the hit efficiency of drift chambers with a large number of channels. The performance of the method under real conditions of the detector operation has been tested analysing the experimental data from the HERA-B drift chambers

Numerical method for two phase flow with a unstable interface

International Nuclear Information System (INIS)

Glimm, J.; Marchesin, D.; McBryan, O.

1981-01-01

The random choice method is used to compute the oil-water interface for two dimensional porous media equations. The equations used are a pair of coupled equations; the (elliptic) pressure equation and the (hyperbolic) saturation equation. The equations do not include the dispersive capillary pressure term and the computation does not introduce numerical diffusion. The method resolves saturation discontinuities sharply. The main conclusion of this paper is that the random choice is a correct numerical procedure for this problem even in the highly fingered case. Two methods of inducing fingers are considered: deterministically, through choice of Cauchy data and heterogeneity, through maximizing the randomness of the random choice method

An implicit second order numerical method for two-fluid models

International Nuclear Information System (INIS)

Toumi, I.

1995-01-01

We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)

NUMERICAL WITHOUT ITERATION METHOD OF MODELING OF ELECTROMECHANICAL PROCESSES IN ASYNCHRONOUS ENGINES

Directory of Open Access Journals (Sweden)

D. G. Patalakh

2018-02-01

Full Text Available Purpose. Development of calculation of electromagnetic and electromechanic transients is in asynchronous engines without iterations. Methodology. Numeral methods of integration of usual differential equations, programming. Findings. As the system of equations, describing the dynamics of asynchronous engine, contents the products of rotor and stator currents and product of rotation frequency of rotor and currents, so this system is nonlinear one. The numeral solution of nonlinear differential equations supposes an iteration process on every step of integration. Time-continuing and badly converging iteration process may be the reason of calculation slowing. The improvement of numeral method by the way of an iteration process removing is offered. As result the modeling time is reduced. The improved numeral method is applied for integration of differential equations, describing the dynamics of asynchronous engine. Originality. The improvement of numeral method allowing to execute numeral integrations of differential equations containing product of functions is offered, that allows to avoid an iteration process on every step of integration and shorten modeling time. Practical value. On the basis of the offered methodology the universal program of modeling of electromechanics processes in asynchronous engines could be developed as taking advantage on fast-acting.

Numerical methods for differential equations and applications

International Nuclear Information System (INIS)

Ixaru, L.G.

1984-01-01

This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)

Applying multi-resolution numerical methods to geodynamics

Science.gov (United States)

Davies, David Rhodri

Computational models yield inaccurate results if the underlying numerical grid fails to provide the necessary resolution to capture a simulation's important features. For the large-scale problems regularly encountered in geodynamics, inadequate grid resolution is a major concern. The majority of models involve multi-scale dynamics, being characterized by fine-scale upwelling and downwelling activity in a more passive, large-scale background flow. Such configurations, when coupled to the complex geometries involved, present a serious challenge for computational methods. Current techniques are unable to resolve localized features and, hence, such models cannot be solved efficiently. This thesis demonstrates, through a series of papers and closely-coupled appendices, how multi-resolution finite-element methods from the forefront of computational engineering can provide a means to address these issues. The problems examined achieve multi-resolution through one of two methods. In two-dimensions (2-D), automatic, unstructured mesh refinement procedures are utilized. Such methods improve the solution quality of convection dominated problems by adapting the grid automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. Thermal and thermo-chemical validation tests illustrate that the technique is robust and highly successful, improving solution accuracy whilst increasing computational efficiency. These points are reinforced when the technique is applied to geophysical simulations of mid-ocean ridge and subduction zone magmatism. To date, successful goal-orientated/error-guided grid adaptation techniques have not been utilized within the field of geodynamics. The work included herein is therefore the first geodynamical application of such methods. In view of the existing three-dimensional (3-D) spherical mantle dynamics codes, which are built upon a quasi-uniform discretization of the sphere and closely coupled

A numerical test of the collective coordinate method

International Nuclear Information System (INIS)

Dobrowolski, T.; Tatrocki, P.

2008-01-01

The purpose of this Letter is to compare the dynamics of the kink interacting with the imperfection which follows from the collective coordinate method with the numerical results obtained on the ground of the field theoretical model. We showed that for weekly interacting kinks the collective coordinate method works similarly well for low and extremely large speeds

An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks

KAUST Repository

Yucel, Abdulkadir C.

2015-05-05

An efficient method for statistically characterizing multiconductor transmission line (MTL) networks subject to a large number of manufacturing uncertainties is presented. The proposed method achieves its efficiency by leveraging a high-dimensional model representation (HDMR) technique that approximates observables (quantities of interest in MTL networks, such as voltages/currents on mission-critical circuits) in terms of iteratively constructed component functions of only the most significant random variables (parameters that characterize the uncertainties in MTL networks, such as conductor locations and widths, and lumped element values). The efficiency of the proposed scheme is further increased using a multielement probabilistic collocation (ME-PC) method to compute the component functions of the HDMR. The ME-PC method makes use of generalized polynomial chaos (gPC) expansions to approximate the component functions, where the expansion coefficients are expressed in terms of integrals of the observable over the random domain. These integrals are numerically evaluated and the observable values at the quadrature/collocation points are computed using a fast deterministic simulator. The proposed method is capable of producing accurate statistical information pertinent to an observable that is rapidly varying across a high-dimensional random domain at a computational cost that is significantly lower than that of gPC or Monte Carlo methods. The applicability, efficiency, and accuracy of the method are demonstrated via statistical characterization of frequency-domain voltages in parallel wire, interconnect, and antenna corporate feed networks.

Efficient orbit integration by manifold correction methods.

Science.gov (United States)

Fukushima, Toshio

2005-12-01

Triggered by a desire to investigate, numerically, the planetary precession through a long-term numerical integration of the solar system, we developed a new formulation of numerical integration of orbital motion named manifold correct on methods. The main trick is to rigorously retain the consistency of physical relations, such as the orbital energy, the orbital angular momentum, or the Laplace integral, of a binary subsystem. This maintenance is done by applying a correction to the integrated variables at each integration step. Typical methods of correction are certain geometric transformations, such as spatial scaling and spatial rotation, which are commonly used in the comparison of reference frames, or mathematically reasonable operations, such as modularization of angle variables into the standard domain [-pi, pi). The form of the manifold correction methods finally evolved are the orbital longitude methods, which enable us to conduct an extremely precise integration of orbital motions. In unperturbed orbits, the integration errors are suppressed at the machine epsilon level for an indefinitely long period. In perturbed cases, on the other hand, the errors initially grow in proportion to the square root of time and then increase more rapidly, the onset of which depends on the type and magnitude of the perturbations. This feature is also realized for highly eccentric orbits by applying the same idea as used in KS-regularization. In particular, the introduction of time elements greatly enhances the performance of numerical integration of KS-regularized orbits, whether the scaling is applied or not.

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

Directory of Open Access Journals (Sweden)

Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

A more efficient implementation of the discrete-ordinates method for an approximate model of particle transport in a duct

International Nuclear Information System (INIS)

Ganapol, B.D.

2015-01-01

Highlights: • Method of doubling solution for the pipe problem. • Uses convergence acceleration. • Fully discretized solution. • Improvement over ADO. - Abstract: We consider transport of light, neutrons, or any uncharged particles in a straight duct of circular cross section. This problem first came to fashion some 30 years ago when Pomraning and Prinja formulated their so called “pipe problem”. In the years to follow, investigators applied essentially every known method of numerical solution, including MMRW’s Wiener–Hopf – except possibly one. This presentation concerns that particular numerical solution, which arguably seems to be the most efficient of all.

RELAP-7 Numerical Stabilization: Entropy Viscosity Method

Energy Technology Data Exchange (ETDEWEB)

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

2014-06-01

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

Investigation of the Dynamic Contact Angle Using a Direct Numerical Simulation Method.

