Asymptotic preserving and all-regime Lagrange-Projection like numerical schemes: application to two-phase flows in low mach regime

International Nuclear Information System (INIS)

Girardin, Mathieu

2014-01-01

Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author) [fr

Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

KAUST Repository

Chen, Huangxin

2017-09-01

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.

On the properties of energy stable flux reconstruction schemes for implicit large eddy simulation

Science.gov (United States)

Vermeire, B. C.; Vincent, P. E.

2016-12-01

We begin by investigating the stability, order of accuracy, and dispersion and dissipation characteristics of the extended range of energy stable flux reconstruction (E-ESFR) schemes in the context of implicit large eddy simulation (ILES). We proceed to demonstrate that subsets of the E-ESFR schemes are more stable than collocation nodal discontinuous Galerkin methods recovered with the flux reconstruction approach (FRDG) for marginally-resolved ILES simulations of the Taylor-Green vortex. These schemes are shown to have reduced dissipation and dispersion errors relative to FRDG schemes of the same polynomial degree and, simultaneously, have increased Courant-Friedrichs-Lewy (CFL) limits. Finally, we simulate turbulent flow over an SD7003 aerofoil using two of the most stable E-ESFR schemes identified by the aforementioned Taylor-Green vortex experiments. Results demonstrate that subsets of E-ESFR schemes appear more stable than the commonly used FRDG method, have increased CFL limits, and are suitable for ILES of complex turbulent flows on unstructured grids.

Analyzing numerics of bulk microphysics schemes in community models: warm rain processes

Directory of Open Access Journals (Sweden)

I. Sednev

2012-08-01

Full Text Available Implementation of bulk cloud microphysics (BLK parameterizations in atmospheric models of different scales has gained momentum in the last two decades. Utilization of these parameterizations in cloud-resolving models when timesteps used for the host model integration are a few seconds or less is justified from the point of view of cloud physics. However, mechanistic extrapolation of the applicability of BLK schemes to the regional or global scales and the utilization of timesteps of hundreds up to thousands of seconds affect both physics and numerics.

We focus on the mathematical aspects of BLK schemes, such as stability and positive-definiteness. We provide a strict mathematical definition for the problem of warm rain formation. We also derive a general analytical condition (SM-criterion that remains valid regardless of parameterizations for warm rain processes in an explicit Eulerian time integration framework used to advanced finite-difference equations, which govern warm rain formation processes in microphysics packages in the Community Atmosphere Model and the Weather Research and Forecasting model. The SM-criterion allows for the existence of a unique positive-definite stable mass-conserving numerical solution, imposes an additional constraint on the timestep permitted due to the microphysics (like the Courant-Friedrichs-Lewy condition for the advection equation, and prohibits use of any additional assumptions not included in the strict mathematical definition of the problem under consideration.

By analyzing the numerics of warm rain processes in source codes of BLK schemes implemented in community models we provide general guidelines regarding the appropriate choice of time steps in these models.

Conservative numerical schemes for Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada

1999-05-01

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

A new numerical scheme for the simulation of active magnetic regenerators

DEFF Research Database (Denmark)

Torregrosa-Jaime, B.; Engelbrecht, Kurt; Payá, J.

2014-01-01

A 1D model of a parallel-plate active magnetic regenerator (AMR) has been developed based on a new numerical scheme. With respect to the implicit scheme, the new scheme achieves accurate results, minimizes computational time and prevents numerical errors. The model has been used to check the boun...

Simple Numerical Schemes for the Korteweg-deVries Equation

International Nuclear Information System (INIS)

McKinstrie, C. J.; Kozlov, M.V.

2000-01-01

Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves

Simple Numerical Schemes for the Korteweg-deVries Equation

Energy Technology Data Exchange (ETDEWEB)

C. J. McKinstrie; M. V. Kozlov

2000-12-01

Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.

Numerical dissipation and dispersion of the homogenenous and complete flux schemes

NARCIS (Netherlands)

Thije Boonkkamp, ten J.H.M.; Anthonissen, M.J.H.

2014-01-01

We analyse numerical dissipation and dispersion of the homogeneous ¿ux (HF) and complete ¿ux (CF) schemes, ¿nite volume methods introduced in [1]. To that purpose we derive the modi¿ed equation of both schemes. We show that the HF scheme suffers from numerical diffusion for dominant advection, which

Canonical, stable, general mapping using context schemes.

Science.gov (United States)

Novak, Adam M; Rosen, Yohei; Haussler, David; Paten, Benedict

2015-11-15

Sequence mapping is the cornerstone of modern genomics. However, most existing sequence mapping algorithms are insufficiently general. We introduce context schemes: a method that allows the unambiguous recognition of a reference base in a query sequence by testing the query for substrings from an algorithmically defined set. Context schemes only map when there is a unique best mapping, and define this criterion uniformly for all reference bases. Mappings under context schemes can also be made stable, so that extension of the query string (e.g. by increasing read length) will not alter the mapping of previously mapped positions. Context schemes are general in several senses. They natively support the detection of arbitrary complex, novel rearrangements relative to the reference. They can scale over orders of magnitude in query sequence length. Finally, they are trivially extensible to more complex reference structures, such as graphs, that incorporate additional variation. We demonstrate empirically the existence of high-performance context schemes, and present efficient context scheme mapping algorithms. The software test framework created for this study is available from https://registry.hub.docker.com/u/adamnovak/sequence-graphs/. anovak@soe.ucsc.edu Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Hybrid flux splitting schemes for numerical resolution of two-phase flows

Energy Technology Data Exchange (ETDEWEB)

Flaatten, Tore

2003-07-01

This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

Science.gov (United States)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Numerical study of a hybrid jet impingement/micro-channel cooling scheme

International Nuclear Information System (INIS)

Barrau, Jérôme; Omri, Mohammed; Chemisana, Daniel; Rosell, Joan; Ibañez, Manel; Tadrist, Lounes

2012-01-01

A new hybrid jet impingement/micro-channel cooling scheme is studied numerically for use in high-heat-flux thermal management of electronic and power devices. The device is developed with the objective of improving the temperature uniformity of the cooled object. A numerical model based on the k–ω SST turbulent model is developed and validated experimentally. This model is used to carry out a parametrical characterization of the heat sink. The study shows that variations in key parameters of jet impingement and micro-channel technologies allow for the cooling scheme to obtain a wide range of temperature profiles for the cooled object. - Highlights: ► A new hybrid cooling scheme is numerically studied. ► The cooling scheme combines the benefits of jet impingement and micro-channel flows. ► The numerical model is validated by comparison with experimental results. ► The temperature distribution can be adapted to the needs of the cooled system.

CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR ...

African Journals Online (AJOL)

This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give ...

Cures for the shock instability: Development of a shock-stable Roe scheme

CERN Document Server

Kim, S S; Rho, O H; Kyu-Hong, S

2003-01-01

This paper deals with the development of an improved Roe scheme that is free from the shock instability and still preserves the accuracy and efficiency of the original Roe's Flux Difference Splitting (FDS). Roe's FDS is known to possess good accuracy but to suffer from the shock instability, such as the carbuncle phenomenon. As the first step towards a shock-stable scheme, Roe's FDS is compared with the HLLE scheme to identify the source of the shock instability. Through a linear perturbation analysis on the odd-even decoupling problem, damping characteristic is examined and Mach number-based functions f and g are introduced to balance damping and feeding rates, which leads to a shock-stable Roe scheme. In order to satisfy the conservation of total enthalpy, which is crucial in predicting surface heat transfer rate in high-speed steady flows, an analysis of dissipation mechanism in the energy equation is carried out to find out the error source and to make the proposed scheme preserve total enthalpy. By modif...

Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results

International Nuclear Information System (INIS)

Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young

2007-12-01

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor

Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results

Energy Technology Data Exchange (ETDEWEB)

Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young

2007-12-15

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor.

Linearly decoupled energy-stable numerical methods for multi-component two-phase compressible flow

KAUST Repository

Kou, Jisheng

2017-12-06

In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are constructed based on the scalar auxiliary variable (SAV) approaches for Helmholtz free energy and the intermediate velocities that are designed to decouple the tight relationship between velocity and molar densities. The intermediate velocities are also involved in the discrete momentum equation to ensure a consistency relationship with the mass balance equations. Moreover, we propose a component-wise SAV approach for a multi-component fluid, which requires solving a sequence of linear, separate mass balance equations. We prove that the methods have the unconditional energy-dissipation feature. Numerical results are presented to verify the effectiveness of the proposed methods.

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%....

A stable penalty method for the compressible Navier-Stokes equations: II: One-dimensional domain decomposition schemes

DEFF Research Database (Denmark)

Hesthaven, Jan

1997-01-01

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...

Numerical schemes for the hybrid modeling approach of gas-particle turbulent flows

International Nuclear Information System (INIS)

Dorogan, K.

2012-01-01

Hybrid Moments/PDF methods have shown to be well suitable for the description of poly-dispersed turbulent two-phase flows in non-equilibrium which are encountered in some industrial situations involving chemical reactions, combustion or sprays. They allow to obtain a fine enough physical description of the poly-dispersity, non-linear source terms and convection phenomena. However, their approximations are noised with the statistical error, which in several situations may be a source of a bias. An alternative hybrid Moments-Moments/PDF approach examined in this work consists in coupling the Moments and the PDF descriptions, within the description of the dispersed phase itself. This hybrid method could reduce the statistical error and remove the bias. However, such a coupling is not straightforward in practice and requires the development of accurate and stable numerical schemes. The approaches introduced in this work rely on the combined use of the up-winding and relaxation-type techniques. They allow to obtain stable unsteady approximations for a system of partial differential equations containing non-smooth external data which are provided by the PDF part of the model. A comparison of the results obtained using the present method with those of the 'classical' hybrid approach is presented in terms of the numerical errors for a case of a co-current gas-particle wall jet. (author)

A new scheme to treat the numerical Tcherenkov instability for electromagnetic particle simulations

International Nuclear Information System (INIS)

Assous, F.; Degond, P.; Segre, J.; Degond, P.

1997-10-01

The aim of this paper is to present a new explicit time scheme for electromagnetic particle simulations. The main property of this new scheme, which depends on a parameter, is to reduce and in some cases to suppress numerical instabilities that can appear in this context, and are widely described in the literature. Other numerical properties are also investigated, and a numerical example is finally given to illustrate our purpose. This scheme is expected to be useful in the field of plasma modelling. (authors)

Development of orthogonal 2-dimensional numerical code TFC2D for fluid flow with various turbulence models and numerical schemes

Energy Technology Data Exchange (ETDEWEB)

Park, Ju Yeop; In, Wang Kee; Chun, Tae Hyun; Oh, Dong Seok [Korea Atomic Energy Research Institute, Taejeon (Korea)

2000-02-01

The development of orthogonal 2-dimensional numerical code is made. The present code contains 9 kinds of turbulence models that are widely used. They include a standard k-{epsilon} model and 8 kinds of low Reynolds number ones. They also include 6 kinds of numerical schemes including 5 kinds of low order schemes and 1 kind of high order scheme such as QUICK. To verify the present numerical code, pipe flow, channel flow and expansion pipe flow are solved by this code with various options of turbulence models and numerical schemes and the calculated outputs are compared to experimental data. Furthermore, the discretization error that originates from the use of standard k-{epsilon} turbulence model with wall function is much more diminished by introducing a new grid system than a conventional one in the present code. 23 refs., 58 figs., 6 tabs. (Author)

Two-level schemes for the advection equation

Science.gov (United States)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

Stable radio frequency dissemination by simple hybrid frequency modulation scheme.

Science.gov (United States)

Yu, Longqiang; Wang, Rong; Lu, Lin; Zhu, Yong; Wu, Chuanxin; Zhang, Baofu; Wang, Peizhang

2014-09-15

In this Letter, we propose a fiber-based stable radio frequency transfer system by a hybrid frequency modulation scheme. Creatively, two radio frequency signals are combined and simultaneously transferred by only one laser diode. One frequency component is used to detect the phase fluctuation, and the other one is the derivative compensated signal providing a stable frequency for the remote end. A proper ratio of the frequencies of the components is well maintained by parameter m to avoid interference between them. Experimentally, a stable 200 MHz signal is transferred over 100 km optical fiber with the help of a 1 GHz detecting signal, and fractional instability of 2×10(-17) at 10(5) s is achieved.

Preliminary Study of 1D Thermal-Hydraulic System Analysis Code Using the Higher-Order Numerical Scheme

Energy Technology Data Exchange (ETDEWEB)

Lee, Won Woong; Lee, Jeong Ik [KAIST, Daejeon (Korea, Republic of)

2016-05-15

The existing nuclear system analysis codes such as RELAP5, TRAC, MARS and SPACE use the first-order numerical scheme in both space and time discretization. However, the first-order scheme is highly diffusive and less accurate due to the first order of truncation error. So, the numerical diffusion problem which makes the gradients to be smooth in the regions where the gradients should be steep can occur during the analysis, which often predicts less conservatively than the reality. Therefore, the first-order scheme is not always useful in many applications such as boron solute transport. RELAP7 which is an advanced nuclear reactor system safety analysis code using the second-order numerical scheme in temporal and spatial discretization is being developed by INL (Idaho National Laboratory) since 2011. Therefore, for better predictive performance of the safety of nuclear reactor systems, more accurate nuclear reactor system analysis code is needed for Korea too to follow the global trend of nuclear safety analysis. Thus, this study will evaluate the feasibility of applying the higher-order numerical scheme to the next generation nuclear system analysis code to provide the basis for the better nuclear system analysis code development. The accuracy is enhanced in the spatial second-order scheme and the numerical diffusion problem is alleviated while indicates significantly lower maximum Courant limit and the numerical dispersion issue which produces spurious oscillation and non-physical results in the higher-order scheme. If the spatial scheme is the first order scheme then the temporal second-order scheme provides almost the same result with the temporal firstorder scheme. However, when the temporal second order scheme and the spatial second-order scheme are applied together, the numerical dispersion can occur more severely. For the more in-depth study, the verification and validation of the NTS code built in MATLAB will be conducted further and expanded to handle two

Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification

Energy Technology Data Exchange (ETDEWEB)

Blottner, F.G.; Lopez, A.R.

1998-10-01

This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation

KAUST Repository

Liu, Yang; Sen, Mrinal K.

2010-01-01

We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.

A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation

KAUST Repository

Liu, Yang

2010-03-01

We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.

Numerical study of read scheme in one-selector one-resistor crossbar array

Science.gov (United States)

Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin

2015-12-01

A comprehensive numerical circuit analysis of read schemes of a one selector-one resistance change memory (1S1R) crossbar array is carried out. Three schemes-the ground, V/2, and V/3 schemes-are compared with each other in terms of sensing margin and power consumption. Without the aid of a complex analytical approach or SPICE-based simulation, a simple numerical iteration method is developed to simulate entire current flows and node voltages within a crossbar array. Understanding such phenomena is essential in successfully evaluating the electrical specifications of selectors for suppressing intrinsic drawbacks of crossbar arrays, such as sneaky current paths and series line resistance problems. This method provides a quantitative tool for the accurate analysis of crossbar arrays and provides guidelines for developing an optimal read scheme, array configuration, and selector device specifications.

Implicit and semi-implicit schemes in the Versatile Advection Code : numerical tests

NARCIS (Netherlands)

Tóth, G.; Keppens, R.; Bochev, Mikhail A.

1998-01-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing

A stable higher order space time Galerkin marching-on-in-time scheme

KAUST Repository

Pray, Andrew J.; Shanker, Balasubramaniam; Bagci, Hakan

2013-01-01

We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order

Application of stable adaptive schemes to nuclear reactor systems, (1)

International Nuclear Information System (INIS)

Fukuda, Toshio

1978-01-01

Parameter identification and adaptive control schemes are presented for a point reactor with internal feedbacks which lead to the nonlinearity of the overall system. Both are shown stable with new representation of the system, which corresponds to the nonminimal system representation, in the vein of the Model Reference Adaptive System (MRAS) via the Lyapunov's method. For the sake of the parameter identification, model parameters can be adjusted adaptively as soon as measurements start, while plant parameters can also adaptively be compensated through control input to reduce the output error between the model and the plant for the case of the adaptive control. In the case of the adaptive control, control schemes are presented for two cases, the case of the unknown decay constant of the delayed neutron and the case of the known constant. The adaptive control scheme for the latter case is shown extremely simpler than that for the former. Furthermore, when plant parameters vary slowly with time, computer simulations show that the proposed adaptive control scheme works satisfactorily enough to stabilize an unstable reactor and that it does even in the noise with small variance. (auth.)

Ferrofluids: Modeling, numerical analysis, and scientific computation

Science.gov (United States)

Tomas, Ignacio

This dissertation presents some developments in the Numerical Analysis of Partial Differential Equations (PDEs) describing the behavior of ferrofluids. The most widely accepted PDE model for ferrofluids is the Micropolar model proposed by R.E. Rosensweig. The Micropolar Navier-Stokes Equations (MNSE) is a subsystem of PDEs within the Rosensweig model. Being a simplified version of the much bigger system of PDEs proposed by Rosensweig, the MNSE are a natural starting point of this thesis. The MNSE couple linear velocity u, angular velocity w, and pressure p. We propose and analyze a first-order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier-Stokes equations. Moving onto the much more complex Rosensweig's model, we provide a definition (approximation) for the effective magnetizing field h, and explain the assumptions behind this definition. Unlike previous definitions available in the literature, this new definition is able to accommodate the effect of external magnetic fields. Using this definition we setup the system of PDEs coupling linear velocity u, pressure p, angular velocity w, magnetization m, and magnetic potential ϕ We show that this system is energy-stable and devise a numerical scheme that mimics the same stability property. We prove that solutions of the numerical scheme always exist and, under certain simplifying assumptions, that the discrete solutions converge. A notable outcome of the analysis of the numerical scheme for the Rosensweig's model is the choice of finite element spaces that allow the construction of an energy-stable scheme. Finally, with the lessons learned from Rosensweig's model, we develop a diffuse-interface model describing the behavior of two-phase ferrofluid flows and present an energy-stable numerical scheme for this model. For a

On a Stable and Consistent Finite Difference Scheme for a Time ...

African Journals Online (AJOL)

NJABS

established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion .... the rate at which signals in the numerical scheme travel will be faster than their real world counterparts and this unrealistic expectation leads ...

Numerical Schemes for Rough Parabolic Equations

Energy Technology Data Exchange (ETDEWEB)

Deya, Aurelien, E-mail: deya@iecn.u-nancy.fr [Universite de Nancy 1, Institut Elie Cartan Nancy (France)

2012-04-15

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489-1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H>1/3.

Numerical investigation of sixth order Boussinesq equation

Science.gov (United States)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

A numerical scheme for the one-dimensional pressureless gases system

OpenAIRE

Boudin , Laurent; Mathiaud , Julien

2012-01-01

International audience; In this work, we investigate the numerical solving of the one-dimensional pressureless gases system. After briefly recalling the mathematical framework of the duality solutions introduced by Bouchut and James, we point out that the upwind scheme for the density and momentum does not satisfy the one-sided Lipschitz (OSL) condition on the expansion rate required for the duality solutions. Then we build a diffusive scheme which allows to recover the OSL condition by follo...

Convergent Difference Schemes for Hamilton-Jacobi equations

KAUST Repository

Duisembay, Serikbolsyn

2018-05-07

In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet and Neumann type boundary conditions in arbitrary two-dimensional domains. First, we introduce the notion of viscosity solutions in both continuous and discontinuous frameworks. Next, we review Barles-Souganidis approach using monotone, consistent, and stable schemes. In particular, we show that these schemes converge locally uniformly to the unique viscosity solution of the first-order Hamilton-Jacobi equations under mild assumptions. To solve the scheme numerically, we use Euler map with some initial guess. This iterative method gives the viscosity solution as a limit. Moreover, we illustrate our numerical approach in several two-dimensional examples.

Generalized Roe's numerical scheme for a two-fluid model

International Nuclear Information System (INIS)

Toumi, I.; Raymond, P.

1993-01-01

This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,

Generating Unstable Resonances for Extraction Schemes Based on Transverse Splitting

CERN Document Server

Giovannozzi, M; Turchetti, G

2009-01-01

A few years ago, a novel multi-turn extraction scheme was proposed, based on particle trapping inside stable resonances. Numerical simulations and experimental tests have confirmed the feasibility of such a scheme for low order resonances. While the third-order resonance is generically unstable and those higher than fourth-order are generically stable, the fourth-order resonance can be either stable or unstable depending on the specifics of the system under consideration. By means of the Normal Form a general approach to control the stability of the fourth-order resonance has been derived. This approach is based on the control of the amplitude detuning and the general form for a lattice with an arbitrary number of sextupole and octupole families is derived in this paper. Numerical simulations have confirmed the analytical results and have shown that, when crossing the unstable fourth-order resonance, the region around the centre of the phase space is depleted and particles are trapped in only the four stable ...

Numerical analysis of boosting scheme for scalable NMR quantum computation

International Nuclear Information System (INIS)

SaiToh, Akira; Kitagawa, Masahiro

2005-01-01

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC'99) (ACM Press, New York, 1999), pp. 322-329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result--namely, that there is such a significant growth in the total binary entropy--disagrees with that of their analysis

A Semi-implicit Numerical Scheme for a Two-dimensional, Three-field Thermo-Hydraulic Modeling

International Nuclear Information System (INIS)

Hwang, Moonkyu; Jeong, Jaejoon

2007-07-01

The behavior of two-phase flow is modeled, depending on the purpose, by either homogeneous model, drift flux model, or separated flow model, Among these model, in the separated flow model, the behavior of each flow phase is modeled by its own governing equation, together with the interphase models which describe the thermal and mechanical interactions between the phases involved. In this study, a semi-implicit numerical scheme for two-dimensional, transient, two-fluid, three-field is derived. The work is an extension to the previous study for the staggered, semi-implicit numerical scheme in one-dimensional geometry (KAERI/TR-3239/2006). The two-dimensional extension is performed by specifying a relevant governing equation set and applying the related finite differencing method. The procedure for employing the semi-implicit scheme is also described in detail. Verifications are performed for a 2-dimensional vertical plate for a single-phase and two-phase flows. The calculations verify the mass and energy conservations. The symmetric flow behavior, for the verification problem, also confirms the momentum conservation of the numerical scheme

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

KAUST Repository

Calatroni, Luca

2013-08-01

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

KAUST Repository

Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane

2013-01-01

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

Numerical investigation on compressible flow characteristics in axial compressors using a multi block finite-volume scheme

International Nuclear Information System (INIS)

Farhanieh, B.; Amanifard, N.; Ghorbanian, K.