Science.gov (United States)

Zhu, Guangpu; Yao, Jun; Zhang, Lei; Sun, Hai; Li, Aifen; Shams, Bilal

2016-11-15

A large amount of residual oil, which exists as isolated oil slugs, remains trapped in reservoirs after water flooding. Numerous numerical studies are performed to investigate the fundamental flow mechanism of oil slugs to improve flooding efficiency. Dynamic contact angle models are usually introduced to simulate an accurate contact angle and meniscus displacement of oil slugs under a high capillary number. Nevertheless, in the oil slug flow simulation process, it is unnecessary to introduce the dynamic contact angle model because of a negligible change in the meniscus displacement after using the dynamic contact angle model when the capillary number is small. Therefore, a critical capillary number should be introduced to judge whether the dynamic contact model should be incorporated into simulations. In this study, a direct numerical simulation method is employed to simulate the oil slug flow in a capillary tube at the pore scale. The position of the interface between water and the oil slug is determined using the phase-field method. The capacity and accuracy of the model are validated using a classical benchmark: a dynamic capillary filling process. Then, different dynamic contact angle models and the factors that affect the dynamic contact angle are analyzed. The meniscus displacements of oil slugs with a dynamic contact angle and a static contact angle (SCA) are obtained during simulations, and the relative error between them is calculated automatically. The relative error limit has been defined to be 5%, beyond which the dynamic contact angle model needs to be incorporated into the simulation to approach the realistic displacement. Thus, the desired critical capillary number can be determined. A three-dimensional universal chart of critical capillary number, which functions as static contact angle and viscosity ratio, is given to provide a guideline for oil slug simulation. Also, a fitting formula is presented for ease of use.

76 FR 21673 - Alternative Efficiency Determination Methods and Alternate Rating Methods

Science.gov (United States)

2011-04-18

... EERE-2011-BP-TP-00024] RIN 1904-AC46 Alternative Efficiency Determination Methods and Alternate Rating Methods AGENCY: Office of Energy Efficiency and Renewable Energy, Department of Energy. ACTION: Notice of... and data related to the use of computer simulations, mathematical methods, and other alternative...

Advanced Numerical and Theoretical Methods for Photonic Crystals and Metamaterials

Science.gov (United States)

Felbacq, Didier

2016-11-01

This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.

Development and verification of an efficient spatial neutron kinetics method for reactivity-initiated event analyses

International Nuclear Information System (INIS)

Ikeda, Hideaki; Takeda, Toshikazu

2001-01-01

A space/time nodal diffusion code based on the nodal expansion method (NEM), EPISODE, was developed in order to evaluate transient neutron behavior in light water reactor cores. The present code employs the improved quasistatic (IQS) method for spatial neutron kinetics, and neutron flux distribution is numerically obtained by solving the neutron diffusion equation with the nonlinear iteration scheme to achieve fast computation. A predictor-corrector (PC) method developed in the present study enabled to apply a coarse time mesh to the transient spatial neutron calculation than that applicable in the conventional IQS model, which improved computational efficiency further. Its computational advantage was demonstrated by applying to the numerical benchmark problems that simulate reactivity-initiated events, showing reduction of computational times up to a factor of three than the conventional IQS. The thermohydraulics model was also incorporated in EPISODE, and the capability of realistic reactivity event analyses was verified using the SPERT-III/E-Core experimental data. (author)

A asymptotic numerical method for the steady-state convection diffusion equation

International Nuclear Information System (INIS)

Wu Qiguang

1988-01-01

In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size

Numerical methods and computers used in elastohydrodynamic lubrication

Science.gov (United States)

Hamrock, B. J.; Tripp, J. H.

1982-01-01

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

A first course in ordinary differential equations analytical and numerical methods

CERN Document Server

Hermann, Martin

2014-01-01

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed t...

Efficient improvement of virtual crack extension method by a derivative of the finite element stiffness matrix

International Nuclear Information System (INIS)

Ishikawa, H.; Nakano, S.; Yuuki, R.; Chung, N.Y.

1991-01-01

In the virtual crack extension method, the stress intensity factor, K, is obtained from the converged value of the energy release rate by the difference of the finite element stiffness matrix when some crack extension are taken. Instead of the numerical difference of the finite element stiffness, a new method to use a direct dirivative of the finite element stiffness matrix with respect to crack length is proposed. By the present method, the results of some example problems, such as uniform tension problems of a square plate with a center crack and a rectangular plate with an internal slant crack, are obtained with high accuracy and good efficiency. Comparing with analytical results, the present values of the stress intensity factors of the problems are obtained with the error that is less than 0.6%. This shows the numerical assurance of the usefulness of the present method. A personal computer program for the analysis is developed

Direct numerical methods of mathematical modeling in mechanical structural design

International Nuclear Information System (INIS)

Sahili, Jihad; Verchery, Georges; Ghaddar, Ahmad; Zoaeter, Mohamed

2002-01-01

Full text.Structural design and numerical methods are generally interactive; requiring optimization procedures as the structure is analyzed. This analysis leads to define some mathematical terms, as the stiffness matrix, which are resulting from the modeling and then used in numerical techniques during the dimensioning procedure. These techniques and many others involve the calculation of the generalized inverse of the stiffness matrix, called also the 'compliance matrix'. The aim of this paper is to introduce first, some different existing mathematical procedures, used to calculate the compliance matrix from the stiffness matrix, then apply direct numerical methods to solve the obtained system with the lowest computational time, and to compare the obtained results. The results show a big difference of the computational time between the different procedures

Toward cost-efficient sampling methods

Science.gov (United States)

Luo, Peng; Li, Yongli; Wu, Chong; Zhang, Guijie

2015-09-01

The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper proposes two new sampling methods based on the idea that a small part of vertices with high node degree could possess the most structure information of a complex network. The two proposed sampling methods are efficient in sampling high degree nodes so that they would be useful even if the sampling rate is low, which means cost-efficient. The first new sampling method is developed on the basis of the widely used stratified random sampling (SRS) method and the second one improves the famous snowball sampling (SBS) method. In order to demonstrate the validity and accuracy of two new sampling methods, we compare them with the existing sampling methods in three commonly used simulation networks that are scale-free network, random network, small-world network, and also in two real networks. The experimental results illustrate that the two proposed sampling methods perform much better than the existing sampling methods in terms of achieving the true network structure characteristics reflected by clustering coefficient, Bonacich centrality and average path length, especially when the sampling rate is low.

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 New Method to Solve Numeric Solution of Nonlinear Dynamic System

Directory of Open Access Journals (Sweden)

Min Hu

2016-01-01

Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

On numerical solution of Burgers' equation by homotopy analysis method

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

Theoretical and applied aerodynamics and related numerical methods

CERN Document Server

Chattot, J J

2015-01-01

This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including: -The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics. - The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings to minimize wave drag. Unsteady flow is also briefly discussed. Numerical simulations based on relaxation mixed-finite difference methods are presented and explained. - Boundary layer theory for all Mach number regimes and viscous/inviscid interaction procedures used in practical aerodynamics calculations. There are also four chapters covering special topics, including wind turbines and propellers, airplane design, flow analogies and h...

A numerical method to compute interior transmission eigenvalues

International Nuclear Information System (INIS)

Kleefeld, Andreas

2013-01-01

In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available. (paper)

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.

On the potential of computational methods and numerical simulation in ice mechanics

International Nuclear Information System (INIS)

Bergan, Paal G; Cammaert, Gus; Skeie, Geir; Tharigopula, Venkatapathi

2010-01-01

This paper deals with the challenge of developing better methods and tools for analysing interaction between sea ice and structures and, in particular, to be able to calculate ice loads on these structures. Ice loads have traditionally been estimated using empirical data and 'engineering judgment'. However, it is believed that computational mechanics and advanced computer simulations of ice-structure interaction can play an important role in developing safer and more efficient structures, especially for irregular structural configurations. The paper explains the complexity of ice as a material in computational mechanics terms. Some key words here are large displacements and deformations, multi-body contact mechanics, instabilities, multi-phase materials, inelasticity, time dependency and creep, thermal effects, fracture and crushing, and multi-scale effects. The paper points towards the use of advanced methods like ALE formulations, mesh-less methods, particle methods, XFEM, and multi-domain formulations in order to deal with these challenges. Some examples involving numerical simulation of interaction and loads between level sea ice and offshore structures are presented. It is concluded that computational mechanics may prove to become a very useful tool for analysing structures in ice; however, much research is still needed to achieve satisfactory reliability and versatility of these methods.