2002-01-01

An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Mon tonic Upstream Scheme for Conservation Laws was added to flux splitting schemes. The Baldwin-Lo max (B L) turbulence model was implemented to solve the turbulent case studies. Implicit solution was also provided using Lower and Upper (L U) decomposition technique to compare with explicit solutions. To validate the numerical procedure, two test cases are prepared and flow over a Na Ca 0012 airfoil was investigated and the pressure coefficients were compared to the reference data. The numerical solver was implemented to study the flow passing over a compressor cascade. The results of various combinations of splitting schemes and the Mon tonic Upstream Scheme for Conventional Laws limiter were compared with each other to find the suitable methods in cascade problems. Finally the convergence histories of implemented schemes were compared to each other to show the behavior of the solver in using various methods before implementation of them in flow instability studies

Stable multi-domain spectral penalty methods for fractional partial differential equations

Science.gov (United States)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Numerical schemes for one-point closure turbulence models

International Nuclear Information System (INIS)

Larcher, Aurelien

2010-01-01

First-order Reynolds Averaged Navier-Stokes (RANS) turbulence models are studied in this thesis. These latter consist of the Navier-Stokes equations, supplemented with a system of balance equations describing the evolution of characteristic scalar quantities called 'turbulent scales'. In so doing, the contribution of the turbulent agitation to the momentum can be determined by adding a diffusive coefficient (called 'turbulent viscosity') in the Navier-Stokes equations, such that it is defined as a function of the turbulent scales. The numerical analysis problems, which are studied in this dissertation, are treated in the frame of a fractional step algorithm, consisting of an approximation on regular meshes of the Navier-Stokes equations by the nonconforming Crouzeix-Raviart finite elements, and a set of scalar convection-diffusion balance equations discretized by the standard finite volume method. A monotone numerical scheme based on the standard finite volume method is proposed so as to ensure that the turbulent scales, like the turbulent kinetic energy (k) and its dissipation rate (ε), remain positive in the case of the standard k - ε model, as well as the k - ε RNG and the extended k - ε - ν 2 models. The convergence of the proposed numerical scheme is then studied on a system composed of the incompressible Stokes equations and a steady convection-diffusion equation, which are both coupled by the viscosities and the turbulent production term. This reduced model allows to deal with the main difficulty encountered in the analysis of such problems: the definition of the turbulent production term leads to consider a class of convection-diffusion problems with an irregular right-hand side belonging to L 1 . Finally, to step towards the unsteady problem, the convergence of the finite volume scheme for a model convection-diffusion equation with L 1 data is proved. The a priori estimates on the solution and on its time derivative are obtained in discrete norms, for

A modified symplectic PRK scheme for seismic wave modeling

Science.gov (United States)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

A study to reduce the numerical diffusion of upwind scheme in two dimensional convection phenomena analysis

International Nuclear Information System (INIS)

Lee, Goung Jin; Kim, Soong Pyung

1990-01-01

In solving the convection-diffusion phenomena, it is common to use central difference scheme or upwind scheme. The central difference scheme has second order accuracy, while the upwind scheme is only first order accurate. However, since the variation rising in the convection-diffusion problem is exponential, central difference scheme ceased to be a good method for anything but extremely small values of Δx. At large values of Δx, which is all one can afford in most practical problems, it is the upwind scheme that gives more reasonable results than the central scheme. But in the conventional upwind scheme, since the accuracy is only first order, false diffusion is somewhat large, and when the real diffusion is smaller than the numerical diffusion, solutions may be very errorneous. So in this paper, a method to reduce the numerical diffusion of upwind scheme is studied. Developed scheme uses same number of nodes as conventional upwind scheme, but it considers the direction of flow more sophistically. As a conclusion, the developed scheme shows very good results. It can reduce false diffusion greatly with the cost of small complexity. Also, algorithm of the developed scheme is presented at appendix. (Author)

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

Science.gov (United States)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

Ballooning stable high beta tokamak equilibria

International Nuclear Information System (INIS)

Tuda, Takashi; Azumi, Masafumi; Kurita, Gen-ichi; Takizuka, Tomonori; Takeda, Tatsuoki

1981-04-01

The second stable regime of ballooning modes is numerically studied by using the two-dimensional tokamak transport code with the ballooning stability code. Using the simple FCT heating scheme, we find that the plasma can locally enter this second stable regime. And we obtained equilibria with fairly high beta (β -- 23%) stable against ballooning modes in a whole plasma region, by taking into account of finite thermal diffusion due to unstable ballooning modes. These results show that a tokamak fusion reactor can operate in a high beta state, which is economically favourable. (author)

Novel communication scheme based on chaotic Roessler circuits

International Nuclear Information System (INIS)

GarcIa-Lopez, J H; Jaimes-Reategui, R; Pisarchik, A N; MurguIa-Hernandez, A; Medina-Gutierrez, C; Valdivia-Hernadez, R; Villafana-Rauda, E

2005-01-01

We present a novel synchronization scheme for secure communication with two chaotic unidirectionally coupled Roessler circuits. The circuits are synchronized via one of the variables, while a signal is transmitted through another variable. We show that this scheme allows more stable communications. The system dynamics is studied numerically and experimentally in a wide range of a control parameter. The possibility of secure communications with an audio signal is demonstrated

Efficient and stable model reduction scheme for the numerical simulation of broadband acoustic metamaterials

DEFF Research Database (Denmark)

Hyun, Jaeyub; Kook, Junghwan; Wang, Semyung

2015-01-01

) as a basis vector. The proposed AQSRV-based model reduction scheme has the following two representative features: (1) Multiple frequency subintervals and (2) Adaptive selection of the subinterval information (i.e., the proper number and location of the center frequencies) and basis vector at each subinterval...

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

Science.gov (United States)

Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

2018-04-01

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual

Generating unstable resonances for extraction schemes based on transverse splitting

Directory of Open Access Journals (Sweden)

M. Giovannozzi

2009-02-01

Full Text Available A few years ago, a novel multiturn extraction scheme was proposed, based on particle trapping inside stable resonances. Numerical simulations and experimental tests have confirmed the feasibility of such a scheme for low order resonances. While the third-order resonance is generically unstable and those higher than fourth order are generically stable, the fourth-order resonance can be either stable or unstable depending on the specifics of the system under consideration. By means of the normal form, a general approach to control the stability of the fourth-order resonance has been derived. This approach is based on the control of the amplitude detuning and the general form for a lattice with an arbitrary number of sextupole and octupole families is derived in this paper. Numerical simulations have confirmed the analytical results and have shown that, when crossing the unstable fourth-order resonance, the region around the center of the phase space is depleted and particles are trapped in only the four stable islands. A four-turn extraction could be designed using this technique.

TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

International Nuclear Information System (INIS)

Walters, W.F.

1983-01-01

A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy

Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

International Nuclear Information System (INIS)

Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.

2013-01-01

The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

Analysis of central and upwind compact schemes

International Nuclear Information System (INIS)

Sengupta, T.K.; Ganeriwal, G.; De, S.

2003-01-01

Central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space, numerical stability and dispersion relation preservation. A von Neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously. This allows one to evaluate various boundary closures and their effects on the domain interior. The same method can be used for stability analysis performed for the semi-discrete initial boundary value problems (IBVP). This analysis tells one about the stability for every resolved length scale. Some well-known compact schemes that were found to be G-K-S and time stable are shown here to be unstable for selective length scales by this analysis. This is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming. To demonstrate the asymptotic stability of the resultant schemes, numerical solution of the wave equation is compared with analytical solution. Furthermore, some of these schemes are used to solve two-dimensional Navier-Stokes equation and a computational acoustic problem to check their ability to solve problems for long time. It is found that those schemes, that were found unstable for the wave equation, are unsuitable for solving incompressible Navier-Stokes equation. In contrast, the proposed compact schemes with improved boundary closure and an explicit higher-order upwind scheme produced correct results. The numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite DRP property

Study on the improvement of the convective differencing scheme for the high-accuracy and stable resolution of the numerical solution

International Nuclear Information System (INIS)

Shin, J. K.; Choi, Y. D.

1992-01-01

QUICKER scheme has several attractive properties. However, under highly convective conditions, it produces overshoots and possibly some oscillations on each side of steps in the dependent variable when the flow is convected at an angle oblique to the grid line. Fortunately, it is possible to modify the QUICKER scheme using non-linear and linear functional relationship. Details of the development of polynomial upwinding scheme are given in this paper, where it is seen that this non-linear scheme has also third order accuracy. This polynomial upwinding scheme is used as the basis for the SHARPER and SMARTER schemes. Another revised scheme was developed by partial modification of QUICKER scheme using CDS and UPWIND schemes (QUICKUP). These revised schemes are tested at the well known bench mark flows, Two-Dimensional Pure Convection Flows in Oblique-Step, Lid Driven Cavity Flows and Buoyancy Driven Cavity Flows. For remain absolutely monotonic without overshoot and oscillation. QUICKUP scheme is more accurate than any other scheme in their relative accuracy. In high Reynolds number Lid Driven Catity Flow, SMARTER and SHARPER schemes retain lower computational cost than QUICKER and QUICKUP schemes, but computed velocity values in the revised schemes produced less predicted values than QUICKER scheme which is strongly effected by overshoot and undershoot values. Also, in Buoyancy Driven Cavity Flow, SMARTER, SHARPER and QUICKUP schemes give acceptable results. (Author)

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed

2012-11-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana

2012-01-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

A stable higher order space time Galerkin marching-on-in-time scheme

KAUST Repository

Pray, Andrew J.

2013-07-01

We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order basis functions in time to improve the accuracy of the solver. The method is validated by showing convergence in temporal basis function order, time step size, and geometric discretization order. © 2013 IEEE.

Stable numerical method in computation of stellar evolution

International Nuclear Information System (INIS)

Sugimoto, Daiichiro; Eriguchi, Yoshiharu; Nomoto, Ken-ichi.

1982-01-01

To compute the stellar structure and evolution in different stages, such as (1) red-giant stars in which the density and density gradient change over quite wide ranges, (2) rapid evolution with neutrino loss or unstable nuclear flashes, (3) hydrodynamical stages of star formation or supernova explosion, (4) transition phases from quasi-static to dynamical evolutions, (5) mass-accreting or losing stars in binary-star systems, and (6) evolution of stellar core whose mass is increasing by shell burning or decreasing by penetration of convective envelope into the core, we face ''multi-timescale problems'' which can neither be treated by simple-minded explicit scheme nor implicit one. This problem has been resolved by three prescriptions; one by introducing the hybrid scheme suitable for the multi-timescale problems of quasi-static evolution with heat transport, another by introducing also the hybrid scheme suitable for the multi-timescale problems of hydrodynamic evolution, and the other by introducing the Eulerian or, in other words, the mass fraction coordinate for evolution with changing mass. When all of them are combined in a single computer code, we can compute numerically stably any phase of stellar evolution including transition phases, as far as the star is spherically symmetric. (author)

Unconditionally stable diffusion-acceleration of the transport equation

International Nuclear Information System (INIS)

Larsen, E.W.

1982-01-01

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically large regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

Unconditionally stable diffusion-acceleration of the transport equation

International Nuclear Information System (INIS)

Larson, E.W.

1982-01-01

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

A first generation numerical geomagnetic storm prediction scheme

International Nuclear Information System (INIS)

Akasofu, S.-I.; Fry, C.F.

1986-01-01

Because geomagnetic and auroral disturbances cause significant interference on many electrical systems, it is essential to develop a reliable geomagnetic and auroral storm prediction scheme. A first generation numerical prediction scheme has been developed. The scheme consists of two major computer codes which in turn consist of a large number of subroutine codes and of empirical relationships. First of all, when a solar flare occurs, six flare parameters are determined as the input data set for the first code which is devised to show the simulated propagation of solar wind disturbances in the heliosphere to a distance of 2 a.u. Thus, one can determine the relative location of the propagating disturbances with the Earth's position. The solar wind speed and the three interplanetary magnetic field (IMF) components are then computed as a function of time at the Earth's location or any other desired (space probe) locations. These quantities in turn become the input parameters for the second major code which computes first the power of the solar wind-magnetosphere dynamo as a function of time. The power thus obtained and the three IMF components can be used to compute or infer: the predicted geometry of the auroral oval; the cross-polar cap potential; the two geomagnetic indices AE and Dst; the total energy injection rate into the polar ionosphere; and the atmospheric temperature, etc. (author)

A predictor-corrector scheme for solving the Volterra integral equation

KAUST Repository

Al Jarro, Ahmed

2011-08-01

The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.

Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

Energy Technology Data Exchange (ETDEWEB)

Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)

2014-05-01

This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

Micromagnetic simulations with thermal noise: Physical and numerical aspects

Energy Technology Data Exchange (ETDEWEB)

Martinez, E. [Dept. de Ingenieria Electromecanica, Universidad de Burgos, Plaza Misael Banuelos, s/n, E-09001, Burgos (Spain)]. E-mail: emvecino@ubu.es; Lopez-Diaz, L. [Dept. de Fisica Aplicada, Universidad Salamanca, Plaza de la Merced s/n, Salamanca E-37008 (Spain); Torres, L. [Dept. de Fisica Aplicada, Universidad Salamanca, Plaza de la Merced s/n, Salamanca E-37008 (Spain); Garcia-Cervera, C.J. [Department of Mathematics, University of California, Santa Barbara, CA 93106 (United States)

2007-09-15

Langevin dynamics treats finite temperature effects in micromagnetics framework by adding a thermal fluctuation field to the local effective field. Several works have addressed that the numerical results depend on the cell size used to split the ferromagnetic samples on the nanoscale regime. In this short paper, we analyze a thermally perturbed micromagnetic problem by using an implicit unconditionally stable numerical scheme to integrate the Langevin equation at room temperature. The obtained micromagnetic results for several cell sizes inside the validity range of the micromagnetic formalism, indicate that the addressed cell size dependence could be associated to numerical limitations of the commonly used numerical schemes.

Micromagnetic simulations with thermal noise: Physical and numerical aspects

International Nuclear Information System (INIS)

Martinez, E.; Lopez-Diaz, L.; Torres, L.; Garcia-Cervera, C.J.

2007-01-01

Langevin dynamics treats finite temperature effects in micromagnetics framework by adding a thermal fluctuation field to the local effective field. Several works have addressed that the numerical results depend on the cell size used to split the ferromagnetic samples on the nanoscale regime. In this short paper, we analyze a thermally perturbed micromagnetic problem by using an implicit unconditionally stable numerical scheme to integrate the Langevin equation at room temperature. The obtained micromagnetic results for several cell sizes inside the validity range of the micromagnetic formalism, indicate that the addressed cell size dependence could be associated to numerical limitations of the commonly used numerical schemes

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

Science.gov (United States)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

Science.gov (United States)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

Stable Numerical Approach for Fractional Delay Differential Equations

Science.gov (United States)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Stable schemes for dissipative particle dynamics with conserved energy

Energy Technology Data Exchange (ETDEWEB)

Stoltz, Gabriel, E-mail: stoltz@cermics.enpc.fr

2017-07-01

This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis–Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiple timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.

Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

2017-01-01

This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil

2017-07-31

This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

Development and comparison of different spatial numerical schemes for the radiative transfer equation resolution using three-dimensional unstructured meshes

International Nuclear Information System (INIS)

Capdevila, R.; Perez-Segarra, C.D.; Oliva, A.

2010-01-01

In the present work four different spatial numerical schemes have been developed with the aim of reducing the false-scattering of the numerical solutions obtained with the discrete ordinates (DOM) and the finite volume (FVM) methods. These schemes have been designed specifically for unstructured meshes by means of the extrapolation of nodal values of intensity on the studied radiative direction. The schemes have been tested and compared in several 3D benchmark test cases using both structured orthogonal and unstructured grids.

Additive operator-difference schemes splitting schemes

CERN Document Server

Vabishchevich, Petr N

2013-01-01

Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy

An efficient numerical progressive diagonalization scheme for the quantum Rabi model revisited

International Nuclear Information System (INIS)

Pan, Feng; Bao, Lina; Dai, Lianrong; Draayer, Jerry P

2017-01-01

An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model. (paper)

Application of stable adaptive schemes to nuclear reactor systems, (2)

International Nuclear Information System (INIS)

Kukuda, Toshio

1979-01-01

The parameter identification and adaptive control schemes applied in a previous study to a nonlinear point reactor are extended to the case of a loosely-coupled-core reactor with internal feedbacks, constituting a nonlinear overall system. Both schemes are shown to be stable, with the system newly represented on the pattern of the Model Reference Adaptive System (MRAS) with use made of the Lyapunov's method. For either parameter identification or adaptive control of a loosely-coupled-core reactor, there exists no canonical form of multiple input-multiple output system which can be directly applied for deriving the MRAS with the matrix version of the Kalman-Yakubovich lemma as it was in the case of the point reactor. This difficulty is circumvented by the practical assumption that the neutron density can be directly measured on each core as reactivity change is applied as input into the coupled core as a whole. For parameter identification, the model parameters are adaptively adjusted to those of each core, while for the adaptive control, plant parameters of each core can be adaptively compensated, again through control inputs, to asymptotically reduce the output error between the model and the plant. The point reactor is shown to correspond to a special case. (author)

Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response

International Nuclear Information System (INIS)

Kiefer, B; Bartel, T; Menzel, A

2012-01-01

Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases. (paper)

A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics

Directory of Open Access Journals (Sweden)

E. Kaas

2013-11-01

Full Text Available A new hybrid Eulerian–Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass-conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place; i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.

Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

International Nuclear Information System (INIS)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2015-01-01

Highlights: • Using high-resolution spatial scheme in solving two-phase flow problems. • Fully implicit time integrations scheme. • Jacobian-free Newton–Krylov method. • Analytical solution for two-phase water faucet problem. - Abstract: The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists

A numerical scheme for optimal transition paths of stochastic chemical kinetic systems

International Nuclear Information System (INIS)

Liu Di

2008-01-01

We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples

A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation

Directory of Open Access Journals (Sweden)

Hakon A. Hoel

2007-07-01

Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.

A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos

Directory of Open Access Journals (Sweden)

Shiyun Shen

2017-01-01

Full Text Available One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.

Numerical scheme of WAHA code for simulation of fast transients in piping systems

International Nuclear Information System (INIS)

Iztok Tiselj

2005-01-01

Full text of publication follows: A research project of the 5. EU program entitled 'Two-phase flow water hammer transients and induced loads on materials and structures of nuclear power plants' (WAHA loads) has been initiated in Fall 2000 and ended in Spring 2004. Numerical scheme used in WAHA code is responsibility of 'Jozef Stefan Institute and is briefly described in the present work. Mathematical model is based on a 6-equation two-fluid model for inhomogeneous non-equilibrium two-phase flow, which can be written in vectorial form as: A δΨ-vector/δt + B δΨ-vector/δx = S-vector. Hyperbolicity of the equations is a prerequisite and is ensured with virtual mass term and interfacial pressure term, however, equations are not unconditionally hyperbolic. Flow-regime map used in WAHA code consists of dispersed, and horizontally stratified flow correlations. The closure laws describe interface heat and mass transfer (condensation model, flashing...), the inter-phase friction, and wall friction. For the modeling of water hammer additional terms due to the pipe elasticity are considered. For the calculation of the thermodynamic state a new set of water properties subroutines was created. Numerical scheme of the WAHA code is based on Godunov characteristic upwind methods. Advanced numerical methods based on high-resolution shock-capturing schemes, which were originally developed for high-speed gas dynamics are used. These schemes produce solutions with a substantially reduced numerical diffusion and allow the accurate modeling of flow discontinuities. Code is using non-conservative variables Ψ-vector = (p, α, ν f , ν g , u f , u g ), however, according to current experience, the non-conservation is not a major problem for the fast transients like water hammers. The following operator splitting is used in the code: 1) Convection and non-relaxation source terms: A δΨ-vector/δt + B δΨ-vector/δx S-vector non relaxation 2) Relaxation (inter-phase exchange) source

Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes

Science.gov (United States)

Liu, Yong; Shu, Chi-Wang; Zhang, Mengping

2018-02-01

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.

Monitoring and preventing numerical oscillations in 3D simulations with coupled Monte Carlo codes

International Nuclear Information System (INIS)

Kotlyar, D.; Shwageraus, E.

2014-01-01

Highlights: • Conventional coupling methods used in all MC codes can be numerically unstable. • Application of new stochastic implicit (SIMP) methods may be required. • The implicit methods require additional computational effort. • Monitoring diagnostic of the numerical stability was developed here. • The procedure allows to create an hybrid explicit–implicit coupling scheme. - Abstract: Previous studies have reported that different schemes for coupling Monte Carlo (MC) neutron transport with burnup and thermal hydraulic feedbacks may potentially be numerically unstable. This issue can be resolved by application of implicit methods, such as the stochastic implicit mid-point (SIMP) methods. In order to assure numerical stability, the new methods do require additional computational effort. The instability issue however, is problem-dependent and does not necessarily occur in all cases. Therefore, blind application of the unconditionally stable coupling schemes, and thus incurring extra computational costs, may not always be necessary. In this paper, we attempt to develop an intelligent diagnostic mechanism, which will monitor numerical stability of the calculations and, if necessary, switch from simple and fast coupling scheme to more computationally expensive but unconditionally stable one. To illustrate this diagnostic mechanism, we performed a coupled burnup and TH analysis of a single BWR fuel assembly. The results indicate that the developed algorithm can be easily implemented in any MC based code for monitoring of numerical instabilities. The proposed monitoring method has negligible impact on the calculation time even for realistic 3D multi-region full core calculations

Development of Non-staggered, semi-implicit ICE numerical scheme for a two-fluid, three-field model

Energy Technology Data Exchange (ETDEWEB)

Jeong, Jae Jun; Yoon, H. Y.; Bae, S. W

2007-11-15

A pilot code for one-dimensional, transient, two-fluid, three-field model has been developed. In this code, the semi-implicit ICE numerical scheme has been adapted to a 'non-staggered' grid. Using several conceptual problems, the numerical scheme has been verified. The results of the verifications are summarized below: - It was confirmed that the basic pilot code can simulate various flow conditions (such as single-phase liquid flow, two-phase mixture flow, and single-phase vapor flow) and transitions of the flow conditions. A mist flow was not simulated, but it seems that the basic pilot code can simulate mist flow conditions. - The mass and energy conservation was confirmed for single-phase liquid and single-phase vapor flows. - It was confirmed that the inlet pressure and velocity boundary conditions work properly. - It was confirmed that, for single- and two-phase flows, the velocity and temperature of non-existing phase are calculated as intended. The non-staggered, semi-implicit ICE numerical scheme, which has been developed in this study, will be a starting point of a new code development that adopts an unstructured finite volume method.

Trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by ECMWF operational analyses

Science.gov (United States)

Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars

2018-02-01

The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration

A numerical spectral approach to solve the dislocation density transport equation

International Nuclear Information System (INIS)

Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C

2015-01-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)

RELAP5 two-phase fluid model and numerical scheme for economic LWR system simulation

International Nuclear Information System (INIS)

Ransom, V.H.; Wagner, R.J.; Trapp, J.A.

1981-01-01

The RELAP5 two-phase fluid model and the associated numerical scheme are summarized. The experience accrued in development of a fast running light water reactor system transient analysis code is reviewed and example of the code application are given

Space-Time Transformation in Flux-form Semi-Lagrangian Schemes

Directory of Open Access Journals (Sweden)

Peter C. Chu Chenwu Fan

2010-01-01

Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.

A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations

Directory of Open Access Journals (Sweden)

Zhuo Su

2013-01-01

Full Text Available Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.

Exponential discontinuous numerical scheme for electron transport in the continuous slowing down approximation

International Nuclear Information System (INIS)

Prinja, A.K.

1997-01-01

A nonlinear discretization scheme in space and energy, based on the recently developed exponential discontinuous method, is applied to continuous slowing down dominated electron transport (i.e., in the absence of scattering.) Numerical results for dose and charge deposition are obtained and compared against results from the ONELD and ONEBFP codes, and against exact results from an adjoint Monte Carlo code. It is found that although the exponential discontinuous scheme yields strictly positive and monotonic solutions, the dose profile is considerably straggled when compared to results from the linear codes. On the other hand, the linear schemes produce negative results which, furthermore, do not damp effectively in some cases. A general conclusion is that while yielding strictly positive solutions, the exponential discontinuous method does not show the crude cell accuracy for charged particle transport as was apparent for neutral particle transport problems

A New Numerical Scheme for Cosmic-Ray Transport

Science.gov (United States)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

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

Direct numerical simulation of stable and unstable turbulent thermal boundary layers

International Nuclear Information System (INIS)

Hattori, Hirofumi; Houra, Tomoya; Nagano, Yasutaka

2007-01-01

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence

A hybrid convection scheme for use in non-hydrostatic numerical weather prediction models

Directory of Open Access Journals (Sweden)

Volker Kuell

2008-12-01

Full Text Available The correct representation of convection in numerical weather prediction (NWP models is essential for quantitative precipitation forecasts. Due to its small horizontal scale convection usually has to be parameterized, e.g. by mass flux convection schemes. Classical schemes originally developed for use in coarse grid NWP models assume zero net convective mass flux, because the whole circulation of a convective cell is confined to the local grid column and all convective mass fluxes cancel out. However, in contemporary NWP models with grid sizes of a few kilometers this assumption becomes questionable, because here convection is partially resolved on the grid. To overcome this conceptual problem we propose a hybrid mass flux convection scheme (HYMACS in which only the convective updrafts and downdrafts are parameterized. The generation of the larger scale environmental subsidence, which may cover several grid columns, is transferred to the grid scale equations. This means that the convection scheme now has to generate a net convective mass flux exerting a direct dynamical forcing to the grid scale model via pressure gradient forces. The hybrid convection scheme implemented into the COSMO model of Deutscher Wetterdienst (DWD is tested in an idealized simulation of a sea breeze circulation initiating convection in a realistic manner. The results are compared with analogous simulations with the classical Tiedtke and Kain-Fritsch convection schemes.

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-01

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

Numerical simulations of cellular detonation diffraction in a stable gaseous mixture

Directory of Open Access Journals (Sweden)

Jian Li

2016-09-01

Full Text Available In this paper, the diffraction phenomenon of gaseous cellular detonations emerging from a confined tube into a sudden open space is simulated using the reactive Euler equations with a two-step Arrhenius chemistry model. Both two-dimensional and axisymmetric configurations are used for modeling cylindrical and spherical expansions, respectively. The chemical parameters are chosen for a stable gaseous explosive mixture in which the cellular detonation structure is highly regular. Adaptive mesh refinement (AMR is used to resolve the detonation wave structure and its evolution during the transmission. The numerical results show that the critical channel width and critical diameter over the detonation cell size are about 13±1 and 25±1, respectively. These numerical findings are comparable with the experimental observation and confirm again that the critical channel width and critical diameter differ essentially by a factor close to 2, equal to the geometrical scaling based on front curvature theory. Unlike unstable mixtures where instabilities manifested in the detonation front structure play a significant role during the transmission, the present numerical results and the observed geometrical scaling provide again evidence that the failure of detonation diffraction in stable mixtures with a regular detonation cellular pattern is dominantly caused by the global curvature due to the wave divergence resulting in the global decoupling of the reaction zone with the expanding shock front.

Malfunction diagnosis and applications of stable adaptive schemes for a nuclear reactor system

International Nuclear Information System (INIS)

Fukuda, Toshio; Shibata, Heki.