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

International Nuclear Information System (INIS)

Aylott, Benjamin; Baker, John G; Camp, Jordan; Centrella, Joan; Boggs, William D; Buonanno, Alessandra; Boyle, Michael; Buchman, Luisa T; Chu, Tony; Brady, Patrick R; Brown, Duncan A; Bruegmann, Bernd; Cadonati, Laura; Campanelli, Manuela; Faber, Joshua; Chatterji, Shourov; Christensen, Nelson; Diener, Peter; Dorband, Nils; Etienne, Zachariah B

2009-01-01

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

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

Science.gov (United States)

Rosenbaum, J. S.

1976-01-01

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

Numerical method improvement for a subchannel code

Energy Technology Data Exchange (ETDEWEB)

Ding, W.J.; Gou, J.L.; Shan, J.Q. [Xi' an Jiaotong Univ., Shaanxi (China). School of Nuclear Science and Technology

2016-07-15

Previous studies showed that the subchannel codes need most CPU time to solve the matrix formed by the conservation equations. Traditional matrix solving method such as Gaussian elimination method and Gaussian-Seidel iteration method cannot meet the requirement of the computational efficiency. Therefore, a new algorithm for solving the block penta-diagonal matrix is designed based on Stone's incomplete LU (ILU) decomposition method. In the new algorithm, the original block penta-diagonal matrix will be decomposed into a block upper triangular matrix and a lower block triangular matrix as well as a nonzero small matrix. After that, the LU algorithm is applied to solve the matrix until the convergence. In order to compare the computational efficiency, the new designed algorithm is applied to the ATHAS code in this paper. The calculation results show that more than 80 % of the total CPU time can be saved with the new designed ILU algorithm for a 324-channel PWR assembly problem, compared with the original ATHAS code.

Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models

International Nuclear Information System (INIS)

Jošt, D; Škerlavaj, A; Lipej, A

2012-01-01

Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.

Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models

Science.gov (United States)

Jošt, D.; Škerlavaj, A.; Lipej, A.

2012-11-01

Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.

A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models

Directory of Open Access Journals (Sweden)

Shengwu Zhou

2012-01-01

Full Text Available A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.

Numerical simulation of compressible two-phase flow using a diffuse interface method

International Nuclear Information System (INIS)

Ansari, M.R.; Daramizadeh, A.

2013-01-01

Highlights: ► Compressible two-phase gas–gas and gas–liquid flows simulation are conducted. ► Interface conditions contain shock wave and cavitations. ► A high-resolution diffuse interface method is investigated. ► The numerical results exhibit very good agreement with experimental results. -- Abstract: In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems

Second GAMM-conference on numerical methods in fluid mechanics

International Nuclear Information System (INIS)

Hirschel, E.H.; Geller, W.

1977-01-01

Proceedings of the Second GAMM-Conference on Numerical Methods in Fluid Mechanics held at the DFVLR, Koeln, October 11 to 13, 1977. The conference was attended by approximately 100 participants from 13 European countries representing quite different fields ranging from Aerodynamics to Nuclear Energy. At the meeting 34 papers were presented, many of them concerned with basic problems in the field. It was well demonstrated that Numerical Methods in Fluid Mechanics do not only serve as means for the computation of flow fields but also as tools in the analysis of fluid mechanical phenomena, a role of large future importance if one considers the complexity especially of three-dimensional flows. (orig./RW) [de

Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

International Nuclear Information System (INIS)

Katsaounis, T D

2005-01-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall

An efficient method for evaluation of post-dynamic quasi-stationary states during the island operation of power system parts

Energy Technology Data Exchange (ETDEWEB)

Popovic, D P; Mijailovic, S V [Nikola Tesla Inst., Belgrade (Yugoslavia)

1995-11-01

This paper presents the development and practical examples of an efficient method for the simultaneous solution of post-dynamic quasi-stationary states in each of the islands, using a unique numerical procedure, retaining the same node numeration which existed in the power system before its disintegration. At the same time, the developed method enables a simple incorporation of the effects of primary frequency and voltage control, emergency control devices and a series of possible dispatch actions, both during the monitoring of the disintegration process and during power system restoration with island synchronization, if the necessary conditions are met. 9 refs, 3 figs, 2 tabs

Uniqueness and numerical methods in inverse obstacle scattering

International Nuclear Information System (INIS)

Kress, Rainer

2007-01-01

The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages

An analytical-numerical comprehensive method for optimizing the fringing magnetic field

International Nuclear Information System (INIS)

Xiao Meiqin; Mao Naifeng

1991-01-01

The criterion of optimizing the fringing magnetic field is discussed, and an analytical-numerical comprehensive method for realizing the optimization is introduced. The method mentioned above consists of two parts, the analytical part calculates the field of the shims, which corrects the fringing magnetic field by using uniform magnetizing method; the numerical part fulfils the whole calculation of the field distribution by solving the equation of magnetic vector potential A within the region covered by arbitrary triangular meshes with the aid of finite difference method and successive over relaxation method. On the basis of the method, the optimization of the fringing magnetic field for a large-scale electromagnetic isotope separator is finished

Numerical methods for hyperbolic differential functional problems

Directory of Open Access Journals (Sweden)

Roman Ciarski

2008-01-01

Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.

Numerical analysis method for reheater performance of moisture separator reheater for Nuclear Power Plants

International Nuclear Information System (INIS)

Oda, Tsuyoshi; Fujisawa, Kyosuke; Akamatsu, Hiroshi

2014-01-01

Nuclear power generation uses saturated steam of 6 MPa and 275degC level due to the restrictions imposed by the materials used in the nuclear reactor, and its efficiency, approximately 33-35%, is not high compared with fossil fuel power generation. Therefore, thermal engineers working on nuclear power generation have the important responsibility toward society of achieving the highest efficiency under the given restrictions. The use of a moisture separator reheater (MSR) is one of the measures we can take to achieve higher efficiency. Because the bottom of the MSR tube bundle making contact with the cycle steam at its lowest temperature is subcooled and inadequate drainage of the condensate inside the tubes causes cyclic flooding and temperature oscillations in some cases, it is necessary to have a minimum flow rate of excess heating steam slightly beyond the demand of/what is required for the heat transfer, and the consequent subcooling must be kept below a certain level. This report describes the numerical analysis method developed for the design of heat transfer performance and evaluation of the tube bundle integrity of MSRs. (author)

Energy efficiency vs. performance of the numerical solution of PDEs: An application study on a low-power ARM-based cluster

Science.gov (United States)

Göddeke, Dominik; Komatitsch, Dimitri; Geveler, Markus; Ribbrock, Dirk; Rajovic, Nikola; Puzovic, Nikola; Ramirez, Alex

2013-03-01

Power consumption and energy efficiency are becoming critical aspects in the design and operation of large scale HPC facilities, and it is unanimously recognised that future exascale supercomputers will be strongly constrained by their power requirements. At current electricity costs, operating an HPC system over its lifetime can already be on par with the initial deployment cost. These power consumption constraints, and the benefits a more energy-efficient HPC platform may have on other societal areas, have motivated the HPC research community to investigate the use of energy-efficient technologies originally developed for the embedded and especially mobile markets. However, lower power does not always mean lower energy consumption, since execution time often also increases. In order to achieve competitive performance, applications then need to efficiently exploit a larger number of processors. In this article, we discuss how applications can efficiently exploit this new class of low-power architectures to achieve competitive performance. We evaluate if they can benefit from the increased energy efficiency that the architecture is supposed to achieve. The applications that we consider cover three different classes of numerical solution methods for partial differential equations, namely a low-order finite element multigrid solver for huge sparse linear systems of equations, a Lattice-Boltzmann code for fluid simulation, and a high-order spectral element method for acoustic or seismic wave propagation modelling. We evaluate weak and strong scalability on a cluster of 96 ARM Cortex-A9 dual-core processors and demonstrate that the ARM-based cluster can be more efficient in terms of energy to solution when executing the three applications compared to an x86-based reference machine.