1979-01-01

Malfunction diagnosis concerns a method to detect the abnormal phenomena during nuclear reactor operations, while stable adaptive schemes does the application of Model Reference Adaptive System (MRAS) to the nonlinear dynamics of a reactor for parameter identification and control. The new method for the malfunction diagnosis consists of the following ideas; an index defined as the sum of ratios of the square of a factor score to the contribution weight of the factor, which is evaluated by applying the multi-factor analysis technique to the data of the state of nuclear reactor systems like neutron flux, temperature, flow rate and so on. The excess of the index over some given threshold shows the reactor system would be in an abnormal state. Then a theory of optimal filtering by Kalman with the aid of the stochastic approximation is applied to estimate the neutron flux distribution at its abnormal state and subsequently the squared sum of difference between desirable and estimated flux distributions shows the spot at which the abnormal phenomena would have occurred in terms of the peak of its distribution. Parameter identification and adaptive control schemes are presented for a point reactor and a loosely-coupled-core reactor with internal feedbacks which lead to the nonlinearity of the overall system. Both schemes are shown stable with new representations of the systems, which correspond to the nonminimal system representation, in the vein of the MRAS via the Lyapunov's method. For the sake of the parameter identification, model parameters can be adjusted adaptively as soon as measurements start, while plant parameters can also adaptively be compensated through control input to reduce the output error between the model and the plant for the case of the adaptive control. Some experiments of parameter identification for the thermal-hydraulic system are carried out successfully using a simplified channel in which flow rate is varied in a binary form. (J.P.N.)

Analysis and Application of High Resolution Numerical Perturbation Algorithm for Convective-Diffusion Equation

International Nuclear Information System (INIS)

Gao Zhi; Shen Yi-Qing

2012-01-01

The high resolution numerical perturbation (NP) algorithm is analyzed and tested using various convective-diffusion equations. The NP algorithm is constructed by splitting the second order central difference schemes of both convective and diffusion terms of the convective-diffusion equation into upstream and downstream parts, then the perturbation reconstruction functions of the convective coefficient are determined using the power-series of grid interval and eliminating the truncated errors of the modified differential equation. The important nature, i.e. the upwind dominance nature, which is the basis to ensuring that the NP schemes are stable and essentially oscillation free, is firstly presented and verified. Various numerical cases show that the NP schemes are efficient, robust, and more accurate than the original second order central scheme

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

Science.gov (United States)

Leonard, B. P.; Mokhtari, Simin

1990-01-01

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

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)

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

Science.gov (United States)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

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

Science.gov (United States)

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

2016-06-01

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

A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

Science.gov (United States)

Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.

2015-02-01

Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

Science.gov (United States)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Towards the ultimate variance-conserving convection scheme

International Nuclear Information System (INIS)

Os, J.J.A.M. van; Uittenbogaard, R.E.

2004-01-01

In the past various arguments have been used for applying kinetic energy-conserving advection schemes in numerical simulations of incompressible fluid flows. One argument is obeying the programmed dissipation by viscous stresses or by sub-grid stresses in Direct Numerical Simulation and Large Eddy Simulation, see e.g. [Phys. Fluids A 3 (7) (1991) 1766]. Another argument is that, according to e.g. [J. Comput. Phys. 6 (1970) 392; 1 (1966) 119], energy-conserving convection schemes are more stable i.e. by prohibiting a spurious blow-up of volume-integrated energy in a closed volume without external energy sources. In the above-mentioned references it is stated that nonlinear instability is due to spatial truncation rather than to time truncation and therefore these papers are mainly concerned with the spatial integration. In this paper we demonstrate that discretized temporal integration of a spatially variance-conserving convection scheme can induce non-energy conserving solutions. In this paper the conservation of the variance of a scalar property is taken as a simple model for the conservation of kinetic energy. In addition, the derivation and testing of a variance-conserving scheme allows for a clear definition of kinetic energy-conserving advection schemes for solving the Navier-Stokes equations. Consequently, we first derive and test a strictly variance-conserving space-time discretization for the convection term in the convection-diffusion equation. Our starting point is the variance-conserving spatial discretization of the convection operator presented by Piacsek and Williams [J. Comput. Phys. 6 (1970) 392]. In terms of its conservation properties, our variance-conserving scheme is compared to other spatially variance-conserving schemes as well as with the non-variance-conserving schemes applied in our shallow-water solver, see e.g. [Direct and Large-eddy Simulation Workshop IV, ERCOFTAC Series, Kluwer Academic Publishers, 2001, pp. 409-287

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Science.gov (United States)

Xia, Xilin; Liang, Qiuhua; Ming, Xiaodong; Hou, Jingming

2017-05-01

Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

Explicit solution of the time domain magnetic field integral equation using a predictor-corrector scheme

KAUST Repository

Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric

2012-01-01

An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.

Explicit solution of the time domain magnetic field integral equation using a predictor-corrector scheme

KAUST Repository

Ulku, Huseyin Arda

2012-09-01

An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.

A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

Directory of Open Access Journals (Sweden)

M. T. Johnson

2010-10-01

Full Text Available The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest. Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone, such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases, but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.

A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

Science.gov (United States)

Johnson, M. T.

2010-10-01

The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest). Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone), such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases), but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility) are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.

Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

Science.gov (United States)

Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

2018-01-01

Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme

Energy Technology Data Exchange (ETDEWEB)

Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

1998-03-01

A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

Science.gov (United States)

Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook

1995-01-01

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

High-Order Multioperator Compact Schemes for Numerical Simulation of Unsteady Subsonic Airfoil Flow

Science.gov (United States)

Savel'ev, A. D.

2018-02-01

On the basis of high-order schemes, the viscous gas flow over the NACA2212 airfoil is numerically simulated at a free-stream Mach number of 0.3 and Reynolds numbers ranging from 103 to 107. Flow regimes sequentially varying due to variations in the free-stream viscosity are considered. Vortex structures developing on the airfoil surface are investigated, and a physical interpretation of this phenomenon is given.

Numerical simulation of laser resonators

International Nuclear Information System (INIS)

Yoo, J. G.; Jeong, Y. U.; Lee, B. C.; Rhee, Y. J.; Cho, S. O.

2004-01-01

We developed numerical simulation packages for laser resonators on the bases of a pair of integral equations. Two numerical schemes, a matrix formalism and an iterative method, were programmed for finding numeric solutions to the pair of integral equations. The iterative method was tried by Fox and Li, but it was not applicable for high Fresnel numbers since the numerical errors involved propagate and accumulate uncontrollably. In this paper, we implement the matrix method to extend the computational limit further. A great number of case studies are carried out with various configurations of stable and unstable r;esonators to compute diffraction losses, phase shifts, intensity distributions and phases of the radiation fields on mirrors. Our results presented in this paper show not only a good agreement with the results previously obtained by Fox and Li, but also the legitimacy of our numerical procedures for high Fresnel numbers.

Numerical solution of one-dimensional transient, two-phase flows with temporal fully implicit high order schemes: Subcooled boiling in pipes

Energy Technology Data Exchange (ETDEWEB)

López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es

2017-03-15

Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.

An investigation into the accuracy, stability and parallel performance of a highly stable explicit technique for stiff reaction-transport PDEs

Energy Technology Data Exchange (ETDEWEB)

Franz, A., LLNL

1998-02-17

The numerical simulation of chemically reacting flows is a topic, that has attracted a great deal of current research At the heart of numerical reactive flow simulations are large sets of coupled, nonlinear Partial Differential Equations (PDES). Due to the stiffness that is usually present, explicit time differencing schemes are not used despite their inherent simplicity and efficiency on parallel and vector machines, since these schemes require prohibitively small numerical stepsizes. Implicit time differencing schemes, although possessing good stability characteristics, introduce a great deal of computational overhead necessary to solve the simultaneous algebraic system at each timestep. This thesis examines an algorithm based on a preconditioned time differencing scheme. The algorithm is explicit and permits a large stable time step. An investigation of the algorithm`s accuracy, stability and performance on a parallel architecture is presented

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.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

Energy Technology Data Exchange (ETDEWEB)

Wintermeyer, Niklas [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Winters, Andrew R., E-mail: awinters@math.uni-koeln.de [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Gassner, Gregor J. [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Kopriva, David A. [Department of Mathematics, The Florida State University, Tallahassee, FL 32306 (United States)

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Long-term numerical simulation of the interaction between a neutron field and a neutral meson field by a symplectic-preserving scheme

International Nuclear Information System (INIS)

Kong Linghua; Hong Jialin; Liu Ruxun

2008-01-01

In this paper, we propose a family of symplectic structure-preserving numerical methods for the coupled Klein-Gordon-Schroedinger (KGS) system. The Hamiltonian formulation is constructed for the KGS. We discretize the Hamiltonian system in space first with a family of canonical difference methods which convert an infinite-dimensional Hamiltonian system into a finite-dimensional one. Next, we discretize the finite-dimensional system in time by a midpoint rule which preserves the symplectic structure of the original system. The conservation laws of the schemes are analyzed in succession, including the charge conservation law and the residual of energy conservation law, etc. We analyze the truncation errors and global errors of the numerical solutions for the schemes to end the theoretical analysis. Extensive numerical tests show the accordance between the theoretical and numerical results

Numeric Analysis for Relationship-Aware Scalable Streaming Scheme

Directory of Open Access Journals (Sweden)

Heung Ki Lee

2014-01-01

Full Text Available Frequent packet loss of media data is a critical problem that degrades the quality of streaming services over mobile networks. Packet loss invalidates frames containing lost packets and other related frames at the same time. Indirect loss caused by losing packets decreases the quality of streaming. A scalable streaming service can decrease the amount of dropped multimedia resulting from a single packet loss. Content providers typically divide one large media stream into several layers through a scalable streaming service and then provide each scalable layer to the user depending on the mobile network. Also, a scalable streaming service makes it possible to decode partial multimedia data depending on the relationship between frames and layers. Therefore, a scalable streaming service provides a way to decrease the wasted multimedia data when one packet is lost. However, the hierarchical structure between frames and layers of scalable streams determines the service quality of the scalable streaming service. Even if whole packets of layers are transmitted successfully, they cannot be decoded as a result of the absence of reference frames and layers. Therefore, the complicated relationship between frames and layers in a scalable stream increases the volume of abandoned layers. For providing a high-quality scalable streaming service, we choose a proper relationship between scalable layers as well as the amount of transmitted multimedia data depending on the network situation. We prove that a simple scalable scheme outperforms a complicated scheme in an error-prone network. We suggest an adaptive set-top box (AdaptiveSTB to lower the dependency between scalable layers in a scalable stream. Also, we provide a numerical model to obtain the indirect loss of multimedia data and apply it to various multimedia streams. Our AdaptiveSTB enhances the quality of a scalable streaming service by removing indirect loss.

Development of a moisture scheme for the explicit numerical simulation of moist convection

CSIR Research Space (South Africa)

Bopape, Mary-Jane M

2010-09-01

Full Text Available .kashan.co.za] Development of a moisture scheme for the explicit numerical simulation of moist convection M BOPAPE, F ENGELBRECHT, D RANDALL AND W LANDMAN CSIR Natural Resources and the Environment, PO Box 395, Pretoria, 0001, South Africa Email: mbopape... sigma coordinate model that incorporates moisture effects, so that it can simulate convective clouds and precipitation. moisture terms equivalent to those of the miller and pearce (1974) model are incorporated in the equation set used: ; (1) ; (2...

A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

Science.gov (United States)

Gilchrist, S. A.; Braun, D. C.; Barnes, G.

2016-12-01

Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.

An energy-stable time-integrator for phase-field models

KAUST Repository

Vignal, Philippe

2016-12-27

We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

An energy-stable time-integrator for phase-field models

KAUST Repository

Vignal, Philippe; Collier, N.; Dalcin, Lisandro; Brown, D.L.; Calo, V.M.

2016-01-01

We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

A New Framework to Compare Mass-Flux Schemes Within the AROME Numerical Weather Prediction Model

Science.gov (United States)

Riette, Sébastien; Lac, Christine

2016-08-01

In the Application of Research to Operations at Mesoscale (AROME) numerical weather forecast model used in operations at Météo-France, five mass-flux schemes are available to parametrize shallow convection at kilometre resolution. All but one are based on the eddy-diffusivity-mass-flux approach, and differ in entrainment/detrainment, the updraft vertical velocity equation and the closure assumption. The fifth is based on a more classical mass-flux approach. Screen-level scores obtained with these schemes show few discrepancies and are not sufficient to highlight behaviour differences. Here, we describe and use a new experimental framework, able to compare and discriminate among different schemes. For a year, daily forecast experiments were conducted over small domains centred on the five French metropolitan radio-sounding locations. Cloud base, planetary boundary-layer height and normalized vertical profiles of specific humidity, potential temperature, wind speed and cloud condensate were compared with observations, and with each other. The framework allowed the behaviour of the different schemes in and above the boundary layer to be characterized. In particular, the impact of the entrainment/detrainment formulation, closure assumption and cloud scheme were clearly visible. Differences mainly concerned the transport intensity thus allowing schemes to be separated into two groups, with stronger or weaker updrafts. In the AROME model (with all interactions and the possible existence of compensating errors), evaluation diagnostics gave the advantage to the first group.

A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method

OpenAIRE

Bondesan , Andrea; Boudin , Laurent; Grec , Bérénice

2018-01-01

In this article, we consider a multi-species kinetic model which leads to the Maxwell-Stefan equations under a standard diffusive scaling (small Knudsen and Mach numbers). We propose a suitable numerical scheme which approximates both the solution of the kinetic model in rarefied regime and the one in the diffusion limit. We prove some a priori estimates (mass conservation and nonnegativity) and well-posedness of the discrete problem. We also present numerical examples where we observe the as...

A new unconditionally stable and consistent quasi-analytical in-stream water quality solution scheme for CSTR-based water quality simulators

Science.gov (United States)

Woldegiorgis, Befekadu Taddesse; van Griensven, Ann; Pereira, Fernando; Bauwens, Willy

2017-06-01

Most common numerical solutions used in CSTR-based in-stream water quality simulators are susceptible to instabilities and/or solution inconsistencies. Usually, they cope with instability problems by adopting computationally expensive small time steps. However, some simulators use fixed computation time steps and hence do not have the flexibility to do so. This paper presents a novel quasi-analytical solution for CSTR-based water quality simulators of an unsteady system. The robustness of the new method is compared with the commonly used fourth-order Runge-Kutta methods, the Euler method and three versions of the SWAT model (SWAT2012, SWAT-TCEQ, and ESWAT). The performance of each method is tested for different hypothetical experiments. Besides the hypothetical data, a real case study is used for comparison. The growth factors we derived as stability measures for the different methods and the R-factor—considered as a consistency measure—turned out to be very useful for determining the most robust method. The new method outperformed all the numerical methods used in the hypothetical comparisons. The application for the Zenne River (Belgium) shows that the new method provides stable and consistent BOD simulations whereas the SWAT2012 model is shown to be unstable for the standard daily computation time step. The new method unconditionally simulates robust solutions. Therefore, it is a reliable scheme for CSTR-based water quality simulators that use first-order reaction formulations.

Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes

Science.gov (United States)

Gnedin, Nickolay Y.; Semenov, Vadim A.; Kravtsov, Andrey V.

2018-04-01

An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be "weak" in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves. We use an experimental fluid dynamics code that allows cubic "patches" of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a constraint on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty.

New Numerical Treatment for Solving the KDV Equation

Directory of Open Access Journals (Sweden)

khalid ali

2017-01-01

Full Text Available In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using collocation method with the modified exponential cubic B-spline. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.

A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

Energy Technology Data Exchange (ETDEWEB)

Ku, S., E-mail: sku@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States); Hager, R.; Chang, C.S. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States); Kwon, J.M. [National Fusion Research Institute (Korea, Republic of); Parker, S.E. [University of Colorado Boulder (United States)

2016-06-15

In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

KAUST Repository

Fan, Xiaolin

2017-01-19

This paper presents a componentwise convex splitting scheme for numerical simulation of multicomponent two-phase fluid mixtures in a closed system at constant temperature, which is modeled by a diffuse interface model equipped with the Van der Waals and the Peng-Robinson equations of state (EoS). The Van der Waals EoS has a rigorous foundation in physics, while the Peng-Robinson EoS is more accurate for hydrocarbon mixtures. First, the phase field theory of thermodynamics and variational calculus are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic equations with extremely strong nonlinear source terms. The steady state equations are transformed into a transient system as a numerical strategy on which the scheme is based. The proposed numerical algorithm avoids the indefiniteness of the Hessian matrix arising from the second-order derivative of homogeneous contribution of total Helmholtz free energy; it is also very efficient. This scheme is unconditionally componentwise energy stable and naturally results in unconditional stability for the Van der Waals model. For the Peng-Robinson EoS, it is unconditionally stable through introducing a physics-preserving correction term, which is analogous to the attractive term in the Van der Waals EoS. An efficient numerical algorithm is provided to compute the coefficient in the correction term. Finally, some numerical examples are illustrated to verify the theoretical results and efficiency of the established algorithms. The numerical results match well with laboratory data.

Response of multiferroic composites inferred from a fast-Fourier-transform-based numerical scheme

International Nuclear Information System (INIS)

Brenner, Renald; Bravo-Castillero, Julián

2010-01-01

The effective response and the local fields within periodic magneto-electric multiferroic composites are investigated by means of a numerical scheme based on fast Fourier transforms. This computational framework relies on the iterative resolution of coupled series expansions for the magnetic, electric and strain fields. By using an augmented Lagrangian formulation, a simple and robust procedure which makes use of the uncoupled Green operators for the elastic, electrostatics and magnetostatics problems is proposed. Its accuracy is assessed in the cases of laminated and fibrous two-phase composites for which analytical solutions exist

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

Science.gov (United States)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

Effect of fluid elasticity on the numerical stability of high-resolution schemes for high shearing contraction flows using OpenFOAM

Directory of Open Access Journals (Sweden)

T. Chourushi

2017-01-01

Full Text Available Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme (UDS is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes (HRS were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all HRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number E≈5. Furthermore, by E, a clear relationship between numerical stability of HRS and E was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to E.

Stable and high order accurate difference methods for the elastic wave equation in discontinuous media

KAUST Repository

Duru, Kenneth

2014-12-01

© 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

Science.gov (United States)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

A fully discrete energy stable scheme for a phase filed moving contact line model with variable densities and viscosities

KAUST Repository

Zhu, Guangpu

2018-01-26

In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation with the generalized Navier boundary condition. Variable densities and viscosities are incorporated in this model. A rigorous proof of energy stability is provided for the fully discrete scheme based on a semi-implicit temporal discretization and a finite difference method on the staggered grids for the spatial discretization. A splitting method based on the pressure stabilization is implemented to solve the Navier-Stokes equation, while the stabilization approach is also used for the Cahn-Hilliard equation. Numerical results in both 2-D and 3-D demonstrate the accuracy, efficiency and decaying property of discrete energy of the proposed scheme.

Study on the wind field and pollutant dispersion in street canyons using a stable numerical method.

Science.gov (United States)

Xia, Ji-Yang; Leung, Dennis Y C

2005-01-01

A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the velocity field and the pressure field separately from the governing equations. The Streamline Upwind Petrov-Galerkin (SUPG) method was used to get stable numerical results. Numerical oscillation was minimized and satisfactory results can be obtained for flows at high Reynolds numbers. Simulating the flow over a square cylinder within a wide range of Reynolds numbers validates the wind field model. The Strouhal numbers obtained from the numerical simulation had a good agreement with those obtained from experiment. The wind field model developed in the present study is applied to simulate more complex flow phenomena in street canyons with two different building configurations. The results indicated that the flow at rooftop of buildings might not be assumed parallel to the ground as some numerical modelers did. A counter-clockwise rotating vortex may be found in street canyons with an inflow from the left to right. In addition, increasing building height can increase velocity fluctuations in the street canyon under certain circumstances, which facilitate pollutant dispersion. At high Reynolds numbers, the flow regimes in street canyons do not change with inflow velocity.

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

Development of a 3D cell-centered Lagrangian scheme for the numerical modeling of the gas dynamics and hyper-elasticity systems

International Nuclear Information System (INIS)

Georges, Gabriel

2016-01-01

High Energy Density Physics (HEDP) flows are multi-material flows characterized by strong shock waves and large changes in the domain shape due to rare faction waves. Numerical schemes based on the Lagrangian formalism are good candidates to model this kind of flows since the computational grid follows the fluid motion. This provides accurate results around the shocks as well as a natural tracking of multi-material interfaces and free-surfaces. In particular, cell-centered Finite Volume Lagrangian schemes such as GLACE (Godunov-type Lagrangian scheme Conservative for total Energy) and EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian Hydrodynamics) provide good results on both the modeling of gas dynamics and elastic-plastic equations. The work produced during this PhD thesis is in continuity with the work of Maire and Nkonga [JCP, 2009] for the hydrodynamic part and the work of Kluth and Despres [JCP, 2010] for the hyper elasticity part. More precisely, the aim of this thesis is to develop robust and accurate methods for the 3D extension of the EUCCLHYD scheme with a second-order extension based on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) and GRP (Generalized Riemann Problem) procedures. A particular care is taken on the preservation of symmetries and the monotonicity of the solutions. The scheme robustness and accuracy are assessed on numerous Lagrangian test cases for which the 3D extensions are very challenging. (author) [fr

An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction

International Nuclear Information System (INIS)

Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa

2015-01-01

We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the course of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well

Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

KAUST Repository

Zhu, Guangpu

2018-04-17

In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

KAUST Repository

Zhu, Guangpu; Kou, Jisheng; Sun, Shuyu; Yao, Jun; Li, Aifen

2018-01-01

In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

Science.gov (United States)

Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

2017-11-01

In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

Flux schemes for the two-fluid models of the trio-U code

International Nuclear Information System (INIS)

Kumbaro, A.; Seignole, V.; Ghidaglia, J.M.

2000-01-01

To solve the non-conservative system of the two-phase flow model in the TRIO-U two-phase flow module, a fully unstructured finite volume formulation is chosen, and the discretization is based on the concept of flux-scheme. Our method allows to determine whether hyperbolicity is necessary to have stable and convergent numerical computations. We discuss the necessity or not to consider all the differential transfer terms between the two-phases in the up-winding of the flux. Numerical results are presented in order to study out the influence of the pressure interface term in the stability, as well as in the up-winding of the flux. (author)

Hybrid TE-TM scheme for time domain numerical calculations of wakefields in structures with walls of finite conductivity

Directory of Open Access Journals (Sweden)

Andranik Tsakanian

2012-05-01

Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.

A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

Science.gov (United States)

Johnson, M. T.

2010-02-01

The transfer velocity determines the rate of exchange of a gas across the air-water interface for a given deviation from Henry's law equilibrium between the two phases. In the thin film model of gas exchange, which is commonly used for calculating gas exchange rates from measured concentrations of trace gases in the atmosphere and ocean/freshwaters, the overall transfer is controlled by diffusion-mediated films on either side of the air-water interface. Calculating the total transfer velocity (i.e. including the influence from both molecular layers) requires the Henry's law constant and the Schmidt number of the gas in question, the latter being the ratio of the viscosity of the medium and the molecular diffusivity of the gas in the medium. All of these properties are both temperature and (on the water side) salinity dependent and extensive calculation is required to estimate these properties where not otherwise available. The aim of this work is to standardize the application of the thin film approach to flux calculation from measured and modelled data, to improve comparability, and to provide a numerical framework into which future parameter improvements can be integrated. A detailed numerical scheme is presented for the calculation of the gas and liquid phase transfer velocities (ka and kw respectively) and the total transfer velocity, K. The scheme requires only basic physical chemistry data for any gas of interest and calculates K over the full range of temperatures, salinities and wind-speeds observed in and over the ocean. Improved relationships for the wind-speed dependence of ka and for the salinity-dependence of the gas solubility (Henry's law) are derived. Comparison with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general but significant improvements under certain conditions. The scheme is provided as a downloadable program in the supplementary material, along with input files containing molecular

Numerical solution of the 1D kinetics equations using a cubic reduced nodal scheme

International Nuclear Information System (INIS)

Gomez T, A.M.; Valle G, E. del; Delfin L, A.; Alonso V, G.

2003-01-01

In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as Θ scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)

Numerical simulation of flood inundation using a well-balanced kinetic scheme for the shallow water equations with bulk recharge and discharge

Science.gov (United States)

Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip

2016-04-01

The flow of water in rivers and oceans can, under general assumptions, be efficiently modelled using Saint-Venant's shallow water system of equations (SWE). SWE is a hyperbolic system of conservation laws (HSCL) which can be derived from a starting point of incompressible Navier-Stokes. A common difficulty in the numerical simulation of HSCLs is the conservation of physical entropy. Work by Audusse, Bristeau, Perthame (2000) and Perthame, Simeoni (2001), proposed numerical SWE solvers known as kinetic schemes (KSs), which can be shown to have desirable entropy-consistent properties, and are thus called well-balanced schemes. A KS is derived from kinetic equations that can be integrated into the SWE. In flood risk assessment models the SWE must be coupled with other equations describing interacting meteorological and hydrogeological phenomena such as rain and groundwater flows. The SWE must therefore be appropriately modified to accommodate source and sink terms, so kinetic schemes are no longer valid. While modifications of SWE in this direction have been recently proposed, e.g., Delestre (2010), we depart from the extant literature by proposing a novel model that is "entropy-consistent" and naturally extends the SWE by respecting its kinetic formulation connections. This allows us to derive a system of partial differential equations modelling flow of a one-dimensional river with both a precipitation term and a groundwater flow model to account for potential infiltration and recharge. We exhibit numerical simulations of the corresponding kinetic schemes. These simulations can be applied to both real world flood prediction and the tackling of wider issues on how climate and societal change are affecting flood risk.

stableGP

Data.gov (United States)

National Aeronautics and Space Administration — The code in the stableGP package implements Gaussian process calculations using efficient and numerically stable algorithms. Description of the algorithms is in the...

A Numerical Scheme Based on an Immersed Boundary Method for Compressible Turbulent Flows with Shocks: Application to Two-Dimensional Flows around Cylinders

Directory of Open Access Journals (Sweden)

Shun Takahashi

2014-01-01

Full Text Available A computational code adopting immersed boundary methods for compressible gas-particle multiphase turbulent flows is developed and validated through two-dimensional numerical experiments. The turbulent flow region is modeled by a second-order pseudo skew-symmetric form with minimum dissipation, while the monotone upstream-centered scheme for conservation laws (MUSCL scheme is employed in the shock region. The present scheme is applied to the flow around a two-dimensional cylinder under various freestream Mach numbers. Compared with the original MUSCL scheme, the minimum dissipation enabled by the pseudo skew-symmetric form significantly improves the resolution of the vortex generated in the wake while retaining the shock capturing ability. In addition, the resulting aerodynamic force is significantly improved. Also, the present scheme is successfully applied to moving two-cylinder problems.

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

Numerical methods and analysis of the nonlinear Vlasov equation on unstructured meshes of phase space

International Nuclear Information System (INIS)

Besse, Nicolas

2003-01-01

This work is dedicated to the mathematical and numerical studies of the Vlasov equation on phase-space unstructured meshes. In the first part, new semi-Lagrangian methods are developed to solve the Vlasov equation on unstructured meshes of phase space. As the Vlasov equation describes multi-scale phenomena, we also propose original methods based on a wavelet multi-resolution analysis. The resulting algorithm leads to an adaptive mesh-refinement strategy. The new massively-parallel computers allow to use these methods with several phase-space dimensions. Particularly, these numerical schemes are applied to plasma physics and charged particle beams in the case of two-, three-, and four-dimensional Vlasov-Poisson systems. In the second part we prove the convergence and give error estimates for several numerical schemes applied to the Vlasov-Poisson system when strong and classical solutions are considered. First we show the convergence of a semi-Lagrangian scheme on an unstructured mesh of phase space, when the regularity hypotheses for the initial data are minimal. Then we demonstrate the convergence of classes of high-order semi-Lagrangian schemes in the framework of the regular classical solution. In order to reconstruct the distribution function, we consider symmetrical Lagrange polynomials, B-Splines and wavelets bases. Finally we prove the convergence of a semi-Lagrangian scheme with propagation of gradients yielding a high-order and stable reconstruction of the solution. (author) [fr

Numerical analysis of Markov-perfect equilibria with multiple stable steady states : A duopoly application with innovative firms

NARCIS (Netherlands)

Dawid, H.; Keoula, M.Y.; Kort, Peter

2017-01-01

This paper presents a numerical method for the characterization of Markov-perfect equilibria of symmetric differential games exhibiting coexisting stable steady states. The method relying on the calculation of ‘local value functions’ through collocation in overlapping parts of the state space, is

A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

Directory of Open Access Journals (Sweden)

Liquan Mei

2014-01-01

Full Text Available A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.

A full quantum network scheme

International Nuclear Information System (INIS)

Ma Hai-Qiang; Wei Ke-Jin; Yang Jian-Hui; Li Rui-Xue; Zhu Wu

2014-01-01

We present a full quantum network scheme using a modified BB84 protocol. Unlike other quantum network schemes, it allows quantum keys to be distributed between two arbitrary users with the help of an intermediary detecting user. Moreover, it has good expansibility and prevents all potential attacks using loopholes in a detector, so it is more practical to apply. Because the fiber birefringence effects are automatically compensated, the scheme is distinctly stable in principle and in experiment. The simple components for every user make our scheme easier for many applications. The experimental results demonstrate the stability and feasibility of this scheme. (general)

Construct the stable vendor managed inventory partnership through a profit-sharing approach

Science.gov (United States)

Li, S.; Yu, Z.; Dong, M.

2015-01-01

In real life, the vendor managed inventory (VMI) model is not always a stable supply chain partnership. This paper proposes a cooperative game based profit-sharing method to stabilize the VMI partnership. Specifically, in a B2C setting, we consider a VMI program including a manufacturer and multiple online retailers. The manufacturer provides the finished product at the equal wholesale price to multiple online retailers. The online retailers face the same customer demand information. We offer the model to compute the increased profits generated by information sharing for total possible VMI coalitions. Using the solution concept of Shapley value, the profit-sharing scheme is produced to fairly divide the total increased profits among the VMI members. We find that under a fair allocation scheme, the higher inventory cost of one VMI member increases the surplus of the other members. Furthermore, the manufacturer is glad to increase the size of VMI coalition, whereas, the retailers are delighted to limit the size of the alliance. Finally, the manufacturer can select the appropriate retailer to boost its surplus, which has no effect on the surplus of the other retailers. The numerical examples indicate that the grand coalition is stable under the proposed allocation scheme.

An Efficient Explicit Finite-Difference Scheme for Simulating Coupled Biomass Growth on Nutritive Substrates

Directory of Open Access Journals (Sweden)

G. F. Sun

2015-01-01

Full Text Available A novel explicit finite-difference (FD method is presented to simulate the positive and bounded development process of a microbial colony subjected to a substrate of nutrients, which is governed by a nonlinear parabolic partial differential equations (PDE system. Our explicit FD scheme is uniquely designed in such a way that it transfers the nonlinear terms in the original PDE into discrete sets of linear ones in the algebraic equation system that can be solved very efficiently, while ensuring the stability and the boundedness of the solution. This is achieved through (1 a proper design of intertwined FD approximations for the diffusion function term in both time and spatial variations and (2 the control of the time-step through establishing theoretical stability criteria. A detailed theoretical stability analysis is conducted to reveal that our FD method is indeed stable. Our examples verified the fact that the numerical solution can be ensured nonnegative and bounded to simulate the actual physics. Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme. The present scheme is applicable for solving similar systems of PDEs in the investigation of the dynamics of biological films.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

Science.gov (United States)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

A numerical relativity scheme for cosmological simulations

Science.gov (United States)

Daverio, David; Dirian, Yves; Mitsou, Ermis

2017-12-01

Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3  +  1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.

Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

International Nuclear Information System (INIS)

Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

2015-01-01

Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

The HIRLAM fast radiation scheme for mesoscale numerical weather prediction models

Science.gov (United States)

Rontu, Laura; Gleeson, Emily; Räisänen, Petri; Pagh Nielsen, Kristian; Savijärvi, Hannu; Hansen Sass, Bent

2017-07-01

This paper provides an overview of the HLRADIA shortwave (SW) and longwave (LW) broadband radiation schemes used in the HIRLAM numerical weather prediction (NWP) model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, schemes is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE-AROME NWP system

Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

International Nuclear Information System (INIS)

Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.; Hughes, E.D.; Solbrig, C.W.

1975-11-01

A mathematical model and a numerical solution scheme for thermal-hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media

A stable computational scheme for stiff time-dependent constitutive equations

International Nuclear Information System (INIS)

Shih, C.F.; Delorenzi, H.G.; Miller, A.K.

1977-01-01

Viscoplasticity and creep type constitutive equations are increasingly being employed in finite element codes for evaluating the deformation of high temperature structural members. These constitutive equations frequently exhibit stiff regimes which makes an analytical assessment of the structure very costly. A computational scheme for handling deformation in stiff regimes is proposed in this paper. By the finite element discretization, the governing partial differential equations in the spatial (x) and time (t) variables are reduced to a system of nonlinear ordinary differential equations in the independent variable t. The constitutive equations are expanded in a Taylor's series about selected values of t. The resulting system of differential equations are then integrated by an implicit scheme which employs a predictor technique to initiate the Newton-Raphson procedure. To examine the stability and accuracy of the computational scheme, a series of calculations were carried out for uniaxial specimens and thick wall tubes subjected to mechanical and thermal loading. (Auth.)

Stable water isotope simulation by current land-surface schemes:Results of IPILPS phase 1

Energy Technology Data Exchange (ETDEWEB)

Henderson-Sellers, A.; Fischer, M.; Aleinov, I.; McGuffie, K.; Riley, W.J.; Schmidt, G.A.; Sturm, K.; Yoshimura, K.; Irannejad, P.

2005-10-31

Phase 1 of isotopes in the Project for Intercomparison of Land-surface Parameterization Schemes (iPILPS) compares the simulation of two stable water isotopologues ({sup 1}H{sub 2} {sup 18}O and {sup 1}H{sup 2}H{sup 16}O) at the land-atmosphere interface. The simulations are off-line, with forcing from an isotopically enabled regional model for three locations selected to offer contrasting climates and ecotypes: an evergreen tropical forest, a sclerophyll eucalypt forest and a mixed deciduous wood. Here we report on the experimental framework, the quality control undertaken on the simulation results and the method of intercomparisons employed. The small number of available isotopically-enabled land-surface schemes (ILSSs) limits the drawing of strong conclusions but, despite this, there is shown to be benefit in undertaking this type of isotopic intercomparison. Although validation of isotopic simulations at the land surface must await more, and much more complete, observational campaigns, we find that the empirically-based Craig-Gordon parameterization (of isotopic fractionation during evaporation) gives adequately realistic isotopic simulations when incorporated in a wide range of land-surface codes. By introducing two new tools for understanding isotopic variability from the land surface, the Isotope Transfer Function and the iPILPS plot, we show that different hydrological parameterizations cause very different isotopic responses. We show that ILSS-simulated isotopic equilibrium is independent of the total water and energy budget (with respect to both equilibration time and state), but interestingly the partitioning of available energy and water is a function of the models' complexity.

Numerical simulations of natural or mixed convection in vertical channels: comparisons of level-set numerical schemes for the modeling of immiscible incompressible fluid flows

International Nuclear Information System (INIS)

Li, R.

2012-01-01

The aim of this research dissertation is at studying natural and mixed convections of fluid flows, and to develop and validate numerical schemes for interface tracking in order to treat incompressible and immiscible fluid flows, later. In a first step, an original numerical method, based on Finite Volume discretizations, is developed for modeling low Mach number flows with large temperature gaps. Three physical applications on air flowing through vertical heated parallel plates were investigated. We showed that the optimum spacing corresponding to the peak heat flux transferred from an array of isothermal parallel plates cooled by mixed convection is smaller than those for natural or forced convections when the pressure drop at the outlet keeps constant. We also proved that mixed convection flows resulting from an imposed flow rate may exhibit unexpected physical solutions; alternative model based on prescribed total pressure at inlet and fixed pressure at outlet sections gives more realistic results. For channels heated by heat flux on one wall only, surface radiation tends to suppress the onset of re-circulations at the outlet and to unify the walls temperature. In a second step, the mathematical model coupling the incompressible Navier-Stokes equations and the Level-Set method for interface tracking is derived. Improvements in fluid volume conservation by using high order discretization (ENO-WENO) schemes for the transport equation and variants of the signed distance equation are discussed. (author)

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

Science.gov (United States)

Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

2018-06-01

Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

Energy Technology Data Exchange (ETDEWEB)

Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

2016-02-20

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

A Stable Marching on-in-time Scheme for Solving the Time Domain Electric Field Volume Integral Equation on High-contrast Scatterers

KAUST Repository

Sayed, Sadeed Bin

2015-05-05

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.

A Stable Marching on-in-time Scheme for Solving the Time Domain Electric Field Volume Integral Equation on High-contrast Scatterers

KAUST Repository

Sayed, Sadeed Bin; Ulku, Huseyin; Bagci, Hakan

2015-01-01

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.

Numerical study of the systematic error in Monte Carlo schemes for semiconductors

Energy Technology Data Exchange (ETDEWEB)

Muscato, Orazio [Univ. degli Studi di Catania (Italy). Dipt. di Matematica e Informatica; Di Stefano, Vincenza [Univ. degli Studi di Messina (Italy). Dipt. di Matematica; Wagner, Wolfgang [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)

2008-07-01

The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field calculations, vanishes sufficiently fast. The error due to the approximation of the trajectories of particles depends on the ODE solver used in the algorithm. It is negligible compared to the other sources of time step error, when a second order Runge-Kutta solver is used. The error related to the approximate scattering mechanism is the most significant source of error with respect to the time step. (orig.)

A rational function based scheme for solving advection equation

International Nuclear Information System (INIS)

Xiao, Feng; Yabe, Takashi.

1995-07-01

A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author)

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

Science.gov (United States)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Age-of-Air, Tape Recorder, and Vertical Transport Schemes

Science.gov (United States)

Lin, S.-J.; Einaudi, Franco (Technical Monitor)

2000-01-01

A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

Numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1982-01-01

There are many recent developments in numerical relativity, but there remain important unsolved theoretical and practical problems. The author reviews existing numerical approaches to solution of the exact Einstein equations. A framework for classification and comparison of different numerical schemes is presented. Recent numerical codes are compared using this framework. The discussion focuses on new developments and on currently open questions, excluding a review of numerical techniques. (Auth.)

2D Numerical Modelling of the Resin Injection Pultrusion Process Including Experimental Resin Kinetics and Temperature Validation

DEFF Research Database (Denmark)

Rasmussen, Filip Salling; Sonne, Mads Rostgaard; Larsen, Martin

In the present study, a two-dimensional (2D) transient Eulerian thermo-chemical analysis of a carbon fibre epoxy thermosetting Resin Injection Pultrusion (RIP) process is carried out. The numerical model is implemented using the well known unconditionally stable Alternating Direction Implicit (ADI......) scheme. The total heat of reaction and the cure kinetics of the epoxy thermosetting are determined using Differential Scanning Calorimetry (DSC). A very good agreement is observed between the fitted cure kinetic model and the experimental measurements. The numerical steady state temperature predictions...

Numerical investigation of complex flooding schemes for surfactant polymer based enhanced oil recovery

Science.gov (United States)

Dutta, Sourav; Daripa, Prabir

2015-11-01

Surfactant-polymer flooding is a widely used method of chemical enhanced oil recovery (EOR) in which an array of complex fluids containing suitable and varying amounts of surfactant or polymer or both mixed with water is injected into the reservoir. This is an example of multiphase, multicomponent and multiphysics porous media flow which is characterized by the spontaneous formation of complex viscous fingering patterns and is modeled by a system of strongly coupled nonlinear partial differential equations with appropriate initial and boundary conditions. Here we propose and discuss a modern, hybrid method based on a combination of a discontinuous, multiscale finite element formulation and the method of characteristics to accurately solve the system. Several types of flooding schemes and rheological properties of the injected fluids are used to numerically study the effectiveness of various injection policies in minimizing the viscous fingering and maximizing oil recovery. Numerical simulations are also performed to investigate the effect of various other physical and model parameters such as heterogeneity, relative permeability and residual saturation on the quantities of interest like cumulative oil recovery, sweep efficiency, fingering intensity to name a few. Supported by the grant NPRP 08-777-1-141 from the Qatar National Research Fund (a member of The Qatar Foundation).

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

KAUST Repository

Kou, Jisheng

2018-02-25

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager\\'s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2018-01-01

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

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.

Rayleigh-Benard convection in a Hele-Shaw cell - a numerical study

International Nuclear Information System (INIS)

Guenther, C.; Mueller, U.

1987-05-01

Free convection in narrow vertical gaps heated from below gives rise to several different flow patterns as has been demonstrated by previous experimental investigations. A numerical study is presented aimed at simulating the observed flow phenomena in Hele-Shaw cells of small lateral extend. The numerical study is based on the assumption that the flow is essentially two-dimensional. This allows an approach using a one-term Galerkin approximation with respect to the direction perpendicular to the gap and a finite difference scheme with regard to the coordinates in the plane of the gap. The calculations result in realistic values of the critical Rayleigh numbers for the onset of steady and oscillatory convection. Most of the observed unsteady flow patterns can be simulated numerically. It is shown that five different stable flow patterns can occur at one particular Rayleigh number. The different stable flow patterns are coupled by a variety of complex transitions. Moreover the calculations show that a realistic description of the observed flow phenomena can not be obtained by a simplified model using the Darcy law in the momentum equation and implying slip flow at the small confining boundaries. (orig.) [de

Numerical performance of the parabolized ADM formulation of general relativity

International Nuclear Information System (INIS)

Paschalidis, Vasileios; Hansen, Jakob; Khokhlov, Alexei

2008-01-01

In a recent paper [Vasileios Paschalidis, Phys. Rev. D 78, 024002 (2008).], the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner (ADM) formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM formulation turns it into a well-posed system which resembles the structure of mixed hyperbolic-second-order parabolic partial differential equations. The surface of constraints of PADM becomes a local attractor for all solutions and all possible well-posed gauge conditions. This paper describes a numerical implementation of PADM and studies its accuracy and stability in a series of standard numerical tests. Numerical properties of PADM are compared with those of standard ADM and its hyperbolic Kidder, Scheel, Teukolsky (KST) extension. The PADM scheme is numerically stable, convergent, and second-order accurate. The new formulation has better control of the constraint-violating modes than ADM and KST.

On usage of CABARET scheme for tracer transport in INM ocean model

International Nuclear Information System (INIS)

Diansky, Nikolay; Kostrykin, Sergey; Gusev, Anatoly; Salnikov, Nikolay

2010-01-01

The contemporary state of ocean numerical modelling sets some requirements for the numerical advection schemes used in ocean general circulation models (OGCMs). The most important requirements are conservation, monotonicity and numerical efficiency including good parallelization properties. Investigation of some advection schemes shows that one of the best schemes satisfying the criteria is CABARET scheme. 3D-modification of the CABARET scheme was used to develop a new transport module (for temperature and salinity) for the Institute of Numerical Mathematics ocean model (INMOM). Testing of this module on some common benchmarks shows a high accuracy in comparison with the second-order advection scheme used in the INMOM. This new module was incorporated in the INMOM and experiments with the modified model showed a better simulation of oceanic circulation than its previous version.

Numerical Comparison of Optimal Charging Schemes for Electric Vehicles

DEFF Research Database (Denmark)

You, Shi; Hu, Junjie; Pedersen, Anders Bro

2012-01-01

of four different charging schemes, namely night charging, night charging with V2G, 24 hour charging and 24 hour charging with V2G, on the basis of real driving data and electricity price of Denmark in 2003. For all schemes, optimal charging plans with 5 minute resolution are derived through the solving...... of a mixed integer programming problem which aims to minimize the charging cost and meanwhile takes into account the users' driving needs and the practical limitations of the EV battery. In the post processing stage, the rainflow counting algorithm is implemented to assess the lifetime usage of a lithium...

Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

Science.gov (United States)

Rihan, Fathalla A.; Al-Salti, Nasser S.

2017-09-01

In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

Numerical Hydrodynamics in General Relativity

Directory of Open Access Journals (Sweden)

Font José A.

2003-01-01

Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.

Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term

International Nuclear Information System (INIS)

Johnston, Hans; Liu Jianguo

2004-01-01

We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C 0 elements to implement

A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

Science.gov (United States)

Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled

2017-02-01

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

On a free-surface problem with moving contact line: From variational principles to stable numerical approximations

Science.gov (United States)

Fumagalli, Ivan; Parolini, Nicola; Verani, Marco

2018-02-01

We analyze a free-surface problem described by time-dependent Navier-Stokes equations. Surface tension, capillary effects and wall friction are taken into account in the evolution of the system, influencing the motion of the contact line - where the free surface hits the wall - and of the dynamics of the contact angle. The differential equations governing the phenomenon are first derived from the variational principle of minimum reduced dissipation, and then discretized by means of the ALE approach. The numerical properties of the resulting scheme are investigated, drawing a parallel with the physical properties holding at the continuous level. Some instability issues are addressed in detail, in the case of an explicit treatment of the geometry, and novel additional terms are introduced in the discrete formulation in order to damp the instabilities. Numerical tests assess the suitability of the approach, the influence of the parameters, and the effectiveness of the new stabilizing terms.

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering—Application to circular footing and deep tunnel in saturated ground

Directory of Open Access Journals (Sweden)

Simon Heru Prassetyo

2018-04-01

Full Text Available Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical (H-M interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit (ADE scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in non-uniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourth-order finite difference (FD approximation to the spatial derivatives of the axisymmetric fluid–diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua (FLAC. This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%–50% that of FLAC's basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%�

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

Science.gov (United States)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations

Science.gov (United States)

Shishkin, G. I.

2015-11-01

An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.

Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes

Directory of Open Access Journals (Sweden)

A. R. Appadu

2013-01-01

for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to the L1 norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values of k and h. Two optimisation techniques are then implemented to find the optimal values of k when h=0.02 for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Science.gov (United States)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1990-01-01

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Tradable schemes

NARCIS (Netherlands)

J.K. Hoogland (Jiri); C.D.D. Neumann

2000-01-01

textabstractIn this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing

A strong shock tube problem calculated by different numerical schemes

Science.gov (United States)

Lee, Wen Ho; Clancy, Sean P.

1996-05-01

Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods.

An efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity

KAUST Repository

Gao, Min

2014-09-01

In this paper, we develop an efficient numerical method for the two phase moving contact line problem with variable density, viscosity, and slip length. The physical model is based on a phase field approach, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition [1,2,5]. To overcome the difficulties due to large density and viscosity ratio, the Navier-Stokes equations are solved by a splitting method based on a pressure Poisson equation [11], while the Cahn-Hilliard equation is solved by a convex splitting method. We show that the method is stable under certain conditions. The linearized schemes are easy to implement and introduce only mild CFL time constraint. Numerical tests are carried out to verify the accuracy, stability and efficiency of the schemes. The method allows us to simulate the interface problems with extremely small interface thickness. Three dimensional simulations are included to validate the efficiency of the method. © 2014 Elsevier Inc.

An efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity

KAUST Repository

Gao, Min; Wang, Xiao-Ping

2014-01-01

In this paper, we develop an efficient numerical method for the two phase moving contact line problem with variable density, viscosity, and slip length. The physical model is based on a phase field approach, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition [1,2,5]. To overcome the difficulties due to large density and viscosity ratio, the Navier-Stokes equations are solved by a splitting method based on a pressure Poisson equation [11], while the Cahn-Hilliard equation is solved by a convex splitting method. We show that the method is stable under certain conditions. The linearized schemes are easy to implement and introduce only mild CFL time constraint. Numerical tests are carried out to verify the accuracy, stability and efficiency of the schemes. The method allows us to simulate the interface problems with extremely small interface thickness. Three dimensional simulations are included to validate the efficiency of the method. © 2014 Elsevier Inc.

A SECOND-ORDER DIVERGENCE-CONSTRAINED MULTIDIMENSIONAL NUMERICAL SCHEME FOR RELATIVISTIC TWO-FLUID ELECTRODYNAMICS

Energy Technology Data Exchange (ETDEWEB)

Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, 113-0033 (Japan)

2016-11-01

A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron–positron or an electron–proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten–Lax–Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.

A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model

Energy Technology Data Exchange (ETDEWEB)

Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr [CMAP, École Polytechnique CNRS, UMR 7641, Route de Saclay, F-91128 Palaiseau cedex (France); Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr [EDF-R& D, Département MFEE, 6 Quai Watier, F-78401 Chatou Cedex (France); Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr [Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 bd 11 novembre 1918, F-69622 Villeurbanne cedex (France)

2017-02-01

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

Tempered stable laws as random walk limits

OpenAIRE

Chakrabarty, Arijit; Meerschaert, Mark M.

2010-01-01

Stable laws can be tempered by modifying the L\\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.

Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme

International Nuclear Information System (INIS)

Ma Jun; Wang Chunni; Li Yanlong; Pu Zhongsheng; Jin Wuyin

2008-01-01

This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhugh–Nagumo (MFHN) model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally. (general)

Numerical Simulations of Reacting Flows Using Asynchrony-Tolerant Schemes for Exascale Computing

Science.gov (United States)

Cleary, Emmet; Konduri, Aditya; Chen, Jacqueline

2017-11-01

Communication and data synchronization between processing elements (PEs) are likely to pose a major challenge in scalability of solvers at the exascale. Recently developed asynchrony-tolerant (AT) finite difference schemes address this issue by relaxing communication and synchronization between PEs at a mathematical level while preserving accuracy, resulting in improved scalability. The performance of these schemes has been validated for simple linear and nonlinear homogeneous PDEs. However, many problems of practical interest are governed by highly nonlinear PDEs with source terms, whose solution may be sensitive to perturbations caused by communication asynchrony. The current work applies the AT schemes to combustion problems with chemical source terms, yielding a stiff system of PDEs with nonlinear source terms highly sensitive to temperature. Examples shown will use single-step and multi-step CH4 mechanisms for 1D premixed and nonpremixed flames. Error analysis will be discussed both in physical and spectral space. Results show that additional errors introduced by the AT schemes are negligible and the schemes preserve their accuracy. We acknowledge funding from the DOE Computational Science Graduate Fellowship administered by the Krell Institute.