A dynamic optimization on economic energy efficiency in development: A numerical case of China

International Nuclear Information System (INIS)

Wang, Dong

2014-01-01

This paper is based on dynamic optimization methodology to investigate the economic energy efficiency issues in developing countries. The paper introduces some definitions about energy efficiency both in economics and physics, and establishes a quantitative way for measuring the economic energy efficiency. The linkage between economic energy efficiency, energy consumption and other macroeconomic variables is demonstrated primarily. Using the methodology of dynamic optimization, a maximum problem of economic energy efficiency over time, which is subjected to the extended Solow growth model and instantaneous investment rate, is modelled. In this model, the energy consumption is set as a control variable and the capital is regarded as a state variable. The analytic solutions can be derived and the diagrammatic analysis provides saddle-point equilibrium. A numerical simulation based on China is also presented; meanwhile, the optimal paths of investment and energy consumption can be drawn. The dynamic optimization encourages governments in developing countries to pursue higher economic energy efficiency by controlling the energy consumption and regulating the investment state as it can conserve energy without influencing the achievement of steady state in terms of Solow model. If that, a sustainable development will be achieved. - Highlights: • A new definition on economic energy efficiency is proposed mathematically. • A dynamic optimization modelling links economic energy efficiency with other macroeconomic variables in long run. • Economic energy efficiency is determined by capital stock level and energy consumption. • Energy saving is a key solution for improving economic energy efficiency

A virtual component method in numerical computation of cascades for isotope separation

International Nuclear Information System (INIS)

Zeng Shi; Cheng Lu

2014-01-01

The analysis, optimization, design and operation of cascades for isotope separation involve computations of cascades. In analytical analysis of cascades, using virtual components is a very useful analysis method. For complicated cases of cascades, numerical analysis has to be employed. However, bound up to the conventional idea that the concentration of a virtual component should be vanishingly small, virtual component is not yet applied to numerical computations. Here a method of introducing the method of using virtual components to numerical computations is elucidated, and its application to a few types of cascades is explained and tested by means of numerical experiments. The results show that the concentration of a virtual component is not restrained at all by the 'vanishingly small' idea. For the same requirements on cascades, the cascades obtained do not depend on the concentrations of virtual components. (authors)

Numerical methods for axisymmetric and 3D nonlinear beams

Science.gov (United States)

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

Methods for enhancing numerical integration

International Nuclear Information System (INIS)

Doncker, Elise de

2003-01-01

We give a survey of common strategies for numerical integration (adaptive, Monte-Carlo, Quasi-Monte Carlo), and attempt to delineate their realm of applicability. The inherent accuracy and error bounds for basic integration methods are given via such measures as the degree of precision of cubature rules, the index of a family of lattice rules, and the discrepancy of uniformly distributed point sets. Strategies incorporating these basic methods often use paradigms to reduce the error by, e.g., increasing the number of points in the domain or decreasing the mesh size, locally or uniformly. For these processes the order of convergence of the strategy is determined by the asymptotic behavior of the error, and may be too slow in practice for the type of problem at hand. For certain problem classes we may be able to improve the effectiveness of the method or strategy by such techniques as transformations, absorbing a difficult part of the integrand into a weight function, suitable partitioning of the domain, transformations and extrapolation or convergence acceleration. Situations warranting the use of these techniques (possibly in an 'automated' way) are described and illustrated by sample applications

Investigating Convergence Patterns for Numerical Methods Using Data Analysis

Science.gov (United States)

Gordon, Sheldon P.

2013-01-01

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

Solutions manual to accompany An introduction to numerical methods and analysis

CERN Document Server

Epperson, James F

2014-01-01

A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp

A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations

International Nuclear Information System (INIS)

Saurel, Richard; Franquet, Erwin; Daniel, Eric; Le Metayer, Olivier

2007-01-01

A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures

A simple and rational numerical method of two-phase flow with volume-junction model. 2. The numerical method for general condition of two-phase flow in non-equilibrium states

International Nuclear Information System (INIS)

Okazaki, Motoaki

1997-11-01

In the previous report, the usefulness of a new numerical method to achieve a rigorous numerical calculation using a simple explicit method with the volume-junction model was presented with the verification calculation for the depressurization of a saturated two-phase mixture. In this report, on the basis of solution method above, a numerical method for general condition of two-phase flow in non-equilibrium states is presented. In general condition of two-phase flow, the combinations of saturated and non-saturated conditions of each phase are considered in the each flow of volume and junction. Numerical evaluation programs are separately prepared for each combination of flow condition. Several numerical calculations of various kinds of non-equilibrium two-phase flow are made to examine the validity of the numerical method. Calculated results showed that the thermodynamic states obtained in different solution schemes were consistent with each other. In the first scheme, the states are determined by using the steam table as a function of pressure and specific enthalpy which are obtained as the solutions of simultaneous equations. In the second scheme, density and specific enthalpy of each phase are directly calculated by using conservation equations of mass and enthalpy of each phase, respectively. Further, no accumulation of error in mass and energy was found. As for the specific enthalpy, two cases of using energy equations for the volume are examined. The first case uses total energy conservation equation and the second case uses the type of the first law of thermodynamics. The results of both cases agreed well. (author)

A novel and efficient analytical method for calculation of the transient temperature field in a multi-dimensional composite slab

International Nuclear Information System (INIS)

Lu, X; Tervola, P; Viljanen, M

2005-01-01

This paper provides an efficient analytical tool for solving the heat conduction equation in a multi-dimensional composite slab subject to generally time-dependent boundary conditions. A temporal Laplace transformation and novel separation of variables are applied to the heat equation. The time-dependent boundary conditions are approximated with Fourier series. Taking advantage of the periodic properties of Fourier series, the corresponding analytical solution is obtained and expressed explicitly through employing variable transformations. For such conduction problems, nearly all the published works necessitate numerical work such as computing residues or searching for eigenvalues even for a one-dimensional composite slab. In this paper, the proposed method involves no numerical iteration. The final closed form solution is straightforward; hence, the physical parameters are clearly shown in the formula. The accuracy of the developed analytical method is demonstrated by comparison with numerical calculations

A detailed survey of numerical methods for unconstrained minimization. Pt. 1

International Nuclear Information System (INIS)

Mika, K.; Chaves, T.

1980-01-01

A detailed description of numerical methods for unconstrained minimization is presented. This first part surveys in particular conjugate direction and gradient methods, whereas variable metric methods will be the subject of the second part. Among the results of special interest we quote the following. The conjugate direction methods of Powell, Zangwill and Sutti can be best interpreted if the Smith approach is adopted. The conditions for quadratic termination of Powell's first procedure are analyzed. Numerical results based on nonlinear least squares problems are presented for the following conjugate direction codes: VA04AD from Harwell Subroutine Library and ZXPOW from IMSL, both implementations of Powell's second procedure, DFMND from IBM-SILMATH (Zangwill's method) and Brent's algorithm PRAXIS. VA04AD turns out to be superior in all cases, PRAXIS improves for high-dimensional problems. All codes clearly exhibit superlinear convergence. Akaike's result for the method of steepest descent is derived directly from a set of nonlinear recurrence relations. Numerical results obtained with the highly ill conditioned Hilbert function confirm the theoretical predictions. Several properties of the conjugate gradient method are presented and a new derivation of the equivalence of steepest descent partan and the CG method is given. A comparison of numerical results from the CG codes VA08AD (Fletcher-Reeves), DFMCG (the SSP version of the Fletcher-Reevens algorithm) and VA14AD (Powell's implementation of the Polak-Ribiere formula) reveals that VA14AD is clearly superior in all cases, but that the convergence rate of these codes is only weakly superlinear such that high accuracy solutions require extremely large numbers of function calls. (orig.)

Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...

Numerical Methods for Free Boundary Problems

CERN Document Server

1991-01-01

About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff­ mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...

Numerical model CCC

International Nuclear Information System (INIS)

Bodvarsson, G.S.; Lippmann, M.J.

1980-01-01

The computer program CCC (conduction-convection-consolidation), developed at Lawrence Berkeley Laboratory, solves numerically the heat and mass flow equations for a fully saturated medium, and computes one-dimensional consolidation of the simulated systems. The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated medium and formulating the governing equations. The sets of equations are solved either by an iterative solution technique (old version) or an efficient sparse solver (new version). The deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. In this paper, the numerical code is described, validation examples given and areas of application discussed. Several example problems involving flow through fractured media are also presented

How to Overcome Numerical Challenges to Modeling Stirling Engines

Science.gov (United States)

Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.

2004-01-01

Nuclear thermal to electric power conversion carries the promise of longer duration missions and higher scientific data transmission rates back to Earth for a range of missions, including both Mars rovers and deep space missions. A free-piston Stirling convertor is a candidate technology that is considered an efficient and reliable power conversion device for such purposes. While already very efficient, it is believed that better Stirling engines can be developed if the losses inherent in current designs could be better understood. However, they are difficult to instrument and so efforts are underway to simulate a complete Stirling engine numerically. This has only recently been attempted and a review of the methods leading up to and including such computational analysis is presented. And finally it is proposed that the quality and depth of Stirling loss understanding may be improved by utilizing the higher fidelity and efficiency of recently developed numerical methods. One such method, the Ultra HI-FI technique is presented in detail.

A numerical method for two-dimensional anisotropic transport problem in cylindrical geometry

International Nuclear Information System (INIS)

Du Mingsheng; Feng Tiekai; Fu Lianxiang; Cao Changshu; Liu Yulan

1988-01-01

The authors deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A prior estimate of the numerical solution is given. Stability is proved. The authors have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experimental results obtained by others both at home and abroad, the method is satisfactory

Effects of Conjugate Gradient Methods and Step-Length Formulas on the Multiscale Full Waveform Inversion in Time Domain: Numerical Experiments

Science.gov (United States)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José; Liu, Qinya; Zhou, Bing

2017-05-01

We carry out full waveform inversion (FWI) in time domain based on an alternative frequency-band selection strategy that allows us to implement the method with success. This strategy aims at decomposing the seismic data within partially overlapped frequency intervals by carrying out a concatenated treatment of the wavelet to largely avoid redundant frequency information to adapt to wavelength or wavenumber coverage. A pertinent numerical test proves the effectiveness of this strategy. Based on this strategy, we comparatively analyze the effects of update parameters for the nonlinear conjugate gradient (CG) method and step-length formulas on the multiscale FWI through several numerical tests. The investigations of up to eight versions of the nonlinear CG method with and without Gaussian white noise make clear that the HS (Hestenes and Stiefel in J Res Natl Bur Stand Sect 5:409-436, 1952), CD (Fletcher in Practical methods of optimization vol. 1: unconstrained optimization, Wiley, New York, 1987), and PRP (Polak and Ribière in Revue Francaise Informat Recherche Opertionelle, 3e Année 16:35-43, 1969; Polyak in USSR Comput Math Math Phys 9:94-112, 1969) versions are more efficient among the eight versions, while the DY (Dai and Yuan in SIAM J Optim 10:177-182, 1999) version always yields inaccurate result, because it overestimates the deeper parts of the model. The application of FWI algorithms using distinct step-length formulas, such as the direct method ( Direct), the parabolic search method ( Search), and the two-point quadratic interpolation method ( Interp), proves that the Interp is more efficient for noise-free data, while the Direct is more efficient for Gaussian white noise data. In contrast, the Search is less efficient because of its slow convergence. In general, the three step-length formulas are robust or partly insensitive to Gaussian white noise and the complexity of the model. When the initial velocity model deviates far from the real model or the

MATH: A Scientific Tool for Numerical Methods Calculation and Visualization

Directory of Open Access Journals (Sweden)

Henrich Glaser-Opitz

2016-02-01

Full Text Available MATH is an easy to use application for various numerical methods calculations with graphical user interface and integrated plotting tool written in Qt with extensive use of Qwt library for plotting options and use of Gsl and MuParser libraries as a numerical and parser helping libraries. It can be found at http://sourceforge.net/projects/nummath. MATH is a convenient tool for use in education process because of its capability of showing every important step in solution process to better understand how it is done. MATH also enables fast comparison of similar method speed and precision.

Design of steel energy absorbing restrainers and their incorporation into nuclear power plants for enhanced safety. Volume 1C. Numerical method for dynamic substructure analysis

International Nuclear Information System (INIS)

Dickens, J.M.; Wilson, E.L.

1980-06-01

This report presents several new or improved numerical methods for the dynamic response analysis of large complex structural systems. The methods presented are primarily concerned with linear dynamic analysis. However, one of the significant results of the research is the development of efficient numerical methods for large systems with a small number of non-linear members. The technique of dynamic substructure analysis is used to accurately model the behavior of the linear part of the system. This approach allows the behavior of the linear structural members to be reduced to a small number of generalized dynamic coordinates. Those linear dynamic coordinates are then used in direct combination with the nonlinear members to approximate the solution of the large nonlinear problem. The methods presented can be applied to structures of arbitrary geometry. However, the use of techniques such as cyclic symmetry can further decrease the numerical effort

Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

Directory of Open Access Journals (Sweden)

Sandvik Leiv

2011-04-01

Full Text Available Abstract Background The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables. Methods Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure. Results The Welch U test (the T test with adjustment for unequal variances and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group. The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily. Conclusions The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

Numerical method for partial equilibrium flow

International Nuclear Information System (INIS)

Ramshaw, J.D.; Cloutman, L.D.; Los Alamos, New Mexico 87545)

1981-01-01

A numerical method is presented for chemically reactive fluid flow in which equilibrium and nonequilibrium reactions occur simultaneously. The equilibrium constraints on the species concentrations are established by a quadratic iterative procedure. If the equilibrium reactions are uncoupled and of second or lower order, the procedure converges in a single step. In general, convergence is most rapid when the reactions are weakly coupled. This can frequently be achieved by a judicious choice of the independent reactions. In typical transient calculations, satisfactory accuracy has been achieved with about five iterations per time step

Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures

Science.gov (United States)

2017-10-04

to the memory architectures of CPUs and GPUs to obtain good performance and result in good memory performance using cache management. These methods ...Accomplishments: The PI and students has developed new methods for path and ray tracing and their Report Date: 14-Oct-2017 INVESTIGATOR(S): Phone...The efficiency of our method makes it a good candidate for forming hybrid schemes with wave-based models. One possibility is to couple the ray curve

On the numerical stability analysis of pipelined Krylov subspace methods

Czech Academy of Sciences Publication Activity Database

Carson, E.T.; Rozložník, Miroslav; Strakoš, Z.; Tichý, P.; Tůma, M.

submitted 2017 (2018) R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : Krylov subspace methods * the conjugate gradient method * numerical stability * inexact computations * delay of convergence * maximal attainable accuracy * pipelined Krylov subspace methods * exascale computations

Towards Cost-efficient Sampling Methods

OpenAIRE

Peng, Luo; Yongli, Li; Chong, Wu

2014-01-01

The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper presents two new sampling methods based on the perspective that a small part of vertices with high node degree can possess the most structure information of a network. The two proposed sampling methods are efficient in sampling the nodes with high degree. The first new sampling method is improved on the basis of the stratified random sampling method and...