A strong shock tube problem calculated by different numerical schemes

International Nuclear Information System (INIS)

Lee, W.H.; Clancy, S.P.

1996-01-01

Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 10 9 and density ratio of 10 3 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods. copyright 1996 American Institute of Physics

Large eddy simulation of spray and combustion characteristics with realistic chemistry and high-order numerical scheme under diesel engine-like conditions

International Nuclear Information System (INIS)

Zhou, Lei; Luo, Kai Hong; Qin, Wenjin; Jia, Ming; Shuai, Shi Jin

2015-01-01

Highlights: • MUSCL differencing scheme in LES method is used to investigate liquid fuel spray and combustion process. • Using MUSCL can accurately capture the gas phase velocity distribution and liquid spray features. • Detailed chemistry mechanism with a parallel algorithm was used to calculate combustion process. • Increasing oxygen concentration can decrease ignition delay time and flame LOL. - Abstract: The accuracy of large eddy simulation (LES) for turbulent combustion depends on suitably implemented numerical schemes and chemical mechanisms. In the original KIVA3V code, finite difference schemes such as QSOU (Quasi-second-order upwind) and PDC (Partial Donor Cell Differencing) cannot achieve good results or even computational stability when using coarse grids due to large numerical diffusion. In this paper, the MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) differencing scheme is implemented into KIVA3V-LES code to calculate the convective term. In the meantime, Lu’s n-heptane reduced 58-species mechanisms (Lu, 2011) is used to calculate chemistry with a parallel algorithm. Finally, improved models for spray injection are also employed. With these improvements, the KIVA3V-LES code is renamed as KIVALES-CP (Chemistry with Parallel algorithm) in this study. The resulting code was used to study the gas–liquid two phase jet and combustion under various diesel engine-like conditions in a constant volume vessel. The results show that using the MUSCL scheme can accurately capture the spray shape and fuel vapor penetration using even a coarse grid, in comparison with the Sandia experimental data. Similarly good results are obtained for three single-component fuels, i-Octane (C8H18), n-Dodecanese (C12H26), and n-Hexadecane (C16H34) with very different physical properties. Meanwhile the improved methodology is able to accurately predict ignition delay and flame lift-off length (LOL) under different oxygen concentrations from 10% to 21

Experimental and numerical investigations of stable crack growth of axial surface flaws in a pressure vessel

International Nuclear Information System (INIS)

Brocks, W.; Krafka, H.; Mueller, W.; Wobst, K.

1988-01-01

In connection with the problem of the transferability of parameters obtained experimentally with the help of fracture-mechanical test specimens and used for the initiation and the stable propagation of cracks in cases of pulsating stress and of the elasto-plastic behaviour of construction components, a pressure vessel with an inside diameter of 1500 mm, a cylindrical length of 3000 mm and a wall thickness of 40 mm was hydraulically loaded with the help of internal pressure in the first stage, to attain an average crack growth of 1 mm at Δ a ≅, the loading taking place at about 21deg C. This stress-free annealed vessel exhibited an axial semielliptical vibration-induced surface crack about 181 mm long and 20 mm deep, as a test defect, in a welded circular blank made of the steel 20MnMoNi 55. The fractographic analysis of the first stable crack revealed that its growth rate of Δa was highest in the area of transition from the weak to the strong bend of the crack front (55deg m /σ v (average principal stress: σ m , Mises' reference stress: σ v v). A comparison of the experimental with the numerical results from the first stable crack shows that the local stable crack growth Δa cannot be calculated solely with reference to J, because Δa appears to depend essentially on the quotient σ m /σ v . (orig./MM) [de

Central upwind scheme for a compressible two-phase flow model.

Science.gov (United States)

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Central upwind scheme for a compressible two-phase flow model.

Directory of Open Access Journals (Sweden)

Munshoor Ahmed

Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

High-order asynchrony-tolerant finite difference schemes for partial differential equations

Science.gov (United States)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method

Directory of Open Access Journals (Sweden)

Feng Wu

Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

Science.gov (United States)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

2018-03-01

The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

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

Science.gov (United States)

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

2015-01-01

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

Long-term stable time integration scheme for dynamic analysis of planar geometrically exact Timoshenko beams

Science.gov (United States)

Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed

2017-05-01

In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.

Numerical methods for incompressible viscous flows with engineering applications

Science.gov (United States)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

Energy Technology Data Exchange (ETDEWEB)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integration methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.

Optimized difference schemes for multidimensional hyperbolic partial differential equations

Directory of Open Access Journals (Sweden)

Adrian Sescu

2009-04-01

Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

International Nuclear Information System (INIS)

Kriventsev, Vladimir

2000-09-01

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

Science.gov (United States)

Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis

2009-10-01

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

High Order Semi-Lagrangian Advection Scheme

Science.gov (United States)

Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

2014-11-01

In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

Nitrogen Fate in a Phreatic Fluviokarst Watershed: a Stable Isotope, Sediment Tracing, and Numerical Modeling Approach

Science.gov (United States)

Husic, A.; Fox, J.; Ford, W. I., III; Agouridis, C.; Currens, J. C.; Taylor, C. J.

2017-12-01

Sediment tracing tools provide an insight into provenance, fate, and transport of sediment and, when coupled to stable isotopes, can elucidate in-stream biogeochemical processes. Particulate nitrogen fate in fluviokarst systems is a relatively unexplored area of research partially due to the complex hydrodynamics at play in karst systems. Karst topography includes turbulent conduits that transport groundwater and contaminants at speeds more typical of open channel flows than laminar Darcian flows. While it is accepted that karst hydro-geomorphology represents a hybrid surface-subsurface system for fluid, further investigation is needed to determine whether, and to what extent, karst systems behave like surface agricultural streams or porous media aquifers with respect to their role in nitrogen cycling. Our objective is to gain an understanding of in-conduit nitrogen processes and their effect on net nitrogen-exports from karst springs to larger waterbodies. The authors apply water, sediment, carbon, and nitrogen tracing techniques to analyze water for nitrate, sediment carbon and nitrogen, and stable sediment nitrogen isotope (δ15N). Thereafter, a new numerical model is formulated that: simulates dissolved inorganic nitrogen and sediment nitrogen transformations in the phreatic karst conduit; couples carbon turnover and nitrogen transformations in the model structure; and simulates the nitrogen stable isotope mass balance for the dissolved and sediment phases. Nitrogen tracing data results show a significant increase in δ15N of sediment nitrogen at the spring outlet relative to karst inputs indicating the potential for isotope fractionation during dissolved N uptake by bed sediments in the conduit and during denitrification within bed sediments. The new numerical modeling structure is then used to reproduce the data results and provide an estimate of the relative dominance of N uptake and denitrification within the surficial sediments of the karst conduit system

Numerical simulation of the debris flow dynamics with an upwind scheme and specific friction treatment

Science.gov (United States)

Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier

2014-05-01

Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the numerical solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit scheme, and the friction contribution to the dynamics is treated with a suited numerical scheme [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by

Nested Hilbert schemes on surfaces: Virtual fundamental class

DEFF Research Database (Denmark)

Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung

We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of Durr-Kabanov-Okonek and the stable pair invariants of Kool......-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial...

Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

International Nuclear Information System (INIS)

Botchorishvili, Ramaz; Pironneau, Olivier

2003-01-01

We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points

Numerical design of RNnν symmetry-based RF pulse schemes for recoupling and decoupling of nuclear spin interactions at high MAS frequencies

International Nuclear Information System (INIS)

Herbst, Christian; Herbst, Jirada; Leppert, Joerg; Ohlenschlaeger, Oliver; Goerlach, Matthias; Ramachandran, Ramadurai

2009-01-01

An approach for the efficient implementation of RN n ν symmetry-based pulse schemes that are often employed for recoupling and decoupling of nuclear spin interactions in biological solid state NMR investigations is demonstrated at high magic-angle spinning frequencies. RF pulse sequences belonging to the RN n ν symmetry involve the repeated application of the pulse sandwich {R φ R -φ }, corresponding to a propagator U RF = exp(-i4φI z ), where φ = πν/N and R is typically a pulse that rotates the nuclear spins through 180 o about the x-axis. In this study, broadband, phase-modulated 180 o pulses of constant amplitude were employed as the initial 'R' element and the phase-modulation profile of this 'R' element was numerically optimised for generating RN n ν symmetry-based pulse schemes with satisfactory magnetisation transfer characteristics. At representative MAS frequencies, RF pulse sequences were implemented for achieving 13 C- 13 C double-quantum dipolar recoupling and through bond scalar coupling mediated chemical shift correlation and evaluated via numerical simulations and experimental measurements. The results from these investigations are presented here

Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

KAUST Repository

Parsani, Matteo

2012-01-01

Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.

Exact Jacobians of Roe-type flux difference splitting of the equations of radiation hydrodynamics (and Euler equations) for use in time-implicit higher-order Godunov schemes

International Nuclear Information System (INIS)

Balsara, D.S.

1999-01-01

In this paper we analyze some of the numerical issues that are involved in making time-implicit higher-order Godunov schemes for the equations of radiation hydrodynamics (and the Euler or Navier-Stokes equations). This is done primarily with the intent of incorporating such methods in the author's RIEMANN code. After examining the issues it is shown that the construction of a time-implicit higher-order Godunov scheme for radiation hydrodynamics would be benefited by our ability to evaluate exact Jacobians of the numerical flux that is based on Roe-type flux difference splitting. In this paper we show that this can be done analytically in a form that is suitable for efficient computational implementation. It is also shown that when multiple fluid species are used or when multiple radiation frequencies are used the computational cost in the evaluation of the exact Jacobians scales linearly with the number of fluid species or the number of radiation frequencies. Connections are made to other types of numerical fluxes, especially those based on flux difference splittings. It is shown that the evaluation of the exact Jacobian for such numerical fluxes is also benefited by the present strategy and the results given here. It is, however, pointed out that time-implicit schemes that are based on the evaluation of the exact Jacobians for flux difference splittings using the methods developed here are both computationally more efficient and numerically more stable than corresponding time-implicit schemes that are based on the evaluation of the exact or approximate Jacobians for flux vector splittings. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness

Directory of Open Access Journals (Sweden)

Tong Zhang

2014-01-01

stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.

TE/TM alternating direction scheme for wake field calculation in 3D

Energy Technology Data Exchange (ETDEWEB)

Zagorodnov, Igor [Institut fuer Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt, Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)]. E-mail: zagor@temf.de; Weiland, Thomas [Institut fuer Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt, Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)

2006-03-01

In the future, accelerators with very short bunches will be used. It demands developing new numerical approaches for long-time calculation of electromagnetic fields in the vicinity of relativistic bunches. The conventional FDTD scheme, used in MAFIA, ABCI and other wake and PIC codes, suffers from numerical grid dispersion and staircase approximation problem. As an effective cure of the dispersion problem, a numerical scheme without dispersion in longitudinal direction can be used as it was shown by Novokhatski et al. [Transition dynamics of the wake fields of ultrashort bunches, TESLA Report 2000-03, DESY, 2000] and Zagorodnov et al. [J. Comput. Phys. 191 (2003) 525]. In this paper, a new economical conservative scheme for short-range wake field calculation in 3D is presented. As numerical examples show, the new scheme is much more accurate on long-time scale than the conventional FDTD approach.

Numerical study of nonspherical black hole accretion

International Nuclear Information System (INIS)

Hawley, J.F.

1984-01-01

This thesis describes in detail a two-dimensional, axisymmetric computer code for calculating fully relativistic ideal gas hydrodynamics around a Kerr black hole. The aim is to study fully dynamic inviscid fluid accretion onto black holes, as well as to study the evolution and development of nonlinear instabilities in pressure supported accretion disks. In order to fully calibrate and document the code, certain analytic solutions for shock tubes and special accretion flows are derived; these solutions form the basis for code testing. The numerical techniques used are developed and discussed. A variety of alternate differencing schemes are compared on an analytic test bed. Some discussion is devoted to general issues in finite differencing. The working code is calibrated using analytically solvable accretion problems, including the radial accretion of dust and of fluid with pressure (Bondi accretion). Two dimensional test problems include the spiraling infall of low angular momentum fluid, the formation of a pressure supported torus, and the stable evolution of a torus. A series of numerical models are discussed and illustrated with selected plots

WENO schemes for balance laws with spatially varying flux

International Nuclear Information System (INIS)

Vukovic, Senka; Crnjaric-Zic, Nelida; Sopta, Luka

2004-01-01

In this paper we construct numerical schemes of high order of accuracy for hyperbolic balance law systems with spatially variable flux function and a source term of the geometrical type. We start with the original finite difference characteristicwise weighted essentially nonoscillatory (WENO) schemes and then we create new schemes by modifying the flux formulations (locally Lax-Friedrichs and Roe with entropy fix) in order to account for the spatially variable flux, and by decomposing the source term in order to obtain balance between numerical approximations of the flux gradient and of the source term. We apply so extended WENO schemes to the one-dimensional open channel flow equations and to the one-dimensional elastic wave equations. In particular, we prove that in these applications the new schemes are exactly consistent with steady-state solutions from an appropriately chosen subset. Experimentally obtained orders of accuracy of the extended and original WENO schemes are almost identical on a convergence test. Other presented test problems illustrate the improvement of the proposed schemes relative to the original WENO schemes combined with the pointwise source term evaluation. As expected, the increase in the formal order of accuracy of applied WENO reconstructions in all the tests causes visible increase in the high resolution properties of the schemes

The Relationship between Nonconservative Schemes and Initial Values of Nonlinear Evolution Equations

Institute of Scientific and Technical Information of China (English)

林万涛

2004-01-01

For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.

Closed loop identification using a modified Hansen scheme

DEFF Research Database (Denmark)

Sekunda, André Krabdrup; Niemann, Hans Henrik; Poulsen, Niels Kjølstad

2015-01-01

in closed loop [4], and one such method is the Hansen scheme [1]. Standard identification using Hansen scheme demands generating the identification signals indirectly. In this paper it is instead proposed to use the relationship between the Youla factorization of a plant and its stabilizing controller...... in order to keep the system stable. Furthermore because the dynamics of such a system depends on the rotational speed it is needed to conduct an identification while the system is part of a closed loop scheme. The authors believe the paper able to contribute towards a simpler and more direct way...... of identifying closed loop plants using Hansen scheme....

Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation

International Nuclear Information System (INIS)

Sha, Wei; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng

2007-01-01

An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources

An Energy Decaying Scheme for Nonlinear Dynamics of Shells

Science.gov (United States)

Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

Solution of Euler unsteady equations using a second order numerical scheme

International Nuclear Information System (INIS)

Devos, J.P.

1992-08-01

In thermal power plants, the steam circuits experience incidents due to the noise and vibration induced by trans-sonic flow. In these configurations, the compressible fluid can be considered the perfect ideal. Euler equations therefore constitute a good model. However, processing of the discontinuities induced by the shockwaves are a particular problem. We give a bibliographical synthesis of the work done on this subject. The research by Roe and Harten leads to TVD (Total Variation Decreasing) type schemes. These second order schemes generate no oscillation and converge towards physically acceptable weak solutions. (author). 12 refs

IMPROVED ENTROPY-ULTRA-BEE SCHEME FOR THE EULER SYSTEM OF GAS DYNAMICS

Institute of Scientific and Technical Information of China (English)

Rongsan Chen; Dekang Mao

2017-01-01

The Entropy-Ultra-Bee scheme was developed for the linear advection equation and extended to the Euler system of gas dynamics in [13].It was expected that the technology be applied only to the second characteristic field of the system and the computation in the other two nonlinear fields be implemented by the Godunov scheme.However,the numerical experiments in [13] showed that the scheme,though having improved the wave resolution in the second field,produced numerical oscillations in the other two nonlinear fields.Sophisticated entropy increaser was designed to suppress the spurious oscillations by increasing the entropy when there are waves in the two nonlinear fields presented.However,the scheme is then not efficient neither robust with problem-related parameters.The purpose of this paper is to fix this problem.To this end,we first study a 3 × 3 linear system and apply the technology precisely to its second characteristic field while maintaining the computation in the other two fields be implemented by the Godunov scheme.We then follow the discussion for the linear system to apply the Entropy-Ultra-Bee technology to the second characteristic field of the Euler system in a linearlized field-byfield fashion to develop a modified Entropy-Ultra-Bee scheme for the system.Meanwhile a remark is given to explain the problem of the previous Entropy-Ultra-Bee scheme in [13].A reference solution is constructed for computing the numerical entropy,which maintains the feature of the density and flats the velocity and pressure to constants.The numerical entropy is then computed as the entropy cell-average of the reference solution.Several limitations are adopted in the construction of the reference solution to further stabilize the scheme.Designed in such a way,the modified Entropy-Ultra-Bee scheme has a unified form with no problem-related parameters.Numerical experiments show that all the spurious oscillations in smooth regions are gone and the results are better than that

Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.

Science.gov (United States)

Li, Q; Luo, K H; Li, X J

2012-07-01

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.

A Conditionally Stable Scheme for a Transient Flow of a Non-Newtonian Fluid Saturating a Porous Medium

KAUST Repository

El-Amin, Mohamed

2012-06-02

The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.

A Conditionally Stable Scheme for a Transient Flow of a Non-Newtonian Fluid Saturating a Porous Medium

KAUST Repository

El-Amin, Mohamed; Salama, Amgad; Sun, Shuyu

2012-01-01

The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.

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

Modeling and numerical analysis of non-equilibrium two-phase flows

International Nuclear Information System (INIS)

Rascle, P.; El Amine, K.

1997-01-01

We are interested in the numerical approximation of two-fluid models of nonequilibrium two-phase flows described by six balance equations. We introduce an original splitting technique of the system of equations. This technique is derived in a way such that single phase Riemann solvers may be used: moreover, it allows a straightforward extension to various and detailed exchange source terms. The properties of the fluids are first approached by state equations of ideal gas type and then extended to real fluids. For the construction of numerical schemes , the hyperbolicity of the full system is not necessary. When based on suitable kinetic unwind schemes, the algorithm can compute flow regimes evolving from mixture to single phase flows and vice versa. The whole scheme preserves the physical features of all the variables which remain in the set of physical states. Several stiff numerical tests, such as phase separation and phase transition are displayed in order to highlight the efficiency of the proposed method. The document is a PhD thesis divided in 6 chapters and two annexes. They are entitled: 1. - Introduction (in French), 2. - Two-phase flow, modelling and hyperbolicity (in French), 3. - A numerical method using upwind schemes for the resolution of two-phase flows without exchange terms (in English), 4. - A numerical scheme for one-phase flow of real fluids (in English), 5. - An upwind numerical for non-equilibrium two-phase flows (in English), 6. - The treatment of boundary conditions (in English), A.1. The Perthame scheme (in English) and A.2. The Roe scheme (in English)

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

Science.gov (United States)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Additive Difference Schemes for Filtration Problems in Multilayer Systems

CERN Document Server

Ayrjan, E A; Pavlush, M; Fedorov, A V

2000-01-01

In the present paper difference schemes for solution of the plane filtration problem in multilayer systems are analyzed within the framework of difference schemes general theory. Attention is paid to splitting the schemes on physical processes of filtration along water-carring layers and vertical motion between layers. Some absolutely stable additive difference schemes are obtained the realization of which needs no software modification. Parallel algorithm connected with the solving of the filtration problem in every water-carring layer on a single processor is constructed. Program realization on the multi-processor system SPP2000 at JINR is discussed.

Carbon trading: Current schemes and future developments

International Nuclear Information System (INIS)

Perdan, Slobodan; Azapagic, Adisa

2011-01-01

This paper looks at the greenhouse gas (GHG) emissions trading schemes and examines the prospects of carbon trading. The first part of the paper gives an overview of several mandatory GHG trading schemes around the world. The second part focuses on the future trends in carbon trading. It argues that the emergence of new schemes, a gradual enlargement of the current ones, and willingness to link existing and planned schemes seem to point towards geographical, temporal and sectoral expansion of emissions trading. However, such expansion would need to overcome some considerable technical and non-technical obstacles. Linking of the current and emerging trading schemes requires not only considerable technical fixes and harmonisation of different trading systems, but also necessitates clear regulatory and policy signals, continuing political support and a more stable economic environment. Currently, the latter factors are missing. The global economic turmoil and its repercussions for the carbon market, a lack of the international deal on climate change defining the Post-Kyoto commitments, and unfavourable policy shifts in some countries, cast serious doubts on the expansion of emissions trading and indicate that carbon trading enters an uncertain period. - Highlights: → The paper provides an extensive overview of mandatory emissions trading schemes around the world. → Geographical, temporal and sectoral expansion of emissions trading are identified as future trends. → The expansion requires considerable technical fixes and harmonisation of different trading systems. → Clear policy signals, political support and a stable economic environment are needed for the expansion. → A lack of the post-Kyoto commitments and unfavourable policy shifts indicate an uncertain future for carbon trading.

Multiuser switched diversity scheduling schemes

KAUST Repository

Shaqfeh, Mohammad; Alnuweiri, Hussein M.; Alouini, Mohamed-Slim

2012-01-01

Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback systems in Rayleigh fading conditions. © 2012 IEEE.

Multiuser switched diversity scheduling schemes

KAUST Repository

Shaqfeh, Mohammad

2012-09-01

Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback systems in Rayleigh fading conditions. © 2012 IEEE.

Electrical Injection Schemes for Nanolasers

DEFF Research Database (Denmark)

Lupi, Alexandra; Chung, Il-Sug; Yvind, Kresten

2014-01-01

Three electrical injection schemes based on recently demonstrated electrically pumped photonic crystal nanolasers have been numerically investigated: 1) a vertical p-i-n junction through a post structure; 2) a lateral p-i-n junction with a homostructure; and 3) a lateral p-i-n junction....... For this analysis, the properties of different schemes, i.e., electrical resistance, threshold voltage, threshold current, and internal efficiency as energy requirements for optical interconnects are compared and the physics behind the differences is discussed....

Numerical integration of the Teukolsky equation in the time domain

International Nuclear Information System (INIS)

Pazos-Avalos, Enrique; Lousto, Carlos O.

2005-01-01

We present a fourth-order convergent (2+1)-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in r* and θ directions. The correct power-law tail, ∼1/t 2l+3 , for general initial data, and ∼1/t 2l+4 , for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code

Some New Components of the Moduli Scheme MP3(2; -1; 2; 0 of Stable Coherent Torsion Free Sheaves of Rank 2 on P3

Directory of Open Access Journals (Sweden)

M. A. Zavodchikov

2012-01-01

Full Text Available In this paper we consider Giseker-Maruyama moduli scheme M := MP3(2;¡1; 2; 0 of stable coherent torsion free sheaves of rank 2 with Chern classes c1 = -1, c2 = 2, c3 = 0 on 3-dimensional projective space P3. We will de¯ne two sets of sheaves M1 and M2 in M and we will prove that closures of M1 and M2 in M are irreducible components of dimensions 15 and 19, accordingly.

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin; Bagci, Hakan

2011-01-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

Energy Technology Data Exchange (ETDEWEB)

Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)

2016-06-08

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.

Power corrections in the N-jettiness subtraction scheme

Energy Technology Data Exchange (ETDEWEB)

Boughezal, Radja [High Energy Physics Division, Argonne National Laboratory,Argonne, IL 60439 (United States); Liu, Xiaohui [Department of Physics, Beijing Normal University,Beijing, 100875 (China); Center of Advanced Quantum Studies, Beijing Normal University,Beijing, 100875 (China); Center for High-Energy Physics, Peking University,Beijing, 100871 (China); Maryland Center for Fundamental Physics, University of Maryland,College Park, MD 20742 (United States); Petriello, Frank [Department of Physics & Astronomy, Northwestern University,Evanston, IL 60208 (United States); High Energy Physics Division, Argonne National Laboratory,Argonne, IL 60439 (United States)

2017-03-30

We discuss the leading-logarithmic power corrections in the N-jettiness subtraction scheme for higher-order perturbative QCD calculations. We compute the next-to-leading order power corrections for an arbitrary N-jet process, and we explicitly calculate the power correction through next-to-next-to-leading order for color-singlet production for both qq̄ and gg initiated processes. Our results are compact and simple to implement numerically. Including the leading power correction in the N-jettiness subtraction scheme substantially improves its numerical efficiency. We discuss what features of our techniques extend to processes containing final-state jets.

On the modelling of compressible inviscid flow problems using AUSM schemes

Directory of Open Access Journals (Sweden)

Hajžman M.

2007-11-01

Full Text Available During last decades, upwind schemes have become a popular method in the field of computational fluid dynamics. Although they are only first order accurate, AUSM (Advection Upstream Splitting Method schemes proved to be well suited for modelling of compressible flows due to their robustness and ability of capturing shock discontinuities. In this paper, we review the composition of the AUSM flux-vector splitting scheme and its improved version noted AUSM+, proposed by Liou, for the solution of the Euler equations. Mach number splitting functions operating with values from adjacent cells are used to determine numerical convective fluxes and pressure splitting is used for the evaluation of numerical pressure fluxes. Both versions of the AUSM scheme are applied for solving some test problems such as one-dimensional shock tube problem and three dimensional GAMM channel. Features of the schemes are discussed in comparison with some explicit central schemes of the first order accuracy (Lax-Friedrichs and of the second order accuracy (MacCormack.

Efficient Scheme for Chemical Flooding Simulation

Directory of Open Access Journals (Sweden)

Braconnier Benjamin

2014-07-01

Full Text Available In this paper, we investigate an efficient implicit scheme for the numerical simulation of chemical enhanced oil recovery technique for oil fields. For the sake of brevity, we only focus on flows with polymer to describe the physical and numerical models. In this framework, we consider a black oil model upgraded with the polymer modeling. We assume the polymer only transported in the water phase or adsorbed on the rock following a Langmuir isotherm. The polymer reduces the water phase mobility which can change drastically the behavior of water oil interfaces. Then, we propose a fractional step technique to resolve implicitly the system. The first step is devoted to the resolution of the black oil subsystem and the second to the polymer mass conservation. In such a way, jacobian matrices coming from the implicit formulation have a moderate size and preserve solvers efficiency. Nevertheless, the coupling between the black-oil subsystem and the polymer is not fully resolved. For efficiency and accuracy comparison, we propose an explicit scheme for the polymer for which large time step is prohibited due to its CFL (Courant-Friedrichs-Levy criterion and consequently approximates accurately the coupling. Numerical experiments with polymer are simulated : a core flood, a 5-spot reservoir with surfactant and ions and a 3D real case. Comparisons are performed between the polymer explicit and implicit scheme. They prove that our polymer implicit scheme is efficient, robust and resolves accurately the coupling physics. The development and the simulations have been performed with the software PumaFlow [PumaFlow (2013 Reference manual, release V600, Beicip Franlab].

Explicit TE/TM scheme for particle beam simulations

International Nuclear Information System (INIS)

Dohlus, M.; Zagorodnov, I.

2008-10-01

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version. It does not have dispersion in the longitudinal direction and the dispersion properties in the transversal plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee's explicit method used in the most popular electrodynamics codes. (orig.)

An efficient shock-capturing scheme for simulating compressible homogeneous mixture flow

Energy Technology Data Exchange (ETDEWEB)

Dang, Son Tung; Ha, Cong Tu; Park, Warn Gyu [School of Mechanical Engineering, Pusan National University, Busan (Korea, Republic of); Jung, Chul Min [Advanced Naval Technology CenterNSRDI, ADD, Changwon (Korea, Republic of)

2016-09-15

This work is devoted to the development of a procedure for the numerical solution of Navier-Stokes equations for cavitating flows with and without ventilation based on a compressible, multiphase, homogeneous mixture model. The governing equations are discretized on a general structured grid using a high-resolution shock-capturing scheme in conjunction with appropriate limiters to prevent the generation of spurious solutions near shock waves or discontinuities. Two well-known limiters are examined, and a new limiter is proposed to enhance the accuracy and stability of the numerical scheme. A sensitivity analysis is first conducted to determine the relative influences of various model parameters on the solution. These parameters are adopted for the computation of water flows over a hemispherical body, conical body and a divergent/convergent nozzle. Finally, numerical calculations of ventilated supercavitating flows over a hemispherical cylinder body with a hot propulsive jet are conducted to verify the capabilities of the numerical scheme.

An efficient shock-capturing scheme for simulating compressible homogeneous mixture flow

International Nuclear Information System (INIS)

Dang, Son Tung; Ha, Cong Tu; Park, Warn Gyu; Jung, Chul Min

2016-01-01

This work is devoted to the development of a procedure for the numerical solution of Navier-Stokes equations for cavitating flows with and without ventilation based on a compressible, multiphase, homogeneous mixture model. The governing equations are discretized on a general structured grid using a high-resolution shock-capturing scheme in conjunction with appropriate limiters to prevent the generation of spurious solutions near shock waves or discontinuities. Two well-known limiters are examined, and a new limiter is proposed to enhance the accuracy and stability of the numerical scheme. A sensitivity analysis is first conducted to determine the relative influences of various model parameters on the solution. These parameters are adopted for the computation of water flows over a hemispherical body, conical body and a divergent/convergent nozzle. Finally, numerical calculations of ventilated supercavitating flows over a hemispherical cylinder body with a hot propulsive jet are conducted to verify the capabilities of the numerical scheme

Experimental and numerical investigation of form-stable dodecane/hydrophobic fumed silica composite phase change materials for cold energy storage

International Nuclear Information System (INIS)

Chen, Jiajie; Ling, Ziye; Fang, Xiaoming; Zhang, Zhengguo

2015-01-01

Highlights: • Form-stable dodecane/fumed silica composite for cold storage is prepared. • A suggesting hypothesis that explains infiltration mechanism is proposed. • The performance of the composite phase change material is investigated. • Numerical simulation of system is carried out and results fit well. - Abstract: A kind of form-stable composite phase change materials used for cold thermal energy storage is prepared by absorbing dodecane into the hydrophobic fumed silica. With relatively suitable pore diameter and hydrophobic groups, hydrophobic fumed silica is beneficial to the penetration and infiltration of dodecane and the leakage problem solving. Scanned by electron micrographs and Fourier transformation infrared, the composite phase change material is characterized to be just physical penetration. Besides, the differential scanning calorimeter and thermo gravimetric analysis reveals the high enthalpy, good thermal stability and cycling performance of this composite phase change material. What’s more, Hot-Disk thermal constants analyzer demonstrates that the composite phase change material has low thermal conductivity which is desired in cold storage application. In the experiment, a cold energy storage system is set up and the results from the experiment show that the system has excellent performance of cold storage by incorporating composite phase change material. Apart from that, the experimental data is found to have a great agreement with the numerical simulation which is carried out by using the commercial computational fluid dynamics software FLUENT.

Sensitivity analysis of numerical weather prediction radiative schemes to forecast direct solar radiation over Australia

Science.gov (United States)

Mukkavilli, S. K.; Kay, M. J.; Taylor, R.; Prasad, A. A.; Troccoli, A.

2014-12-01

The Australian Solar Energy Forecasting System (ASEFS) project requires forecasting timeframes which range from nowcasting to long-term forecasts (minutes to two years). As concentrating solar power (CSP) plant operators are one of the key stakeholders in the national energy market, research and development enhancements for direct normal irradiance (DNI) forecasts is a major subtask. This project involves comparing different radiative scheme codes to improve day ahead DNI forecasts on the national supercomputing infrastructure running mesoscale simulations on NOAA's Weather Research & Forecast (WRF) model. ASEFS also requires aerosol data fusion for improving accurate representation of spatio-temporally variable atmospheric aerosols to reduce DNI bias error in clear sky conditions over southern Queensland & New South Wales where solar power is vulnerable to uncertainities from frequent aerosol radiative events such as bush fires and desert dust. Initial results from thirteen years of Bureau of Meteorology's (BOM) deseasonalised DNI and MODIS NASA-Terra aerosol optical depth (AOD) anomalies demonstrated strong negative correlations in north and southeast Australia along with strong variability in AOD (~0.03-0.05). Radiative transfer schemes, DNI and AOD anomaly correlations will be discussed for the population and transmission grid centric regions where current and planned CSP plants dispatch electricity to capture peak prices in the market. Aerosol and solar irradiance datasets include satellite and ground based assimilations from the national BOM, regional aerosol researchers and agencies. The presentation will provide an overview of this ASEFS project task on WRF and results to date. The overall goal of this ASEFS subtask is to develop a hybrid numerical weather prediction (NWP) and statistical/machine learning multi-model ensemble strategy that meets future operational requirements of CSP plant operators.

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.

Birkhoffian Symplectic Scheme for a Quantum System

International Nuclear Information System (INIS)

Su Hongling

2010-01-01

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure-preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f. Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system. (general)

A fast resonance interference treatment scheme with subgroup method

International Nuclear Information System (INIS)

Cao, L.; He, Q.; Wu, H.; Zu, T.; Shen, W.

2015-01-01

A fast Resonance Interference Factor (RIF) scheme is proposed to treat the resonance interference effects between different resonance nuclides. This scheme utilizes the conventional subgroup method to evaluate the self-shielded cross sections of the dominant resonance nuclide in the heterogeneous system and the hyper-fine energy group method to represent the resonance interference effects in a simplified homogeneous model. In this paper, the newly implemented scheme is compared to the background iteration scheme, the Resonance Nuclide Group (RNG) scheme and the conventional RIF scheme. The numerical results show that the errors of the effective self-shielded cross sections are significantly reduced by the fast RIF scheme compared with the background iteration scheme and the RNG scheme. Besides, the fast RIF scheme consumes less computation time than the conventional RIF schemes. The speed-up ratio is ~4.5 for MOX pin cell problems. (author)

The same number of optimized parameters scheme for determining intermolecular interaction energies

DEFF Research Database (Denmark)

Kristensen, Kasper; Ettenhuber, Patrick; Eriksen, Janus Juul

2015-01-01

We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave...... as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP...

Spatial and temporal accuracy of asynchrony-tolerant finite difference schemes for partial differential equations at extreme scales

Science.gov (United States)

Kumari, Komal; Donzis, Diego

2017-11-01

Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Science.gov (United States)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

Comparison of reactivity estimation performance between two extended Kalman filtering schemes

International Nuclear Information System (INIS)

Peng, Xingjie; Cai, Yun; Li, Qing; Wang, Kan

2016-01-01

Highlights: • The performances of two EKF schemes using different Jacobian matrices are compared. • Numerical simulations are used for the validation and comparison of these two EKF schemes. • The simulation results show that the EKF scheme adopted by this paper performs better than the one adopted by previous literatures. - Abstract: The extended Kalman filtering (EKF) technique has been utilized in the estimation of reactivity which is a significantly important parameter to indicate the status of the nuclear reactor. In this paper, the performances of two EKF schemes using different Jacobian matrices are compared. Numerical simulations are used for the validation and comparison of these two EKF schemes, and the results show that the Jacobian matrix obtained directly from the discrete-time state model performs better than the one which is the discretization form of the Jacobian matrix obtained from the continuous-time state model.

Hybrid matrix method for stable numerical analysis of the propagation of Dirac electrons in gapless bilayer graphene superlattices

Science.gov (United States)

Briones-Torres, J. A.; Pernas-Salomón, R.; Pérez-Álvarez, R.; Rodríguez-Vargas, I.

2016-05-01

Gapless bilayer graphene (GBG), like monolayer graphene, is a material system with unique properties, such as anti-Klein tunneling and intrinsic Fano resonances. These properties rely on the gapless parabolic dispersion relation and the chiral nature of bilayer graphene electrons. In addition, propagating and evanescent electron states coexist inherently in this material, giving rise to these exotic properties. In this sense, bilayer graphene is unique, since in most material systems in which Fano resonance phenomena are manifested an external source that provides extended states is required. However, from a numerical standpoint, the presence of evanescent-divergent states in the eigenfunctions linear superposition representing the Dirac spinors, leads to a numerical degradation (the so called Ωd problem) in the practical applications of the standard Coefficient Transfer Matrix (K) method used to study charge transport properties in Bilayer Graphene based multi-barrier systems. We present here a straightforward procedure based in the hybrid compliance-stiffness matrix method (H) that can overcome this numerical degradation. Our results show that in contrast to standard matrix method, the proposed H method is suitable to study the transmission and transport properties of electrons in GBG superlattice since it remains numerically stable regardless the size of the superlattice and the range of values taken by the input parameters: the energy and angle of the incident electrons, the barrier height and the thickness and number of barriers. We show that the matrix determinant can be used as a test of the numerical accuracy in real calculations.

Construction of second-order accurate monotone and stable residual distribution schemes for steady problems

International Nuclear Information System (INIS)

Abgrall, Remi; Mezine, Mohamed

2004-01-01

After having recalled the basic concepts of residual distribution (RD) schemes, we provide a systematic construction of distribution schemes able to handle general unstructured meshes, extending the work of Sidilkover. Then, by using the concept of simple waves, we show how to generalize this technique to symmetrizable linear systems. A stability analysis is provided. We formally extend this construction to the Euler equations. Several test cases are presented to validate our approach

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Directory of Open Access Journals (Sweden)

Asad Rehman

Full Text Available An upwind space-time conservation element and solution element (CE/SE scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme. Keywords: Dusty gas flow, Solid particles, Upwind schemes, Rarefaction wave, Shock wave, Contact discontinuity

Numerical analysis of intrinsic bistability and chromatic switching in Tm3+ single-doped systems under photon avalanche pumping scheme

International Nuclear Information System (INIS)

Li Li; Zhang Xinlu; Chen Lixue

2008-01-01

In this paper, we predict and numerically demonstrate the intrinsic intensity bistability, spectra bistability and chromatic switching of visible-infrared emission in Tm 3+ single-doped systems that are pumped by the photon avalanche scheme at 648 nm. Based on the coupled rate equation theory, the evolutions of the populations at various Tm 3+ energy levels, emission spectra and fluorescence intensity versus pump excitation are numerically investigated in detail. The results show that intrinsic optical bistability (IOB) associated with emission spectra and luminescence intensity takes place in the vicinity of the avalanche threshold (∼10 kW cm -2 ). When the pump excitation rises above the switching threshold (∼17.5 kW cm -2 ), the chromatic switching between the infrared (1716 nm) and the visible blue (452/469 nm) spectra can be performed. Moreover, the influences of system parameters on IOB and the origin of chromatic switching are discussed. These unique characteristics of Tm 3+ -doped systems would lead to the new possibility of the development of pump-controlled all-solid-state luminescence switches and optical bistability switches.

Stable cycling in discrete-time genetic models.

OpenAIRE

Hastings, A

1981-01-01

Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.

Stable cycling in discrete-time genetic models.

Science.gov (United States)

Hastings, A

1981-11-01

Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.

TVD schemes in one and two space dimensions

International Nuclear Information System (INIS)

Leveque, R.J.; Goodman, J.B.; New York Univ., NY)

1985-01-01

The recent development of schemes which are second order accurate in smooth regions has made it possible to overcome certain difficulties which used to arise in numerical computations of discontinuous solutions of conservation laws. The present investigation is concerned with scalar conservation laws, taking into account the employment of total variation diminishing (TVD) schemes. The concept of a TVD scheme was introduced by Harten et al. (1976). Harten et al. first constructed schemes which are simultaneously TVD and second order accurate on smooth solutions. In the present paper, a summary is provided of recently conducted work in this area. Attention is given to TVD schemes in two space dimensions, a second order accurate TVD scheme in one dimension, and the entropy condition and spreading of rarefaction waves. 19 references

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

Modified SIMPLE algorithm for the numerical analysis of incompressible flows with free surface

International Nuclear Information System (INIS)

Mok, Jin Ho; Hong, Chun Pyo; Lee, Jin Ho

2005-01-01

While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipment or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented for the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm

Asymptotic behavior of a diffusive scheme solving the inviscid one-dimensional pressureless gases system

OpenAIRE

Boudin , Laurent; Mathiaud , Julien

2012-01-01

In this work, we discuss some numerical properties of the viscous numerical scheme introduced in [Boudin, Mathiaud, NMPDE 2012] to solve the one-dimensional pressureless gases system, and study in particular, from a computational viewpoint, its asymptotic behavior when the viscosity parameter used in the scheme becomes smaller.

An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

KAUST Repository

Bourantas, Georgios

2013-07-01

A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

KAUST Repository

Bourantas, Georgios; Burganos, Vasilis N.

2013-01-01

A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

Implementation of a gust front head collapse scheme in the WRF numerical model

Science.gov (United States)

Lompar, Miloš; Ćurić, Mladjen; Romanic, Djordje

2018-05-01

Gust fronts are thunderstorm-related phenomena usually associated with severe winds which are of great importance in theoretical meteorology, weather forecasting, cloud dynamics and precipitation, and wind engineering. An important feature of gust fronts demonstrated through both theoretical and observational studies is the periodic collapse and rebuild of the gust front head. This cyclic behavior of gust fronts results in periodic forcing of vertical velocity ahead of the parent thunderstorm, which consequently influences the storm dynamics and microphysics. This paper introduces the first gust front pulsation parameterization scheme in the WRF-ARW model (Weather Research and Forecasting-Advanced Research WRF). The influence of this new scheme on model performances is tested through investigation of the characteristics of an idealized supercell cumulonimbus cloud, as well as studying a real case of thunderstorms above the United Arab Emirates. In the ideal case, WRF with the gust front scheme produced more precipitation and showed different time evolution of mixing ratios of cloud water and rain, whereas the mixing ratios of ice and graupel are almost unchanged when compared to the default WRF run without the parameterization of gust front pulsation. The included parameterization did not disturb the general characteristics of thunderstorm cloud, such as the location of updraft and downdrafts, and the overall shape of the cloud. New cloud cells in front of the parent thunderstorm are also evident in both ideal and real cases due to the included forcing of vertical velocity caused by the periodic collapse of the gust front head. Despite some differences between the two WRF simulations and satellite observations, the inclusion of the gust front parameterization scheme produced more cumuliform clouds and seem to match better with real observations. Both WRF simulations gave poor results when it comes to matching the maximum composite radar reflectivity from radar

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin

2011-07-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.

A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation

Science.gov (United States)

Li, Haochen; Sun, Jianqiang

2012-09-01

We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.

Towards a multigrid scheme in SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Gutbrod, F.

1992-12-01

The task of constructing a viable updating multigrid scheme for SU(2) lattice gauge theory is discussed in connection with the classical eigenvalue problem. For a nonlocal overrelaxation Monte Carlo update step, the central numerical problem is the search for the minimum of a quadratic approximation to the action under nonlocal constraints. Here approximate eigenfunctions are essential to reduce the numerical work, and these eigenfunctions are to be constructed with multigrid techniques. A simple implementation on asymmetric lattices is described, where the grids are restricted to 3-dimensional hyperplanes. The scheme is shown to be moderately successful in the early stages of the updating history (starting from a cold configuration). The main results of another, less asymmetric scheme are presented briefly. (orig.)

Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

International Nuclear Information System (INIS)

Khaled, S.M.; Szatmary, Z.

2005-01-01

A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)

Asynchronous Channel-Hopping Scheme under Jamming Attacks

Directory of Open Access Journals (Sweden)

Yongchul Kim

2018-01-01

Full Text Available Cognitive radio networks (CRNs are considered an attractive technology to mitigate inefficiency in the usage of licensed spectrum. CRNs allow the secondary users (SUs to access the unused licensed spectrum and use a blind rendezvous process to establish communication links between SUs. In particular, quorum-based channel-hopping (CH schemes have been studied recently to provide guaranteed blind rendezvous in decentralized CRNs without using global time synchronization. However, these schemes remain vulnerable to jamming attacks. In this paper, we first analyze the limitations of quorum-based rendezvous schemes called asynchronous channel hopping (ACH. Then, we introduce a novel sequence sensing jamming attack (SSJA model in which a sophisticated jammer can dramatically reduce the rendezvous success rates of ACH schemes. In addition, we propose a fast and robust asynchronous rendezvous scheme (FRARS that can significantly enhance robustness under jamming attacks. Our numerical results demonstrate that the performance of the proposed scheme vastly outperforms the ACH scheme when there are security concerns about a sequence sensing jammer.

Stable Flocking of Multiple Agents Based on Molecular Potential Field and Distributed Receding Horizon Control

International Nuclear Information System (INIS)

Zhang Yun-Peng; Duan Hai-Bin; Zhang Xiang-Yin

2011-01-01

A novel distributed control scheme to generate stable flocking motion for a group of agents is proposed. In this control scheme, a molecular potential field model is applied as the potential field function because of its smoothness and unique shape. The approach of distributed receding horizon control is adopted to drive each agent to find its optimal control input to lower its potential at every step. Experimental results show that this proposed control scheme can ensure that all agents eventually converge to a stable flocking formation with a common velocity and the collisions can also be avoided at the same time. (general)

Detection of the onset of numerical chaotic instabilities by lyapunov exponents

Directory of Open Access Journals (Sweden)

Alicia Serfaty De Markus

2001-01-01

Full Text Available It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. We present a procedure that establishes a criterion to select the largest possible step size before the onset of chaotic numerical instabilities, based upon the observation that computational chaos does not occur in a smooth, continuous way, but rather abruptly, as detected by examining the largest Lyapunov exponent as a function of the step size. For completeness, examination of the bifurcation diagrams with the step reveals the complexity imposed by the algorithmic discretization, showing the robustness of a scheme to numerical instabilities, illustrated here for explicit and implicit Euler schemes. An example of numerical suppression of chaos is also provided.

A well-balanced scheme for Ten-Moment Gaussian closure equations with source term

Science.gov (United States)

Meena, Asha Kumari; Kumar, Harish

2018-02-01

In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.

A literature survey on numerical heat transfer

Science.gov (United States)

Shih, T. M.

1982-12-01

Technical papers in the area of numerical heat transfer published from 1977 through 1981 are reviewed. The journals surveyed include: (1) ASME Journal of Heat Transfer, (2) International Journal of Heat and Mass Transfer, (3) AIAA Journal, (4) Numerical Heat Transfer, (5) Computers and Fluids, (6) International Journal for Numerical Methods in Engineering, (7) SIAM Journal of Numerical Analysis, and (8) Journal of Computational Physics. This survey excludes experimental work in heat transfer and numerical schemes that are not applied to equations governing heat transfer phenomena. The research work is categorized into the following areas: (A) conduction, (B) boundary-layer flows, (C) momentum and heat transfer in cavities, (D) turbulent flows, (E) convection around cylinders and spheres or within annuli, (F) numerical convective instability, (G) radiation, (H) combustion, (I) plumes, jets, and wakes, (J) heat transfer in porous media, (K) boiling, condensation, and two-phase flows, (L) developing and fully developed channel flows, (M) combined heat and mass transfer, (N) applications, (O) comparison and properties of numerical schemes, and (P) body-fitted coordinates and nonuniform grids.

Numerical simulation of pulse-tube refrigerators

NARCIS (Netherlands)

Lyulina, I.A.; Mattheij, R.M.M.; Tijsseling, A.S.; Waele, de A.T.A.M.

2004-01-01

A new numerical model has been introduced to study steady oscillatory heat and mass transfer in the tube section of a pulse-tube refrigerator. Conservation equations describing compressible gas flow in the tube are solved numerically, using high resolution schemes. The equation of conservation of

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES

Directory of Open Access Journals (Sweden)

S.ZIBAEI

2016-12-01

Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.

An efficient numerical method for evolving microstructures with strong elastic inhomogeneity

International Nuclear Information System (INIS)

Jeong, Darae; Lee, Seunggyu; Kim, Junseok

2015-01-01

In this paper, we consider a fast and efficient numerical method for the modified Cahn–Hilliard equation with a logarithmic free energy for microstructure evolution. Even though it is physically more appropriate to use a logarithmic free energy, a quartic polynomial approximation is typically used for the logarithmic function due to a logarithmic singularity. In order to overcome the singularity problem, we regularize the logarithmic function and then apply an unconditionally stable scheme to the Cahn–Hilliard part in the model. We present computational results highlighting the different dynamic aspects from two different bulk free energy forms. We also demonstrate the robustness of the regularization of the logarithmic free energy, which implies the time-step restriction is based on accuracy and not stability. (paper)

Scheme for achieving coherent perfect absorption by anisotropic metamaterials

KAUST Repository

Zhang, Xiujuan

2017-02-22

We propose a unified scheme to achieve coherent perfect absorption of electromagnetic waves by anisotropic metamaterials. The scheme describes the condition on perfect absorption and offers an inverse design route based on effective medium theory in conjunction with retrieval method to determine practical metamaterial absorbers. The scheme is scalable to frequencies and applicable to various incident angles. Numerical simulations show that perfect absorption is achieved in the designed absorbers over a wide range of incident angles, verifying the scheme. By integrating these absorbers, we further propose an absorber to absorb energy from two coherent point sources.

A Hybrid DGTD-MNA Scheme for Analyzing Complex Electromagnetic Systems

KAUST Repository

Li, Peng

2015-01-07

A hybrid electromagnetics (EM)-circuit simulator for analyzing complex systems consisting of EM devices loaded with nonlinear multi-port lumped circuits is described. The proposed scheme splits the computational domain into two subsystems: EM and circuit subsystems, where field interactions are modeled using Maxwell and Kirchhoff equations, respectively. Maxwell equations are discretized using a discontinuous Galerkin time domain (DGTD) scheme while Kirchhoff equations are discretized using a modified nodal analysis (MNA)-based scheme. The coupling between the EM and circuit subsystems is realized at the lumped ports, where related EM fields and circuit voltages and currents are allowed to “interact’’ via numerical flux. To account for nonlinear lumped circuit elements, the standard Newton-Raphson method is applied at every time step. Additionally, a local time-stepping scheme is developed to improve the efficiency of the hybrid solver. Numerical examples consisting of EM systems loaded with single and multiport linear/nonlinear circuit networks are presented to demonstrate the accuracy, efficiency, and applicability of the proposed solver.