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.

Workshop on Numerical Methods for Ordinary Differential Equations

CERN Document Server

Gear, Charles; Russo, Elvira

1989-01-01

Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.

Practical design of magnetostatic structure using numerical simulation

CERN Document Server

Wang, Qiuliang

2013-01-01

Covers the practical numerical method for the analysis and design of magnets Extensively covers the magnet design and computation aspects from theories to practical applications, emphasizing design methods of practical structures such as superconducting, electromagnetic and permanent magnet for use in various scientific instruments, industrial processing, biomedicine and special electrical equipments. The computations cover a wide range of numerical techniques and analytical derivation to efficiently provide solutions to complicated problems that are often encountered in practice, where simple analytical calculations are no longer adequate. Chapters include: Introduction of Magnet Technology, Magnetostatic Equation for the Magnet Structure, Finite Element Analysis for Magnetostatic Field, Integral Method for Magnetostatic Field, Numerical Method of Solenoid Coils Design, Series Analysis of Axially Symmetric Magnetic Field, Magnets with High Magnetic Field and High Homogeneity, Permanent Magnet and its App...

An assessment of diagnostic efficiency by Taguchi/DEA methods.

Science.gov (United States)

Taner, Mehmet Tolga; Sezen, Bulent

2009-01-01

The aim of this paper is to propose a new, objective and consistent method for the calculation of the diagnostic efficiency in medical applications. In this study, a hybrid method of Taguchi and DEA is proposed. This method reflects the diversity of inputs and outputs by incorporating the stepwise application of sensitivity, specificity, leveling threshold, and efficiency score. A hypothetical case study is given which involves eight readers of X-ray films in clinical radiology. The selected pairs of sensitivity and specificity yielded two efficient readers. After super efficiency analysis, Reader 6 is found to be the most efficient reader. The paper presents a new, objective and consistent method for the calculation of the diagnostic efficiency in medical applications.

Energy-efficient cooking methods

Energy Technology Data Exchange (ETDEWEB)

De, Dilip K. [Department of Physics, University of Jos, P.M.B. 2084, Jos, Plateau State (Nigeria); Muwa Shawhatsu, N. [Department of Physics, Federal University of Technology, Yola, P.M.B. 2076, Yola, Adamawa State (Nigeria); De, N.N. [Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, TX 76019 (United States); Ikechukwu Ajaeroh, M. [Department of Physics, University of Abuja, Abuja (Nigeria)

2013-02-15

Energy-efficient new cooking techniques have been developed in this research. Using a stove with 649{+-}20 W of power, the minimum heat, specific heat of transformation, and on-stove time required to completely cook 1 kg of dry beans (with water and other ingredients) and 1 kg of raw potato are found to be: 710 {+-}kJ, 613 {+-}kJ, and 1,144{+-}10 s, respectively, for beans and 287{+-}12 kJ, 200{+-}9 kJ, and 466{+-}10 s for Irish potato. Extensive researches show that these figures are, to date, the lowest amount of heat ever used to cook beans and potato and less than half the energy used in conventional cooking with a pressure cooker. The efficiency of the stove was estimated to be 52.5{+-}2 %. Discussion is made to further improve the efficiency in cooking with normal stove and solar cooker and to save food nutrients further. Our method of cooking when applied globally is expected to contribute to the clean development management (CDM) potential. The approximate values of the minimum and maximum CDM potentials are estimated to be 7.5 x 10{sup 11} and 2.2 x 10{sup 13} kg of carbon credit annually. The precise estimation CDM potential of our cooking method will be reported later.

Towards a suite of test cases and a pycomodo library to assess and improve numerical methods in ocean models

Science.gov (United States)

Garnier, Valérie; Honnorat, Marc; Benshila, Rachid; Boutet, Martial; Cambon, Gildas; Chanut, Jérome; Couvelard, Xavier; Debreu, Laurent; Ducousso, Nicolas; Duhaut, Thomas; Dumas, Franck; Flavoni, Simona; Gouillon, Flavien; Lathuilière, Cyril; Le Boyer, Arnaud; Le Sommer, Julien; Lyard, Florent; Marsaleix, Patrick; Marchesiello, Patrick; Soufflet, Yves

2016-04-01

bed to continue research in numerical approaches as well as an efficient tool to maintain any oceanic code and assure the users a stamped model in a certain range of hydrodynamical regimes. Thanks to a common netCDF format, this suite is completed with a python library that encompasses all the tools and metrics used to assess the efficiency of the numerical methods. References - Couvelard X., F. Dumas, V. Garnier, A.L. Ponte, C. Talandier, A.M. Treguier (2015). Mixed layer formation and restratification in presence of mesoscale and submesoscale turbulence. Ocean Modelling, Vol 96-2, p 243-253. doi:10.1016/j.ocemod.2015.10.004. - Soufflet Y., P. Marchesiello, F. Lemarié, J. Jouanno, X. Capet, L. Debreu , R. Benshila (2016). On effective resolution in ocean models. Ocean Modelling, in press. doi:10.1016/j.ocemod.2015.12.004

Methods for fitting of efficiency curves obtained by means of HPGe gamma rays spectrometers

International Nuclear Information System (INIS)

Cardoso, Vanderlei

2002-01-01

The present work describes a few methodologies developed for fitting efficiency curves obtained by means of a HPGe gamma-ray spectrometer. The interpolated values were determined by simple polynomial fitting and polynomial fitting between the ratio of experimental peak efficiency and total efficiency, calculated by Monte Carlo technique, as a function of gamma-ray energy. Moreover, non-linear fitting has been performed using a segmented polynomial function and applying the Gauss-Marquardt method. For the peak area obtainment different methodologies were developed in order to estimate the background area under the peak. This information was obtained by numerical integration or by using analytical functions associated to the background. One non-calibrated radioactive source has been included in the curve efficiency in order to provide additional calibration points. As a by-product, it was possible to determine the activity of this non-calibrated source. For all fittings developed in the present work the covariance matrix methodology was used, which is an essential procedure in order to give a complete description of the partial uncertainties involved. (author)

Analytic-numerical method of determining the freezing front location

Directory of Open Access Journals (Sweden)

R. Grzymkowski

2011-07-01

Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic boundary problems with the moving boundary. Solution of such defined problem requires, most often, to use sophisticated numerical techniques and far advanced mathematical tools. Excellent illustration of the complexity of considered problems, as well as of the variety of approaches used for finding their solutions, gives the papers [1-4]. In the current paper, the authors present the, especially attractive from the engineer point of view, analytic-numerical method for finding the approximate solution of selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of the sought function describing the temperature field into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of the function defining the location of freezing front with the broken line, parameters of which are numerically determined.

Stability of numerical method for semi-linear stochastic pantograph differential equations

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Yu Zhang

2016-01-01

Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

A method for solving the KDV equation and some numerical experiments

International Nuclear Information System (INIS)

Chang Jinjiang.

1993-01-01

In this paper, by means of difference method for discretization of space partial derivatives of KDV equation, an initial value problem in ordinary differential equations of large dimensions is produced. By using this ordinary differential equations the existence and the uniqueness of the solution of the KDV equation and the conservation of scheme are proved. This ordinary differential equation can be solved by using implicit Runge-Kutta methods, so a new method for finding the numerical solution of the KDV equation is presented. Numerical experiments not only describe in detail the procedure of two solitons collision, soliton reflex and soliton produce, but also show that this method is very effective. (author). 7 refs, 3 figs

Computationally efficient methods for digital control

NARCIS (Netherlands)

Guerreiro Tome Antunes, D.J.; Hespanha, J.P.; Silvestre, C.J.; Kataria, N.; Brewer, F.

2008-01-01

The problem of designing a digital controller is considered with the novelty of explicitly taking into account the computation cost of the controller implementation. A class of controller emulation methods inspired by numerical analysis is proposed. Through various examples it is shown that these

An analytically based numerical method for computing view factors in real urban environments

Science.gov (United States)

Lee, Doo-Il; Woo, Ju-Wan; Lee, Sang-Hyun

2018-01-01

A view factor is an important morphological parameter used in parameterizing in-canyon radiative energy exchange process as well as in characterizing local climate over urban environments. For realistic representation of the in-canyon radiative processes, a complete set of view factors at the horizontal and vertical surfaces of urban facets is required. Various analytical and numerical methods have been suggested to determine the view factors for urban environments, but most of the methods provide only sky-view factor at the ground level of a specific location or assume simplified morphology of complex urban environments. In this study, a numerical method that can determine the sky-view factors ( ψ ga and ψ wa ) and wall-view factors ( ψ gw and ψ ww ) at the horizontal and vertical surfaces is presented for application to real urban morphology, which are derived from an analytical formulation of the view factor between two blackbody surfaces of arbitrary geometry. The established numerical method is validated against the analytical sky-view factor estimation for ideal street canyon geometries, showing a consolidate confidence in accuracy with errors of less than 0.2 %. Using a three-dimensional building database, the numerical method is also demonstrated to be applicable in determining the sky-view factors at the horizontal (roofs and roads) and vertical (walls) surfaces in real urban environments. The results suggest that the analytically based numerical method can be used for the radiative process parameterization of urban numerical models as well as for the characterization of local urban climate.

A calculation method for RF couplers design based on numerical simulation by microwave studio

International Nuclear Information System (INIS)

Wang Rong; Pei Yuanji; Jin Kai

2006-01-01

A numerical simulation method for coupler design is proposed. It is based on the matching procedure for the 2π/3 structure given by Dr. R.L. Kyhl. Microwave Studio EigenMode Solver is used for such numerical simulation. the simulation for a coupler has been finished with this method and the simulation data are compared with experimental measurements. The results show that this numerical simulation method is feasible for coupler design. (authors)

Numerical simulation methods for wave propagation through optical waveguides

International Nuclear Information System (INIS)

Sharma, A.

1993-01-01

The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Zhao, Jia, E-mail: zhao62@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States); Wang, Qi, E-mail: qwang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Beijing Computational Science Research Center, Beijing (China); School of Materials Science and Engineering, Nankai University, Tianjin (China)

2017-03-15

The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

A higher order numerical method for time fractional partial differential equations with nonsmooth data

Science.gov (United States)

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.

Efficient Rank Reduction of Correlation Matrices

NARCIS (Netherlands)

I. Grubisic (Igor); R. Pietersz (Raoul)

2005-01-01

textabstractGeometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with the Lagrange multiplier method is established,

Numerical Verification Methods for Spherical $t$-Designs

OpenAIRE

Chen, Xiaojun

2009-01-01

The construction of spherical $t$-designs with $(t+1)^2$ points on the unit sphere $S^2$ in $\\mathbb{R}^3$ can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degree $t$ polynomial in $(t+1)^4$ arguments. This paper reviews numerical verification methods using the Brouwer fixed point theorem and Krawczyk interval operator for solutions of the underdetermined system of nonlinear equations...

Numerical calculations in elementary quantum mechanics using Feynman path integrals

International Nuclear Information System (INIS)

Scher, G.; Smith, M.; Baranger, M.

1980-01-01

We show that it is possible to do numerical calculations in elementary quantum mechanics using Feynman path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical results for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient

Numerical investigations on contactless methods for measuring critical current density in HTS: application of modified constitutive-relation method

International Nuclear Information System (INIS)

Kamitani, A.; Takayama, T.; Itoh, T.; Ikuno, S.

2011-01-01

A fast method is proposed for calculating the shielding current density in an HTS. The J-E constitutive relation is modified so as not to change the solution. A numerical code is developed on the basis of the proposed method. The permanent magnet method is successfully simulated by means of the code. A fast method has been proposed for calculating the shielding current density in a high-temperature superconducting thin film. An initial-boundary-value problem of the shielding current density cannot be always solved by means of the Runge-Kutta method even when an adaptive step-size control algorithm is incorporated to the method. In order to suppress an overflow in the algorithm, the J-E constitutive relation is modified so that its solution may satisfy the original constitutive relation. A numerical code for analyzing the shielding current density has been developed on the basis of this method and, as an application of the code, the permanent magnet method for measuring the critical current density has been investigated numerically.

On a method of numerical calculation of nonlinear radial pulsations of stars

International Nuclear Information System (INIS)

Kosovichev, A.G.

1984-01-01

Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars

Numerical simulation of bubble deformation in magnetic fluids by finite volume method

International Nuclear Information System (INIS)

Yamasaki, Haruhiko; Yamaguchi, Hiroshi

2017-01-01

Bubble deformation in magnetic fluids under magnetic field is investigated numerically by an interface capturing method. The numerical method consists of a coupled level-set and VOF (Volume of Fluid) method, combined with conservation CIP (Constrained Interpolation Profile) method with the self-correcting procedure. In the present study considering actual physical properties of magnetic fluid, bubble deformation under given uniform magnetic field is analyzed for internal magnetic field passing through a magnetic gaseous and liquid phase interface. The numerical results explain the mechanism of bubble deformation under presence of given magnetic field. - Highlights: • A magnetic field analysis is developed to simulate the bubble dynamics in magnetic fluid with two-phase interface. • The elongation of bubble increased with increasing magnetic flux intensities due to strong magnetic normal force. • Proposed technique explains the bubble dynamics, taking into account of the continuity of the magnetic flux density.

Interface COMSOL-PHREEQC (iCP), an efficient numerical framework for the solution of coupled multiphysics and geochemistry

Science.gov (United States)

Nardi, Albert; Idiart, Andrés; Trinchero, Paolo; de Vries, Luis Manuel; Molinero, Jorge

2014-08-01

This paper presents the development, verification and application of an efficient interface, denoted as iCP, which couples two standalone simulation programs: the general purpose Finite Element framework COMSOL Multiphysics® and the geochemical simulator PHREEQC. The main goal of the interface is to maximize the synergies between the aforementioned codes, providing a numerical platform that can efficiently simulate a wide number of multiphysics problems coupled with geochemistry. iCP is written in Java and uses the IPhreeqc C++ dynamic library and the COMSOL Java-API. Given the large computational requirements of the aforementioned coupled models, special emphasis has been placed on numerical robustness and efficiency. To this end, the geochemical reactions are solved in parallel by balancing the computational load over multiple threads. First, a benchmark exercise is used to test the reliability of iCP regarding flow and reactive transport. Then, a large scale thermo-hydro-chemical (THC) problem is solved to show the code capabilities. The results of the verification exercise are successfully compared with those obtained using PHREEQC and the application case demonstrates the scalability of a large scale model, at least up to 32 threads.

Development of the numerical method for liquid metal magnetohydrodynamics (I). Investigation of the method and development of the 2D method

International Nuclear Information System (INIS)

Ohira, H.; Ara, K.

2002-11-01

Advanced electromagnetic components are investigated in Feasibility Studies on Commercialized FR Cycle System to apply to the main cooling systems of Liquid Metal Fast Reactor. Although a lot of experiments and numerical analysis were carried out on both high Reynolds numbers and high magnetic Reynolds numbers, the complex phenomena could not be evaluated in detail. As the first step of the development of the numerical methods for the liquid metal magnetohydrodynamics, we investigated numerical methods that could be applied to the electromagnetic components with both complex structures and high magnetic turbulent field. As a result, we selected GSMAC (Generalized-Simplified MArker and Cell) method for calculating the liquid metal fluid dynamics because it could be easily applied to the complex flow field. We also selected the vector-FEM for calculating the magnetic field of the large components because the method had no interaction procedure. In the high magnetic turbulent field, the dynamic-SGS models would be also a promising model for the good estimation, because it could calculate the field directly without any experimental constant. In order to verify the GSMAC and the vector-FEM, we developed the 2D numerical models and calculated the magnetohydrodynamics in the large electromagnetic pump. It was estimated from these results that the methods were basically reasonable, because the calculated pressure differences had the similar tendencies to the experimental ones. (author)

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

2015-01-01

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

New numerical method for iterative or perturbative solution of quantum field theory

International Nuclear Information System (INIS)

Hahn, S.C.; Guralnik, G.S.