The use of the MacCormack scheme in computational hydraulics

International Nuclear Information System (INIS)

Garcia, R.; Zhang, H.; Kahawita, R.

1985-01-01

This manuscript describes the development of a numerical model that solves shallow water problems based upon an enhanced version of the MacCormack explicit scheme (MS). The MS has been successfully applied to solve numerous problems in gas dynamics. However, the standard application of the MS to solve the shallow water equations can cause in certain test cases non-linear instabilities and non-symmetrical results that eventually destroy the solution. By examining the calculation 'cell' one can show that the MS is not symmetric in space, which explains why it cannot be used directly in the treatment of hydraulic problems most of which possess irregular boundaries thereby resulting in a flow with no 'preferred direction'. This is contrary to what is usually encountered in aerodynamics. The enhanced MacCormack scheme is obtained by a simple modification to the original formulation resulting in a symmetric scheme. The scheme has been applied to the computation of the flowfield in a real life situation with satisfactory results. (author)

Conservative Semidiscrete Difference Schemes for Timoshenko Systems

OpenAIRE

Júnior, D. S. Almeida

2014-01-01

We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. Our method of proof relies on discrete multiplier techniques.

Numerical simulation of interface movement in gas-liquid two-phase flows with Level Set method

International Nuclear Information System (INIS)

Li Huixiong; Chinese Academy of Sciences, Beijing; Deng Sheng; Chen Tingkuan; Zhao Jianfu; Wang Fei

2005-01-01

Numerical simulation of gas-liquid two-phase flow and heat transfer has been an attractive work for a quite long time, but still remains as a knotty difficulty due to the inherent complexities of the gas-liquid two-phase flow resulted from the existence of moving interfaces with topology changes. This paper reports the effort and the latest advances that have been made by the authors, with special emphasis on the methods for computing solutions to the advection equation of the Level set function, which is utilized to capture the moving interfaces in gas-liquid two-phase flows. Three different schemes, i.e. the simple finite difference scheme, the Superbee-TVD scheme and the 5-order WENO scheme in combination with the Runge-Kutta method are respectively applied to solve the advection equation of the Level Set. A numerical procedure based on the well-verified SIMPLER method is employed to numerically calculate the momentum equations of the two-phase flow. The above-mentioned three schemes are employed to simulate the movement of four typical interfaces under 5 typical flowing conditions. Analysis of the numerical results shows that the 5-order WENO scheme and the Superbee-TVD scheme are much better than the simple finite difference scheme, and the 5-order WENO scheme is the best to compute solutions to the advection equation of the Level Set. The 5-order WENO scheme will be employed as the main scheme to get solutions to the advection equations of the Level Set when gas-liquid two-phase flows are numerically studied in the future. (authors)

Recoupling and decoupling of nuclear spin interactions at high MAS frequencies: numerical design of CNnν symmetry-based RF pulse schemes

International Nuclear Information System (INIS)

Herbst, Christian; Herbst, Jirada; Kirschstein, Anika; Leppert, Joerg; Ohlenschlaeger, Oliver; Goerlach, Matthias; Ramachandran, Ramadurai

2009-01-01

The CN n ν class of RF pulse schemes, commonly employed for recoupling and decoupling of nuclear spin interactions in magic angle spinning solid state NMR studies of biological systems, involves the application of a basic 'C' element corresponding to an RF cycle with unity propagator. In this study, the design of CN n ν symmetry-based RF pulse sequences for achieving 13 C- 13 C double-quantum dipolar recoupling and through bond scalar coupling mediated 13 C- 13 C chemical shift correlation has been examined at high MAS frequencies employing broadband, constant-amplitude, phase-modulated basic 'C' elements. The basic elements were implemented as a sandwich of a small number of short pulses of equal duration with each pulse characterised by an RF phase value. The phase-modulation profile of the 'C' element was optimised numerically so as to generate efficient RF pulse sequences. The performances of the sequences were evaluated via numerical simulations and experimental measurements and are presented here

Modeling and numerical simulation of multi-component flow in porous media

International Nuclear Information System (INIS)

Saad, B.

2011-01-01

This work deals with the modelization and numerical simulation of two phase multi-component flow in porous media. The study is divided into two parts. First we study and prove the mathematical existence in a weak sense of two degenerate parabolic systems modeling two phase (liquid and gas) two component (water and hydrogen) flow in porous media. In the first model, we assume that there is a local thermodynamic equilibrium between both phases of hydrogen by using the Henry's law. The second model consists of a relaxation of the previous model: the kinetic of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is no longer instantaneous. The second part is devoted to the numerical analysis of those models. Firstly, we propose a numerical scheme to compare numerical solutions obtained with the first model and numerical solutions obtained with the second model where the characteristic time to recover the thermodynamic equilibrium goes to zero. Secondly, we present a finite volume scheme with a phase-by-phase upstream weighting scheme without simplified assumptions on the state law of gas densities. We also validate this scheme on a 2D test cases. (author)

Boson expansion theory in the seniority scheme

International Nuclear Information System (INIS)

Tamura, T.; Li, C.; Pedrocchi, V.G.

1985-01-01

A boson expansion formalism in the seniority scheme is presented and its relation with number-conserving quasiparticle calculations is elucidated. Accuracy and convergence are demonstrated numerically. A comparative discussion with other related approaches is given

Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

Science.gov (United States)

Jiang, Jiamin; Younis, Rami M.

2017-10-01

In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.

Generalization of binary tensor product schemes depends upon four parameters

International Nuclear Information System (INIS)

Bashir, R.; Bari, M.; Mustafa, G.

2018-01-01

This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes. (author)

Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach

KAUST Repository

Chertock, A.

2012-02-02

Aquatic bacteria like Bacillus subtilis are heavier than water yet they are able to swim up an oxygen gradient and concentrate in a layer below the water surface, which will undergo Rayleigh-Taylor-type instabilities for sufficiently high concentrations. In the literature, a simplified chemotaxis-fluid system has been proposed as a model for bio-convection in modestly diluted cell suspensions. It couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier-Stokes equations subject to a gravitational force proportional to the relative surplus of the cell density compared to the water density. In this paper, we derive a high-resolution vorticity-based hybrid finite-volume finite-difference scheme, which allows us to investigate the nonlinear dynamics of a two-dimensional chemotaxis-fluid system with boundary conditions matching an experiment of Hillesdon et al. (Bull. Math. Biol., vol. 57, 1995, pp. 299-344). We present selected numerical examples, which illustrate (i) the formation of sinking plumes, (ii) the possible merging of neighbouring plumes and (iii) the convergence towards numerically stable stationary plumes. The examples with stable stationary plumes show how the surface-directed oxytaxis continuously feeds cells into a high-concentration layer near the surface, from where the fluid flow (recurring upwards in the space between the plumes) transports the cells into the plumes, where then gravity makes the cells sink and constitutes the driving force in maintaining the fluid convection and, thus, in shaping the plumes into (numerically) stable stationary states. Our numerical method is fully capable of solving the coupled chemotaxis-fluid system and enabling a full exploration of its dynamics, which cannot be done in a linearised framework. © 2012 Cambridge University Press.

Towards stable acceleration in LINACS

CERN Document Server

Dubrovskiy, A D

2014-01-01

Ultra-stable and -reproducible high-energy particle beams with short bunches are needed in novel linear accelerators and, in particular, in the Compact Linear Collider CLIC. A passive beam phase stabilization system based on a bunch compression with a negative transfer matrix element R56 and acceleration at a positive off-crest phase is proposed. The motivation and expected advantages of the proposed scheme are outlined.

Analysis and improvement for the performance of Baptista's cryptographic scheme

International Nuclear Information System (INIS)

Wei Jun; Liao Xiaofeng; Wong, K.W.; Zhou Tsing; Deng Yigui

2006-01-01

Based on Baptista's chaotic cryptosystem, we propose a secure and robust chaotic cryptographic scheme after investigating the problems found in this cryptosystem as well as its variants. In this proposed scheme, a subkey array generated from the key and the plaintext is adopted to enhance the security. Some methods are introduced to increase the efficiency. Theoretical analyses and numerical simulations indicate that the proposed scheme is secure and efficient for practical use

New advection schemes for free surface flows

International Nuclear Information System (INIS)

Pavan, Sara

2016-01-01

The purpose of this thesis is to build higher order and less diffusive schemes for pollutant transport in shallow water flows or 3D free surface flows. We want robust schemes which respect the main mathematical properties of the advection equation with relatively low numerical diffusion and apply them to environmental industrial applications. Two techniques are tested in this work: a classical finite volume method and a residual distribution technique combined with a finite element method. For both methods we propose a decoupled approach since it is the most advantageous in terms of accuracy and CPU time. Concerning the first technique, a vertex-centred finite volume method is used to solve the augmented shallow water system where the numerical flux is computed through an Harten-Lax-Van Leer-Contact Riemann solver. Starting from this solution, a decoupled approach is formulated and is preferred since it allows to compute with a larger time step the advection of a tracer. This idea was inspired by Audusse, E. and Bristeau, M.O. [13]. The Monotonic Upwind Scheme for Conservation Law, combined with the decoupled approach, is then used for the second order extension in space. The wetting and drying problem is also analysed and a possible solution is presented. In the second case, the shallow water system is entirely solved using the finite element technique and the residual distribution method is applied to the solution of the tracer equation, focusing on the case of time-dependent problems. However, for consistency reasons the resolution of the continuity equation must be considered in the numerical discretization of the tracer. In order to get second order schemes for unsteady cases a predictor-corrector scheme is used in this work. A first order but less diffusive version of the predictor-corrector scheme is also introduced. Moreover, we also present a new locally semi-implicit version of the residual distribution method which, in addition to good properties in

User Matching with Relation to the Stable Marriage Problem in Cognitive Radio Networks

KAUST Repository

Hamza, Doha R.

2017-03-20

We consider a network comprised of multiple primary users (PUs) and multiple secondary users (SUs), where the SUs seek access to a set of orthogonal channels each occupied by one PU. Only one SU is allowed to coexist with a given PU. We propose a distributed matching algorithm to pair the network users, where a Stackelberg game model is assumed for the interaction between the paired PU and SU. The selected secondary is given access in exchange for monetary compensation to the primary. The PU optimizes the interference price it charges to a given SU and the power allocation to maintain communication. The SU optimizes its power demand so as to maximize its utility. Our algorithm provides a unique stable matching. Numerical results indicate the advantage of the proposed algorithm over other reference schemes.

Tukey max-stable processes for spatial extremes

KAUST Repository

Xu, Ganggang

2016-09-21

We propose a new type of max-stable process that we call the Tukey max-stable process for spatial extremes. It brings additional flexibility to modeling dependence structures among spatial extremes. The statistical properties of the Tukey max-stable process are demonstrated theoretically and numerically. Simulation studies and an application to Swiss rainfall data indicate the effectiveness of the proposed process. © 2016 Elsevier B.V.

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.

An Implicit Scheme of Lattice Boltzmann Method for Sine-Gordon Equation

International Nuclear Information System (INIS)

Hui-Lin, Lai; Chang-Feng, Ma

2008-01-01

We establish an implicit scheme of lattice Boltzmann method for simulating the sine-Gordon equation, which can be transformed into the explicit one, so the computation of the scheme is simple. Moreover, the parameter θ of the implicit scheme is independent of the relaxation time, which makes the model more flexible. The numerical results show that this method is very effective. (fundamental areas of phenomenology (including applications))

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

Energy Technology Data Exchange (ETDEWEB)

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn [School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Lin, Lin, E-mail: linlin@math.berkeley.edu [Department of Mathematics, University of California, Berkeley, CA 94720 (United States); Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Vigil-Fowler, Derek, E-mail: vigil@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Lischner, Johannes, E-mail: jlischner597@gmail.com [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kemper, Alexander F., E-mail: afkemper@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sharifzadeh, Sahar, E-mail: ssharifz@bu.edu [Department of Electrical and Computer Engineering and Division of Materials Science and Engineering, Boston University, Boston, MA 02215 (United States); Jornada, Felipe H. da, E-mail: jornada@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Deslippe, Jack, E-mail: jdeslippe@lbl.gov [NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Yang, Chao, E-mail: cyang@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); and others

2015-04-01

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

Numerical Investigation of a Heated, Sheared Planetary Boundary Layer

Science.gov (United States)

Liou, Yu-Chieng

1996-01-01

A planetary boundary layer (PBL) developed on 11 July, 1987 during the First International Satellites Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) is investigated numerically by a two dimensional and a three dimensional large eddy simulation (LES) model. Most of the simulated mean and statistical properties are utilized to compare or verify against the observational results extracted from single Doppler lidar scans conducted by Gal-Chen et al. (1992) on the same day. Through the methods of field measurements and numerical simulations, it is found that this PBL, in contrast to the well-known convective boundary layer (CBL), is driven by not only buoyancy but also wind shear. Large eddies produced by the surface heating, as well as internal gravity waves excited by the convection, are both present in the boundary layer. The most unique feature is that in the stable layer, the momentum flux ({overlinerm u^' w^'}), transported by the gravity waves, is counter-gradient. The occurrence of this phenomenon is interpreted by Gal-Chen et al. (1992) using the theory of critical layer singularity, and is confirmed by the numerical simulations in this study. Qualitative agreements are achieved between the model-generated and lidar-derived results. However, quantitative comparisons are less satisfactory. The most serious discrepancy is that in the stable layer the magnitudes of the observed momentum flux ({overlinerm u^ ' w^'}) and vertical velocity variance ({overlinerm w^'^2}) are much larger than their simulated counterparts. Nevertheless, through the technique of numerical simulation, evidence is collected to show inconsistencies among the observations. Thus, the lidar measurements of {overline rm u^' w^'} and {overlinerm w^ '^2} seem to be doubtful. A Four Dimensional Data Assimilation (FDDA) experiment is performed in order to connect the evolution of the model integration with the observations. The results indicate that the dynamical relaxation

An Efficient and Robust Numerical Solution of the Full-Order Multiscale Model of Lithium-Ion Battery

Directory of Open Access Journals (Sweden)

Michal Beneš

2018-01-01

Full Text Available We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the finite difference discretization of the diffusion equations combined with an original iterative scheme for solving the integral formulation of the laws of electrochemical interactions. We demonstrate that our implementation is fast and stable over the expected lifetime of the cell. In contrast to some simplified models, it provides physically consistent results for a wide range of applied currents including high loads. The algorithm forms a solid basis for simulations of cells and battery packs in hybrid electric vehicles, with possible straightforward extensions by aging and heat effects.

Validation of Numerical Schemes in a Thermal-Hydraulic Analysis Code for a Natural Convection Heat Transfer of a Molten Pool

International Nuclear Information System (INIS)

Kim, Jong Tae; Ha, Kwang Soon; Kim, Hwan Yeol; Park, Rae Joon; Song, Jin Ho

2010-01-01

, unsteady turbulence models based on filtered or volume-averaged governing equations have been applied for the turbulent natural convection heat transfer. Tran et al. used large eddy simulation (LES) for the analysis of molten corium coolability. The numerical instability is related to a gravitational force of the molten corium. A staggered grid method on an orthogonal structured grid is used to prohibit a pressure oscillation in the numerical solution. But it is impractical to use the structured grid for a partially filled spherical pool, a cone-type pool or triangular pool. An unstructured grid is an alternative for the nonrectangular pools. In order to remove the checkerboard- like pressure oscillation on the unstructured grid, some special interpolation scheme is required. In order to evaluate in-vessel coolability of the molten corium for a pressurized water reactor (PWR), thermo-hydraulic analysis code LILAC had been developed. LILAC has a capability of multi-layered conjugate heat transfer with melt solidification. A solution domain can be 2-dimensional, axisymmetric, and 3-dimensional. LILAC is based on the unstructured mesh technology to discretized non-rectangular pool geometry. Because of too limited man-power to maintain the code, it becomes more and more difficult to implement new physical and numerical models in the code along with increased complication of the code. Recently, open source CFD code OpenFOAM has been released and applied to many academic and engineering areas. OpenFOAM is based on the very similar numerical schemes to the LILAC code. It has many physical and numerical models for multi-physics analysis. And because it is based on object-oriented programming, it is known that new models can be easily implemented and is very fast with a lower possibility of coding errors. This is a very attractive feature for the development, validation and maintenance of an analysis code. On the contrary to commercial CFD codes, it is possible to modify and add

A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: Towards minimalism

Science.gov (United States)

Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi

2018-06-01

Developed is a high-order accurate shock-capturing scheme for the compressible Euler/Navier-Stokes equations; the formal accuracy is 5th order in space and 4th order in time. The performance and efficiency of the scheme are validated in various numerical tests. The main ingredients of the scheme are nothing special; they are variants of the standard numerical flux, MUSCL, the usual Lagrange's polynomial and the conventional Runge-Kutta method. The scheme can compute a boundary layer accurately with a rational resolution and capture a stationary contact discontinuity sharply without inner points. And yet it is endowed with high resistance against shock anomalies (carbuncle phenomenon, post-shock oscillations, etc.). A good balance between high robustness and low dissipation is achieved by blending three types of numerical fluxes according to physical situation in an intuitively easy-to-understand way. The performance of the scheme is largely comparable to that of WENO5-Rusanov, while its computational cost is 30-40% less than of that of the advanced scheme.

Accuracy of spectral and finite difference schemes in 2D advection problems

DEFF Research Database (Denmark)

Naulin, V.; Nielsen, A.H.

2003-01-01

In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....

Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media

KAUST Repository

Amir, Sahar Z.

2018-01-02

The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.

Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media

KAUST Repository

Amir, Sahar Z.; Sun, Shuyu

2018-01-01

The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.

Linear source approximation scheme for method of characteristics

International Nuclear Information System (INIS)

Tang Chuntao

2011-01-01

Method of characteristics (MOC) for solving neutron transport equation based on unstructured mesh has already become one of the fundamental methods for lattice calculation of nuclear design code system. However, most of MOC codes are developed with flat source approximation called step characteristics (SC) scheme, which is another basic assumption for MOC. A linear source (LS) characteristics scheme and its corresponding modification for negative source distribution were proposed. The OECD/NEA C5G7-MOX 2D benchmark and a self-defined BWR mini-core problem were employed to validate the new LS module of PEACH code. Numerical results indicate that the proposed LS scheme employs less memory and computational time compared with SC scheme at the same accuracy. (authors)

Nonoscillatory shock capturing scheme using flux limited dissipation

International Nuclear Information System (INIS)

Jameson, A.

1985-01-01

A method for modifying the third order dissipative terms by the introduction of flux limiters is proposed. The first order dissipative terms can then be eliminated entirely, and in the case of a scalar conservation law the scheme is converted into a total variation diminishing scheme provided that an appropriate value is chosen for the dissipative coefficient. Particular attention is given to: (1) the treatment of the scalar conservation law; (2) the treatment of the Euler equations for inviscid compressible flow; (3) the boundary conditions; and (4) multistage time stepping and multigrid schemes. Numerical results for transonic flows suggest that a central difference scheme augmented by flux limited dissipative terms can lead to an effective nonoscillatory shock capturing method. 20 references

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 solution of modified differential equations based on symmetry preservation.

Science.gov (United States)

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

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

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

Directory of Open Access Journals (Sweden)

Moutassem El Rafei

2017-12-01

Full Text Available The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES. The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT. All combinations of numerical methods produce a k − 4 spectrum

Numerical vs. turbulent diffusion in geophysical flow modelling

International Nuclear Information System (INIS)

D'Isidoro, M.; Maurizi, A.; Tampieri, F.

2008-01-01

Numerical advection schemes induce the spreading of passive tracers from localized sources. The effects of changing resolution and Courant number are investigated using the WAF advection scheme, which leads to a sub-diffusive process. The spreading rate from an instantaneous source is compared with the physical diffusion necessary to simulate unresolved turbulent motions. The time at which the physical diffusion process overpowers the numerical spreading is estimated, and is shown to reduce as the resolution increases, and to increase as the wind velocity increases.

On the numerical simulation of tracer flows in porous media

International Nuclear Information System (INIS)

Aquino, J.; Pereira, F.; Amaral Souto, H.P.; Francisco, A.S.

2007-01-01

We discuss in detail a new Lagrangian, locally conservative procedure which has been proposed for the numerical solution of linear transport problems in porous media. The new scheme is computationally efficient, virtually free of numerical diffusion, and can be applied to investigate numerically the time evolution of radionuclide contaminant plumes. Results of two-dimensional simulations of tracer flows will be presented to show the influence on the computed solutions of distinct interpolation functions for evaluating the velocity field at any position of the physical domain, as required by the Lagrangian scheme. (author)

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

OpenAIRE

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-01-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller–Pearce–White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which res...

A robust trust establishment scheme for wireless sensor networks.

Science.gov (United States)

Ishmanov, Farruh; Kim, Sung Won; Nam, Seung Yeob

2015-03-23

Security techniques like cryptography and authentication can fail to protect a network once a node is compromised. Hence, trust establishment continuously monitors and evaluates node behavior to detect malicious and compromised nodes. However, just like other security schemes, trust establishment is also vulnerable to attack. Moreover, malicious nodes might misbehave intelligently to trick trust establishment schemes. Unfortunately, attack-resistance and robustness issues with trust establishment schemes have not received much attention from the research community. Considering the vulnerability of trust establishment to different attacks and the unique features of sensor nodes in wireless sensor networks, we propose a lightweight and robust trust establishment scheme. The proposed trust scheme is lightweight thanks to a simple trust estimation method. The comprehensiveness and flexibility of the proposed trust estimation scheme make it robust against different types of attack and misbehavior. Performance evaluation under different types of misbehavior and on-off attacks shows that the detection rate of the proposed trust mechanism is higher and more stable compared to other trust mechanisms.

A Robust Trust Establishment Scheme for Wireless Sensor Networks

Directory of Open Access Journals (Sweden)

Farruh Ishmanov

2015-03-01

Full Text Available Security techniques like cryptography and authentication can fail to protect a network once a node is compromised. Hence, trust establishment continuously monitors and evaluates node behavior to detect malicious and compromised nodes. However, just like other security schemes, trust establishment is also vulnerable to attack. Moreover, malicious nodes might misbehave intelligently to trick trust establishment schemes. Unfortunately, attack-resistance and robustness issues with trust establishment schemes have not received much attention from the research community. Considering the vulnerability of trust establishment to different attacks and the unique features of sensor nodes in wireless sensor networks, we propose a lightweight and robust trust establishment scheme. The proposed trust scheme is lightweight thanks to a simple trust estimation method. The comprehensiveness and flexibility of the proposed trust estimation scheme make it robust against different types of attack and misbehavior. Performance evaluation under different types of misbehavior and on-off attacks shows that the detection rate of the proposed trust mechanism is higher and more stable compared to other trust mechanisms.

A numerical model for diffusion of helium in a hydrogen plasma

International Nuclear Information System (INIS)

Potters, J.H.H.M.

1983-07-01

A quasi-cylindrical steady-state numerical model for the diffusion of helium in a hydrogen plasma is presented, adopting collisional plus either ALCATOR-INTOR- or ASDEX-like anomalous transport for the charged species. The coupled momentum and conservation equations for H + , He + and He ++ are solved to obtain radial profiles of their densities, consistent with those of the neutral species. For the neutrals, a diffusion equation is used for the transport of H, whereas He is assumed to enter the plasma with an energy equal to the temperature of the plasma immediately in front of the wall. A stable numerical scheme for the solution of the coupled ion and electron energy balances is discussed. Results are presented for the JET-tokamak, using prescribed temperature profiles. Collisional effects are shown to produce an enhancement of the alpha particle density about 10 centimetres in front of the wall, especially in combination with ALCATOR-INTOR-like scaling. The neutral helium density that accumulates in the outer plasma is too low to allow for pumping helium from a cool plasma/gas blanket

Two split cell numerical methods for solving 2-D non-equilibrium radiation transport equations

International Nuclear Information System (INIS)

Feng Tinggui

2004-11-01

Two numerically positive methods, the step characteristic integral method and subcell balance method, for solving radiative transfer equations on quadrilateral grids are presented. Numerical examples shows that the schemes presented are feasible on non-rectangle grid computation, and that the computing results by the schemes presented are comparative to that by the discrete ordinate diamond scheme on rectangle grid. (author)

The use of the MacCormack scheme in computational hydraulics

Energy Technology Data Exchange (ETDEWEB)

Garcia, R. [Universidad Central de Venezuela, Inst. de Mecanica de Fluidos, Caracas (Venezuela); Zhang, H.; Kahawita, R. [Ecole Polytechnique, Dept. of Civil Engineering, Montreal, Quebec (Canada)

1985-07-01

This manuscript describes the development of a numerical model that solves shallow water problems based upon an enhanced version of the MacCormack explicit scheme (MS). The MS has been successfully applied to solve numerous problems in gas dynamics. However, the standard application of the MS to solve the shallow water equations can cause in certain test cases non-linear instabilities and non-symmetrical results that eventually destroy the solution. By examining the calculation 'cell' one can show that the MS is not symmetric in space, which explains why it cannot be used directly in the treatment of hydraulic problems most of which possess irregular boundaries thereby resulting in a flow with no 'preferred direction'. This is contrary to what is usually encountered in aerodynamics. The enhanced MacCormack scheme is obtained by a simple modification to the original formulation resulting in a symmetric scheme. The scheme has been applied to the computation of the flowfield in a real life situation with satisfactory results. (author)

Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter

DEFF Research Database (Denmark)

Fjelde, Tina; Kloch, Allan; Wolfson, David

2001-01-01

We present a novel scheme for all-optical label swapping that relies on logic exclusive-OR (XOR) in an integrated SOA-based Michelson interferometer. The scheme allows simple, efficient and mechanically stable operation, while relaxing the requirements on packet format and simplifying switch...

Numerical and experimental study on temperature control of solar panels with form-stable paraffin/expanded graphite composite PCM

International Nuclear Information System (INIS)

Luo, Zigeng; Huang, Zhaowen; Xie, Ning; Gao, Xuenong; Xu, Tao; Fang, Yutang; Zhang, Zhengguo

2017-01-01

Highlights: • A passive cooling PV-PCM system was developed. • Form-stable paraffin/EG composite PCM with high thermal conductivity was utilized. • Numerical simulation on the temperature of PV-PCM panel was carried out. • Effects of density were studied under the given weather conditions. - Abstract: Performance of photovoltaic (PV) panels is greatly affected by its operating temperature. And traditional active and passive cooling methods usually suffer from the disadvantages of external energy consumption, uneven temperature distribution and low thermal conductivity of phase change materials (PCMs). In this work, a PV-PCM system was developed to control the temperature of a PV panel by applying high thermal conductive form-stable paraffin (ZDJN-28)/EG composite PCM. The temperature, output voltage and power of a conventional PV panel and the PV-PCM panel were measured and compared. A numerical simulation model established by CFD software FLUENT was used to simulate the temperature change process of the PV-PCM panel with different material densities under the same conditions as experiment. The experiment results showed that compared with the temperature of the conventional PV panel, the temperature of the PV-PCM panel is kept below 50 °C for 200 min extended by 146 min with output power averagely increased by 7.28% in heating process. Simulated temperatures were in good agreement with experimental temperatures and indicated that the higher the density of the PCM is, the better the temperature management performance the PV panel could achieve. Besides, the PCM with density of 900 kg/m 3 was found sufficient to achieve a good temperature management performance when the average ambient temperature below 25 °C with the highest solar irradiation of 901 w/m 2 . In summary, this work is of great importance in the design of a PV-PCM system for temperature management of PV panels.

Support schemes and market design in international offshore grids

DEFF Research Database (Denmark)

Schröder, Sascha Thorsten

2013-01-01

International offshore grids can combine the grid connection of offshore wind parks with the possibility for international power trading in the future. This paper investigates the choice of support scheme and power market design in international offshore grids and derives resulting incentives...... support. For a stable investment framework in the near future, a tendering/feed-in tariff may be the best choice. It avoids exposing wind farms to balancing with multiple countries. In the long run, also other support scheme options may be of interest....

Chance and stability stable distributions and their applications

CERN Document Server

Uchaikin, Vladimir V

1999-01-01

An introduction to the theory of stable distributions and their applications. It contains a modern outlook on the mathematical aspects of the theory. The authors explain numerous peculiarities of stable distributions and describe the principle concept of probability theory and function analysis. A significant part of the book is devoted to applications of stable distributions. Another notable feature is the material on the interconnection of stable laws with fractals, chaos and anomalous transport processes.

Designing synchronization schemes for chaotic fractional-order unified systems

International Nuclear Information System (INIS)

Wang Junwei; Zhang Yanbin

2006-01-01

Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

KAUST Repository

Auzinger, Winfried; Hofstä tter, Harald; Ketcheson, David I.; Koch, Othmar

2016-01-01

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

KAUST Repository

Auzinger, Winfried

2016-07-28

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

Assessment of some high-order finite difference schemes on the scalar conservation law with periodical conditions

Directory of Open Access Journals (Sweden)

Alina BOGOI

2016-12-01

Full Text Available Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

Science.gov (United States)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

A second-order iterative implicit-explicit hybrid scheme for hyperbolic systems of conservation laws

International Nuclear Information System (INIS)

Dai, Wenlong; Woodward, P.R.

1996-01-01

An iterative implicit-explicit hybrid scheme is proposed for hyperbolic systems of conservation laws. Each wave in a system may be implicitly, or explicitly, or partially implicitly and partially explicitly treated depending on its associated Courant number in each numerical cell, and the scheme is able to smoothly switch between implicit and explicit calculations. The scheme is of Godunov-type in both explicit and implicit regimes, is in a strict conservation form, and is accurate to second-order in both space and time for all Courant numbers. The computer code for the scheme is easy to vectorize. Multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step. The feature of the scheme is shown through numerical examples. 38 refs., 12 figs

Projection scheme for a reflected stochastic heat equation with additive noise

Science.gov (United States)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

Science.gov (United States)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

2017-04-01

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

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....

Numerical simulations for radiation hydrodynamics. 2: Transport limit

International Nuclear Information System (INIS)

Dai, W.W.; Woodward, P.R.

2000-01-01

A finite difference scheme is proposed for two-dimensional radiation hydrodynamical equations in the transport limit. The scheme is of Godunov-type, in which the set of time-averaged flux needed in the scheme is calculated through Riemann problems solved. In the scheme, flow signals are explicitly treated, while radiation signals are implicitly treated. Flow fields and radiation fields are updated simultaneously. An iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme. The sweeping method used in the scheme significantly reduces the number of iterations or computer CPU time needed. A new approach to further accelerate the convergence is proposed, which further reduces the number of iterations needed by more than one order. No matter how many cells radiation signals propagate in one time step, only an extremely small number of iterations are needed in the scheme, and each iteration costs only about 0.8% of computer CPU time which is needed for one time step of a second order accurate and fully explicit scheme. Two-dimensional problems are treated through a dimensionally split technique. Therefore, iterations for solving the set of algebraic equations are carried out only in each one-dimensional sweep. Through numerical examples it is shown that the scheme keeps the principle advantages of Godunov schemes for flow motion. In the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme. The acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems. This study is important for laser fusion and astrophysics

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Science.gov (United States)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Directory of Open Access Journals (Sweden)

Shahid Hasnain

2017-07-01

Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

Science.gov (United States)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

Adaptive transmission schemes for MISO spectrum sharing systems

KAUST Repository

Bouida, Zied

2013-06-01

We propose three adaptive transmission techniques aiming to maximize the capacity of a multiple-input-single-output (MISO) secondary system under the scenario of an underlay cognitive radio network. In the first scheme, namely the best antenna selection (BAS) scheme, the antenna maximizing the capacity of the secondary link is used for transmission. We then propose an orthogonal space time bloc code (OSTBC) transmission scheme using the Alamouti scheme with transmit antenna selection (TAS), namely the TAS/STBC scheme. The performance improvement offered by this scheme comes at the expense of an increased complexity and delay when compared to the BAS scheme. As a compromise between these schemes, we propose a hybrid scheme using BAS when only one antenna verifies the interference condition and TAS/STBC when two or more antennas are illegible for communication. We first derive closed-form expressions of the statistics of the received signal-to-interference-and-noise ratio (SINR) at the secondary receiver (SR). These results are then used to analyze the performance of the proposed techniques in terms of the average spectral efficiency, the average number of transmit antennas, and the average bit error rate (BER). This performance is then illustrated via selected numerical examples. © 2013 IEEE.

A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

KAUST Repository

Bao, Kai

2012-10-01

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

KAUST Repository

Bao, Kai; Shi, Yi; Sun, Shuyu; Wang, Xiaoping

2012-01-01

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

Progress with multigrid schemes for hypersonic flow problems

International Nuclear Information System (INIS)

Radespiel, R.; Swanson, R.C.

1995-01-01

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 X 10 6 and Mach numbers up to 25. 32 refs., 31 figs., 1 tab

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.

Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model

Science.gov (United States)

Calatroni, L.; Estatico, C.; Garibaldi, N.; Parisotto, S.

2017-10-01

We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in [10] for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented.

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

Science.gov (United States)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

MIMO transmit scheme based on morphological perceptron with competitive learning.

Science.gov (United States)

Valente, Raul Ambrozio; Abrão, Taufik

2016-08-01

This paper proposes a new multi-input multi-output (MIMO) transmit scheme aided by artificial neural network (ANN). The morphological perceptron with competitive learning (MP/CL) concept is deployed as a decision rule in the MIMO detection stage. The proposed MIMO transmission scheme is able to achieve double spectral efficiency; hence, in each time-slot the receiver decodes two symbols at a time instead one as Alamouti scheme. Other advantage of the proposed transmit scheme with MP/CL-aided detector is its polynomial complexity according to modulation order, while it becomes linear when the data stream length is greater than modulation order. The performance of the proposed scheme is compared to the traditional MIMO schemes, namely Alamouti scheme and maximum-likelihood MIMO (ML-MIMO) detector. Also, the proposed scheme is evaluated in a scenario with variable channel information along the frame. Numerical results have shown that the diversity gain under space-time coding Alamouti scheme is partially lost, which slightly reduces the bit-error rate (BER) performance of the proposed MP/CL-NN MIMO scheme. Copyright © 2016 Elsevier Ltd. All rights reserved.

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Energy Technology Data Exchange (ETDEWEB)

Pebay, Philippe [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Terriberry, Timothy B. [Xiph.Org Foundation, Arlington, VA (United States); Kolla, Hemanth [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Bennett, Janine [Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

2016-03-29

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Formulas such as these, are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

TE/TM scheme for computation of electromagnetic fields in accelerators

International Nuclear Information System (INIS)

Zagorodnov, Igor; Weiland, Thomas

2005-01-01

We propose a new two-level economical conservative scheme for short-range wake field calculation in three dimensions. The scheme does not have dispersion in the longitudinal direction and is staircase free (second order convergent). Unlike the finite-difference time domain method (FDTD), it is based on a TE/TM like splitting of the field components in time. Additionally, it uses an enhanced alternating direction splitting of the transverse space operator that makes the scheme computationally as effective as the conventional FDTD method. Unlike the FDTD ADI and low-order Strang methods, the splitting error in our scheme is only of fourth order. As numerical examples show, the new scheme is much more accurate on the long-time scale than the conventional FDTD approach

Active Fault Tolerant Control of Livestock Stable Ventilation System

DEFF Research Database (Denmark)

Gholami, Mehdi

2011-01-01

Modern stables and greenhouses are equipped with different components for providing a comfortable climate for animals and plant. A component malfunction may result in loss of production. Therefore, it is desirable to design a control system, which is stable, and is able to provide an acceptable d...... are not included, while due to the physical limitation, the input signal can not have any value. In continuing, a passive fault tolerant controller (PFTC) based on state feedback is proposed to track a reference signal while the control inputs are bounded....... of fault. Designing a fault tolerant control scheme for the climate control system. In the first step, a conceptual multi-zone model for climate control of a live-stock building is derived. The model is a nonlinear hybrid model. Hybrid systems contain both discrete and continuous components. The parameters...... affine (PWA) components such as dead-zones, saturation, etc or contain piecewise nonlinear models which is the case for the climate control systems of the stables. Fault tolerant controller (FTC) is based on a switching scheme between a set of predefined passive fault tolerant controller (PFTC...

A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation

Directory of Open Access Journals (Sweden)

Jinsong Hu

2013-01-01

Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.

On the integration scheme along a trajectory for the characteristics method

International Nuclear Information System (INIS)

Le Tellier, Romain; Hebert, Alain

2006-01-01

The issue of the integration scheme along a trajectory which appears for all tracking-based transport methods is discussed from the point of view of the method of characteristics. The analogy with the discrete ordinates method in slab geometry is highlighted along with the practical limitation in transposing high-order S N schemes to a trajectory-based method. We derived an example of such a transposition starting from the linear characteristic scheme. This new scheme is compared with the standard flat-source approximation of the step characteristic scheme and with the diamond differencing scheme. The numerical study covers a 1D analytical case, 2D one-group critical and fixed-source benchmarks and finally a realistic multigroup calculation on a BWR-MOX assembly

The analytical evolution of NLS solitons due to the numerical discretization error

Science.gov (United States)

Hoseini, S. M.; Marchant, T. R.

2011-12-01

Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank-Nicolson scheme and a scheme, due to Taha [1], based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t^{-{1\\over 2}}, which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank-Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found.

The analytical evolution of NLS solitons due to the numerical discretization error

International Nuclear Information System (INIS)

Hoseini, S M; Marchant, T R

2011-01-01

Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank–Nicolson scheme and a scheme, due to Taha, based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t -1/2 , which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank–Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found. (paper)

Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

KAUST Repository

Parsani, Matteo

2013-04-10

Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

KAUST Repository

Parsani, Matteo; Ketcheson, David I.; Deconinck, W.

2013-01-01

Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

Pressure correction schemes for compressible flows: application to baro-tropic Navier-Stokes equations and to drift-flux model

International Nuclear Information System (INIS)

Gastaldo, L.

2007-11-01

We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they

A Multiserver Biometric Authentication Scheme for TMIS using Elliptic Curve Cryptography.

Science.gov (United States)

Chaudhry, Shehzad Ashraf; Khan, Muhammad Tawab; Khan, Muhammad Khurram; Shon, Taeshik

2016-11-01

Recently several authentication schemes are proposed for telecare medicine information system (TMIS). Many of such schemes are proved to have weaknesses against known attacks. Furthermore, numerous such schemes cannot be used in real time scenarios. Because they assume a single server for authentication across the globe. Very recently, Amin et al. (J. Med. Syst. 39(11):180, 2015) designed an authentication scheme for secure communication between a patient and a medical practitioner using a trusted central medical server. They claimed their scheme to extend all security requirements and emphasized the efficiency of their scheme. However, the analysis in this article proves that the scheme designed by Amin et al. is vulnerable to stolen smart card and stolen verifier attacks. Furthermore, their scheme is having scalability issues along with inefficient password change and password recovery phases. Then we propose an improved scheme. The proposed scheme is more practical, secure and lightweight than Amin et al.'s scheme. The security of proposed scheme is proved using the popular automated tool ProVerif.

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

Science.gov (United States)

Mickens, Ronald E.

1989-01-01

A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

Numerical solutions of the Vlasov equation

International Nuclear Information System (INIS)

Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

1985-01-01

A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)

2D deblending using the multi-scale shaping scheme

Science.gov (United States)

Li, Qun; Ban, Xingan; Gong, Renbin; Li, Jinnuo; Ge, Qiang; Zu, Shaohuan

2018-01-01

Deblending can be posed as an inversion problem, which is ill-posed and requires constraint to obtain unique and stable solution. In blended record, signal is coherent, whereas interference is incoherent in some domains (e.g., common receiver domain and common offset domain). Due to the different sparsity, coefficients of signal and interference locate in different curvelet scale domains and have different amplitudes. Take into account the two differences, we propose a 2D multi-scale shaping scheme to constrain the sparsity to separate the blended record. In the domain where signal concentrates, the multi-scale scheme passes all the coefficients representing signal, while, in the domain where interference focuses, the multi-scale scheme suppresses the coefficients representing interference. Because the interference is suppressed evidently at each iteration, the constraint of multi-scale shaping operator in all scale domains are weak to guarantee the convergence of algorithm. We evaluate the performance of the multi-scale shaping scheme and the traditional global shaping scheme by using two synthetic and one field data examples.

Godunov-type schemes for hydrodynamic and magnetohydrodynamic modeling

International Nuclear Information System (INIS)

Vides-Higueros, Jeaniffer

2014-01-01

The main objective of this thesis concerns the study, design and numerical implementation of finite volume schemes based on the so-Called Godunov-Type solvers for hyperbolic systems of nonlinear conservation laws, with special attention given to the Euler equations and ideal MHD equations. First, we derive a simple and genuinely two-Dimensional Riemann solver for general conservation laws that can be regarded as an actual 2D generalization of the HLL approach, relying heavily on the consistency with the integral formulation and on the proper use of Rankine-Hugoniot relations to yield expressions that are simple enough to be applied in the structured and unstructured contexts. Then, a comparison between two methods aiming to numerically maintain the divergence constraint of the magnetic field for the ideal MHD equations is performed and we show how the 2D Riemann solver can be employed to obtain robust divergence-Free simulations. Next, we derive a relaxation scheme that incorporates gravity source terms derived from a potential into the hydrodynamic equations, an important problem in astrophysics, and finally, we review the design of finite volume approximations in curvilinear coordinates, providing a fresher view on an alternative discretization approach. Throughout this thesis, numerous numerical results are shown. (author) [fr

Numerical Analysis of Dusty-Gas Flows

Science.gov (United States)

Saito, T.

2002-02-01

This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.

A new numerically stable implementation of the T-matrix method for electromagnetic scattering by spheroidal particles

Science.gov (United States)

Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.

2013-07-01

We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.

Low-Dissipation Advection Schemes Designed for Large Eddy Simulations of Hypersonic Propulsion Systems

Science.gov (United States)

White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.

2012-01-01

The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

Science.gov (United States)

Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.

2013-12-01

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1

IR subtraction schemes. Integrating the counterterms at NNLO in QCD

Energy Technology Data Exchange (ETDEWEB)

Bolzoni, Paolo; Somogyi, Gabor

2010-06-15

We briefly review a subtraction scheme for computing radiative corrections to QCD jet cross sections that can be defined at any order in perturbation theory. Hereafter we discuss the computational methods used to evaluate analytically and numerically the integrated counterterms arising from such a subtraction scheme. Basically these methods the Mellin-Barnes (MB) representations technique together with the harmonic summation and the sector decomposition. (orig.)

IR subtraction schemes. Integrating the counterterms at NNLO in QCD

International Nuclear Information System (INIS)

Bolzoni, Paolo; Somogyi, Gabor

2010-06-01

We briefly review a subtraction scheme for computing radiative corrections to QCD jet cross sections that can be defined at any order in perturbation theory. Hereafter we discuss the computational methods used to evaluate analytically and numerically the integrated counterterms arising from such a subtraction scheme. Basically these methods the Mellin-Barnes (MB) representations technique together with the harmonic summation and the sector decomposition. (orig.)

An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities

Science.gov (United States)

Gong, Yuezheng; Zhao, Jia; Wang, Qi

2017-10-01

A quasi-incompressible hydrodynamic phase field model for flows of fluid mixtures of two incompressible viscous fluids of distinct densities and viscosities is derived by using the generalized Onsager principle, which warrants the variational structure, the mass conservation and energy dissipation law. We recast the model in an equivalent form and discretize the equivalent system in space firstly to arrive at a time-dependent ordinary differential and algebraic equation (DAE) system, which preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we develop a temporal discretization scheme for the DAE system, where the mass conservation and the energy dissipation law are once again preserved at the fully discretized level. We prove that the fully discretized algorithm is unconditionally energy stable. Several numerical examples, including drop dynamics of viscous fluid drops immersed in another viscous fluid matrix and mixing dynamics of binary polymeric solutions, are presented to show the convergence property as well as the accuracy and efficiency of the new scheme.

Asynchronous schemes for CFD at extreme scales

Science.gov (United States)

Konduri, Aditya; Donzis, Diego

2013-11-01

Recent advances in computing hardware and software have made simulations an indispensable research tool in understanding fluid flow phenomena in complex conditions at great detail. Due to the nonlinear nature of the governing NS equations, simulations of high Re turbulent flows are computationally very expensive and demand for extreme levels of parallelism. Current large simulations are being done on hundreds of thousands of processing elements (PEs). Benchmarks from these simulations show that communication between PEs take a substantial amount of time, overwhelming the compute time, resulting in substantial waste in compute cycles as PEs remain idle. We investigate a novel approach based on widely used finite-difference schemes in which computations are carried out asynchronously, i.e. synchronization of data among PEs is not enforced and computations proceed regardless of the status of messages. This drastically reduces PE idle time and results in much larger computation rates. We show that while these schemes remain stable, their accuracy is significantly affected. We present new schemes that maintain accuracy under asynchronous conditions and provide a viable path towards exascale computing. Performance of these schemes will be shown for simple models like Burgers' equation.

A positive and multi-element conserving time stepping scheme for biogeochemical processes in marine ecosystem models

Science.gov (United States)

Radtke, H.; Burchard, H.

2015-01-01

In this paper, an unconditionally positive and multi-element conserving time stepping scheme for systems of non-linearly coupled ODE's is presented. These systems of ODE's are used to describe biogeochemical transformation processes in marine ecosystem models. The numerical scheme is a positive-definite modification of the Runge-Kutta method, it can have arbitrarily high order of accuracy and does not require time step adaption. If the scheme is combined with a modified Patankar-Runge-Kutta method from Burchard et al. (2003), it also gets the ability to solve a certain class of stiff numerical problems, but the accuracy is restricted to second-order then. The performance of the new scheme on two test case problems is shown.

Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

KAUST Repository

Peng, Qiujin; Qiao, Zhonghua; Sun, Shuyu

2017-01-01

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L-infinity convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

KAUST Repository

Peng, Qiujin

2017-09-18

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L-infinity convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

A numerical solution for a class of time fractional diffusion equations with delay

Directory of Open Access Journals (Sweden)

Pimenov Vladimir G.

2017-09-01

Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

Comments on numerical simulations

International Nuclear Information System (INIS)

Sato, T.

1984-01-01

The author comments on a couple of things about numerical simulation. One is just about the philosophical discussion that is, spontaneous or driven. The other thing is the numerical or technical one. Frankly, the author didn't want to touch on the technical matter because this should be a common sense one for those who are working at numerical simulation. But since many people take numerical simulation results at their face value, he would like to remind you of the reality hidden behind them. First, he would point out that the meaning of ''driven'' in driven reconnection is different from that defined by Schindler or Akasofu. The author's definition is closer to Axford's definition. In the spontaneous case, for some unpredicted reason an excess energy of the system is suddenly released at a certain point. However, one does not answer how such an unstable state far beyond a stable limit is realized in the magnetotail. In the driven case, there is a definite energy buildup phase starting from a stable state; namely, energy in the black box increases from a stable level subject to an external source. When the state has reached a certain position, the energy is released suddenly. The difference between driven and spontaneous is whether the cause (plasma flow) to trigger reconnection is specified or reconnection is triggered unpredictably. Another difference is that in driven reconnection the reconnection rate is dependent on the speed of the external plasma flow, but in spontaneous reconnection the rate is dependent on the internal condition such as the resistivity

Finite-difference schemes for anisotropic diffusion

Energy Technology Data Exchange (ETDEWEB)

Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)

2014-09-01

In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.

Homogenization scheme for acoustic metamaterials

KAUST Repository

Yang, Min

2014-02-26

We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial\\'s structural unit cell with a piece of homogenized material. From the Green\\'s theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme\\'s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.

A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke

2001-01-01

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``

Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows

Science.gov (United States)

Wang, Wei; Yee, H. C.; Sjogreen, Bjorn; Magin, Thierry; Shu, Chi-Wang

2009-01-01

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.

Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations

Energy Technology Data Exchange (ETDEWEB)

Bank, Randolph E. [Univ. of California, San Diego, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Bulgarian Academy of Sciences, Sofia (Bulgaria)

2016-01-20

This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space-time domain demonstrate the feasibility of the proposed approach.

NUMERICAL RESEARCH ON THE THREE-DIMENSIONAL FIBER ORIENTATION DISTRIBUTION IN PLANAR SUSPENSION FLOWS

Directory of Open Access Journals (Sweden)

Qihua Zhang

Full Text Available Abstract To describe flow-induced fiber orientation, the Fokker-Planck equation is widely applied in the processing of composites and fiber suspensions. The analytical solution only exists when the Péclet number is infinite. So developing a numerical method covering a full range of Péclet number is of great significance. To accurately solve the Fokker-Planck equation, a numerical scheme based on the finite volume method is developed. Using spherical symmetry, the boundary is discretized and formulated into a cyclic tridiagonal matrix which is further solved by the CTDMA algorithm. To examine its validity, benchmark tests over a wide range of Péclet number are performed in a simple shear flow. For Pe=∞, the results agree well with the analytical solutions. For the other Pe numbers, the results are compared to results available in the literature. The tests show that this algorithm is accurate, stable, and globally conservative. Furthermore, this algorithm can be extended and used to predict the three-dimensional orientation distribution of complex suspension flows.

Analytical reconstruction schemes for coarse-mesh spectral nodal solution of slab-geometry SN transport problems

International Nuclear Information System (INIS)

Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.

2009-01-01

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

Science.gov (United States)