1999-01-01

A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

Power and thermal efficient numerical processing

DEFF Research Database (Denmark)

Liu, Wei; Nannarelli, Alberto

2015-01-01

Numerical processing is at the core of applications in many areas ranging from scientific and engineering calculations to financial computing. These applications are usually executed on large servers or supercomputers to exploit their high speed, high level of parallelism and high bandwidth...

Numerical determination of transmission probabilities in cylindrical geometry

International Nuclear Information System (INIS)

Queiroz Bogado Leite, S. de.

1989-11-01

Efficient methods for numerical calculation of transmission probabilities in cylindrical geometry are presented. Relative errors of the order of 10 -5 or smaller are obtained using analytical solutions and low order quadrature integration schemes. (author) [pt

Contributions to reinforced concrete structures numerical simulations

International Nuclear Information System (INIS)

Badel, P.B.

2001-07-01

In order to be able to carry out simulations of reinforced concrete structures, it is necessary to know two aspects: the behaviour laws have to reflect the complex behaviour of concrete and a numerical environment has to be developed in order to avoid to the user difficulties due to the softening nature of the behaviour. This work deals with these two subjects. After an accurate estimation of two behaviour models (micro-plan and mesoscopic models), two damage models (the first one using a scalar variable, the other one a tensorial damage of the 2 order) are proposed. These two models belong to the framework of generalized standard materials, which renders their numerical integration easy and efficient. A method of load control is developed in order to make easier the convergence of the calculations. At last, simulations of industrial structures illustrate the efficiency of the method. (O.M.)

A family of four stages embedded explicit six-step methods with eliminated phase-lag and its derivatives for the numerical solution of the second order problems

Science.gov (United States)

Simos, T. E.

2017-11-01

A family of four stages high algebraic order embedded explicit six-step methods, for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating solutions, are studied in this paper. The free parameters of the new proposed methods are calculated solving the linear system of equations which is produced by requesting the vanishing of the phase-lag of the methods and the vanishing of the phase-lag's derivatives of the schemes. For the new obtained methods we investigate: • Its local truncation error (LTE) of the methods.• The asymptotic form of the LTE obtained using as model problem the radial Schrödinger equation.• The comparison of the asymptotic forms of LTEs for several methods of the same family. This comparison leads to conclusions on the efficiency of each method of the family.• The stability and the interval of periodicity of the obtained methods of the new family of embedded finite difference pairs.• The applications of the new obtained family of embedded finite difference pairs to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc. The above applications lead to conclusion on the efficiency of the methods of the new family of embedded finite difference pairs.

Achieving better cooling of turbine blades using numerical simulation methods

Science.gov (United States)

Inozemtsev, A. A.; Tikhonov, A. S.; Sendyurev, C. I.; Samokhvalov, N. Yu.

2013-02-01

A new design of the first-stage nozzle vane for the turbine of a prospective gas-turbine engine is considered. The blade's thermal state is numerically simulated in conjugate statement using the ANSYS CFX 13.0 software package. Critical locations in the blade design are determined from the distribution of heat fluxes, and measures aimed at achieving more efficient cooling are analyzed. Essentially lower (by 50-100°C) maximal temperature of metal has been achieved owing to the results of the performed work.

Discrete variational derivative method a structure-preserving numerical method for partial differential equations

CERN Document Server

Furihata, Daisuke

2010-01-01

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

An efficient preconditioning technique using Krylov subspace methods for 3D characteristics solvers

International Nuclear Information System (INIS)

Dahmani, M.; Le Tellier, R.; Roy, R.; Hebert, A.

2005-01-01

The Generalized Minimal RESidual (GMRES) method, using a Krylov subspace projection, is adapted and implemented to accelerate a 3D iterative transport solver based on the characteristics method. Another acceleration technique called the self-collision rebalancing technique (SCR) can also be used to accelerate the solution or as a left preconditioner for GMRES. The GMRES method is usually used to solve a linear algebraic system (Ax=b). It uses K(r (o) ,A) as projection subspace and AK(r (o) ,A) for the orthogonalization of the residual. This paper compares the performance of these two combined methods on various problems. To implement the GMRES iterative method, the characteristics equations are derived in linear algebra formalism by using the equivalence between the method of characteristics and the method of collision probability to end up with a linear algebraic system involving fluxes and currents. Numerical results show good performance of the GMRES technique especially for the cases presenting large material heterogeneity with a scattering ratio close to 1. Similarly, the SCR preconditioning slightly increases the GMRES efficiency

A numeric-analytic method for approximating the chaotic Chen system

International Nuclear Information System (INIS)

Mossa Al-sawalha, M.; Noorani, M.S.M.

2009-01-01

The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge-Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic-numeric scheme is effective and accurate.

Numerical analysis for multi-group neutron-diffusion equation using Radial Point Interpolation Method (RPIM)

International Nuclear Information System (INIS)

Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong

2017-01-01

Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and

Numerical precision calculations for LHC physics

International Nuclear Information System (INIS)

Reuschle, Christian Andreas

2013-01-01

In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N c ) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N c limit.

Numerical precision calculations for LHC physics

Energy Technology Data Exchange (ETDEWEB)

Reuschle, Christian Andreas

2013-02-05

In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N{sub c}) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N{sub c} limit.

GPUs, a new tool of acceleration in CFD: efficiency and reliability on smoothed particle hydrodynamics methods.

Directory of Open Access Journals (Sweden)

Alejandro C Crespo

Full Text Available Smoothed Particle Hydrodynamics (SPH is a numerical method commonly used in Computational Fluid Dynamics (CFD to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs or Graphics Processor Units (GPUs, a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability.

A rapid, efficient, and economic device and method for the isolation and purification of mouse islet cells.

Directory of Open Access Journals (Sweden)

Yin Zongyi

Full Text Available Rapid, efficient, and economic method for the isolation and purification of islets has been pursued by numerous islet-related researchers. In this study, we compared the advantages and disadvantages of our developed patented method with those of commonly used conventional methods (Ficoll-400, 1077, and handpicking methods. Cell viability was assayed using Trypan blue, cell purity and yield were assayed using diphenylthiocarbazone, and islet function was assayed using acridine orange/ethidium bromide staining and enzyme-linked immunosorbent assay-glucose stimulation testing 4 days after cultivation. The results showed that our islet isolation and purification method required 12 ± 3 min, which was significantly shorter than the time required in Ficoll-400, 1077, and HPU groups (34 ± 3, 41 ± 4, and 30 ± 4 min, respectively; P 1000 islets. In summary, the MCT method is a rapid, efficient, and economic method for isolating and purifying murine islet cell clumps. This method overcomes some of the shortcomings of conventional methods, showing a relatively higher quality and yield of islets within a shorter duration at a lower cost. Therefore, the current method provides researchers with an alternative option for islet isolation and should be widely generalized.

Calculation method of efficiency factor in Alford's force

Energy Technology Data Exchange (ETDEWEB)

Ding, X.; Yang, Y.; Chen, W.; Huang, S.; Zheng, C. [Huazhong University of Science and Technology, Wuhan (China). College of Energy and Power Engineering

2006-07-01

The mechanism of gas excitation for wheel eccentricity and to calculate Alford's force are introduced. On the basis of the blade-and-flow parameters a new formulation is derived and validated. The calculation results are consistent with current theory and experimental conclusions. The physical meaning of the ranges of numerical values of the efficiency factor are discussed. This gets rid of the difficulty of selecting the efficiency factor in Alford's formulation and lays a theoretical foundation for the stability analysis to increases turbine rotor stability. (author)

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.